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ÍNDICE

Nonparametric specifi cation testing for continuous time models for interest rates in MexicoJosé A. Núñez Mora y Carlos A. Martínez Reyes....................................... 7

Innovation on nanomaterials across countries in a triple helix framework: The case oxide of hafniumAlenka Guzmán Chávez ............................................................................. 29

Dependencia de largo plazo en los rendimientos de acciones mexicanas selectasAgustín I. Cabrera Llanos, Samantha S. López Gil y Francisco López Herrera .................................... 59

Opciones reales e incentivosEsteban Colla De Robertis........................................................................... 79

Reciprocal dumping and environmental taxesSalvador Sandoval Bravo, Semei L. Coronado Ramírez y Jesús Porras Serrano.................................. 97

Migration and remitt ances eff ects on consumption of the poorest: The mexican caseJosé J. Mora Rivera y Jesús Arellano González .......................................... 121

Volumen VII, No. 14, Enero-Junio, 2012, pp. 7-27

AUTORES 1

NONPARAMETRIC SPECIFICATION TESTING FOR CONTINUOUS TIME MODELS

FOR INTEREST RATES IN MEXICO

José A. Núñez Mora*Carlos A. Martínez Reyes**

Resumen

En este artículo se propone una prueba estadística para la especifi cación de los modelos paramétricos de dos factores. Se presentan tres pruebas diferentes. Las dos primeras se basan en una comparación de la estimación de la densidad de núcleo de la función de densidad desconocida y la estimación de la función de densidad marginal mediante el método Delta. La última prueba se basa en la idea de la comparación entre la estimación de la densidad de núcleo y el modelo paramétrico de la densidad de núcleo suavizado para evitar los efectos de sesgo. En particular, esta prueba se aplicó para determinar si la dinámica de la estructura temporal de tasa de interés de Cetes en México para el período 2002-2009 puede ser modelada a partir de los supuestos de los dos modelos, el de Brennan-Schwartz y el de Schaefer y Schwartz ; los resultados de la prueba muestran que ambos modelos continuos son rechazados y por lo tanto no son capaces de describir los datos de los Cetes en México.Palabras clave: modelo de tiempo continuo, función de densidad marginal, método Delta, estimación no paramétrica, proceso de difusiónClasifi cación JEL: C14, C44, C51

* Instituto Tecnológico y de Estudios Superiores de Monterrey, Campus Ciudad de México. Electronic mail: <[email protected]>.

** Instituto Tecnológico y de Estudios Superiores de Monterrey, Campus Estado de México. Electronic mail: <[email protected]>.

(Recibido: Julio 2011 / Aprobado: Diciembre 2011)

JOSÉ A. NÚÑEZ / CARLOS A. MARTÍNEZ

8

Abstract

In this paper we propose a statistical test for the specifi cation of parametric models of two factors. We present three diff erent tests. The fi rst two are based on a comparison between the estimate of kernel density of the unknown density function and the estimate of marginal density function by the Delta method. The last test is based on the idea of comparison between the estimate of kernel density and the parametric model of the smoothed kernel density to avoid skew eff ects. Particularly, this test was applied to determine if the dynamic of the term structure of the Mexican Cetes interest rate in the period 2002-2009 can be modeled from the assumptions of two models, that of Brennan-Schwartz and that of Schaefer-Schwart; the test results show that both continuous models are rejected and therefore are unable to describe the data of the Mexican Cetes.Keywords: continuous-time model, marginal density function, Delta method, nonparameter estimation, diff usion processJEL Classifi cation: C14, C44, C51

1. Introduction

A common approach to model the term structure of interest rates is such that express the interest rate in terms of one or more stochastic factors, which in turn follow continuous time stochastic processes. Several studies by Dybvig (1989) and Steeley (1991) have concluded that the variability of rates with diff erent maturity dates can be best explained more than one stochastic factor. This has lead researchers to develop time structure models that use two or more stochastic factors. Multi factor models are proposed by Brennan and Schwartz (1979), Schaefer and Schwartz (l984), Longstaff and Schwartz (l992), Hull and White (1990), Fong and Vasicek (1991), Heath, Jarrow and Morton (1992), Duffi e and Kan (1995). The mod-el of Brennan y Schwartz (1979) assumes that the short and long rates are the driving forces for the time structure, while the model advanced by Fong y Vasicek (1991) include the short rate and volatility as the main fac-tors.

In the absence of a theoretical framework that defi nes in detail the term structure of interest rates, can be testing diff erent models with real data,

CONTENIDO 1

NONPARAMETRIC SPECIFICATION TESTING FOR CONTINUOUS TIME MODELS FOR INTEREST RATES IN MEXICO

9

without using any observation that coming from a set of prices derived from interest rates. Aït-Sahalia (1996) proposes an approach in this direction, it is assumed that the properties of a model that gives structure to terms is determined completely by a difusion process. This process is characterized by its two fi rst moments of time continuum, tendency and diff usion. Each parametric model of the term structure has a certain density function characterized by the tendency and diff usion functions.

The statistical test is based in a comparison between the density function obtained from a parametric model of the time structure and a non-parametric estimate of the density function, which in turn is derived form data. The density function is valid even if the parametric model of the time structure is not well specifi ed.

Nevertheless it should be pointed out that there are limits to this statistical test: fi rst, it is only applied to one-factor models for term structure. Second, the most important assumption for this test is that data are smoothed when the non-parametric estimate of the density function is constructed, that means, it possess a high variance so the estimate introduces too much “noise” expressed by many “illegitimate” modes (relative maximums) which in turn do not appear in the desired density calculation, in this case, the non-parametric estimate is less than optimal. Therefore is not clear what happens to this test when the data are over smoothed. Thirdly, the test do no consider the skew eff ects inherent to the non parametric estimate of the density function. Next, the test of Yacine Aït-Sahalia (1996) will be explored in the aforementioned directions.

2. The model and null hypothesis

For a complete probability space ),,( PF and augmented fi ltration 0}:{ tFt generated by a standard Brownian movement W in Rd, a time continuum model tipically depends on a stationary diff usion process X that takes values from some open subset D of Rd, with a dynamics represented by the Ito stochastic diff erential equation,

tttt dWXdtXdX ),(),(= (1)

So that for any in a bounded subset dR , ( , ) dR and ( , ) d×dR are the tendency and difussion functions respectively. The distribuition of


10

the process is completely characterized by its tendency and its diff usion. For example, for a one dimension stationary diff usion process, the marginal density function can be writt en as

2 20

( ) 2 ( , )( , ) = { }

( , ) ( , )

x

x

ux exp du

x u

(2)

Where the process is distributed over R and )( is a standarization constant that ensures that density integrates to one.

Generally, for any we use ),( x to express the marginal density function which is implicit in the parametric model )(x to express the true marginal density function. The null hypothesis and alternative hypothesis are:

0 0 0: ( , ) = ( ) H exists such that x x

anyforH )(),(:1

As in Aït-Sahalia (1996), our statistical test is based in a pondered integral of the squared diff erence between )(x and ),(

0 x ,

dxxxxI )()),()((= 2 (3)

We can use the measure I as a pointer of the incorrect specifi cation of the model, because 0I and I = 0 if and only if the marginal density function implied by the model is correctly specifi ed. In order to obtain a consistent of parameter

0 , a non parametric method is use the Delta method of nonparametric kernel functionals of Yacine Aït-Sahalia (1992) as follows,

)(min=ˆ

nn L

(4)

where

2

1=

))(ˆ),((1

=)( ii

n

in xx

nL (5)


11

and )(ˆ x represents the kernel estimate of the marginal density function )(x , i.e.,

h

XxK

hnx i

n

id

1=

1=)(̂

(6)

where )(K is a kernel function and h = hn is a smoothing parameter, bandwidth or window that does not depend on the data. Therefore, under H0 the estimate of the Delta method of ),( x is )ˆ,( nx and the true and unknown marginal density function of x, )(x , can be estimated consistently with the kernel estimate )(ˆ x regardless to the correct specifi cation of the parametric model.

If the estimates of )(x and ),( x are )(ˆ x and )ˆ,( nx respectively, they can be substituted in the defi nition of I producing the following estimate of I,

dxxxxI nn )(ˆ))ˆ,()(ˆ(= 2 (7)

3. The limit distribution of In under H0

The foll owing assumptions are used to obtain the limit distribution of In.

Premise 1. For any , ),( is locally bounded and is Borel measurable.

Premise 2. Let be q a measure of induced probability over Rd by X0 and = 0dR

dq for any bounded and continous function )(x in Rd , where is the infi nitesimal

generator created by the diff usion process 0},{ tX t .

Premise 3. The kernel function )(K is a symmetric and bounded function in Rd that satisfi es:

,||||0|)(|||||,<|)(| uwhenuKuduuK d

( ) = 0, ( ) = 2 , 1 , ,i i j iju K u du u u K u du k for i j d k R


12

Premise 4. The density function )( and its partial derivative of second order are bounded and uniformly continuous in BBRd.

Premise 5. The smoothing parameter h = hn satisfi e 0h , dnh when n .

Premise 6. The function of parametric density ),( u and its partial derivative of second order respect are uniformely bounded and uniformly continuous. ),( u and its partial derivative of second degree respect x are bounded and uniformly continuous in Rd. Also, <|),(| dxuD' , where ),( uD' is a px1 partial derivative vector of fi rst degree of the function ),( u respect .

Premise 7. The succesion of observed data ,1iX i n is strictly stationary.

Premise 8. Exist * such that *ˆ n a.s and

21

* ))()(()(=ˆ nouFuFdu pnFn

21

1=* )()(

1= noXEX

n piFiF

n

i

(8)

where )(F and )(F are the function of cumulative density and the derivative of )(F respectively, associated with the unknown function of marginal density )( .

Premise 9. The parameters space dR is compact and ))/,()()/,(( 00 'uuE has a full range.

• Premise 1 guarantees the existence and uniqueness of a solution for the stochastic diff erential equation. Given that our model is a stochastical homogeneus diff erential equation in time and of Markovian type, also this premise is condition enough to ensure a non explosive solution.• Premise 2 ensures that the solution process is stationary.• Premises 3, 4 and 5 are used to obtain a limit distribution of the integral of the squared error for the estimate of the kernel density.


13

• Premises 6 and 8 are used to examine the eff ect of the estimate of ),( 0 u by )(~ x over the limit distribution In. In particular, the last term,

(1)Po , from the right side of the equation (8), can be guaranteed assuming that the derivative )(F is a cadlag bounded function.• Premise 7 serves the purpose to limit the dependence of the discrete observations so that asymptotic theory can be used.• Premise 9 ensures that the linear term in the Taylor expansion of a functional is not degenerate. If the linear term degenerates then the asyntotic distribution might be given by a term of greater degree present in the Taylor expansion.

From equation (7) we can write the squared integrable diff erence between )(ˆ x and )(~ x as follows,

dxxxxdxxxxIn )(ˆ))()(~()(ˆ))()(ˆ(= 22 dxxxxxx )(ˆ))()(~))(()(ˆ(2

nnn III 321 2= (9)

Theorem 1. Let be dxxxxEdxxdxxKnhnc d )()))()(ˆ()()()(=)( 2221 , 22

1=)/(=)( i

d

ixxx and we defi ne

0si

si =)(

4/2

4 21/2

dd

d

nhnh

nhhnnd

then, under the conditions established over )(K and )( and assuming that dnh2 , when n , we have

),())((2=))()((1

1221 jin

nji

dn XXHhnndncInd

))(()())()(ˆ))((ˆ)(ˆ()(2 /233/2 dp hnndOdxxxxExExnd

where

dxxh

XxEK

h

XxK

hXx

EKhXx

KXXH jjiijin )(=),(


14

NXXHhnnhd

jinnji

dd2

1

122/2 2),(

2222221/2 })()]([{)()](ˆ[ dxxxdxxxhn

where 2222222

1 )()]([)()]([= dxxxdxxx

dvduvuKuKdxx242

2 )()()(=

0si2

si2))()((

42

41

1 d

dd

nnhN

nhNkncInd

Theorem 1 implies that the limit distribution of the integrable squared error of )(ˆ x , I1n depends upon the amount of smoothing that is applied to the data. The limit distributions form Theorem 1 can be used to construct of proof for the null hypothesis )(=)( 0 xx against the alternative )()( 0 xx , where )(0 x is a density function which is completely unknown. Furthermore, in order to Theorem 1 to be observed, the smoothing parameter h must satisfy dnh2 or 04 dnh (under smoothing data) or 4dnh (over smoothing data). So d must satisfy 3d for under smoothing data. Nevertheless, when the null hypothesis is composite, that is, there are a fi nite number of unknown parameters, the last two terms of the right side of the equation (9) must be taken under consideration. For this purpose, the Taylor expansion and premise 8, under H0, we have

)())()((1

),(=),()(~ 1/200

noXEXn

xD'xx piFiF

then we express I3n as follows,

)()( 02013 nnn JJI where

dxxxxxExJ n )(ˆ)],()(~)][(ˆ)(ˆ[=)( 001 (10)and


15

dxxxxxxEJ n )(ˆ)],()(~)][()(ˆ[=)( 002 (11)

The following lemma summarizes the behavior of )( 01 nJ and )( 02 nJ , and therfore that of I3n.

Lemma 1. Under premises 1-9, for any 1<<0 we have

a) whereNkJhnalsoandnOJ

d

npn 30221/2

01 )()(=)(

dxxxDVdxxxD' )(),()(),(= 200

200

23

))(),(())((= 111=

1 kFFk

F XXCovxVarV

1/2 2

3 2 0 3 3= ( ) ( )d

n n p nconsequently I J O n y n h I k N

b) If the null hypothesis is satisfi ed, then )(= 12

nOI pn and also

NkIhnd

n 3321/2

If the null hypothesis is satisfi ed from equation (11) and Lemma 1 we

obtain the following expression,

1 2 0= 2n n n pI I J O n (12)

this equation lays down that the parametric estimate of ),(0

x under the eff ects of the null hypothesis is the limit distribution of In only through )( 02 nJ . Therefore if the fi rst term of the right side of equation (12) dominates the second term asimptotically, which is the case for under smoothed data, the parametric estimate of ),(

0 x under the null hypothesis does not

aff ect the limit distribuition of In as Yacine Aït-Sahalia (1996) demonstrates for d = 1. Nevertheless, if data are over smoothed, the limit distribution of A will be aff ected by non parametric estimates as the following theorem shows.

Theorem 2. Under the assumptions of Lemma 1, if the null hypothesis is satisfi ed and

1<

4)2(

dd , then we have


16

0si2

si2))()((

42

44

d

dd

nnhN

nhNkncInd

where 22

21 ,),(),( ndnc are the same as in Lemma 1, 21

24 2= VV and:

dyyyDXVarV ' )(),(2))((= 21

21

dyyyDXVardyyyD F

' )(),())(()(),( 21

2 (13)

))(),(())(),((= 221

2

2=2 dxxyDXXCovV '

kk

))(),(())(),(( 2

12=

dyyyDXXCov kFFk

(14)

))(),(()(),( 12

2=

2kF

k

' XXCovdyyyD

))(),(()(),( 1

2

2=

2 XXCovdyyyD Fkk

'

(15)

Corollary 1. Under the assumptions of Lemma 1, and if the null hypothesis is satisfi ed, we have

a)

NkdxxxxEIhnthennhIfd

nd

42

021/24 2])(ˆ)],()(ˆ[[,

b)

NduuduuKnh

InhthennhIfd

dndd

222/24/2 2])()(

1[0,

4. Statistical test and its asymptotical distributions

The following statistical tests are based upon the estimates of 22 and 2

242

can be consistently estimated by

dvduvuKuKXn i

n

i

23

1=])()([)(ˆ

1 . To ob-

tain consistent estimates of 24 , we defi ne


17

};)(ˆ))(ˆ({)(ˆ))(ˆ(=))(( 222

12 dxxxdxxxXarV

=))(),(( 111=

kFFkXXCov

;)(

1)(

11

22

ˆ1=

ˆ1=1=

inF

n

ikinF

kn

in

nG

k

Xn

XnGk

=))(),(( 12

12

1=

kkXXCov

;)(ˆ

1)(ˆ)(ˆ

11

22

2

1=

22

1=1=

i

n

ikii

kn

in

nG

k

Xn

XXnGk

=))(),(( 112

1=

kFkXXCov

;)()(ˆ

1)()(ˆ

11

2ˆ

1=

2

1=2ˆ

2

1=1=

kinF

n

ii

n

ikinFi

kn

in

nG

k

XXn

XXnGk

=))(),(( 112

1=XXCov Fkk

,)()(ˆ

1)()(ˆ

11

2ˆ

1=

2

1=2ˆ

2

1=1=

inF

n

iki

n

iinFki

kn

in

nG

k

XXn

XXnGk

where Gn is a delay of a selected truncate such that =lim nG y )(= 1/3nOGn

. This is the estimate of the spectral density at zero see (Yacine Aït-Sahalia, 1992). It is possible to fi nd consistent estimates of V1 and V2 substituing the previous estimates in equations (13) and (14). Using the results obtained tests values for ),(=)(: 00 xxH against the general alternative ),()(:1 xxH for any .


18

5. Extension of the statistical test of Yacine Aït-Sahalia

Now we defi ne the statistical tests as follows

4

221/2

1ˆ2

})(ˆ)](~)(~*[{=

k

dxxxxKIhnT

hn

n

(16)

2

22/2

2ˆ2

])()([=

dzzdzzKInhhT

ndd

n

(17)

where

duuh

uxKhxK d

h )(~=)(~*

Theorem 3. Under premises 1 to 9, if H0 is satis fi ed and

1<4)2(

dd

then

a) NTthennhIfd

nd

14/2

b)

NTthennhIfd

nd

24/2 0

Theorem 3 stablishes that a statistical test can be constructed to a

signifi cant level to prove H0 against H1 that correspond to a diverse amount of smoothing applied to data. Also it is pointed that the statistical test T2n is an extension Yacine Aït-Sahalia (1996) test that can be applied to two factors model, by the small value of the smoothed parameter.

6. Statistical test for skew correction

As established before, the skew introduced by the kernel estimate of the density function has a signifi cant infl uence in the test of H0 based upon the es timate of the squared error integral. The skew eff ects are refl ected upon the restriction of the smoothing parameter, which can decrease to zero and cannot decrease too fast or too slow when the size of the sample tends to infi nite. Based upon diff erent restrictions in the smoothing parameter, two diff erent tests can be obtained. Now, we present a statistical test that applies to any diff usion process of fi nite dimension, but also does not depend on the amount of smoothing


19

applied to data. Under H0, the expected value of the non parametric estimate )(ˆ x is

duu

hux

KhxKxE dh ),()(=),(*=)(ˆ 00 . Therefore, to eliminate

the skew eff ects, we can construct an statistical test for adjusted skew based upon the weighted integral of the square diff erence divided by the non parametric estimate of the marginal density function implied in the data and the estimate of smoothed kernel of the function of marginal density implied by the parametric model,

dxxKxJ hn2)](~*)(ˆ[=

We can decompose Jn as follows

dxxxKxEdxxxExJ hn )(ˆ)](~*)(~[)(ˆ)](~)(ˆ[= 22 dxxxKxExEx h )(ˆ)](~*)(~)][(~)(ˆ[2

1211

2 2)(ˆ)](~)(ˆ[= JJdxxxEx

Theorem 4. Under premises 1 to 9, if H0 is observed and

1<)2(

dd , then

NdzzpidzzK

nhJnh

Tddn

d

n

2

22/2

ˆ2

])()(1

[=

(18)

where 22̂ is defi ned as before.

The asymptotic distribution of the adjusted skew test is the same regardless of the nature of the data as under or over smoothing. It is also important to note that the adjusted skew test can be applied to de marginal density function of any diff usion process of fi nite dimensions.

7. Parametric models of two factors

There is a general acceptance that one factor models of the term structure cannot succesfully explain several characteristics of bond returns. The


20

reason for this is tha t the factor of the term structure and the returns and outcomes of the bonds must be perfectly correlated. As we have seen in the Introduction, several authors accept that moved by two uncertainty factors at least. So actual research focus into models of term structure that uses two state variables or stochastic factors. These models are mutually exclusive and do create diff erent values when used to predict the price derived from diff erent rates. From the two model research we can fi nd that of Brennan y Schwartz (1979) and that of Schaefer Schwartz (1984) that create their specifi cations based upon stochastic processes using two interest rates. Before we use the specifi cation test of Brennan-Schwartz and the model of Schaefer-Schwartz , we will fi nd the marginal density functions of such models.

7.1 Models of term structure of Brennan-Schwartz and Schaefer-Schwartz

7.1.1 Model of Term Structure of Brennan-Schwartz

Brennan and Schwartz (1979) developed a straddle model for term structure of inte rest rates under the assumption that all the term structure can be expressed at any time in terms of the outcomes of instruments of short and long terms. If r defi nes the instant interest rate and l is the long term interest rate its model can be expressed as,

1

2 )(]1/2)lnln([= dWrdtrplrdr trrttt (19)

2

2 )(]1/2)ln(([= dWldtlkldl tllttt (20)

where p is the diff erence between the middle levels of 1nl and 1nr; is the adjustment coeffi cient for the speed in which 1nr returns to )ln( pl ; k is the adjustment coeffi cient for the speed in which 1nl returns to the mean level of ; and =)( 21dWdWE Using the Ito´s lemma, the previous equations can be writt en as,

1)ln)ln((=ln dWdtrplrd rttt (21)

2)ln(=ln dWdtlkld ltt (22)


21

To put into practice our test, we have to estimate the unknown parameters assumed under the null hypothesis. The bivariate processes for 1nr and 1nl is stationary in a joint form if and k are greater than zero. Also, the solution of equations (21) and (22) is a Gaussian process if and only if the initial value is constant or normaly distributed. As a matt er of fact the solution of the linear stochastic diff erential equation (21) and (22) can be expressed as dWBstAXttAX tt

1/2

00 ))((exp)())((exp= (23)

where

2

1

2

2

=,0

0=,

0= ,=,

ln

ln=

dW

dWdWB

kA

p

l

rX

l

r

t

tt

Otherwise, if and k are greater than zero, then the solution follows a Gaussian stationary process. For a stochastic stationary process, the marginal density function equals the density of the initial observation, therefore, we can obtain a stationary marginal density function of this process once we have the density function of the initial random variable. The marginal density can be obtained with equation (22) as follows,

))())((exp

||21

=)( 11/2

XXXf ' (24)

where

t

t

l

rX

ln

ln= ,=

2221

1211

)

21

)(2

21

())(

()

21

)(

1)((2

2= 2222

2

11

kkkkk llr

r

)

)(1

21

)(()1

(2= 212 kkkk llr


22

1221 =

kl

2=

2

22

7.1.2 Model of term structure of Schaefer-Schwartz

Schaefer and Schwartz (1984) use the same information of the interest rate as Brennan and Schwartz (1979), but express its model in terms of the long term interest rate and the diff erenc e between it and the short term interest rate. This is a redefi nition of the variables that make possible to obtain an analytical solution for the problem of valuation. Furthermore, Schaefer and Schwartz assume that the diff erence follows the process of Ornstein-Uhlenbeck (a process of the reversion of the mean and the constant diff usion function). In fi nancial research, the Ornstein-Uhlenbeck process has been used to model the short term interest rate. Nevertheless, it is reasonable to assumme a bett er probability that it is the diff erence and not the short term rate what follows this kind of process due to the fact that the model allows negative values. The specifi c form of the stochastic process of Schaefer and Schwartz is,

1)(= dWdtSdS tt (25)

22 )(),,(= dWldttlSdl ttt (26)

where dW1 and dW2 are standard Wiener processes with dtdWdWdWEdWE ==0,=][=][ 2

22

121 . As in the model of Brennan-Schwartz , Schaefer and Schwartz assume that the difusion function of the console rate depends on its level. The tendency function of the console rate stays as in its general form. The process of Ornstein-Uhlenbeck, 1)(= dWdtSdS tt , has a transition density function given by

})(2

))(({exp

)(2

1=),=|,=( 2

2)0(

0

2000 tess

ttsStsSf

tt

tt


23

where

].[12

=)()0(2

22 tt

et

Let us suppose that the spread process shows the property of reversion to the mean ( 0> ), then when 0t or )( 0tt , the marginal density of the stochastic process is invariant through time, i.e., the spread process is stationary and the marginal density function can be expressed as follows:

2

22 )(exp

s

For stationary diff usion processes, the only stationary processes with explicit transition density functions are those who have the linear functional specifi cation for the tendency function and the specifi cation of the cuadratic function for the diff usion function.

7.2 Empirical tests and specifi cation analysis of the term structure of the models of Brennan-Schwartz and Schaefer-Schwartz

The time series used in this analysis include daily observations of Cetes for 1 day to 10 years of maturity. The analyzed sample period covers from july 9th of 2002 up to december 7th of 2009, which comprises 1 867 observations for each term. Based upon the stationary density functions derived previously, we can estimate the unknown parameters, reducing to a minimal expression the cuadratic error between the estimate of the non parametric density and the density of the parametric model. The results of the parametric estimate of both models are shown in tables 1 and 2.

The estimates of ))()()(( 22 dxxdzzK and ))()())()((( 42 dxxduxuKuK are respectively:

))(log),(log(ˆ

1)()( 0

1=

2ii

n

i

lrn

dzzK

)))(log),(log(ˆ

1)())()((( 3

01=

2ii

n

i

lrn

dxduxuKuK


24

Tabla 1Parameter values estimated with the Brennan and Schwarts model

Parameter k p r l

Estimate 0.98725 0.23873 0.10191 -0.01533

0.4956 0.21096 0.24627

Tabla 2Values of the parameters estimate with the Schaefer and Schwartz model

Parameter

Estimate 1.7612 1.50114 0.1796

Taking a critical value of 6.32 to obtain a test level of 0.05%. For the normal kernel, the two kernel constants are:

1 1

2 ,1

24

d

z dz

d

2

if K =

if

2

1 12 2

128

d

K u K u x du dx

d

if

if

To estimate the marginal density, the smoothed parameter hn = h is selected such that =lim

2nhn and 0=lim5nh . The quality of the estimate of the

density depends mainly on the selection of the smoothing parameter rather than on the kernel. We select 1/5= nch n , where )(ln(= nccn . c is choosed such that it minimizes the mean cuadratic integrable error of the estimate. The results of this test are shown in Table 3. Both models Brennan-Schwartz and Schaefer-Schwartz are rejected with a signifi cance level of 0.05%. The main reasons for rejection of both models are: fi rst, the constant diff usions limit volatilities to be uniformly increasing. Second, if a model has a linear especifi cation for the drift and also has a constant diff usion, as in the case of Brennan-Schwartz and Schwartz -Schaefer, the parameters founded in the tendency and difussion functions might not be homogeneous, that is, shifts in the economical regime implies the possible lack of stationarity of the parameters during the modeling process.


25

Tabla 3Tests of parametric specifi cation of two factor models of time continuum

Brennan-Schwartz Function of Tendency Function of

Diffusion Statistical Test I Statistical Test II Critical

Value Result

nT2 nT

2[ (ln ln ) 1/ 2 rr l p r rr 46.2792 1.645 Reject 2[ ( ( ln ) 1/ 2 )]ll k l ll 21.48973 1.645 Reject

Schaefer-Schwartz

( ) , ,tS s l t 75.07685 1.645 Reject

l 123.97681 1.645 Reject

8. Conclusions It was proposed a statistical test for the specifi cation of parametric models of two factors. We present three diff erent tests. The fi rst two are based upon a comparison between the estimate of the kernel density of the unknown density function and the estimate of ),( x by the Delta method. The last test is based upon the idea of comparison between the estimate of the kernel density and the parametric model of the smoothed density kernel to avoid skew eff ects. The advantage of the last test respect the fi rst two tests is its validity for under smoothed data and also over smoothed data. This test can be applied in many fi nancial process which of research importance. Particularly, this test was applied to determine if the dynamic of the term structure of Cetes can be modeled from the assumptions of two models, that of Brennan-Schwartz (1979) and that of Schaefer-Schwartz (1984), the test results show that both continuous models are rejected at a 5% level as accurate describing the dynamic of Cetes. Finally the causes for rejection were analyzed for both models.


26

References

Aït-Sahalia, Y. (1996), “Testing Continuous-Time Models of The Spot Interest Rate”. Review of Financial Studies, vol. 9, num. 2, pp. 385-426.

Aït-Sahalia, Y. (l992), “The Delta Method for Nonparametric Kernel Functionals”, Working paper, MIT.

Bakshi G. S. and Z. Chen (1996), “Infl ation, asset prices and the term structure of interest rates in monetary economies”, The Review of Financial Studies 9, pp. 241-275.

Buraschi, A. and A. Jiltsov (2001), “Time-varying infl ation risk premia and the expectations hypothesis: a monetary model of the treasury yield curve”. Journal of Financial Economics.

Chen, L. (1996), “Stochastic mean and stochastic volatility-a three factor model of the term structure of interest rates and its application in derivatives pricing and risk management”, Financial Markets, Institutions and Instruments, 5, pp. 1-87.

Chen, R. R. and L. Scott (1993), “Maximum Likelihood Estimation for a Multifactor Equilibrium Model of the Term Structure of Interest Rates”, Journal of Fixed Income, 3, pp. 14-31.

Cortázar, G. and E. Schwartz (1994), “The valuation of commodity-contingent claims”, Journal of Derivatives, vol. 1, num. 4, pp. 27-39 77.

Cox, J. C., J. E. Ingersoll and S. A. Ross (1985), “A Theory of the Term Structure of Interest Rates”, Econometrica, 53, pp. 385-407.

Cultberson, J. (1957), “The term structure of interest rates”, Quarterly Journal of Economics, vol. 71, pp. 485-517.

Dai, Q. and K. Singleton (2002), “Expectation puzzles, time-varying risk premia, and affi ne models of the term structure”, Journal of Financial Economics, 63, 415-441.

D´Ecclesia, R. L. and S. A. Zenios (1994), “Risk Factor Analysis and Portfolio Immunization in the Italian Bond Market”, Journal of Fixed Income, vol. 4, num. 2, pp. 51-58.

Duffi e, D. and R. Kan (1996), “A Yield-Factor Model of Interest Rates”, Mathematical Finance, vol. 6, num. 4, pp. 379-406.

Dybvig, P. H. (1989), “Bond and Option Pricing Based on The Current Term Structure”, Working paper, Washington University.

Elton, E. J., M. Gruber and R. Michaely (1990), “The Structure of Spot Rates and Immunization”, The Journal of Finance, vol. 45, num. 2, pp. 629-642.


27

Fisher, I. (1896), “Appreciation and interest”, AEA Publications, vol. 3, num. 11, pp. 331-442.

Hicks, J. (1939), Value and Capital, Segunda Edición, Londres: Oxford University Press.

Knez, J., R. Litt erman and J. Scheinkman (1996), “Exploration into Factors Explaining Money Markets Returns”, Journal of Finance, vol. 49, num. 5, pp. 1861-1881.

Litt erman, R. and J. A. Scheinkman (1991), “Common Factors Aff ecting Bond Returns”, Journal of Fixed Income, 1, pp. 54-61.

Lund, J. (1997), Non-Linear Kalman Filtering Techniques for Term Structure Models, Aarhus School of Business.

Pearson, N. D. and T. S. Sun (1994), “Exploiting the Conditional Density in Estimating the Term Structure:An Application to the Cox, Ingersoll, and Ross Model”, Journal of Finance, 49, pp. 1279-1304.

Steeley, J. M. (1990), “Modelling the dynamics of the term structure of interest rates”, Economic and Social Review, vol. 21, num. 4, pp. 337-361.Svensson, L. (1994), “Estimating and interpreting forward interest rates:

Sweden 1992-94”, CEPR Discussion Paper 1051.Vasicek, O. A. (1997), “An equilibrium Characterization of the Term

Structure”, Journal of Financial Economics, 5, pp. 177-188.79.


INNOVATION ON NANOMATERIALSACROSS COUNTRIES IN A

TRIPLE HELIX FRAMEWORK:THE CASE OXIDE OF HAFNIUM

Alenka Guzmán Chávez*

Resumen

El objetivo de este artículo es identifi car las capacidades de innovación y los fl ujos de conocimiento de fi rmas, universidades e institutos de investigación en el campo de nanomateriales en diversos países, particularmente de nanomateriales basados en hafnium. Mediante del análisis de las patentes concedidas en la Ofi cina de Patentes y Marcas de los Estados Unidos (USPTO) en el campo de hafnium, se busca conocer la contribución de los empresarios, gobierno e instituciones universitarias y de investigación a la innovación y cómo los fl ujos de conocimiento se expresan en el ámbito de los inventores. Asimismo, nos proponemos explorar cómo en México, las fi rmas, universidades y gobierno contribuyen a desarrollar capacidades científi cas y tecnológicas para desplegar este nuevo paradigma tecnológico y, por tanto, a favorecer el alcance tecnológico en el campo de los nanomateriales.Palabras clave: Hafnium nanomateriales, I&D, patentes USPTO, inventores, papel de fi rmas-universidad-gobierno de México en innovación y alcance tecnológicoClasifi cación JEL: O31, O34

* Professor at Economics Department of Universidad Autónoma Metropolitana, Campus Iztapalapa. Electronic mail: <[email protected]>.

A preliminar version was the paper: “Is it possible for the developing countries to catch up technolo-gically in the nanotechnology fi eld in a Triple Helix Model? The case of nanomaterials in Mexico”, presented at VIII Triple Helix Conference, Triple Helix in the Development of Cities of Knowledge, Expanding Communities and Connecting Regions, Madrid, 20-22 October 2010.

(Recibido: Agosto 2011 / Aprobado: Diciembre 2011)

ALENKA GUZMÁN

30

Abstract

The aim of this paper is to identify the innovation capabilities and knowl-edge fl ows of fi rms, universities and research institutes in the nanomaterials fi eld across countries, particularly in the “hafnium” nanomaterial. Through the analysis of patents granted at the United States Patent and Trademark Offi ce (USPTO) in hafnium fi eld we want to know how the entrepreneurs, government and academic and research institutions are concern to innovate and how the knowledge fl ows are manifested at the inventors level. As same, we want to explore how in Mexico the fi rms, universities and government are contributing to build scientifi c and technological capabilities in this new scientifi c and technological paradigm. Taking into account the international innovation gaps in hafnium nanomaterial, we discus about the main insti-tutional policies that Mexico could foster to build scientifi c and technologi-cal capabilities, to spread the new technological paradigm and, therefore, to favor the technological catch up in nanomaterials fi eld.Keywords: Hafnium nanomaterial, R&D, patents, Mexican fi rms-university-government role on innovation and technological catching upJEL Classifi cation: O31, O34

1. Introduction

The remarkable scientifi c progress on knowledge of the atomic and molecular material properties has driven to the convergence of a wide scope of scientifi c disciplines. Since the development of the nanosciences fi eld and the emergence of nanotechnologies as a new technological paradigm, the role of the governmental policies has became of crucial importance to foster a virtuous circle where universities, fi rms and government institutions could interact to innovate.

Nanotechnology innovation has been particularly dynamic in the information and communication technologies (ICT). “Since the invention of silicon based transistors, … hafnium (HfO2) emerges from all likely candidates to become the new gold standard in the microelectronics industry. HfO2 based materials have emerged as the designated dielectrics for future generation of nano-electronics with a gate length less than 45nm” (Choi, Mao and Chang, 2011). The progress of this hafnium nanomaterials

CONTENIDO 2

INNOVATION ON NANOMATERIALS ACROSS COUNTRIES IN A TRIPLE HELIX FRAMEWORK: THE CASE OXIDE OF HAFNIUM

31

could be entail the end of the silicon age and to pass towards an effi cient and competitive new technological paradigm by: i) improving the control of logical nanocircuits; ii) reducing radically the size and increasing the capacity of computer processors and, iii) improving the performance and speed of nanochips for data transmission and communications.

The aim of this paper is to identify which countries are moving to the frontier nanotechnologies, and specifi cally in nanomaterials. By analyzing patents granted at USPTO in hafnium fi eld (a new nanomaterial) we want to know how the entrepreneurs, government and institutions are concern to innovate in this fi eld and how the knowledge fl ows are manifested at the inventors level. Likewise we want to know if Mexico is building capabilities to develop frontier nanotechnologies, such as in hafnium or other nanomaterials, by considering universities, government and entrepreneurial scopes. Particularly, we want to analyze the nature of the innovation of this emerging sector in Mexico, identifying the R&D and innovation eff orts, the communicating vessels between the universities, fi rms and governmental agencies in a national, regional and international context. We set out the next questions: How the universities, research institutes and entrepreneurs across countries are concern to develop innovation in the nanosciences and nanotechnology? In the case of Mexico is the government fostering policies to encourage this new scientifi c and technological paradigm by supporting research projects and education programs, incentive the entrepreneurial investment and promoting the links and cooperation between universities and fi rms? What are the challenges for Mexico to be capable of appropriating the new knowledge generated regarding the new nanomaterials, as the hafnium, to boost the industrial activity? In this sense, we state the following hypothesis: the path of innovation in nanotechnologies, specially in hafnium nanomaterial, suggest that universities and research institutions, fi rms and government are key actors to develop scientifi c and technological knowledge, to create new process and new products impacting the industrial and market scopes and to foster R&D and innovation policies to assure to be at technological frontier. In this sense, in Mexico, as other developing countries, characterized by a lack of fi nancial resources, the new knowledge generated in nanotechnologies by the research teams could be appropriated by the multinational fi rms (without having benefi ts for the country) if there is no fi nancial support, alongside institutional policies to develop a new local industry based on the nanotechnology paradigm.

ALENKA GUZMÁN

32

Firstly, we discuss the main issues concerning the debate of the institutional innovations or innovation policies to promote the closer links between academia and entrepreneurial sectors by considering mainly the National System of Innovation approach and the Triple Helix framework. Next, in the second section we analyze the emergence of the hafnium (new nanomaterial) replacing the silicon oxide. In the third section we identify the technological gap in nanomaterials across countries, including the eff orts on R&D, the innovation capabilities (patents and scientifi c production), and research networks. Finally, in the last section we identify the nature of the university-fi rm-government linkage building capabilities in the sector of nanosciences and nanotechnology in Mexico. We point out some elements and strategies, which might contribute to the design of public policies in Mexico.

2. Theoretical framework

The increasing importance achieved by the knowledge economy has focused the necessity to discus about the role of universities in the economic development and the institutional policies to generate an adequate environment that favors the closer relations between university and fi rms. As producer of the scientifi c and technological knowledge, the universities play a catalytic role in the innovation process (Etz kowitz and Leydesdorff , 2000). Nevertheless fi rms are recognized to have the leading role on innovation, according to National System of Innovation (Lundvall, 1992; Nelson, 1993) and the statal policies could have a promoter leadership role, following Triangle of Sabato Model (Sábato and Mackenzi, 1982), the interaction between universities, fi rms and governmental agencies through institutionals arrangements are essential to foster and to increase the knowledge-based societes, from the Triple Helix point of view (Etz kowitz and Leydesdorff , 2000).

Although the networks between science and technology are the key element for knowledge production in fi elds such as biotechnology and nanotechnology (Freeman, 1974; Gibbons et al., 1994; Foray, 2000) and consequently, to the national and regional developments, there has been a strong debate concerning the academic technology transfer (Mowery, Nelson, Sampat and Ziedonis, 2004). The several obstacles to develop successfully the industry and sience links are associated to diff erent kind of arguments,


33

mainly those focused to institutional changes, and more precisely to the new mission of university and the appropriaton of benefi ts generated derived from the new knowledge and technological change.1

Firstly, it is important to identify the nature of collaboration of universities and fi rms with regard to the market. While fi rms which are collaborating compete in the output market, the universites-fi rms collaboration are not characterized by a logic of competition, specially because “…the universities are not being able to apppropiate exclusively the benefi ts from the new know how… unless the know how would leak out the competitors indirectly through common partners” (Veugelers and Cassiman, 2005: 359).

Secondly, the joint R&D projects between universities and industry are arranged with a “...high uncertainty, high information asymmetries between partners, high transaction cost for knowledge exchange requiring the presence of absorptive capacity, high spillovers to other market actors and, restrictions for fi nancing knowledge production and exchange activities due to risk-averse and short-term oriented fi nancial markets”2 (Veugelers and Cassiman, 2005: 359). The uncertaintity in this kind of cooperation could be explained by the nature of scientifi c knowledge. But regarding the transaction costs derived from academic technology-transfer, they are seen by Swedish academics as unnnecesary because once the knowledge is patented, it cannot go freely to industry (Etz kowitz and Leydesdorff , 2000). Otherwise, the regulation of intellectual property rigths (IPR) and tecnological transfer regulation at universites, specially those referring the new organizational mechanisms, is appreciated as necessary to incentive scientifi c and technological innovation and assure the knowledge fl ows and the innovation returns.3

Thirdly, in a university-industry-governement relation framework aiming an alternative strategy for an innovative path, economic growth and

1 The establishment of links between university and fi rm has been the outcome of a process in which, on the one hand, the university has transformed the environment of its mission and, on the other, fi rms have internalized the need for cooperation in order to strengthen R&D with the idea of developing new products and processes in the context of the innovation economy.

2 The uncertainty is present in this kind of cooperation because the nature of scientifi c knowledge and therefore the demand of the universities scientifi c know how will be localized in some particular fi rms associated to specifi c technologies as biotecnology and nanotechnology.

3 The Act Bayh Dole has been a reference for developed countries as same of developing countries as a statal policy to endorse academic institutions to be involved in patenting and transferring technology. The evidence about the impact of the Bayh Dole Act in the growth of patenting activity in the univer-sities is not conclusive. If it is true that patents from universities have grown during the 80s and 90s, also is true that other factors could have infl uenced in this tendency (Mowery et al. 2004).

ALENKA GUZMÁN

34

social transformation, the analysis must be focused on the factors explaining the universities R&D collaborations, as the fi rm size, the government support, the patenting and scientifi c industry, the strategies to choose the complementarity between the internal and external technological sources (Arora and Gambardella, 1990). Hence, the fi rm builds absorption of external knowledge as it increases the internal R&D eff ort (Cohen and Levin, 1989; Kamien and Zang, 2000), meanwhile the fortress of internal R&D facilitates the adoption of imported technologies.4 At the same time, the acquisition of external technologies favors the optimization of a fi rm’s R&D eff orts and consequently contributes to improve its technological capabilities to undertake an endogenous innovation path (Kamien and Zang, 2000; Kaiser, 2002). Concerning the links university-fi rms, Veugelers and Cassiman (2005: 361) state that “fi rms being engaged in other innovation strategies will have a larger incentive to engage in industry-science cooperation”. The hypothesis expecting fi rms having more R&D activities, both basic and applied, will benefi t more from the basic capabilities developed through R&D cooperation with universities is confi rmed in specifi c science industries. They founded that “fi rms impeded by cost to innovate are more likely to cooperate with universities, att racted by the often government subsidized cost-sharing in public-private partnerships.” (Veugelers and Cassiman, 2005: 373). Another fi nding is that the fact of fi rms protecting their properties rights does not aff ect the decision to cooperate with universities.

The literature regarding innovative activity in developing countries has identifi ed diff erent factors that block the R&D investment and stop the innovative eff orts of the companies; among them are: unlikely access to fi nancing and macroeconomic instability, low level of human capital, lack of policies promoting the interactions between the diff erent institutional scopes, necessity to make regulatory and institutional reforms. The developed countries fi rms and universities are internalizing the need to undertake R&D collaboration, promote university spin-off fi rms, transferring specialized knowledge. The joint R&D and innovation eff orts from developing countries must be higher to develop absorption capabilities that allow profi ting from foreign technologies and further developing endogenous scientifi c and technological knowledge. Specially, in these countries, these two helices

4 For the case of developing countries see: Caves and Ukesa, 1976; Katrak, 1997; and Arora, 1997.


35

need of a third one: the government support and institutional policies leading the interaction of knowledge networks (even in a global context) and incentive the industrial activity, therefore improving the economic and social development.

3. The emergence of hafnium oxide as nanomaterial in semiconductor fi eld

There are four nanotechnologies that converge with scientifi c and technological disciplines and they have several application sectors: i) nanometrology/nanoanalysis; ii) nanobiotechnology/nanomedicine; iii) nanomaterials/nano chemical/nanoelectronic and iv) nano-optic (Abricht et al., 2004: 17).

In electronic fi eld, nanotechnology augur a big fertility to the semiconductors devices, spurring economically from 10 to 15 years more than 300 thousands of millions of dollars by year for each area (Doering, 2001: 74).

The silicon dioxide, SiO2, and the silicon oxynitride were essential mate-rials for semiconductor devices development, key of technological revolu-tion in the ICT, more the three decades ago. As semiconductors have got-ten smaller, the limiting factor in further size reduction has been the ability of the silicon oxide gate to perform below 10 angstroms where leakage oc-curs (Keita, Keisuke, Yasuhito and Hiroshi, 2011). Therefore, these materi-als risk to be replaced by gate dielectric materials with signifi cantly higher dielectric constant (Sparks, Lysaght and Rhoad, 2005). The future generation semiconductor devices, as CMOS architectures and Metal-Insulator-Metal architectures for DRAM applications, need new materials such as having high dielectric constant oxides. In that sense, SiO2 reaches its physical limits, by the fact it has equivalent thickness of about 1nm. Among various metal compositions having the materials requirements as k, (leakage current, crys-tallization temperature, charge trapping) and the integration requirements (thermal stability on interface, dry etching feasibility), Hafnium based ox-ides is one of the most promising candidates (Stéphane, 2008). The eff ort to introduce a high-k gate dielectric thin fi lm with equivalent electrical silicon oxide thickness (EOT) less than 1nm that meets required performance char-acteristics including low leakage current and high electron mobility, while

ALENKA GUZMÁN

36

demonstrating the capability of continued scaling, has evolved with the re-alization that the combination of many specifi c chemical treatments in con-junction with variations in Hf silicate (HfSiO) composition may be necessary (Sparks, Lysaght and Rhoad, 2005)

Hafnium could replace polysilicon as the principal gate or electrode mate-rial in metal oxide semiconductor fi eld eff ect transistors (MOSFETs), because they have become essential for all modern semiconductors. “Using hafnium based alloys, as this di-electric gate has allowed for the development of MOS-FET gates smaller than 10 angstroms. This allows for further size reduction, reduced switching power requirements and improved performance”.5

Therefore, Hafnium based materials seems to be the designated dielec-trics for the new paradigm of nano-electronics, passing from thermal pro-cesses to atomic layer deposition processes. These new materials provide a physically thicker layer to suppress the quantum mechanical tunneling through the dielectric layer. They have a thin gate length less than 45nm. (Choi, Mao and Chang, 2011).

Hafnium is obtained by refi ning various zirconic mineral deposits and was discovered by Dirk Coster in 1923. “Hafnium is available as metal and compounds with purities from 99% to 99.999% (ACS grade to ultra-high pu-rity); metals in the form of foil, sputt ering target, and rod, and compounds as submicron and nanopowder. It’s primary uses are due to its ability as a nuclear ‘gett er’ or absorber of neutrons. It is a primary component in nuclear control rods for this purpose. It also fi nds uses as a dopant in the alloy of steel and titanium. It is also used in the production of mantles for high inten-sity incandescent lamps”.6

The progress of nanoparticles and nanopowders allows to hafnium ox-ides other properties and benefi ts with clear advantages linked to the fact that Hafnium is available in soluble forms including chloride, nitrates and acetates. These compounds are also manufactured as solutions at specifi ed stoichiometries.7

Given the importance of the emergence of nanotechnologies, govern-ments and multinationals are making gross investments on R&D in this fi eld.

5 <htt p://www.americanelements.co.uk/hf.htm>.6 Hafnium is a Block D, Group 4, Period 6 element. The electronic confi guration is [Xe] 4f14 5d2 6s2. In its

elemental form hafnium’s CAS number is 7440-58-6. The hafnium atom has a radius of 156.4.pm and it’s Van der Waals radius is 200.pm. (Ibídem).

7 Ibídem.


37

By 2005 their R&D spending on nanotechnologies reached 9 billion dollars and 0.5 billion came from venture capital fi rms. Specially in the nanomateri-als, where the market has registered an enormous growth,8 multinationals, such as IBM, Texas Instruments and Intel are hugely fi nancing on HfO2 research and development of systems and also have start to launch the fi rst innovative hafnium based products into the market. The speed at which the new era of hafnium could displace older technology based on silicon will depend largely on the accuracy and precision with which ultrathin fi lms can be elaborated and used for manufacturing the computer processors, hard drives and the other MOS devices.

4. Technological gaps betweendeveloped and developing countries in nanomaterials

The public R&D investment in nanotechnologies is relatively recent. Since the second half of the 90s, the United States, countries of European Union and Japan started to support R&D activities focused on nanotechnologies and increased even more from the beginning of the XXI century. Between 1997 to 2006 we observe three facts in the evolution of R&D expenditure: i) the R&D has growth 30.3 per cent in annual average rate ii) the leadership of United States, who has cumulated one quarter of total R&D and iii) the notable increasing participation of Asian countries as China, Korea and Taiwan on global R&D, with a contribution of 660 millions of dollars in 2004, which means two thirds of that invested as whole by the group of other countries including Australia, Canada, Singapore, Israel and East European.

According to the nature of the diff erent National Systems of Innovation of the countries, in the US the private support to R&D in nanotech is slightly higher (54.4%) than the public; in Japan is even higher (63.2%). In contrast, in the European countries the importance of public funding is bigger than the private.

In accordance to the bigger R&D eff orts of US, this country maintains an extensive leadership in nanotechnology inventive activity over the other

8 In 2006 was predicted for two year later a total demand for nanoscale materials, device and tools more than 28 billion of dollars. Meanwhile, the US nanotech market is predicted to reach 3.3 billion by 2008 and cross 19.8 billion by 2013 (The World Nanotechnology Market, 2006).

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38

industrialized countries and some Emerging countries from 1980 to 2009 in nonomaterials patents. Patents are an expression of the capacity of creating new knowledge. Following the increased tendency of R&D spending in nanotechnologies the number of applications and patents granted by the USPTO to residents and no residents have raised. Between 1980 and 2009 we have found 5 830 patents granted in the class 977 of USPTO, referring to nanotechnologies. From these patents 952 belong to patents in seminconductor fi eld of the nanomaterial sector.

Graphic 1R&D spending in nanotechnology sector by sector funding, 2004-2006

(Millions US dls)

Source: Plamberg et al. (2009: p.33).

The patents granted by USPTO to residents and non residents in nanomaterial fi eld concerning hafnium are 153 since 1982 to July 2010. Of these patentes, 83% belong to the United States and only four countries have applied and granted patents in this emerging technology. Japan is a follower with 10.2% of the total patents. The contribution of Germany (3.3%), Korea (3.3%) and France (2.0%) is marginal. Mexico doesn’t have any USPTO patent in hafnium nanomaterials until now.

From the middle of the 90s, the inventive in hafnium fi eld has increased remarkably in the United States, stressing the technological gaps respect to other developed countries. In the United States, the main locations of


39

hafnium innovative fi rms or institutions are located in California and New York, with 30 and 21 patents respectively; Texas and Missouri with less patents (9 each one).

Graphic 2Patents granted to residents and non residents in

nanotechnology fi eld by USPTO,1980-2008

Source: USPTO, patents data base, class 977.

Graphic 3Patents in nanomaterial fi eld, hafnium applied for USPTO countries,

1982-2009

Source: USPTO, patents data base, class 977.

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40

Graphic 4Technological gaps of countries based in the

number of patents granted in USPTO, 1980-2009

Source: USPTO patents data base class 977/hafnium.

Near to the half of the total patents in hafnium are assigned to fi rms. The universities or research institutes have contributed near to two thirds and individuals have 13% of the patents granted. The joint patents assigny are marginal; only 2% of patents belong jointly to fi rms and individuals and 1% to fi rms and institutions.

We identify, only fi rms among those that have more patents and mainly Americans. Those who have one patent are either fi rms of the other countries or institutions/universities.

We have build a symmetrical matrix associating the total number of the inventors of hafnium nanomaterials patents granted to residents and non residents of the United States with the origin of the inventor, either country or region (US state), with USPTO patents data base class 977/hafnium nanomaterials. We identify from where are coming the inventors that take part of the research teams of the novelty in hafnium fi eld. We take into account not only countries but also we include the diff erent American states in order to notice researcher mobility not only across countries but also across the Unites States. The number of countries in the matrix is bigger than those that have patents granted in hafnium because they are only indicating the origin


41

of the researchers that have contributed to the creation of the patent that is the case of Netherlands, Norway, India and China.

Graphic 5Patents granted by USPTO in hafnium nanomaterials fi eld by assigny type,

1988-2009

Source: USPTO patents data base, class 977/hafnium.

This research mobility could be explained by the individual migration of researchers highly skilled to regions of the United States or other countries, but also could be on account of collaborating research networks. Most of the total patents of each country or American states have inventors from the place, but also have inventors coming from other regions or countries. We identify that researcher mobility is higher to California, New York, Illinois, Ohio and Texas. The inventors of patents assigned to California come from six diff erent regions of the US (Delaware, Illinois, Minnesota, Oregon and from other countries as Korea and Norway), but the researchers are mainly residents from California (80.1%). Meanwhile, to New York are coming researchers from seven US regions (California, Connecticut, Delaware, Vermont) and from India, but almost four fi fths parties of the inventors are residents of New York. Even if Japan has a contribution to the knowledge progress of hafnium, his innovative activity is made almost without having foreign inventors; among the 34 inventors only there is an American from Ohio. France has similar phenomenon. In the total patents where Korea is the fi rst assignee, there 12 are Korean inventors and 2 are Americans from New York; Samsung, a Korean fi rm, shares with General

ALENKA GUZMÁN

42

Electric, an American fi rm, a patent. Although India does not have any patent in hafnium technology, for Indian researchers are inventors in American patents. Although is wider the mobility of the inventors across the Unites States, taking into account the residence of the inventor, we notice that an important number of inventors are native of the Asian countries (mostly from China and India).

Table 1The top ten fi rms with more patents granted by USPTO to

residents and non residents in hafnium nanomaterials fi eld, 1980-2009

Firms

Number

of

patents

1 International Business Machines Corporation 11

2 Mallinckrodt Medical, Inc./ Micron Technology,

Inc. 7

3 Micron Technology, Inc. 7

4 Motorola, Inc. 6

5 Intel Corporation 5

6 NanoProducts Corporation 4

7 Hewlett-Packard Development Company, L.P./

NanoProducts Corporation 4

8 Samsung Electronics Co., Ltd. 3

9 General Electric Company / Samsung Electronics

Co., Ltd. 3

10 Allied-Signal Inc. 2

10 APS Laboratory 2

10 E. I. du Pont de Nemours and Company 2

10 Everspin Technologies, Inc. 2

10 Honeywell International Inc. 2

10 Hyperion Catalysis International, Inc. 2

10 Kabushiki Kaisha Toshiba 2

10 Keesmann; Till 2

10 Kennametal Inc. 2

10 Mecagis 2

10 Qimonda AG 2

10 Shin-Etsu Chemical Co., Ltd. 2

10 U.S. Philips Corporation 2

Source: own elaboration based on USPTO.


43

Table

2M

atri

x of

ori

gin

of th

e in

vent

ors

in th

e to

tal i

nven

tors

of h

afni

um n

anom

ater

ials

pat

ents

by

coun

try

or U

S St

ate,

19

80-2

009

Source

: ow

n el

abor

atio

n ba

sed on

USP

TO p

atents

dat

a ba

se.

ALENKA GUZMÁN

44

Either by individual decision or in the context of institutional collaboration networks, the mobility of the researcher, using patent indicator is still weak. This is probably because the research in hafnium is emerging. Probably, the collaboration networks could be identifi ed through current projects or scientifi c publication.

Patent citations reveal the sources of technological knowledge. A greater number of consulted citations show the ability of inventors to accede to a vast fi eld of technological knowledge. Given the leadership of US in patenting in hafnium, this country has the biggest number of patent citations. Therefore, the Unites States also register the largest patent citation average, in contrast to other countries; the 121 US patents granted in hafnium since 1982 to July 2010, have cited 3 068 patents, that means 24.5 citation patents per patent. By its side, Korea, only having 5 patents, has 10.4 citation patents per patent in average, more than Japan, even if this country has more patents.

Graphic 6Patents, citation patents and patent citation average

Source: own elaboration with USPTO patents data base class 977/hafnium.

Developing countries have a small research base, and do not have any program that can substantially increase the training of qualifi ed personnel in nanomaterials. Most of the Latin Americans researchers working in nanomaterials make it so dispersed maintaining only weak contacts among themselves and with international peers. Mexico has the second place, after


45

Brazil, in Latin America on the number of articles published in nanosciences and nanotechnology fi eld, according to the Science Citation Index data base, but is far away from the Emerging Asian countries as India Korea and China. Even if Mexico has doubled the scientifi c articles from the period 2000-2003 to the period 2004-2007, still remains low in comparison to other Emerging countries.

Graphic 7ISI articles in nanosciences and nanotechnology fi eld of Emerging countries,

by periods

Source: Science Citation Index.

5. Nanotechnology sector in Mexico and the NAFTA region scope. The case of nanomaterials/hafnium

Nevertheless the Mexican government has expressed its interest to develop nanotechnologies in Mexico through the Science and Technology Special Program (pecyt-Programa Especial de Ciencia y Tecnología) 2001-2006 and 2008-2012 and has supported several projects, until now there has not been any Nanotechnology National Plan (Záyago-Lau and Foladori, 2010). Indeed, Mexican government has admitt ed the potential benefi ts of nanotechnologies development to improve the technologies in the energy sector and mainly in the petroleum industry, and consequently contributing to increase their competitiveness.

ALENKA GUZMÁN

46

Although the Science and Technology National Council (conacyt-Con-sejo Nacional de Ciencia y Tecnología) has given fi nancial funds to create research centers on nanotechnology and research projects, there has been ab-sence of an articulated and strategic policy assuring a high R&D investment, giving priority to the most urgent technological needs of the country and the opportunities niches, fostering the research networks in nanotech and sup-porting the creation of education programs to diff use nanotech knowledge and develop skills in this scientifi c and technological fi eld. conacyt has sup-ported 152 project on nanotechnologies, spending 14.4 millions of US dollars between 1998 and 2004 (Secretaría de Economía, 2008); this amount is far away from the expenditure destinated to R&D in nanotech in industrialized countries and even some Emerging countries, as China and India, that have spend 510 and 50 million of dollars in 2008, respectively. So, if Mexico has registered a relative technological backwardness in the new Information and Communication Technologies paradigm with respect to industrialized coun-tries and Emerging Asian countries, Mexico must undertake a wide R&D ef-forts but building an active policy creating the network of actors and institu-tions in the public and the private sectors in order to develop and to diff use the new nanotechnology paradigm.

Role of universities In Mexico there are around 56 institutions and 159 laboratories, where 449 researchers are involved in 340 issues of nanotech research (Secretaría de Economía, 2008). Among the institutions the more relevant, by taking into account their articles of the International Scientifi c Index, are the National Autonomous University of Mexico (unam-Universidad Nacional Autónoma de México) and the Research and Advanced Studies Center of the National Polythecnic Institute (cinvestav-Centro de Investigaciones y de Estudios Avanzados del Instituto Politécnico Nacional), which concentrate the 40 and 16.4% of the total articles on nanotech in 1995-2007, respectively. From these articles, the nanomaterials is the most fi eld tackled, surely it is associated to the fact that nanomaterials includes a wide scope of scientifi c issues. Among them we identify more than 380 frontier research articles about nanomaterials/hafnium fi eld in the science citation index, where stands up the contribution of the Condensed Matt er and Nanoparticles Laboratory of Physics Department at cinvestav.


47

Nevertheless the relative active article’s production of the Mexican institutions, concerning patents, the institutional inventive activity is still weak. According to World Intellectual Property Offi ce (wipo), the number of patents granted at the Patent Cooperation Treat (pct) by Mexican is 28, where ipn has 4 and unam has 2. But regarding the hafnium there is not any patent granted nor at the pct, uspto or even at the Industrial Property Mexican Institute (impi-Instituto Mexicano de la Propiedad Industrial).

Tabla 3Main universities and research centers involved in

nanosciences and nanotechnologies in Mexico

Institutiton Number of laboratories

CPI-CONACYT (Public Research Centers-Science and Technology National Council; not including CIMAV and IPICYT)

45

UNAM (National Autonomous University of Mexico, including faculties and institutes)

23

CIMAV (Advanced Materials Research Center)

18

IMP (Petroleum Mexican Institute)

16

IPN (National Polytechnic Institute, including CINVESTAV)

7

IPICYT (Scientific and Technological Research Institute of Potosi)

6

University of Sonora 6 University of Guadalajara 6 UAM (Autonomous Metropolitan University)

5

UACH (Autonomous University of Chihuahua)

3

135

Source: Záyago-Lau and Foladori, 2010.

The laboratories identifi ed as having capabilities to study frontier knowledge in nanotechnology and nanosciences are mainly those of the unam, the National Center of Metrology (cenam-Centro Nacional de Metrología), some research public institutes of conacyt as the Chemical Applied Research Center (ciqa-Centro de Investigación en Química Aplicada), also the Advanced Materials Research Center (cimav-Centro de Investigación en Materiales Avanzados₎,

ALENKA GUZMÁN

48

the fi rst national laboratory funded by conacyt in nanotech and is located in Chihuahua, the National Laboratory in Nanosciences and Nanotechnology Research (linan-Laboratorio Nacional de Investigaciones en Nanociencias y Nanotecnología), was the second laboratory supported by conacyt located too in the Scientifi c and Technological Research Institute of Potosi (ipicyt-Instituto Potosino de Investigación Científi ca y Tecnológica₎ headquarter in San Luis Potosi.

The diff erent universities or research centers in Mexico have created 6 bachelor’s degree programs, 33 master programs and 33 PhD programs on nanotechnologies or linked to them. The unam is most active institution worried to bring up graduates in nanosciences and nanotechnologies fi elds through 10 masters and 10 PhD programs. The second one is the ipn, having 6 masters and 5 PhD programs. The University of San Luis Potosi, the city where are placed the ipicyt/linan, has 3 bachelor’s degree, 4 master and 5 PhD programs. Also the University of Sonora stands up with 5 master and 3 PhD programs. Other institutions have academic programs but still are few extended in their university campus as uam, uanl, udla and the ug. Given the role of the universities and research centers as source of knowledge in this scientifi c technological paradigm, the academic programs are relevant to spread a new culture of nanotech in the entrepreneurial scope through professionals or research highly skilled.

As we have seen, the research in nanosciences and nanotechnology Mexico takes part of the scientifi c and technological goals of several universities and research centers. Many of them have undertaken projects on nanotech fi eld under the support of the conacyt, states fi nancial funds or even of international institutions. Some of them have internalized the necessity of building research networks with national and foreign institutes. The model of technological collaboration has been important to joint eff orts between institutions with similar purposes.

Because the geographical and commercial closeness to the United States, the main international connections of Mexican institutions are with the similar American ones. The Mexico-Unites States Foundation for Science (fumec-Fundación México-Estados Unidos para la Ciencia), which promotes the scientifi c linkages between these two countries of North American region, has contributed the create a network of universities and superior institutes called Design Centers Network. Through this network, the institutions are engaged to develop industrial projects and


49

Inst

itutio

n L

ocal

izat

ion

Mai

n pu

rpos

es a

nd r

esea

rch

proj

ects

C

IMA

V/N

AN

OT

EC

H

(Nat

iona

l L

abor

ator

y of

N

anot

echn

olog

y)

Chi

huah

ua

To

deve

lop

nano

tech

spe

cifi

c ap

plic

atio

n fo

r in

dust

rial

pro

duct

s en

hanc

ing

the

coll

abor

atio

n w

ith

nati

onal

an

d in

tern

atio

nal

inst

itutio

ns

and

firm

s an

d im

prov

ing

indu

stri

al

com

petit

iven

ess.

Nan

otec

h ai

ms

to b

ecom

e th

e m

ain

cent

er o

f lin

kage

of

all

the

Mex

ican

na

note

chno

logy

act

iviti

es w

ith t

he f

orei

gn o

nes.

The

y ha

ve e

stab

lishe

d re

sear

ch n

etw

orks

w

ith N

orth

Am

eric

an r

egio

n in

stitu

tions

as

Ari

zona

Sta

te U

nive

rsit

y, T

exas

Uni

vers

ity,

U

Alb

any

Col

lege

of

Nan

osca

le S

cien

ce a

nd E

ngin

eeri

ng o

f A

lban

o N

anot

ech,

aim

ing

to

crea

te a

reg

iona

l clu

ster

. Als

o th

ere

is a

pro

ject

with

the

colla

bora

tion

of B

razi

l and

Arg

entin

a to

cre

ate

Tri

-Nat

iona

l C

ente

r of

Nan

otec

hnol

ogy

(CN

T).

The

foc

us r

esea

rch

of N

anot

ech

will

be

on

m

ater

ials

sy

nthe

sis,

m

ater

ials

ch

arac

teri

stic

s,

deve

lopm

ent

of

new

m

ater

ials

, co

nsul

tanc

y an

d tr

aini

ng to

fir

ms

and

inst

itute

s.

IPIC

YT/L

INA

N

San

Lui

s P

otos

i R

esea

rch

focu

sed

to b

ring

up

and

to t

rain

hum

an r

esou

rces

hig

hly

skill

ed a

nd t

o co

ntri

bute

w

ith th

e fi

rms

deve

lopm

ent t

o be

com

e in

tern

atio

nal c

ompe

titiv

e. M

aste

r an

d P

hD p

rogr

ams

in

nano

scie

nces

an

d na

note

chno

logy

fo

cusi

ng

on

issu

es

such

as

: na

nost

ruct

ures

sy

nthe

sis,

bi

omim

etri

cs,

mag

neti

c na

nom

ater

ials

an

d ap

plic

atio

ns,

nano

biot

echn

olog

y,

biom

ater

ials

na

nost

ruct

ures

cha

ract

eris

tics

, na

noco

mpo

unds

, el

ectr

onic

s es

tim

atio

ns o

f na

nosy

stem

s. T

he

colla

bora

tion

with

int

erna

tiona

l in

stitu

tions

(N

AS

A,

MIT

, U

SDC

-Uni

tes

Stat

es D

epar

tmen

t of

C

omm

erce

, th

e Sh

in S

hu U

nive

rsity

of

Japa

n) a

nd n

atio

nal

inst

ituti

ons

(UN

AM

, IM

P, I

TE

SM-

Mon

terr

ey S

uper

ior

Stud

ies

Tec

hnol

ogic

al I

nstit

ute,

Phi

sycs

Ins

titut

e of

IPN

, am

ong

othe

rs).

U

NA

M

Mai

nly

in

Mex

ico

City

U

nive

rsit

y E

nvir

onm

enta

l N

anot

echn

olog

y P

roje

ct

(PU

NT

A-P

roye

cto

Uni

vers

itari

o de

N

anot

ecno

logí

a A

mbi

enta

l) t

o fo

ster

mul

tidis

cipl

inar

y re

sear

ch a

imin

g to

sol

ve n

atio

nal

prob

lem

s w

ith

the

part

icip

atio

n of

30

expe

rts.

Net

wor

k of

Res

earc

h G

roup

s in

Nan

osci

ence

s (R

EG

INA

- R

ed d

e G

rupo

s de

Inv

esti

gaci

ón e

n N

anoc

ienc

ias)

wit

h m

ore

than

50

rese

arch

ers,

se

arch

ing

on

issu

es

such

as

: na

nopa

rtic

les

synt

hesi

s us

ing

coll

oida

l m

etho

ds,

nano

biot

echn

olog

y,

nano

stru

ctur

ed

syst

ems

wit

h ap

plic

atio

n to

ca

taly

sis,

na

nom

ater

ials

co

mpu

ter

phys

ics,

nan

omac

hine

s, a

mon

g ot

hers

. N

anos

cien

ce a

nd N

anot

echn

olog

y C

ente

r lo

cate

d in

Ens

enad

a, B

aja

Cal

ifor

nia.

IM

P

Mex

ico

City

In

stitu

tion

focu

sed

on e

nerg

y se

ctor

, m

ainl

y on

pet

role

um i

ndus

try

thro

ugh

Pem

ex l

inka

ge.

Aim

s to

dev

elop

nan

otec

hnol

ogy

rese

arch

in o

rder

to f

ind

out m

ore

effi

cien

t use

of

petr

oleu

m

deri

vate

s an

d lo

ok f

or n

ew s

ourc

es o

f en

ergy

. The

mai

n re

sear

ch is

sues

are

new

mat

eria

ls a

nd

nano

stru

ctur

es.

Table

4R

esea

rch

proj

ects

in n

anos

cien

cies

and

nan

otec

hnol

ogy

in M

exic

o by

inst

itutio

n/la

bora

tory

Sou

rce:

Záy

ago-

Lau

and

Fola

dori

, 201

0.

ALENKA GUZMÁN

50

Table

4R

esea

rch

proj

ects

in n

anos

cien

cies

and

nan

otec

hnol

ogy

in M

exic

o by

inst

itutio

n/la

bora

tory

(Con

tinue

d)

CIN

VE

STA

V

Mex

ico

Cit

y A

dvan

ced

Lab

orat

ory

for

the

stud

y of

sem

icon

duct

ors

nano

stru

ctur

es, d

epar

tmen

t of

Phy

sics

. M

aste

r an

d Ph

D

in

Nan

osci

ence

s an

d N

anot

echn

olog

ies

focu

sing

in

na

nom

ater

ials

, na

node

vice

s, n

anos

yste

ms

and

nano

biot

echn

olog

y. T

his

labo

rato

ry h

as u

nder

take

n th

e R

&D

in

nan

omat

eria

ls/h

afni

um.

CE

NA

M (

Nat

iona

l C

ente

r of

M

etro

logy

)

Que

reta

ro

Aim

s to

fos

ter

know

ledg

e an

d to

use

of

met

rolo

gy t

o st

reng

then

ind

ustr

ial

com

peti

tive

ness

, eq

uity

in

m

arke

t tr

ansa

ctio

ns,

heal

th

envi

ronm

ent

prot

ectio

n an

d sc

ient

ific

re

sear

ch.

The

refo

re,

CE

NA

M e

stab

lish

es t

he m

easu

re s

tand

ards

, in

clud

ing

norm

s fo

r na

note

chno

logy

. C

olla

bora

tes

join

tly w

ith t

he N

atio

nal

Inst

itute

of

Mea

sure

men

t St

anda

rds

(NIM

S) f

rom

C

anad

a an

d th

e N

atio

nal

Inst

itute

of

Stan

dard

s an

d T

echn

olog

y (N

IST)

from

the

US

in a

Tri

-N

atio

nal

Wor

ksho

p di

scus

sing

ab

out

the

risk

s of

th

e us

e of

na

note

chno

logi

es

for

the

envi

ronm

ent,

heal

th, a

nd c

onsu

mer

s an

d fo

r th

e w

hole

soc

iety

. B

UA

P (M

erito

riou

s A

uton

omou

s U

nive

rsit

y of

Pu

ebla

)

Pueb

la

Res

earc

h st

ress

ing

on s

emic

ondu

ctor

s. H

eadq

uart

er o

f th

e In

tern

atio

nal

Nan

osci

ence

s an

d N

anot

echn

olog

y, w

ith r

esea

rche

r of

the

IPN

(M

echa

nica

l an

d E

lect

rica

l E

ngin

eeri

ng S

uper

ior

Scho

ol,

Posg

rade

Stu

dies

Sec

tion

, U

AM

Izt

apal

apa,

CIN

VE

STA

V,

Nuc

lear

Res

earc

h N

atio

nal

Inst

itute

(IN

IN-I

nstit

uto

Nac

iona

l de

Inve

stig

acio

nes

Nuc

lear

es),

Neu

rolo

gy a

nd N

euro

surg

ery

Nat

iona

l Ins

titut

e (I

NN

N-I

nsti

tuto

Nac

iona

l de

Neu

rolo

gía

y N

euro

ciru

gía)

. IN

AO

E/L

NN

(E

lect

roni

cal,

Opt

ic

and

Ast

roph

isyc

s N

atio

nal

Inst

itute

/ N

anoe

lect

roni

c N

atio

nal

Lab

orat

ory)

Pueb

la

Aim

s to

bec

ome

the

linka

ge b

etw

een

high

tec

hnol

ogic

al r

esea

rch

and

the

indu

stri

al s

ecto

r to

pr

omot

e th

e el

ectr

onic

s in

dust

ry d

evel

opm

ent,

in f

avor

ing

a un

iver

sity

-ind

ustr

y-go

vern

men

t m

odel

. T

hey

star

ted

sinc

e th

e do

natio

n of

Mot

orol

a In

c co

mpa

ny o

f a

prod

uctio

n lin

e of

de

vice

s an

d ci

rcui

ts

Sou

rce:

Záy

ago-

Lau

and

Fola

dori

, 201

0.


51

academic programs specialized in Micro and Nano electromechanical systems (mems/nems). Also with the intervention of fumec was created de Productive Articulation Center to infl uence industry-academia policy maker collaboration to undertake the development of new projects and business. In the fumec framework was creating Bi-national Sustainability Laboratory (bnsl) aiming to boost the sustainable development in the frontier territory enhancing local capabilities and favoring successful entrepreneurial environment of the Paso del Norte Packaging Cluster. Through the collaboration of Mexican and American institutions, bnsl looks for having complementarities in R&D of products and their commercialization, energy and advanced materials, packaging mems. Collaboration is that made by Texas University-Austin and the cimav; both have made an agreement and therefore creating the International Center for Nanotechnology and Advance Materials (icnam). Likewise the Center for Nano and Molecular Science and Technology in the Texas University search for the stay academic exchange with the R&D purposes, specially the researcher coming from the Hispanic community.

Universities and fi rms linkage

Although the Mexican fi rms have been characterized by having scarce R&D eff orts and innovation capabilities, their specialization is not identifi ed by the high technology and register important gaps with respect to industrialized and some Emerging countries, few of them have started to incorporate to their production process and products the nanotechnology knowledge. Near of three fi fths of the 30 fi rms are using nanoparticles in the chemical and electrical industries. Comex, a Mexican fi rm with a larger business of paint and coating products is using nano clay and the fi rms Prolec GE/Xignux Group and General Electric are working with nanomaterials in Nuevo Leon. One third of fi rms using nanotech have the headquarter at Mexico City, less than one third are located at Nuevo Leon state, three in Coahuila, Jalisco and State of Mexico and fi nally, 5 companies (21.7%) are multinationals coming from Minnesota, South Carolina and Texas (United States), Tokio (Japan) and Glucksburg (Germany) (Záyago-Lau and Foladori, 2010).

Following the initiative to develop research networks and foster industrial clusters in nanotech undertaken by Mexican research centers and

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universities, there have been the linkage with foreign and national fi rms as Cementos de Chihuahua, Peñoles, Delphi, Lexmark, Mabe and Cydsa and other fi rms belonging to industrial parks or clusters. Several of these cases are launched under the joint agreements, mostly, with American institutions and in some cases with the public funds.

Among the projects to build industrial parks or clusters profi ting of the nanotechnology knowledge generated at the universities or research centers are:

i) The Silicon Border Development Science Park (sbdsp) located in Mexicali, Baja California, specialized in nanocomponents in order to supply the semiconductors industry chain and other industry of high technology. The fi nancial support is coming from federal Mex-ican government, state of Baja California and California US State.

ii) High technology park of Huejotz ingo, located in Puebla. The mea-sures planned by government include profi ting of the nanotech knowledge produce by the inaoe and inn for the medical and auto-motive industries (García, 2007).

iii) Innovation and Transfer Center, project to be placed in Puebla with the support of itesm of Puebla looking for fostering innovation to improve the regional industrial competitiveness (cit-items, cited by Záyago-Lau and Foladori, 2010).

iv) Technological Research and Innovation Park (piit-Parque de In-vestigación e Innovación Tecnológica), knowledge city project in course since 2005 in Nuevo Leon state with the collaboration of the uanl and the laboratory of nanotechnology and nanosciences of the Engineering and Technology R&D and Innovation Center, likewise other conacyt research centers (cimav), the itesm, the uaem and the ipn. The piit aims to create a high technology fi rms incubator, including a software cluster and fi rms as Sigma, Pepsico and Mo-torola.

v) The Paso el Norte mems/nems Packaging Cluster aims to build an industrial park between Alburqueque, Nuevo Mexico and Chihua-hua city. The R&D activities on nanotech are focused to military ac-tivities with the support of Sandia military laboratories and fumec and the activities are those contributing to the development and competitiveness of the frontier business.


53

6. Conclusions

Nanotechnologies will have a huge impact on production process and there-fore on economic and social development. They have became a scientifi c and technological paradigm and it is predicted to become the next technological revolution. Its difussion is noticed by the growing nano products and nano components diversity. The most industrialized countries have been involved in funding R&D nanotechnologies without precedent. Therefore nanotech-nologies are rapidly making progress on new scientifi and technological knowledge, registered in articles and patents.

Nanomaterials linked to on chemical and nano electronic are one of the four fi elds of nanotechnology that has been dynamic. It is predicted that in electronics and specially in semiconductors, the progress in nanotechnology will give enormous benefi ts to corporates by increasing the effi ciency and quality of this sector.

In nanomaterials fi eld, the research on hafnium oxide as a new material for semiconductor and electronic sector has been placed at the frontier state of art. We have found that only few countries have developed innovation capabilities in this emerging technology associated to an important eff ort of government, fi rms and research institutions, including universities on R&D spending. United States stands out as an innovation leader in hafnium nanomaterials fi eld, with their fi rms and research institutions at the head of patenting. France, Germany and Korea are distant followers. Nevertheless, among the community of inventors in the United States there is an interesting mobility and even if the inventors nationality is mostly American, several of them come from other countries by identifying their names. It is remarkable the number of inventors of Chinese origin. The fl ows of knowledge are signifi cant in the United States taking into account patent citation.

Mexico is characterized by a disarticulated national innovation in the nanotech system with still low eff orts in R&D and patents fi elds. In the nano material sector, the poor performance of these two innovation indicators provides evidence of the important technological gap that Mexico has vis a vis the industrialized countries, and even with some other emerging countries. Nevertheless, there is some strength in the frontier scientifi c research of the universities. Even if the international scientifi c leadership of some research teams is atypical, it provides a technological opportunity to develop a local industry that could be the beginning of a converging path. In the absence

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of active, institutional and supportive government policies, multinational fi rms could appropriate the innovative eff orts of the research teams without having any local benefi ts, or the rest forgott en.

The role of government policies is crucial to fostering the development of the entrepreneurial activity in nanomaterials applied to information processing. The government’s policies will be addressed to build technological capabilities so as to assure the linkages between fi rms and universities as well as assure fi nancial support. All this, in order to make profi ts, from the technological opportunities resulting to the scientifi c progress of the research teams leaders in this kind of knowledge. By considering the important amounts of R&D investment, the Mexican government has to consider the possibility of promoting some technological cooperation agreements with international fi rms, but, at the same time, making sure that Mexico can be a benefi ciary of the innovation activity carried out by university researchers.

Policy implications

By identifying the relative scientifi c strength of some university research teams on the innovation of nanomaterials fi eld applied to the ICT in the context of a weak NIS and a sector few developed, the government must facilitate the communicating vessels between universities and local enterprises in order to foster the local fi rms investment (demand factors), the technological collaboration, the absorption of knowledge spillovers and probably the strategic alliances with foreign fi rms, leaders in this fi eld. The government has to play a crucial role in this process of technological innovation, where the R&D of the raw material hafnium oxide (HfO2) stands out as an important technological opportunity, which could improve effi ciency, stability and manufacturing costs in the ICT sector.


55

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DEPENDENCIA DE LARGO PLAZO EN LOSRENDIMIENTOS DE

ACCIONES MEXICANAS SELECTAS

Agustín Ignacio Caberra Llanos*Samantha Sofía López Gil**Francisco López Herrera***

Resumen

Este artículo muestra los resultados del análisis de los rendimientos de cinco acciones que cotizan en la Bolsa Mexicana de Valores y un tracker que son activos subyacentes de opciones que se comercian en el mercado mexicano de opciones. El objetivo del análisis es encontrar evidencia de la presencia de dependencia de largo plazo o memoria larga en dichos rendimientos y en proxies de las volatilidades de los mismos, mediante diversas pruebas estadísticas que han sido comúnmente utilizadas para este propósito. De acuerdo con los resultados del análisis efectuado, se encuentra evidencia estadísticamente signifi cativa acerca de la presencia de dependencia de largo plazo (memoria larga), tanto en los rendimientos como en los proxies de sus volatilidades, para todos los activos sujetos al análisis.Palabras clave: Dependencia de largo plazo, memoria larga, coefi ciente (exponente) de Hurst, rendimientos accionarios, volatilidadClasifi cación JEL: G10, G12, G14

(Recibido: Septiembre 2011 / Aprobado: Febrero 2012)

AUTORES 3

* Unidad Profesinal Interdisciplinaria de Biotecnología, Instituto Politécnico Nacional. Correo electró-nico: <[email protected]>.

** Escuela Superior de Economía, Instituto Politécnico Nacional. Correo electrónico: <[email protected]>.

*** División de Investigación, Facultad de Contaduría y Administración, Universidad Nacional Autóno-ma de México. Correo electrónico: <[email protected]>.

AGUSTÍN I. CABRERA / SAMANTHA S. LÓPEZ / FRANCISCO LÓPEZ

60

Abstract

This paper shows the results of the analysis of the returns of fi ve shares quoted in the Bolsa Mexicana de Valores and a tracker that are underlying asets of options traded in the Mexican options market. The objective of the analysis is to fi nd evidence of the presence of long run dependence or long memory in such returns and in proxies of their volatilities by means of statistical tests commonly used for this purpose. Accordingly with the results of the analysis carried out, statistically signifi cant evidence about long run dependence (long memory) is found, both in the returns and the proxies of their volatilities, for all assets subject to analysis.Keywords: Long run dependence, long memory, Hurst coeffi cient (exponent), stock returns, volatilityJEL Classifi cation: G10, G12, G14

1. Introducción

La primera evidencia sobre la presencia de procesos estocásticos con dependencia de largo plazo entre los valores observados de series de tiempo fue proporcionada por el hidrólogo británico Harold Edwin Hurst, quien llevó a cabo su trabajo de investigación como consecuencia de sus observaciones sobre el comportamiento de los niveles del agua contenida por la Presa Aswan del Río Nilo, luego de estudiar la capacidad del almacenaje de largo plazo de dicha presa. En Hurst (1951) se presentaron los resultados del estudio de 690 series de tiempo de variables geofísicas tales como temperatura, precipitación pluvial y el número de manchas solares. Los resultados del análisis empírico mostraron que en la mayor parte de las series existía un efecto de dependencia de largo plazo, o memoria larga, el cual fue bautizado como el efecto Hurst, en honor de su descubridor. De acuerdo con Mesa y Poveda (1993), el efecto Hurst se constituyó en uno de los principales problemas de la hidrología estocástica, motivando la publicación de una cantidad considerable de artículos de investigación al respecto.

El impacto de los hallazgos de Hurst no sólo alcanzó el campo de los hidrólogos, sino que se extendió a otros campos de estudio y sirvió de inspiración para el trabajo de otros investigadores de distintas áreas del

CONTENIDO 3

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61

conocimiento. Por ejemplo, Mandelbrot (1982) declaró que la investigación que él llevó a cabo en relación con el efecto Hurst fue una de las fuentes que le inspiraron en el desarrollo de su Teoría de los Fractales, la cual por su importancia es, a su vez, una de las piedras angulares de la Teoría del Caos.

Como se ha señalado con anterioridad, la motivación original del trabajo llevado a cabo por Hurst fue un problema relacionado con el diseño de una presa. Sin embargo, en investigaciones efectuadas posteriormente, por ejemplo Kleměs et al. (1981), se encontró que a pesar del gran revuelo inicial que los hallazgos de Hurst habían causado en al campo de la hidrología, el efecto Hurst era relevante únicamente para unos cuantos casos. A pesar de esos resultados, el interés por dicho efecto no menguó del todo pues el uso de distintos modelos hidrológicos tiene implicaciones económicas, de igual forma que las tiene el cómo se modele la persistencia.

En el análisis de series de tiempo se ha encontrado la presencia de procesos de dependencia de largo plazo en campos diferentes a la hidrología, como son por ejemplo la economía fi nanciera, el análisis de series macroeconómicas y del tráfi co de redes, entre otros. Las series en las cuales se encuentra presente la dependencia de largo plazo, asociada con la memoria larga, se pueden caracterizar por valores altos en las autocorrelaciones (autocovarianzas) entre observaciones cuya distancia en el tiempo es relativamente grande. El patrón del decaimiento de las autocorrelaciones en una serie de tiempo con dependencia o memoria de largo plazo es hiperbólico, no geométrico o exponencial como en el caso de las series que pueden caracterizarse mediante procesos de memoria corta, por ejemplo los modelos ARMA estacionarios. Dicho en otras palabras, las autocorrelaciones entre los valores de las observaciones de las series en las que sólo existe dependencia de corto plazo, es decir series con memoria corta, decaen hacia cero en forma rápida conforme se incrementa la distancia en el tiempo. Por su parte, la fuerte asociación entre las observaciones en series con memoria larga, a pesar de encontrarse distantes en el tiempo, produce un decaimiento más lento en el transcurso del tiempo.

Desde la perspectiva teórica de la economía fi nanciera, es importante destacar que la presencia de memoria larga o de dependencia de largo plazo en los rendimientos de los activos fi nancieros no es consistente con la famosa hipótesis de los mercados efi cientes. En caso de la existencia de memoria larga, conocida también como “caminata aleatoria sesgada”, implica la existencia de una dependencia no lineal en el primer momento


62

de la distribución y, por lo tanto, existe un componente de predecibilidad en la dinámica de la serie. La dependencia estadística persistente en el largo plazo también implica que los cambios de precios no sigan un proceso de martingala y tengan varianza infi nita. Por lo anterior se desprende que, la presencia de ese fenómeno tiene también implicaciones trascendentes para la valuación de activos con base en el supuesto de que el proceso estocástico que rige la dinámica del movimiento de los precios de los activos puede ser descrito de manera adecuada por el movimiento browniano.

En forma particular debe considerarse que, la evidencia sobre la existencia de memoria larga en los rendimientos accionarios implica que las realizaciones de esas series no son independientes en el tiempo, por lo que los rendimientos que se han observado en un pasado relativamente distante podrían ser útiles para pronosticar los rendimientos futuros, abriendo así la puerta a la posibilidad de obtener rendimientos especulativos. Es decir, la dependencia de largo plazo o memoria larga podría presentar una contradicción a la forma débil de la hipótesis de los mercados efi cientes, según la cual los rendimientos futuros de los activos no son predecibles si se condicionan a los rendimientos históricos, pues se supone que la distribución probabilística de estos rendimientos es idéntica e independiente del momento del tiempo en que se observe.

Los procesos que muestran dependencia de largo plazo también han recibido especial atención en la literatura fi nanciera puesto que su existencia en los rendimientos de los activos tiene consecuencias de suma importancia práctica, como lo son las decisiones de inversión de portafolio, la valuación de activos y el diseño de estrategias para la cobertura de los riesgos asociados. Greene y Fielitz (1979) muestran que, si la memoria larga se encuentra presente en los rendimientos accionarios puede afectar a los modelos fi nancieros del riesgo y rendimiento pues, en su presencia, tanto la clasifi cación de las acciones y de los portafolios de acuerdo con su nivel de riesgo, como los portafolios efi cientes en riesgo-rendimiento, tienden a variar cuando los rendimientos se miden en diferentes frecuencias temporales. En Islas y Venegas-Martínez (2003) se muestran los efectos que la memoria larga puede tener para la cobertura con opciones europeas de compra en el mercado mexicano.

En este trabajo se analizan tanto los rendimientos de cinco acciones que cotizan en el mercado bursátil mexicano como un tracker, extendiendo el análisis a proxies de las volatilidades de los rendimientos de esos activos


63

fi nancieros. El objetivo perseguido es verifi car si existe evidencia de que en los procesos estocásticos de esos rendimientos hay presencia de dependencia de largo plazo o memoria larga. Por una parte es importante estudiar las series de rendimientos de estos activos pues, el análisis en sí mismo puede proporcionar un mayor conocimiento de sus características y contribuir a una mejor comprensión del funcionamiento del mercado mexicano de capitales. Además, también es importante este estudio sobre la memoria larga de las cinco acciones y el tracker bajo estudio, toda vez que son activos subyacentes para opciones que se comercian en el mercado mexicano de ese tipo de derivados fi nancieros.

Con base en el objetivo que se persigue, el presente trabajo está organizado de la manera que se describe a continuación. Después de esta introducción, en la sección uno se presenta la revisión de literatura relevante sobre la dependencia de largo plazo en los rendimientos y volatilidades de los rendimientos fi nancieros. Posteriormente, en la sección dos se presentan los elementos metodológicos en los que se sustenta el análisis, cuyos resultados se muestran y discuten en la sección tres de. La última sección está dedicada a las conclusiones.

2. Revisión de literatura

Al mostrar que para la existencia del arbitraje perfecto se requiere que la dependencia estadística entre los precios decrezca rápidamente a medida que se incrementa la distancia temporal, Mandelbrot (1971) estuvo entre los primeros que tomaron en cuenta la posibilidad de que en los rendimientos de los activos fi nancieros se encontrasen presentes procesos de dependencia de largo plazo o memoria larga que pudiese impedir el arbitraje perfecto de los precios accionarios. Posteriormente, Greene y Fielitz (1977) proporcionaron apoyo empírico al planteamiento establecido por Mandelbrot, pues al estudiar los rendimientos diarios de 200 acciones negociadas en la bolsa estadounidense encontraron evidencia de que los rendimientos de varias de las acciones bajo estudio se caracterizaban por la dependencia de largo plazo.

Aunque Lo (1991) pone en duda la existencia de memoria larga en el mercado estadounidense, pues no encuentra evidencia de su presencia en los rendimientos accionarios diarios, otros estudios como los de Peters


64

(1992, 1994) y Goetz mann (1993) muestran evidencia de su presencia en esos mercados. Por su parte, Teverovsky, Taqqu y Willinger (1999) muestran que la prueba de Lo (1991) está sesgada al rechazo de dependencia de largo plazo aunque en los datos ésta sea el único tipo de dependencia presente.

Otros estudios que se han llevado a cabo en mercados accionarios desarrollados han proporcionado evidencia no concluyente sobre la existencia de memoria larga en los rendimientos accionarios. Los resultados de Aydogan y Booth (1988) les llevaron a la conclusión de que no había evidencia estadísticamente signifi cativa sobre la presencia de memoria larga en los rendimientos accionarios. El estudio de Mills (1993) ofrece evidencia débil de su presencia en el mercado bursátil del Reino Unido. Crato (1994) encuentra evidencia únicamente para el caso del mercado accionario alemán pero no para los índices accionarios de los demás países del G-7. Cheung y Lai (1995) en su estudio sobre diversos mercados del mundo también encuentran alguna evidencia sobre la existencia de memoria larga. Barkoulas y Baum (1996) muestran pruebas signifi cativas de la presencia de memoria larga únicamente en algunas acciones integrantes del Índice Industrial Dow Jones. Lux (1996) no encontró evidencia de memoria larga en los rendimientos del índice DAX, sin embargo sí encuentra evidencia de dependencia de largo plazo en la volatilidad en los rendimientos de ese índice del mercado alemán. Por su parte, Hiemstra y Jones (1997) encuentran poca evidencia de memoria larga en su estudio sobre acciones individuales de la bolsa estadounidense. Lobato y Savin (1997) tampoco encuentran evidencia sobre la presencia de memoria larga en esa bolsa, pero sí la encuentran para los cuadrados de los rendimientos.

La investigación sobre la presencia de memoria larga se ha extendido de manera más o menos profusa a diferentes mercados accionarios, incluyendo incluso mercados más pequeños entre los cuales se encuentran los llamados mercados emergentes. Madhusoodanan (1998) encuentra evidencia débil de dependencia de largo plazo al estudiar el comportamiento de índices bursátiles de la India y también acciones de ese país. Barkoulas, Baum y Travlos (2000) encuentran evidencia sobre la existencia de dependencia positiva de largo plazo en los rendimientos del mercado accionario de Atenas. McKenzie (2001) identifi có la presencia de memoria larga en el mercado accionario de Australia. Henry (2002) estudió la memoria larga en los rendimientos accionarios, también desde una perspectiva de mercados accionarios internacionales y tampoco encontró evidencia de ella en los mercados de Australia, Estados Unidos, Hong Kong, Reino Unido y Singapur.


65

No obstante, Henry encontró evidencias de memoria larga en los mercados accionarios de Alemania, Corea del Sur, Japón y Taiwan. En Cajueiro y Tabak (2004) se muestra evidencia de dependencia de largo plazo en las bolsas de valores de China, Singapur y Taiwan. Por su parte, Tolvi (2003) estudia los rendimientos diarios de tres índices generales, tres índices por industria y 40 acciones del mercado bursátil fi nlandés, encontrando evidencia de memoria larga en muchos de los casos. Chang y Kim (2004), detectaron memoria larga en los rendimientos semanales y diarios del mercado accionario coreano y Yoon y Kang (2008) ofrecen nuevamente evidencia de memoria larga en los rendimientos diarios de ese mercado.

A partir del estudio de Ding, Granger y Engle (1993), quienes encuentran indicios de memoria larga en la volatilidad de los rendimientos del índice SP500, la evidencia sobre memoria larga en las volatilidades de los rendimientos ha sido mucho más consistente, señalando su presencia en forma signifi cativa en diferentes mercados en los que se ha llevado a cabo investigación. Islas y Venegas-Martínez (2003) muestran evidencia de la presencia de memoria larga en la volatilidad del mercado accionario mexicano. Venegas-Martínez e Islas (2005) examinan también varios mercados accionarios encontrando evidencia de memoria larga en las volatilidades de los índices bursátiles de Argentina, Brasil, Chile, México y Estados Unidos. Kasman y Torun (2007), en su estudio sobre el mercado accionario turco, documentan evidencia sobre memoria larga tanto en los rendimientos diarios como en su volatilidad. Quan et al. (2008) sugiere presencia de memoria larga en la volatilidad del mercado accionario chino. Los resultados de Conrad (2007) muestran efectos signifi cativos de memoria larga en la volatilidad de los rendimientos de la Bolsa de Valores de Nueva York. De forma similar, Wen (2008) encuentra la presencia de memoria larga cuando estudia el comportamiento de la volatilidad de la bolsa de Malasia.

En estudios recientes relacionados con la presencia de memoria larga en el mercado accionario mexicano se ha encontrado evidencia de memoria larga. Por ejemplo, se puede señalar entre otros a López, Venegas y Sánchez (2009) y López, Villagómez y Venegas (2011), en los cuales se muestra evidencia de presencia signifi cativa de memoria larga tanto en los rendimientos del IPC como en las volatilidades de dichos rendimientos. Sin embargo, es conveniente señalar que los resultados de Sierra (2010) sugieren que no existe memoria larga en los rendimientos del IPC pero sí en sus volatilidades. En López, Villagómez y Venegas (2009) se encuentra evidencia de memoria larga en los rendimientos


66

de algunas acciones mexicanas pero no en otras, en tanto que en todos los casos se encuentra evidencia signifi cativa de memoria larga en las volatilidades de dichos rendimientos. En los resultados de Villagómez (2010) se observa que los rendimientos y volatilidades de algunas acciones mexicanas de la muestra estudiada exhiben presencia de memoria larga en tanto que otras no.

3. Aspectos metodológicos

En el trabajo de Hurst (1951) antes mencionado se propuso el análisis del rango reescalado, actualmente conocido simplemente como análisis R/S, para detectar la presencia de memoria larga o dependencia de largo plazo. Posteriormente esta prueba fue reconsiderada y reformulada por Mandelbrot y Wallis (1969). El objetivo del análisis del rango reescalado es estimar el parámetro H, comúnmente conocido como coefi ciente o exponente de Hurst en honor del célebre hidrólogo inglés. La importancia de dicho parámetro radica en que da cuenta de la (in)dependencia de una serie.

Si H = 0.5 se tiene una serie aleatoria y las observaciones no están correlacionadas, lo que corresponde al comportamiento esperado de un movimiento browniano. Cuando se tiene que 0 < H < 0.5, entonces en las series se observa un comportamiento que puede caracterizarse como antipersistente, pues presentan correlaciones con valores positivos y negativos alternados produciendo un comportamiento al que comúnmente se le denomina reversión de la media. La característica de este tipo de series es que, si el sistema ha estado arriba en el periodo anterior es más probable que esté abajo en el siguiente y viceversa. Finalmente, si 0.5 < H < 1 entonces la serie es persistente en el sentido de que refuerza su tendencia puesto que las observaciones están correlacionadas de manera positiva (con correlación más alta mientras más cercano a la unidad se encuentre el valor de H) y se tiene entonces series que exhiben dependencia de largo plazo o memoria larga.

Para estimar el coefi ciente de Hurst antes se calcula el rango reescalado. Entonces, primero se divide la serie de tiempo de tamaño T, en V intervalos de longitud n, es decir Vn = T. A cada intervalo se le denomina Iv con v = 1,2,…,V. Cada elemento del intervalo se llama Tk,v con k = 1,2,…n. Se calcula la media de los elementos de cada subintervalo de longitud n obteniendo así v medias calculadas; según:

,1

1 n

im T

n .


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Enseguida se calculan las desviaciones acumuladas respecto a la media para cada subintervalo, es decir:

, ,1( )

kIi

X T Mk n n n== -å para k = 1,2,…,n.

Después se defi ne el rango para cada subintervalo RI,v como la diferencia entre el valor máximo y mínimo de , , , ,: max mink v I v k v k vX R X X .

Se calcula la desviación típica muestral para cada subintervalo Iv:

1

22

,1

1( )

n

I kk

S T mn

.

Se divide cada rango por la desviación típica y se obtiene el rango

reescalado R/S para cada intervalo. Se calcula ahora el valor medio de R/S

para los intervalos de longitud n: , ,

1/ ( / )

T

I InR S R S

V

.

Se aumenta la longitud del intervalo hasta el siguiente valor que verifi que que N/n sea un número entero y se repite todo el proceso desde el paso número uno para todos los valores posibles de n. Al dividir cada valor del rango entre su desviación estándar, se obtiene el rango reescalado R/S, el cual mantiene la siguiente relación con el coefi ciente de Hurst: R/S = anH, donde R/S es el rango que corresponde a una escala seleccionada, a es una constante de proporcionalidad, n es el número de observaciones o tamaño de la escala. Al tomar logaritmos se obtiene ln(R/S) = ln(a) + H ln(n) y entonces se puede estimar el coefi ciente de Hurst mediante una regresión.

La función de autocorrelación k de una serie estacionaria con memoria larga se comporta asintóticamente como 2 1dk ck , para la cual 0.5d . En este caso, d mide el grado de intensidad de la memoria larga. Es conveniente señalar que entre el coefi ciente H y el parámetro d existe la relación: H = d + 1/2. Cuando d es igual a cero se tiene una serie estacionaria, defi nida en el léxico de las series de tiempo como una serie con grado de integración igual a cero o simplemente I(0).

Geweke y Porter-Hudak (1983), en lo sucesivo GPH, proponen la estimación del parámetro de memoria larga, d, mediante la regresión:

1

log 2logsin2

Jk J

k j J kj

I c d U

, 2 ,...,k L J L J M


68

donde jI es el j-ésimo punto del periodograma y 2 /j j T . El valor de J es fi jo y L y M deben divergir con el tamaño de la muestra.

Otra alternativa para estimar el parámetro de memoria larga es el estimador local gaussiano de Whitt le, el cual consiste en maximizar la función:

2

1 1

1 12 log log

M Md

T j j jj j

L d d IM M

donde 2 /j j T al igual que en el caso del estimador de GPH.1

4. Análisis empírico

Las series analizadas son las de las acciones AMXL, CEMEXCPO, GMEXICOB, TLEVISA CPO y WALMEX, así como la del NAFTAC02, tracking que fue emitido en abril de 2002 por Nacional Financiera para reproducir el comportamiento del IPC. Los datos de los precios diarios se obtuvieron de la página web de Yahoo México, Finanzas. Todas las series de precios, exceptuando la de NAFTRAC02, van del tres de enero de 2000 hasta el seis de octubre de 2011. Los precios de NAFTRAC02 van del 17 de abril de 2002 a la misma fecha que las otras series. En la Figura 1 se muestran las series.

Con los precios de las series se estimaron los rendimientos logarítmicos rt = lnPt - lnPt - 1. En la Tabla 1 se puede observar que los rendimientos de los activos analizados muestran, como es de esperarse, alejamientos de la normalidad como lo evidencian sus sesgos y niveles altos de curtosis.

En la Tabla 2 se observan los resultados de las estimaciones del coefi ciente de Hurst, los valores esperados de dicho coefi ciente y el valor de la prueba z que resulta de la prueba de Anis y Lloyd (1976) que se llevó a cabo bajo la hipótesis nula de que las series son ruidos blancos gaussianos (H = 0.5). Esta prueba se construye estimando primero el valor esperado de R/S:

1/2 1

1

12[( / ) ] .

2

n

nr

n n n rR S

n r

E

1 Al respecto se puede consultar a Robinson (1995), por ejemplo.


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Figura 1Precios de los activos

AMXL

CMEXCPO

GMEXICOB


70

Figura 1Precios de los activos

(Continuación)

NAFTRAC02

TLEVISACPO

WALMEXV

Fuente: elaboración propia.


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Tabla 1Estadísticas descriptivas de los rendimientos

AMXL CEMEXCPO GMEXICOB NAFTRAC02 TLEVISACPO WALMEX Media -0.00014 0.0000314 0.015894 0.011305 0.017794 0.013085 Desv. estándar 0.034028 0.032541 0.48598 0.31338 0.85611 0.93116 Mínimo -0.83367 -0.21010 - 3.3300 -2.1500 -3.4400 -30.130 Máximo 0.12608 0.68236 2.6600 1.9700 26.950 13.480 Asimetría -11.758 4.2201 -0.35938 -0.21887 10.963 -14.380 Curtosis 254.50 98.079 7.8025 8.4716 342.12 533.15


Siguiendo el mismo proceso que se enunció en la sección previa para la estimación del coefi ciente de Hurst, se estima ahora el valor esperado de éste: E(H) y se calcula el siguiente estadístico de prueba:

0,1)1

H HN

T

E

Al igual que se ha hecho en otros estudios, en el análisis se incluyeron los cuadrados de los rendimientos y los valores absolutos de los rendimientos como proxies de su volatilidad. Como puede verse en la Tabla 1, según la prueba de Anis y Lloyd (1976), ni los rendimientos ni las volatilidades de los activos analizados se pueden caracterizar como series de ruido blanco gaussiano. Sin embargo, es de hacerse notar que los valores estimados del coefi ciente de Hurst sugieren que los rendimientos de CEMEXCPO, TLEVISA y WALMEX son procesos antipersistentes (H < 0.5), es decir, que en esos rendimientos se tienen procesos con reversión a la media. De acuerdo con el estadístico de prueba, los valores estimados de los coefi cientes de Hurst para los rendimientos de los otros tres activos sugieren procesos persistentes (H > 0.5), consistentes con procesos en los cuales hay presencia de memoria larga. En el caso de los cuadrados y los valores absolutos de los rendimientos, se observan valores numéricos más elevados para el coefi ciente de Hurst estimado. Con excepción de los cuadrados de los rendimientos de TLEVISA, la prueba de Anis y Lloyd sugiere procesos persistentes, es decir, con memoria larga.

En la Tabla 3 se presentan las estimaciones del parámetro d mediante los métodos de GPH y el estimador local gaussiano de Whitle. Es conveniente


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Tabla 2Estimaciones del coefi ciente de Hurst

H E(H) z AMXL Rendimientos 0.6038 0.5390 183.311

Rendimientos al cuadrado

0.6802 0.5390 399.444

Rendimientos absolutos

0.8005 0.5390 739.035

CEMEX Rendimientos 0.5182 0.5436 54.874 Rendimientos al cuadrado

0.7417 0.5436 427.847


0.9059 0.5436 782.371

GMEXICOB Rendimientos 0.6012 0.5454 109.840 Rendimientos al cuadrado

0.8405 0.5454 580.930


0.8893 0.5454 676.903

NAFTRAC Rendimientos 0.6088 0.5425 152.189 Rendimientos al cuadrado

0.8607 0.5425 731.032


0.8434 0.5425 691.408

TLEVISA Rendimientos 0.5047 0.5386 98.156 Rendimientos al cuadrado

0.7053 0.5386 482.616


0.8130 0.5386 794.611

WALMEX Rendimientos 0.4963 0.5437 101.956 Rendimientos al cuadrado

0.5148 0.5437 62.127


0.6898 0.5437 313.947


señalar que en ambos casos la selección de M, el número de ordenadas del periodograma es importante pues la estimación de d es sensible a dicha selección, pero es un problema de carácter práctico porque no hay guías simples para seleccionar sus valores. En tanto que Geweke y Porter-Hudak (1983) sugieren un ancho de banda M = T v con v = 0.5, donde T es el tamaño de la muestra, Sowell (1992) argumenta que cuando se selecciona M se debería considerar el ciclo más corto asociado con el comportamiento de largo plazo. Hurvich et al. (1998) muestran que la M óptima que minimiza el error cuadrático medio asintótico es del orden de T 0.8 y probaron con esta regla la normalidad asintótica del parámetro de memoria larga estimado mediante el método de GPH. Por su parte, Kim y Phillips (2000) sugieren que 0.7 < v < 0.8 es deseable. Por lo anterior, en este trabajo se decidió utilizar M = T 0.5.


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Tabla 3Estimaciones del parámetro d

Rendimientos


Rendimientos al cuadrado

GPHa Local Whittlea

GPHa Local Whittlea

GPHa Local Whittlea

AMXL 0.04162 (< 0.01)

0.01719 (< 0.01)

0.12755 (< 0.01)

0.1297 (< 0.01)

0.02241 (< 0.01)

0.01254 (< 0.01)

CEMEXCPO -0.0007 (< 0.01)

0.02381 (< 0.01)

0.30806 (< 0.01)

0.29593 (< 0.01)

0.02298 (< 0.01)

0.06775 (< 0.01)

GMEXICOB 0.00327 (< 0.01)

-0.00728 (< 0.01)

0.28523 (< 0.01)

0.30643 (< 0.01)

0.28512 (< 0.01)

0.28551 (< 0.01)

NAFTRAC02 -0.0410 (< 0.01)

-0.0266 (< 0.01)

0.3343 (< 0.01)

0.33984 (< 0.01)

0.40033 (< 0.01)

0.36576 (< 0.01)

TLEVISACPO -0.0099 (< 0.01)

-0.02377 (< 0.01)

0.09987 (< 0.01)

0.12479 (< 0.01)

0.00366 (< 0.01)

0.00375 (< 0.01)

WALMEXV -0.0076 (< 0.01)

-0.01717 (< 0.01)

0.06852 (< 0.01)

0.1188 (< 0.01)

0.01879 (< 0.01)

-0.00347 (< 0.01)

a Las pruebas se llevaron a cabo estableciendo M = T 0.75 Los números entre paréntesis son valores p


En todos los casos y de acuerdo con los resultados de las pruebas efectuadas, tanto para los rendimientos como para las proxies de las volatilidades, los valores de los parámetros d estimados son estadísticamente diferentes de cero con un alto nivel de signifi cancia. Sin embargo, resalta el hecho de que únicamente para los rendimientos de AMXL ambas pruebas sugieren presencia de memoria larga, aunque en el caso del estimador local gaussiano el valor estimado del parámetro d es de una magnitud no muy importante. En el caso de GMEXICOB el método de GPH sugiere evidencia de memoria larga, aunque también de forma muy débil; para todos los demás se encuentran valores estimados de d negativos, sugiriendo procesos de reversión a la media. En el caso del estimado local gaussiano se encuentra que, además del caso ya mencionado, sugiere presencia de efectos de memoria larga para los rendimientos de CEMEXCPO y en los casos restantes los signos negativos de los parámetros d estimados también sugieren la posibilidad de procesos con reversión a la media.

De manera semejante al caso de la prueba sobre el exponente de Hurst, en las estimaciones de las d correspondientes a los procesos de las volatilidades de los rendimientos, se pueden observar valores estimados


74

mucho más altos, en particular cuando se toman los valores absolutos de los rendimientos como proxies de las volatilidades. Prácticamente en todos los casos se pueden considerar los resultados como indicios de memoria larga en las volatilidades de los rendimientos de los activos sujetos a estudio, sin embargo, se observa que en la serie de los cuadrados de los rendimientos de WALMEXV el parámetro d estimado muestra un signo negativo, aunque también es necesario destacar que su valor numérico es de magnitud muy pequeña.

5. Conclusiones

Con el objetivo de verifi car si existe evidencia de que hay presencia de dependencia de largo plazo o memoria larga en los procesos estocásticos de los rendimientos de cinco acciones mexicanas y un tracker, también mexicano, se llevó a cabo un análisis basado en el estadístico R/S y los estimadores de Geweke y Porter-Hudak.

De manera general, en línea con hallazgos previos de otras investigaciones cuyos resultados se han enunciado en este trabajo, se puede decir que los resultados de las pruebas llevadas a cabo en esta investigación sugieren que únicamente los rendimientos de algunos activos mexicanos podrían caracterizarse como procesos de memoria larga, en tanto que los rendimientos de otros activos podrían caracterizarse como procesos con reversión a la media.

Sin embargo, los resultados aquí mostrados no son concluyentes pues, en tanto que las pruebas de Hurst sugieren que en los rendimientos de la mayoría de los activos analizados existe dependencia de largo plazo o memoria larga, la evidencia de memoria larga en los rendimientos es muy débil según las otras pruebas efectuadas. Esta situación plantea la necesidad de estudiar los fundamentos teóricos del problema con mayor detalle. Una posibilidad a explorar es si el proceso de reversión a la media obedece a la dependencia que se ha observado en otros mercados como consecuencia de la sobre-reacción de los participantes del mercado a eventos y a los posteriores movimientos de corrección, como fue planteado originalmente por De Bondt y Thaler (1985). Por otra parte, se debe incluir también, el análisis de la necesidad y conveniencia de utilizar mejores técnicas de estimación de los parámetros pertinentes.


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También de manera congruente con los resultados de otras investigaciones, se encuentra mayor evidencia de efectos de memoria larga en las volatilidades de los rendimientos de los activos analizados. Como consecuencia, es importante tomar en cuenta esta situación para las decisiones fi nancieras de portafolio, de valuación de activos y de administración de riesgos. De manera particular se deben tomar en cuenta estos efectos en los modelos relacionados con el análisis de esas decisiones.

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OPCIONES REALES E INCENTIVOS

Esteban Colla De Robertis*

Resumen

Administrar efi cientemente una opción real implica establecer si conviene ejecutar el proyecto de benefi cios inciertos, o diferir la ejecución al futuro, cuando aparece nueva información útil y la incertidumbre sobre los benefi cios se reduce o desaparece. Con frecuencia esta decisión se basa en la recomendación de un experto, con capacidad para determinar la rentabilidad del proyecto en caso de ejecutarse. En el presente trabajo analizamos el contrato óptimo que el dueño de la opción real debe proponer al experto para que involucre recursos costosos que le permitan recabar información de utilidad para decidir sobre el timing óptimo, y para que efectúe una recomendación consistente con la información recabada.Palabras clave: opciones reales, información asimétrica, incentivos, contratos, agencia, expertoClasifi cación JEL: D82, D86, D92, L26

Abstract

Effi cient management of a real option involves establishing the convenience of undertaking a proyect with uncertain benefi ts versus deferring decision


* Universidad Panamericana, Escuela de Ciencias Económicas y Empresariales. Correo electrónico: <[email protected]>.

Se agredecen los comentarios y sugerencias de Andrei Gomberg y César Martinelli. Cualquier error del presente trabajo es exclusiva responsabilidad del autor.

(Recibido: Octubre 2011 / Aprobado: Enero 2012)

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and waiting for new useful information to appear and uncertainty to dissapear. Frequently, this decision is based on the recommendation of an expert, with the ability to determine the benefi ts of the proyect if it is undertaken. In this paper we analyze the optimal contract that the owner of the real option should propose to the expert in order to give her incentives to use costly resources in order to acquire useful information, and to make a recommendation which is consistent with the information acquired.Keywords: real options, asymmetric information, incentives, contracts, agency, expertJEL Classifi cation: D82, D86, D92, L26

1. Introducción

Buena parte de los proyectos de inversión que se llevan a cabo en una economía están caracterizados por la confl uencia de tres factores: (i) La inversión necesaria para ejecutar el proyecto es irreversible (por ejemplo, cuando el capital invertido en el proyecto no puede recuperarse porque los activos tienen alto grado de especifi cidad). (ii) Es posible postergar la ejecución del proyecto. (iii) Los benefi cios del proyecto son inciertos y pueden variar a lo largo del tiempo. Proyectos con estas características suelen recibir el nombre de opciones reales, por la analogía con las opciones fi nancieras. El dueño de una opción real tiene el derecho de ejecutar un proyecto en algún momento a lo largo de un periodo, pero no está obligado a ejecutarlo, del mismo modo que el dueño de una opción fi nanciera tiene el derecho a realizar una determinada operación sobre un activo subyacente, en o antes de una fecha de vencimiento, pero no está obligado a realizar dicha operación.

Ejercer en el presente una opción real involucra un tradeoff : se obtienen benefi cios inmediatos pero se pierde la posibilidad de ejecutar el proyecto en el futuro, con el costo de oportunidad asociado si los benefi cios son mayores. Cuando los benefi cios del proyecto, en caso de ejecutarse, dependen de alguna variable observable (por ejemplo precios de mercado), la regla de decisión suele involucrar un umbral: llevar e cabo el proyecto solo si la variable observada es mayor que un determinado valor umbral, y esperar en caso contrario (McDonald y Siegel, 1986; Dixit y Pindyck, 1994). La espera tiene valor porque puede permitir resolver incertidumbre sobre

CONTENIDO 4


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los benefi cios futuros del proyecto, pero también tiene costo de oportunidad, que corresponde a los benefi cios perdidos por no ejecutar inmediatamente el proyecto. La regla óptima es la que logra un balance adecuado entre los benefi cios y los costos de esperar. La industria del petróleo y la industria farmacéutica son dos ejemplos de industrias en las que las carteras de proyectos de las fi rmas que las conforman tienen un fuerte componente de opciones reales. (Para otros casos referirse a Dixit y Pindyck, 1994; Smit y Trigeorgis, 2004, presentan casos en los que el ejercicio de la opción real depende de la interacción estratégica entre varias fi rmas).

Las opciones reales en las que nos enfocamos en el presente trabajo son aquellas en las que los benefi cios subyacentes (en caso de ejecutarse el proyecto) no son fácilmente observables. Tal es el caso, por ejemplo, del desarrollo de nuevos productos cuya demanda es incierta y difícilmente estimable. En estos casos, para la decisión de ejecutar o esperar suele ser útil contar con la opinión de un experto, que cuenta con una tecnología (know-how) para estimar el benefi cio subyacente del proyecto (usualmente involucrando recursos costosos o incurriendo en desutilidades debido al esfuerzo). En tales situaciones, el dueño de la opción real deberá diseñar un contrato que incentive al experto a esforzarse por conocer con la mayor precisión posible los benefi cios subyacentes, y que también incentive al experto a comunicar verazmente dicha información.

Gromb y Martimort (2007), desde ahora GM, analizan en detalle los incentivos a expertos, y la posibilidad de colusión entre ellos. GM defi nen a un experto como un agente que realiza una acción o esfuerzo para obtener determinada información. Tanto la acción como la información adquiridas son privadas del experto y no verifi cables, por lo que no pueden exigirse en contratos. Como consecuencia, los incentivos dados a los expertos tienen como fi nalidad inducirlos a que se esfuercen por adquirir información, y a revelarla verazmente; sin embargo, no pueden requerir del experto el reporte del esfuerzo ni de la información adquirida. GM consideran contratos que especifi can una recomendación del experto y un pago, que puede (y óptimamente debe) estar condicionado a cualquier variable observable que se produzca al implementar la recomendación del experto, y estudian la forma del contrato que incentiva al experto a esforzarse y a efectuar una recomendación en línea con la información adquirida, a modo de administrar efi cientemente el proyecto. El modelo es de un solo periodo y las dos decisiones posibles son ejecutar o abandonar el proyecto.

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A diferencia del modelo de un solo periodo considerado por GM, en este trabajo consideramos una opción real cuya administración efi ciente requiere decidir entre ejecutar inmediatamente un proyecto con benefi cios inciertos, o esperar a que se resuelva la incertidumbre. El inversor puede delegar la búsqueda de información útil en un experto, con capacidad para obtener una señal informativa pero imperfecta sobre los benefi cios del proyecto. El diseño del contrato óptimo entre el inversor y el experto es el objetivo del presente trabajo, para lo cual construimos un modelo sencillo basado en el de GM. Mostramos que si el experto recomienda la ejecución inmediata, el contrato establece una recompensa sólo si el proyecto tiene éxito. Si en cambio el experto recomienda postergar la decisión en espera de mayor información, el pago en el segundo periodo debe hacerse contingente a la información que se revela al postergar el proyecto. Además, mostramos que el pago esperado al experto es mayor que su costo de esfuerzo, ya que es necesaria una prima para incentivar al experto a revelar la información adquirida efectuando una recomendación consistente.

En la siguiente sección presentamos el modelo. En la sección 3 obtenemos el contrato óptimo y ofrecemos un análisis del mismo. Por último presentamos las conclusiones. Todas las demostraciones se relegan al Apéndice.

2. Modelo

El modelo considera un inversor con derecho a ejecutar un proyecto irreversible de benefi cios inciertos. La inversión puede efectuarse en dos periodos posibles: t = 1, 2. En cada periodo hay dos estados de la naturaleza posibles: el estado favorable (St = H) y el estado desfavorable (St = L). Concretamente, suponemos que en el estado favorable, el proyecto reporta ganancias G > 0, y en el estado desfavorable reporta pérdidas iguales a P.

El estado de la naturaleza no es observable en el primer periodo, pero es observable en el segundo periodo. Es decir, la incertidumbre en el segundo periodo desaparece. Este supuesto nos permite modelar de forma estilizada el tradeoff esencial de una opción real: ejecutar inmediatamente versus esperar la llegada de más información. En el primer periodo, un experto tiene acceso a una señal correlacionada con el estado de la naturaleza, condicional a la realización de esfuerzo, de costo e > 0. Este costo puede interpretarse directamente como la desutilidad del experto debido al esfuerzo, o como el costo de los recursos utilizados por la tecnología para recabar información. La precisión de la


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señal si el experto se esfuerza es 1Pr( | )s S e . Suponemos 1/ 2 1 ; es

decir, la señal es informativa pero imperfecta. El estado de la naturaleza en cada periodo está caracterizado por las probabilidades no condicionales )Pr( 1 HS y 1)Pr( 1 LS , y por las probabilidades condicionales )|Pr( 12 HSHSH , que es la probabilidad de permanencia en el estado favorable, y )|Pr( 12 LSLSL , que es la probabilidad de permanencia en el estado desfavorable. Las probabilidades no condicionales en el segundo periodo se denotan )Pr( 2 HS y 1)Pr( 2 LS . La probabilidad no condicional de la señal s, se denota )1)(|Pr()|Pr()( 11 LSsHSssp , la probabilidad de que el estado de la naturaleza en t sea el favorable dada la señal s se denota )|Pr()( sHSsq tt , y la probabilidad de que la señal sea la favorable, condicional al estado de la naturaleza St , se denota )|Pr()( SSHsS tt .

Tanto el inversor como el experto son neutrales al riesgo (maximizan benefi cios esperados) y el experto tiene responsabilidad limitada, por lo que el contrato no puede especifi car penalidades o pagos del experto al inversor. (Si el experto no tuviera responsabilidad limitada, la administración efi ciente puede implementarse a través de un contrato que equivale a vender los derechos de propiedad sobre la opción real al experto.)

El timing es el siguiente:

1. El inversor propone un contrato al experto, y el experto decide si aceptarlo o no aceptarlo.

2. La naturaleza determina el estado S1. 3. El experto decide si observa una señal correlacionada con el estado de

la naturaleza. 4. El experto efectúa una recomendación al inversor respecto de la

ejecución del proyecto. La recomendación puede ser esperar o ejecutar inmediatamente.

5. Si el proyecto se ejecuta inmediatamente, se observan los benefi cios, y el inversor paga al experto lo estipulado en el contrato, en función de los benefi cios observados.

6. Si la recomendación del experto es esperar, la naturaleza determina el estado S2, observado por todos.

7. Si el estado en el segundo periodo es favorable, se ejecuta el proyecto; si es desfavorable, se abandona el proyecto.

8. El inversor paga al experto lo estipulado en el contrato, en función de la decisión del inversor de ejecutar o abandonar.

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3. El contrato óptimo

La señal recibida por el experto es información privada de él, y por lo tanto no es verifi cable. El estado de la naturaleza en el primer periodo no es observable, y en el segundo periodo sí es observable, pero no es verifi cable. La idea es que un tercero -árbitro o juez- no puede, o le resulta muy costoso, certifi car dicha información. En cambio, el resultado del proyecto, si se ejecuta, es información pública y además es verifi cable por terceros (por ejemplo, mediante la auditoría de los estados contables). En consecuencia, el contrato no puede especifi car acciones o pagos condicionales a la señal o al estado de la naturaleza, pero puede especifi car pagos contingentes a acciones de cada parte y a información que pueda ser verifi cable por terceros. En nuestro contexto, el contrato exige al experto una recomendación (ejecutar inmediatamente o diferir para el periodo siguiente), y exige al inversor un pago al experto en el primer periodo si el experto recomienda ejecutar inmediatamente, condicionado a los benefi cios del proyecto. Denotamos a estos pagos t1H y t1L. Además el contrato especifi ca un pago al experto en el segundo periodo, si su recomendación es diferir, condicionado a la decisión del inversor de ejecutar o abandonar el proyecto. Al desaparecer la incertidumbre, el inversor puede conocer con certeza si el proyecto es rentable (S2 = H) o no (S2 = L), y utilizar esta información para decidir si lo ejecuta o lo abandona (en la jerga fi nanciera “deja morir la opción”). Suponemos que el estado de la naturaleza no es verifi cable por terceros (por ejemplo por un juez en caso de disputas), aún cuando en el segundo periodo sea información pública. Por lo tanto, los pagos no pueden condicionarse a dicho estado. Sin embargo, el contrato puede especifi car pagos en función de acciones verifi cables del inversor. Como las acciones del inversor en el segundo periodo son ejecutar o dejar morir la opción, y óptimamente estas decisiones se toman respectivamente si el estado de la naturaleza es favorable o desfavorable, el inversor puede en la práctica pagar al experto en función del estado. Denotamos a estos pagos por t2H y t2L.

A efectos de formular las restricciones de incentivos que debe verifi car el contrato, denotamos por )(R al valor actual de los pagos esperados por el experto si su recomendación es R (= Ejecutar o Diferir) sin haber observado la señal, y denotamos por )|( SR el pago esperado si el experto recomienda ejecutar o diferir habiendo observado una señal favorable ( HE |


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y HD | ) o una señal desfavorable ( LE | y LD | ). Por ejemplo, los pagos esperados al efectuar una recomendación consistente con la señal son

LH tHqtHqHE 1111 )](1[)()|(

y

LH tLqtLqLD 2222 )](1[)()|(

Defi nimos como costo delegación el pago esperado al experto:

)|()()|()( LDLpHEHpCD

El contrato debe ser atractivo para el experto si éste decide esforzarse y efectuar la recomendación consistente con la señal que observa.

0 eCD (PP)

El lado izquierdo es el el pago esperado si el experto decide participar, esforzarse y efectuar una recomendación consistente con la señal, menos el costo de esfuerzo: el lado derecho es la utilidad de reserva del agente, normalizada a cero.

El contrato también debe incentivar al experto a esforzarse por adquirir información. Por lo tanto, los pagos deben satisfacer la siguiente restricción de incentivos al esfuerzo:

)}(),(max{ DEeCD (IF)

El lado derecho representa el máximo pago esperado que el experto puede obtener si debe efectuar una recomendación sin haberse informado. Si esta recomendación es ejecutar inmediatamente, el pago esperado es

LH ttE 11 )1()(

y si la recomendación es diferir, el pago esperado es

LH ttD 22 )1()(

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La condición (IF) es equivalente a las dos condiciones siguientes:

)(EeCD (IFE) y

)(DeCD (IFD)

Además, el contrato debe incentivar al experto a efectuar una recomendación consistente con la señal observada. Por lo tanto, los pagos deben satisfacer las siguientes restricciones:

)|()|( HDHE (RCE)

y

)|()|( LELD (RCD)

La primera de estas dos restricciones establece que si el experto observa una señal favorable (s = H), debe preferir débilmente recomendar la ejecución inmediata; similarmente, la segunda establece que si el experto observa una señal desfavorable, debe preferir débilmente recomendar la postergación de la decisión.

Finalmente, el contrato debe especifi car pagos no negativos, debido a que el experto tiene responsabilidad limitada:

0,,, 2211 LHLH tttt (RL)

Defi nición: El contrato es incentivo factible (FACT) si verifi ca las restricciones (PP), (IFE), (IFD), (RCE), (RCD) y (RL).

El problema del inversor es diseñar el contrato incentivo factible que maximize su utilidad esperada, que es

)|()()|()( LDLpHEHp II

donde )|( HEI es el benefi cio actual esperado, neto de pagos al experto, que obtiene el inversor al ejecutar inmediatamente el proyecto, si el experto luego de esforzarse y observar la señal favorable, así lo recomienda, y )|( LDI es


87

el benefi cio neto actual esperado de diferir la ejecución, si el experto luego de esforzarse y observar la señal desfavorable, recomienda esperar al siguiente periodo. Estos pagos son

))]((-1[))(()|( 1111 LHI tPHqtGHqHE

y

)](-1[))(()|( 2222 LqttGLqLD LHI

El estado de la naturaleza en t = 2 es observable. Por lo tanto, el inversor óptimamente decide no ejecutar el proyecto si se observa la señal desfavorable, evitándose la pérdida P. No obstante, a pesar de que el proyecto no se ejecute, dejamos abierta la posibilidad de que el contrato incluya un pago al experto si en el segundo periodo el estado de la naturaleza es desfavorable.

Como el inversor es neutral al riesgo, podemos expresar los benefi cios esperados de los pagos esperados al experto como V - CD, donde

GLqLpPHqHpGHqHpV )()()](1)[()()( 211

es el valor de la opción real si el inversor fuera experto, es decir, tuviera la capacidad para adquirir información en el primer periodo. Como V no depende de los pagos al experto, el problema del inversor puede expresarse como el de elegir los pagos al experto incentivo factibles que minimizan el costo de delegación:

min CD sujeto a (FACT)

Las restricciones al esfuerzo implican las restricciones de consistencia en la recomendación. GM argumentan que si el experto prefi riera efectuar una recomendación inconsistente, no necesitaría la señal para hacerlo, por lo que no tendría sentido esforzarse para obtener dicha señal. Formalmente:

Lema 1. Si un contrato verifi ca las restricciones (IFE) y (IFD) entonces también verifi ca las restricciones (RCE) y (RCD).

Igualmente, las restricciones de esfuerzo implican la restricción de participación.

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Lema 2. Si un contrato verifi ca las restricciones (IFE) y (IFD) entonces también verifi ca la restricción (PP).

Como consecuencia, podemos omitir las restricciones de consistencia en la recomendación y la restricción de participación.

Defi nimos el costo de agencia como la diferencia entre el costo de delegación y el costo de esfuerzo del experto: CA = CD - e

La siguiente proposición establece que el problema del inversor está bien defi nido, y caracteriza el contrato óptimo.

Proposición 1. (i) Existe solución al problema de diseño óptimo del contrato. (ii) Si )()( 22 LH y el experto recomienda la ejecución inmediata, el inversor sólo debe recompesar al experto si el proyecto tiene éxito, con el siguiente pago:

)]()([ 211 LH

et H

y si el experto recomienda la postergación de la decisión, el inversor sólo debe recompensar al experto si al resolverse la incertidumbre, el inversor observa que el estado de la naturaleza en t = 2 es el desfavorable, dejando morir la opción. En tal caso, el pago debe ser

)]()()[1( 212 LH

et L

(iii) Si )()( 22 LH , y el experto recomienda la ejecución inmediata, el inversor sólo debe recompesar al experto si el proyecto tiene éxito, con el siguiente pago:

)]()([ 211 HH

et H

y si el experto recomienda la postergación de la decisión, el inversor sólo debe recompensar al experto si al resolverse la incertidumbre, el inversor observa que el estado de la naturaleza en t = 2 es el favorable, ejerciendo la opción. En tal caso, el pago debe ser

)]()([ 212 HH

et H


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La demostración de la proposición puede verse en el apéndice. La misma se basa en construir un problema (llamado problema primal) cuyo dual es el problema del inversor, mostrar que la solución al primal es positiva, y vincularla con las holguras de las restricciones al esfuerzo utilizando la teoría de dualidad en programación lineal.

Las holguras de las restricciones de incentivos al esfuerzo son

)(* EeCh DE

y

)(* DeCh DD

El teorema de la holgura complementaria (cfr. Vanderbei, 2007, TH 5.3) establece que el producto entre cada variable solución del primal y la correspondiente holgura del dual debe ser igual a cero. En el apéndice mostramos que la solución al primal es positiva. Como consecuencia, las holguras complementarias son cero, por lo que las restricciones de incentivos al esfuerzo se cumplen con igualdad. Por lo tanto, la diferencia entre el costo de delegación y el costo de esfuerzo es

)()( DEeCD

que es positiva en el óptimo, indicando que sea cual fuere su recomendación, el pago esperado del experto debe compensarlo por el esfuerzo, e incentivarlo a efectuar una recomendación consistente con la señal observada con un monto adicional al costo de esfuerzo. Este monto adicional es el costo de agencia, y es igual a )(E y a )(D :

)()( DECA

El inversor compensa al experto por su esfuerzo, y además ofrece la menor prima posible para asegurar consistencia en la recomendación. Esta consistencia en la recomendación se garantiza ofreciéndole al experto benefi cios iguales a los que esperaría si efectúa una recomendación sin esforzarse. Además, los pagos óptimos son tales que si el experto no se esfuerza, estaría indiferente entre recomendar la ejecución inmediata o la postergación de la decisión. (En el óptimo, )(E y )(D son iguales; GM

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obtienen el mismo resultado en su setup de un periodo.) El siguiente corolario se deriva de la proposición anterior.

Corolario 1. El costo de agencia es positivo.

El contrato óptimo es consistente con un principio general en problemas de acción oculta: el pago debe estar vinculado a los eventos más informativos sobre el esfuerzo del agente. Concretamente, la actualización bayesiana que el inversor hace sobre la probabilidad de una recomendación de ejecución inmediata, consistente con la señal observada (s = H), es mayor si el estado de la naturaleza es el favorable, debido a que la señal es informativa:

)(12/1)( 11 LH

Siguiendo el mismo criterio, si el experto recomienda postergar la decisión, en el siguiente periodo se lo deberá recompensar en el evento más informativo sobre el esfuerzo del agente. Este evento puede ser tanto la ocurrencia del estado favorable como la ocurrencia del estado desfavorable (a diferencia del pago en el primer periodo en el que el evento más informativo es siempre el estado favorable). El inversor debe asociar el pago a la ocurrencia del estado favorable en el segundo periodo sólo si )()( 22 LH , o equivalentemente, si )(1)(1 22 LH , es decir, sólo si el evento más informativo sobre la recepción de una señal desfavorable por parte del experto (s = L) es la ocurrencia del estado favorable en el segundo periodo. Si )()( 22 LH , el evento más informativo sobre la recepción de una señal desfavorable por parte del experto es la ocurrencia del estado desfavorable en el periodo t = 2. En tal caso, el inversor debe recompensar al experto sólo si ocurre el estado desfavorable. Aunque puede parecer contraintuitivo, tiene sentido: la idea es incentivar al experto a recomendar la postergación del proyecto sólo si observa una señal desfavorable; si )()( 22 LH , la probabilidad que el inversor asigna a la recepción de una señal favorable por parte del experto (y por lo tanto de haber hecho una recomendación inconsistente) es mayor luego de observar el estado favorable en el segundo periodo. Si quiere desincentivar esta recomendación inconsistente, el inversor no debe recompensar al experto en el estado favorable.

Notar que el pago al experto disminuye con aumentos en la diferencia )()( 221 SH . Intuitivamente, si el experto recomienda la ejecución,


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el problema de asimetría informacional se agrava a menor contenido informativo de los resultados del proyecto sobre el esfuerzo del agente (a menor )(1 H , por lo que el pago al experto debe aumentar; por otro lado, si el experto recomienda la postergación, el pago debe aumentar con )( 22 S , que es la probabilidad de que el experto haya observado una señal favorable, dado que el estado de la naturaleza en el segundo periodo es S2. Mayores valores de esta probabilidad equivalen a menores valores de la probabilidad de que el experto haya observado una señal desfavorable en el primer periodo, y por lo tanto haya efectuado una recomendación consistente. En otras palabras, altos valores )( 22 S signifi can que la ocurrencia del estado S2 es poco informativo sobre la consistencia en la recomendación de esperar. Esto agrava el problema de asimetría informacional, por lo que el pago al experto debe aumentar.

4. Conclusiones

En el presente trabajo hemos obtenido el contrato óptimo que el dueño de una opción real debe proponer al experto para que involucre recursos costosos que le permitan recabar información de utilidad para decidir sobre el timing óptimo, y para que efectúe una recomendación consistente con la información recabada. Si el experto recomienda la ejecución inmediata, el contrato establece una recompensa sólo si el proyecto tiene éxito. Si en cambio el experto recomienda postergar la decisión en espera de mayor información, el pago en el segundo periodo debe hacerse contingente a la información que se revela al postergar el proyecto. El contrato puede considerar un pago si el proyecto se abandona, o si se ejecuta con éxito, dependiendo de cuál sea el estado más informativo sobre la acción del experto en el primer periodo. El pago esperado al experto es mayor que su costo de esfuerzo, ya que es necesaria una prima para incentivar al experto a revelar la información adquirida efectuando una recomendación consistente.

ESTEBAN COLLA

92

Referencias bibliográfi cas

Dixit, A. K., R. S. Pindyck (1994), Investment under Uncertainty, Princeton University Press.

Gromb, D., D. Martimort (2007), “Collusion and the organization of delegated expertise”, Journal of Economic Theory, vol. 137, núm. 1, pp. 271-299.

McDonald, R., D. Siegel (1986), “The value of waiting to invest”, The Quarterly Journal of Economics, vol. 101, núm. 4, pp. 707-27.

Smith, H. T. J., L. Trigeorgis (2004), Strategic Investment: Real Options and Games, Princeton University Press.

Vanderbei, R. (2007), Linear Programming: Foundations and Extensions (International Series in Operations Research & Management Science), 3rd edn. Springer.

Apéndice

A continuación se desarrollan las demostraciones de los resultados del trabajo. En lo que sigue, para simplifi car la exposición de las funciones objetivo y de las restricciones, utilizamos la siguiente notación:

)(1 Ha

)1)(1()1)((1 Lb

)]1()1()1([)](1[ 2 LHHc

)]1()1)(1[()1)]((1[ 2 LHLd

)]1)(1)(1([)](2 LHHf

)]1)(1()1[()1)]((2 LHLg

)1()](1[ 1 Hj

)1()1)]((1[ 1 Lk


93

Lema 1. (IF implica IC y PP) El problema de diseño óptimo del contrato queda expresado de la siguiente manera:

LHLH dtctbtat 2211min

02211 edtctbtat LHLH

0)]1([)( 2211 edtcttbta LHLH

0)]1([)( 2211 etdtcbtat LHLH

LHLH ktjtdtct 1122

LHLH gtftbtat 2211

0,,, 2211 LHLH tttt

Como el costo de esfuerzo es no negativo, edtctdtct LHLH 2222 . Suponer que (IFE) se verifi ca; entonces el lado derecho es mayor o igual a

LH ktjt 11 ; por lo tanto, también se verifi ca (RCD). Similarmente, si (IFD) se verifi ca, entonces

LHLHLHLH gtfttdtcebtatbtat 22221111 ])1([)(

que implica que (RCE) también se verifi ca.

Lema 2. (IF implican PP) Si las restricciones al esfuerzo se cumplen, entonces

eettedtctbtat LHLHLH 112211 )1( y

eetdtedtctbtat LHLHLH 222211 )1([

donde las últimas desigualdades se deben a que los pagos son no negativos. Ambas implican (PP). Proposición 1. (Existencia de solución - Contrato óptimo) Notar que el problema del inversor es el dual del siguiente problema primal:

ESTEBAN COLLA

94

)(max yxe

sujeto a

aayxa )(

bbyxb ])1[(

cyccx )(

ddyxd )]1([

0, yx

Este problema es factible (por ejemplo, )0,0( verifi ca el conjunto de restricciones). Mostraremos que el problema primal está acotado, para lo cual expresamos la primera restricción como xy ]/)1[(1 y la segunda como y xy )]1/([1 . Como la señal es informativa 2/1 , la primera condición implica la segunda que, por lo tanto, podemos omitir. Del mismo modo, la tercera y cuarta restricción pueden expresarse como )1)(/( xfcy y )1)(/( xgdy . La recta xy )]1/([1 tiene ordenada al origen en y=1, y las rectas )1)(/( xfcy y )1)(/( xgdy tienen abcisa al origen en x=1. Notar que sólo estará activa la restricción correspondiente a la recta con la mayor de las pendientes. Por lo tanto, para probar que el problema está acotado, basta con demostrar que la mayor de las pendientes de estas rectas es mayor que /)1( , es decir, basta con demostrar que /)1(}/,/max{ gdfc . Suponer que fcgdfc /}/,/max{ . Entonces, si la señal es informativa,

./)1(/

)1)(1)(1()1()1)(1()1(

)1(2/122

22

fcLHLH

Siguiendo el mismo procedimiento, gdgdfc /}/,/max{ .

./)1(/

)1)(1()1()1()1()1()1(

)1(2/122

22

gdLHLH


95

Por lo tanto, el problema está acotado. El teorema fundamental de la programación lineal (cfr. Vanderbei (2007) TH. 3.4) implica que el dual es factible; por lo tanto, existe solución al problema de diseño del contrato óptimo. La solución al problema primal satisface las siguientes restricciones con igualdad:

xy 1

)1( xy

donde /)1( y }/,/max{ gdfc . Por lo tanto,

0)/()1(* x

0)/()1(* y

Las holguras del problema primal son

01 **1 yxH

0

)(

)1)(1(11

2**

1

yxL

0)1)(1(

1 **2

c

f

yc

fxH

0)1)(1(

1 **2

d

g

yd

gxL

Tanto el problema primal como el dual son factibles. Notar que 01 L implica que 01 Lt . Además, como x* y y* son mayores a cero, el teorema de la holgura complementaria (Vanderbei (2007), TH 5.3) implica que las restricciones de incentivos al esfuerzo se cumplen con igualdad. Si gdfc // , entonces 02 L , y si fcgd // , entonces 02 H . (Note que la desigualdad gdfc /)(/ es equivalente a )()()( 22 LH . Por lo tanto, las restricciones

ESTEBAN COLLA

96

de incentivos al esfuerzo conforman un sistema de dos ecuaciones con dos incógnitas, t1H y t2H o t2H dependiendo de la comparación de )(2 H versus )(2 L , cuya solución corresponde a los pagos de la proposición.

Corolario 1. (El costo de agencia es positivo) El corolario se deriva del teorema fuerte de dualidad (Vanderbei, 2007; TH 5.2), que establece que el costo de delegación del inversor, función objetivo del problema de minimización evaluada en el óptimo, es igual a la función objetivo del primal evaluada en la solución. Sustituyendo x* y y* en la función objetivo del problema primal obtenemos el costo de delegación eCD )]/)21[( . Notar que )1( es menor a 0. Por lo tanto, )1(1 que implica 21 o 1)/()21( . El costo de agencia es

)/()1(}1)]/()21{[( eeCA

que es positivo.

RECIPROCAL DUMPING ANDENVIRONMENTAL TAXES

Salvador Sandoval Bravo*Semei Leopoldo Coronado Ramírez**

Jesús Porras Serrano***

Resumen

En este trabajo se calcula el impuesto óptimo a la emisión de contaminantes en competencia oligopolística y en condiciones de dumping recíproco, en el que las empresas cuentan con la tecnología adecuada para disminuir la contaminación y poder decidir la cantidad de emisiones generadas. En este modelo, el impuesto óptimo depende principalmente de la cantidad de la desutilidad marginal de contaminar, además del costo de abatimiento.Palabras clave: dumping recíproco, impuestos, política medioambiental, competición oligopolísticaClasifi cación JEL: Q52, Q56, F18

Abstract

This paper calculates the optimal tax of the emission of polluting agents in oligopolistic possess and under conditions of the reciprocal dumping, in which the fi rms count on the appropriate technology to decrease the pollution and


* Departamento de Métodos Cuantitativos del Centro Universitario de Ciencias Económico Adminis-trativas, Universidad de Guadalajara. Correo electrónico: <[email protected]>.

** Departamento de Métodos Cuantitativos del Centro Universitario de Ciencias Económico Adminis-trativas, Universidad de Guadalajara. Correo electrónico: <[email protected]>.

*** Escuela Superior de Economía del Instituto Politécnico Nacional. Correo electrónico: <[email protected]>.

(Recibido: Septiembre 2011 / Aprobado: Enero 2012)

SALVADOR SANDOVAL / SEMEI L. CORONADO / JESÚS PORRAS

98

can decide the amount of emissions generated. In this model the optimal tax mainly depends on the amount of the marginal disutility to pollute, as well as the abatement cost.Keywords: reciprocal dumping, taxes, environment policy, oligopolistic competitionJEL Classifi cation: Q52, Q56, F18

1. Introduction

Among the instruments of environmental policy more used by the governments to regulate the emissions of polluting agents to the atmosphere we fi nd the taxes.1 Due to the fact that pollution is a public bad, this can not be corrected by the ordinary mechanisms of the market. Government intervention is required to impose a system of shadow prices for pollution to reduce it; in other words, the agents must pay a price for each unit of emitt ed pollution. In this way, the externality is corrected, at least in theory. Such a price for pollution is implemented by the government through a tax, whose intention is to make fi rms pollute reasonably less, since to pollute will become expensive by the tributary cost to be paid by the polluting agents.

The present work analyses the implementation of a tax on the amount of pollution emitt ed by the fi rms under conditions of the reciprocal dumping. This paper will deal with an apparently paradoxical situation of international trade: the reciprocal dumping.2 Under such conditions commerce between two countries in completely identical goods exists (and that in the absence of comparative advantage and with constant yields on scale).3 And although the force of monopolies and oligopolies is reduced due to the increase of in competition, since the penetration in a country by foreign fi rms tends to reduce power positions of the local fi rms, so that the prices of the goods fall more and more approaching the average production costs, it still remains far away from a perfect competition situation of perfect competition.

1 In the classic work of Cropper and Oates (1992) a more detailed explanation of this instrument of environmental policy can be seen.

2 For more detailed information of the reciprocal dumping model, see Brander (1981), Brander and Krugman (1983), Venables (1985), among others.

3 The most general case of similar goods is known as intraindustry trade, where they emphasize works like Balassa (1966), Krugman (1979) and Lancaster (1980).

RECIPROCAL DUMPING AND ENVIRONMENTAL TAXES

99

This way we developed a Cournot model of oligopolistic competition, which is a partial equilibrium analysis, of reciprocal dumping conditions between two small countries, the typical situation faced by developing economies.4 Both countries produce the same homogenous good under constant economies of scale and diff erent marginal costs of production. We consider in addition that in both countries there are domestic fi rms that assign part of their production to the local consumption and leave the rest to the export market.5 We also suppose that the markets are segmented since constant scale economies exist and there are no capacity restrictions, which imply that for the fi rms the variations in one of the markets do not infl uence the decisions taken in the other. The fi rms generate pollution in their productive processes, yet, they own the proper technology to oppose it, so they can decide the magnitude of the generated pollution; in addition, there exists a social cost to pollute. Under these circumstances the government tries to persuade the fi rms that they pollute the least possible through the imposition of a tax by unit of emitt ed pollution. The proposed model calculates the optimal pollution tax that maximises the welfare in each one of the countries. And therefore, the aforementioned optimal tax determines the application of strategic policies under specifi c conditions that are related to the structure of costs of the fi rms, specifi cally the amount of the abatement cost by unit of pollution and its relation with the marginal disutility of polluting. These policies have important consequences in function of social welfare in both countries that involve the consumer surplus, the benefi t of the fi rms and the social cost to pollute.

For this model we concluded that if the marginal cost of polluting is very high, then the government imposes a positive pollution tax that consequently forces the fi rms to pollute less or to pay it. But if the marginal cost to pollute is not suffi ciently large, then the magnitude of the tax depends on the size of the market of the foreign country with respect to the local one. If the fi rst is very big, then the government will try to favour the competitiveness of the local fi rms establishing a null burden to the emissions of polluting agents, but if the second is much larger, then the principle will prevail to reduce the emission of polluting agents through a tax greater than zero.

4 Some works that analyse the instruments of environmental policy in oligopolistic models, including some specifi c of reciprocal dumping, we have: Barret (1994), Espinosa and Palomera (2003), Lahiri and Ono (1998), Espinosa and Ozgur (2001).

5 Even though there are asymmetries in the cost structure, both countries will import the same homo-geneous good as a result of strategic decisions of the fi rms, Brander (1981).


100

The structure of this work is the following: It begins with the specifi cation and boundary of the model. Next the optimal pollution tax is determined. Finally, from these results applicable environmental policies are set forth.

2. Specifi cation of the model

We consider the trade of a homogenous good between two countries A and B, under conditions of reciprocal dumping. Country A produces for local consumption and to export to country B. Therefore, the production of a particular fi rm from country A of the homogenous marketable good is:

A BX X X (1)

Where, XA is the quantity of the produced good for local consumption in the country A; XB is the quantity of the produced good for export to the country B.

Similarly, for country B,

A BY Y Y (2)

Where, YB is the quantity of the produced good for the local consumption for the country B and YA is the quantity of the produced good for export to the country A.

We can make the assumption that there exist n fi rms in the country A, and m fi rms in the country B; in order that the demand in the country A, DA, is equal to the production for the local consumption combined in their n fi rms, plus the assigned production to the exports combined of the m fi rms of country B, this is,

A A AD nX mY (3)

In the same way, the demand in country B will be

B B BD mY nX (4)

We can assume that both countries have the proper technology to regulate their emissions of pollutants. Let zA be the quantity of pollution per


101

unit produced of the homogeneous good in the country A and let zB be the quantity of pollution per unit produced of the good in the country B.

Therefore, the quantity of polluting emissions in the country A, zA , is equal to the total production of the homogeneous good in the country A, given by the production by each domestic company, times the number of fi rms that participate in the market of the country A, times the quantity of pollution emitt ed per unit of product, zA, i.e., A A A B A A B AZ z n X X nX z mX z (5)

In the same way for country B, B B A B A B B BZ z m Y Y mY z mY z (6)

Let be the marginal disutility caused by the pollution, assuming like Lahiri and Ono (1998) that is constant. Besides let t be the tax per unit of pollution emitt ed.

The welfare of the country A, WA, will be built by the consumers’ surplus of the country A, CSA; the producers’ surplus in the country A, An ; plus the tributary tax collection tA ZA , minus the total disutility times the polluting emissions in the country A, AZ , then,

A SA A A A AW C n t Z Z (7)

Similarly for country B, is defi ned by, B SB B B B BW C m t Z Z (8)

If we consider the marginal costs of production of the good from the country A, sA and the ones from the country B, sB , we assume diff erences in the structures of costs between the two countries. Those costs are constants, and therefore, equivalent to the average variable costs. The prices of the good in each country are respectively pA y pB . In this way the benefi ts of the producer are given by,

A A A A B A Bp s X p s X (9)


102

In other words, the marginal profi t of the good, A Ap s , times the production for the local country A, plus the marginal profi t of the homogeneous good,

B Ap s , times the production of exports to the country B, times the number of local fi rms. In the same way, the producers’ surplus of country B is given by, B B B B A B Ap s Y p s Y (10)

In addition the price to the homogenous good in the country A, is a function of the level of production of this good in the domestic industries for the local consumption, and the import level of production of this good from the foreign country, this way, by simplicity and without loss of majority we can consider the inverse function of the demand as linear and of the form,

A A A Ap D A A A A Ap nX mY (11) B B B Bp D B B B B Bp mY nX (12)

Let be the marginal cost of abatement a unit of pollution, A and B , represent the quantities of pollution emitt ed before implementing any

environmental policies. This way, the cost by each fi rm related with the emission of pollution is given by, A A A A Av z t z (13)

B B B B Bv z t z (14)

So that the unitary cost of production of each company is given by,

A A A A A As c z t z (15) B B B B B Bs c z t z (16)

In these conditions zA and zB , represent an amount of emission of polluting agents imposed by the fi rms to themselves, in the understanding that they possess the technology to abate such pollution it can turn out bett er to reduce the amount of polluting agents that to pay a tax for the emission.


103

It is clear that when the tax by pollution unit is greater or just as the abatement cost the fi rms prefer to reduce the emission of polluting agents completely, whereas if the same tax is minor that the abatement cost, then they are continue emitt ing the same amount of pollution A and B , that is to say, A

AA A

0 si tz si t

B

BB B

0 si tz si t

(17)

And therefore,

A A AA

A A A A

c + si ts c t si t

B B BB

B B B B

c + si ts c t si t

(18)

0 AA

A A B A A

si tz nX nX si t

0 BB

A B B B B

si tz mY mY si t

(19)

The calculus of the optimal tax doesn’t make any sense when At and

Bt , because in this case the quantity of pollution is zero, independently from the tax amount. But when At and Bt all fi rms prefer to pay the tax and the reduction in the polluting emissions doesn´t occur, then in this case W does depends on t.

Under the previous conditions and assuming that each fi rm decides which proportion of the good is consumed locally, and which one is exported. Under the assumptions of Cournot-Nash, the conditions of maximization of fi rst order are,6

0, 0A A

A B

d d

dX dX

(20)

0, 0B B

A B

d d

dY dY

(21)

6 See Appendix 1.


104

From which we get the solutions for variables XA, XB, YA and YB:7

1

A A B AA

A

s m s sX

m n

1

B A B AB

B

s m s sX

m n

1

A B A BA

A

s n s sY

m n

1B B A B

BB

s n s sY

m n

(22)

Therefore the benefi ts from the fi rms in the country A and B in the optimal point are given by

* 2 2A A A B BX X * 2 2

B B B A AY Y (23)

3. Comparative Statics

The welfare of the countries A and B is defi ned as the sum of the consumers’ surplus plus the benefi ts of the fi rms plus the tributary tax collection minus the disutility given by pollution, this is,8 *

A SA A A A AW C n t Z Z *

B SB B B B BW C m t Z Z (24)

Diff erentiating WA and WB with respect to tA and tB respectively we get,9

*SA A A A AA

Z A A A A

d C d n d t Z d ZdW

dt dt dt dt dt

(25)

2 1

1 1A A A A BA A

A

n nX mY n m X XdW

dt m n m n

7 See Appendix 2.8 See Appendix 2. 9 See Appendix 3.


105

21 1

1 1A A A B A A B

A A BA B A B

t m n mn X X

m n m n

(26)

*SB B B B BB

B B B B B

d C d n d t Z d ZdW

dt dt dt dt dt

(27)

2 1

1 1B B B A BB B

B

m nX mY m m Y YdW

dt m n m n

21 1

1 1B B A B B A B

B A BA B A B

t n m nm Y Y

m n m n

(28)

Analysing the eff ects of the pollution tax from the diff erentiated components of the welfare function, we obtain:

The profi t of fi rms

*2 1

1A A B

A A

n m X Xd n dt

m n

(29)

In this case any reduction in the pollution tax reduces the marginal costs of production of the homogeneous good, and therefore, the production in the fi rms is favoured, at the same time the competitiveness of the local country is increased and consequently the exports are stimulated; therefore, the benefi ts of the domestic fi rms grow. In addition, such increase in the production stimulates the employment at the same time.

The consumers’ surplus

1

A A ASA A

n nX mYd C dt

m n

(30)

Since the production costs fall for the domestic fi rms when the pollution tax is reduced, the prices decrease which increases the spending power of the consumers, and therefore the consumers’ surplus.


106

The tax collection

1

1A A A B

A A A A B AA B

t md t Z n X X dt

m n

(31)

Clearly the tax increases the income of the government through collection of the tax from the fi rms and is a direct function of the levels of production of the manufacturers, although this also increases the marginal costs of the good and aff ects the production level negatively, reason why the combined eff ect is ambiguous.

Social cost for polluting

2 1

1A A B

A AA B

n md Z dt

m n

(32)

Evidently, reducing the tax stimulates the emissions of polluting agents to the atmosphere, thus the social cost to pollute also is increased, that is to say,

0A

A

d Z

dt (33)

In the same way an increase in tA , reduces the pollution and therefore it benefi ts to the country. In addition, the magnitude to such benefi t depends on the size of the parameter .

Given the symmetry of the model, the same reasoning is valid for tB , when considering the three components from the point of view of the foreign country.

Optimal tax In order to calculate the optimal tax and to implement the conducive tax policies we make 0A

A

dW

dt and 0B

B

dW

dt , fi nding tA and tB , we have,10

10 See Appendix 4.


107

*

1

1A B B A A B

AA A B

nX mY X X mt

m

(34)

*

1

1A B A B A B

BB A B

mY nX Y Y nt

n

(35)

Besides we can assure that the function is concave,11

2 22

22

2 1 2 10

1

A A BA

A A B

n m md W

dt m n

(36)

2 22

22

2 1 2 10

1

B B AB

B A B

m n nd W

dt m n

(37)

Of the expressions (34) and (35) we can observe since all the parameters are positive, the sign of tA depends on the size of the market and of the sign and value of the parameter .

Proposition 1. In the non-cooperative equilibrium

* 0A A Bt si mY nX

* 0B B At si nX mY

The economic interpretation of the previous result is very intuitive. If the size of market of export of the foreign country is signifi cantly greater than the size of market of the domestic country, then the best policy is tax rate of zero. In this case, the government favours the local fi rms by reducing their costs, which aff ects positively its benefi ts, increasing their competitiveness with respect to the foreign fi rms. At the same time it benefi ts the consumers who pay lower prices as a result of the reduction of marginal cost.

11 See Appendix 5.


108

Although a zero tax on the emissions of polluting agents favours the increase of the pollution rate, since the fi rms do not have any incentive to diminish their emissions, increasing therefore the social cost to pollute. On the other hand, a zero tax prevents to the government of gett ing additional income by the collection of the pollution tax. Even so, in this case, the awaited benefi ts as much of the benefi t of the fi rms as of consumers’ surplus they surpass the adverse eff ects of no tax collection and a considerable increase in the social cost to pollute.

Proposition 2. In the non-cooperative equilibrium * 0At and * 0Bt if the marginal disutility to pollute is signifi cantly elevated.

Such asseveration is obvious. The government values more the adverse eff ects of the pollution when the costs associated to their emission are very high, at the same time it stimulates as well to increase its tributary fundraising through the taxes. Although on the other hand, they reduce the benefi ts of the fi rms and the consumers’ surplus by the increase in the marginal cost of production and consequently increases the prices to the consumer. In addition since

*

0Ad t

d (38)

While greater it is the marginal disutility to pollute greater will be the tax determined by the government.

If we considered the case in which 1m n , that is to say, the situation of monopoly in both countries, we have:

*2

2A B A B A

AA A B

X X Yt

*2

2A B B B A

BB A B

Y X Yt

We notice that the fi rst term of such expressions is negative, reason why the sign of t* depends on the magnitude of , for a value of the very high


109

disutility, a positive tax would prevail, in this case the government weights the adverse eff ects of the pollution against the other components of the welfare function. Whereas if such parameter is not signifi cantly elevated then the tax would be zero, in such a way that the government cares more of the benefi cial eff ect in the consumers’ surplus and the producer’s surplus due to the reduction of the marginal costs and in the price the consumers. Although it represents an increase pollution. This also is consequent with the previous proposition.

On the other hand, the function W not necessarily is continuous with respect to t.

For the way that sA y sB are defi ne, the only possible point of discontinuity is t . Analyzing the likely discontinuity of W in t by calculating unilateral limits and using (17), (18) y (19) we have that,

*t A SA A A A Alim W C n t Z Z (39)

*

t A SA Alim W C n (40)

*t A SA A A A Alim W C n t Z Z (41)

*

t A SA A A A B A A A B Alim W C n nX nX nX nX (42)

*t A SA A A A B Alim W C n nX nX (43)

Therefore from (40) and (43) we have,

t A t A A A B Alim W lim W nX nX

Where we concluded that,

0t A t Alim W lim W si (44)



For a similar reasoning we get,


110

t B t B A B B Blim W lim W mY mY

Where we concluded that,

0t B t Blim W lim W si (47)



Which we can summarize on the next proposition.

Proposition 3. If then the tax *At therefore there´s no polluting

agents emission. And if then the tax *At therefore there´s no

reduccion on the pollutant emission.

Intuitively if the disutility to pollute is very high compared to the abatement cost the benefi t of reducing the emission of pollutants is imposed on other components of the welfare function, implementing the tax is higher than the abatement cost that´s why fi rms prefer not to emit pollutants at all.

While if the marginal disutility is not signifi cantly high compared with the abatement cost, the optimal tax is strictly less than the abatement cost and in this case, fi rms choose not to reduce their emissions.

4. Conclusions

One of the most used instruments for environmental policy to regulate the emission of pollutants into the environment which would not depend on the willingness of fi rms, is the imposition of governments of a tax per unit of pollution emitt ed, i.e., the government put a price on pollution, and fi rms pay the government in proportion to the amount of emissions they generate, as theoretically correct the market failure that causes the production of goods through the pollution, as the government to intervene by imposing a pollution tax must be costly and so the fi rms weighs on purely economic criteria the viability to pollute less.


111

In this project we develop an environmental policy model by taxes to the emission of pollutants under conditions of oligopolistic competition.

We consider trade between two small countries of similar size, assuming that reciprocal dumping exists. So, fi rms dedicate most of their production to the local consumption and the other part to export. We assume that fi rms pollute as part of the production process, but at the same time they must have technology to lower pollutant emissions. Under these circumstances we calculate the optimal pollution tax. Also from the optimal tax derived a series of strategic policies that are related with the costs structure of the fi rms and in particular the abatement cost and disutility from pollution. These environmental policies directly aff ect the welfare function of the countries and their components (consumers’ surplus, fi rms profi ts and social cost for polluting).

The magnitude of the optmimal tax depends mainly on the export market size of countries and the size of the marginal disutility of pollution. In the fi rst case, if the size of the country´s export market is larger than the local market, the government burden on domestic fi rms a zero tax rate, which enhances the competitiveness of such fi rms to reduce the marginal costs of production, inducing a positive eff ect on consumers’ surplus and in fi rms benefi t. Although the zero-tax results in an increase in pollution and social costs that these involve. On the other hand, if the marginal inutility for pollution is very high, then the government values more the adverse eff ects of pollution, which at the same time increases tax collection by means of the pollution tax, although this sacrifi ces in some way the benefi t to companies and consumer well-being. The above result is also true in the case of monopolies in both countries.

Finally, if we compare the marginal disutility with the abatement cost we conclude that if the fi rst is greater than the second, then the optimal tax must be greater than the abatement cost and in this case the fi rms decide not to pollute at all, because clearly it is cheaper to cover the cost of not polluting than pay an expensive tax.

In the opposite case, when the marginal disutility of pollution is less than the abatement cost, then the optimal tax should be less than the abatement cost, in which case fi rms choose not to reduce the least emission of pollutants, because bringing down the abatement cost the pollution is clearly much more expensive than paying the taxes on the emission of pollutants.


112

References

Balassa, B. (1966), "Tariff Reductions and Trade in Manufactures", American Economics Review, vol. 56, no. 3, 466-473.

Barret, S. (1994), "Self-Enforcing International Environmental Agreements", Oxford Economics Papers, no. 46, 878-894.

Brander, J. (1981), "Intraindustry Trade in Identical Commodities", Journal of International Economics, no. 11, 1-14.

Brander, J. and P. Krugman (1983), "A Reciprocal Dumping Model of International Trade", Journal of International Economics, vol. 15, nos. 3-4, 313-321.

Cropper, M. and W. Oates (1992), "Environmental Economics: A Survey", Journal of Economics Literature, vol. 30, no. 2, 675-740.

Espinosa, R. and G. Palomera (2003), "Políticas Ambientales en la Presencia de Inversión Extranjera Directa y Fusiones", CUCEA, U. de G.

Espinosa, R. and M. Ozgur (2001), "Strategic Environmental Policies and Mergers", LACEA 2001, Montevideo, Uruguay.

Krugman, P. (1979), "Increasing Returns, Monopolistic Competition and International Trade", Journal of International Economics, vol. 9, no. 4, 469-479.

Lahiri, S. and Y. Ono (2000), "Protecting environment in the presence of foreign direct investment: tax versus quantity restriction", Mimeo Department of Economics, University of Essex.

Lancaster, K. (1980), "Intra-Industry Trade under Perfect Monopolistic Competition", Journal of International Economics, vol. 10, no. 2, 151-175.

Venables, J. (1985), "Trade and Trade Policy with Imperfect Competition:. The Case of Identical Products and Free Entry", Journal of International Economics vol. 19, nos. 1-2, 1-19.


113

Appendix

1. First order conditions

The profi ts of the fi rms in the country A and B are given by,

A A A A B A Bp s X p s X

B B B B A B Ap s Y p s Y

We also know that,

A A A Ap D A A A A Ap nX mY

B B B Bp D B B B B Bp mY nX

Replacing pA, pB, sA y sB, en A y B we have:

A A A A A A A B B B B A BnX mY s X mY nX s X

(50)

B B B B B B B A A A A B AmY nX s Y nX mY s Y (51)

Diff erentiating with respect to XA, XB, YA and YB to obtain the values of those variables that maximize the profi ts of the fi rms in both countries we have,

2A

A A A A A i A A A iA

ds X X m Y n X

dX


114

2A

A A A A A A A A A AA

ds X X m Y n X

dX

0AA A A A A A A

A

ds X mY nX

dX

(52)

But, A A A A Ap nX mY , then

A A A AX p s (53)

Similarly, performing the same calculations for,

A

B

d

dX

,

B

A

d

dY

y

B

B

d

dY

results

0BB A B B B B B

B

ds X mY nX

dX

(54)

B B B AX p s (55)

0BA B A A A A A

B

ds Y mY nX

dY

(56)

A A A BY p s (57)

0BB B B B B B B

B

ds Y mY nX

dY

(58)

B B B BX p s (59)

2. Closed solutions for the variables XA, XB, YA and YB

Solving the system of simultaneous equations given by the reaction curves, expressed by the equations (52), (54), (56) y (58), that express the Cournot


115

equilibrium, we fi nd the optimal choice of output level XA, XB, YA and YB for the fi rms of the country A and the country B.

1A A B A

AA

s m s sX

m n

(60)

1B A B A

BB

s m s sX

m n

(61)

1A B A B

AA

s n s sY

m n

(62)

1B B A B

BB

s n s sY

m n

(63)

Replacing (60), (61), (62), (63) in (50) and (51), we get the company´s benefi ts in the country A and B at the optimal point, * 2 2

A A A B BX X (64)

* 2 2B B B A AY Y (65)

3. Total diff erentiation of the welfare function

We will diff erentiate the functions of welfare for the country A and the country B

*A SA A A A AW C n t Z Z (66)

*B SB B B B BW C m t Z Z (67)

But before XA, XB, YA and YB respect to taxes in the respective countries (will be use in the next calculations). Replacing (15) and (16) in (60), (61), (62), (63) and diff erentiating with respect to tA and tB, we get,


116

1

1AA

A A

mdX

dt m n

(68)

1A B

B A

dX m

dt m n

(69)

1A A

A A

dY n

dt m n

(70)

1

1BA

B A

ndY

dt m n

(71)

1

1AB

A B

ndX

dt m n

(72)

1B B

B B

dX m

dt m n

(73)

1B A

A B

dY n

dt m n

(74)

1

1BB

B B

ndY

dt m n

(75)

Consumers’ surplusTo derive the fi rst term of (66) and (67), given the demand of the countries A and B, consumers’ surplus is given by,

2

2

2 2A A AA A

SA

nX mYDC

(76)

22

2 2B B BB B

SB

nX mYDC

(77)

Diff erentiating the above equations respect to tA and tB, and using (68), (70), (73) y (75) we get,


117

1A A ASA

A

n nX mYdC

dt m n

(78)

1B B BSB

B

m nX mYdC

dt m n

(79)

The benefi t of the fi rmsIn order to derive the second term of (66) and (67), given the benefi ts of the fi rms in the countries A and B (64) and (65); and using again (68), (71), (72) and (75) we get,

* * 2 2 2 1

1A A A A B B A A B

A A A

d n d d X X n m X Xn n

dt dt dt m n

(80)

* * 2 2 2 1

1B B B B A A B A B

B B B

d n d d Y Y m n Y Ym m

dt dt dt m n

(81)

The tributary componentDiff erentiating the fourth term from (66) and (67), and starting off of the total emission of polluting agents in the countries A and B by the disutility to pollute .

A A A A A B At Z t nX nX

B B B A B B Bt Z t mY mY

And using (68), (71), (72) and (75) we have the following thing,

A A A B AA A

A A

d t nX nXd t Z

dt dt

1

1A A A B

A A BA B

t mn X X

m n

(82)


118

B A B B BB B

B B

d t mY mYd t Z

dt dt

1

1B B A B

B A BA B

t nm Y Y

m n

(83)

Social cost to polluteDiff erentiating the third term from (66) and (67), and starting off to the total emission of polluting agents in the countries A and B by the disutility to pollute .

A A A B AZ nX nX

B A B B BZ mY mY

thus, using again (68), (71), (72) and (75) we get the following,

A A

A A

d Z d Z

dt dt

2 1

1A A B A A A B

A A B

d nX nX n m

dt m n

(84)

B B

B B

d Z d Z

dt dt

2 1

1A B B B B A B

B A B

d mY mY m n

dt m n

(85)

Therefore,

A

A

dW

dt is

*SA A A A AA

A A A A A

d C d n d t Z d ZdW

dt dt dt dt dt

2 1

1 1A A A A A BA

A

n nX mY n m X XdW

dt m n m n

21 1

1 1A A A B A A B

A A BA B A B

t m n mn X X

m n m n

(86)


119

And similarly

B

B

dW

dt we get ,

*SB B B B BB

B B B B B

d C d n d t Z d ZdW

dt dt dt dt dt

2 1

1 1B B B B A BB

B

m nX mY n m Y YdW

dt m n m n

21 1

1 1B B A B B A B

B A BA B A B

t n m nm Y Y

m n m n

(87)

4. Optimal tax of pollution

If we do

A

A

dW

dt y

B

B

dW

dt in order to fi nd the optimal tax in (86) and in (87),

clearing tA y tB, we get,

*

1

1A B B A A B

AA A B

nX mY X X mt

m

(88)

*

1

1A B A B A B

BA A B

mY nX Y Y nt

m

(89)

5. Concavity of the welfare functionObtaining the second derivative from the welfare function with respect to the tax to determine the conditions of concavity we have,

2 22

22

2 1 2 10

1

A A BA

A A B

n m md W

dt m n

(90)

2 22

22

2 1 2 10

1

B B AB

B A B

m n nd W

dt m n

(91)

Then, W is concave.

MIGRATION AND REMITTANCES EFFECTS ON CONSUMPTION OF THE POOREST:

THE MEXICAN CASE

José Jorge Mora Rivera*Jesús Arellano González**

Resumen

Este trabajo presenta evidencia empírica sobre el efecto de las remesas en los patrones de gasto de hogares rurales que viven en algunas de las zonas más pobres de México. Utilizando datos de las encuestas del programa Progresa-Oportunidades de los años 1997 al 2000, se desarrolla un modelo econométrico que considera el proceso de autoselección involucrado en el fenómeno migratorio, para estimar el impacto que tiene la probabilidad de recibir remesas, internas y externas, en los patrones de gasto de estos hogares. Los resultados señalan que existen efectos signifi cativos en ciertas categorías de gasto. Dichos hallazgos indican que los hogares con mayor probabilidad de recibir remesas tienen mayor propensión a gastar en categorías de gasto relacionadas con la inversión física y humana. Palabras clave: migración, remesas, consumo, hogares mexicanosClasifi cación JEL: D12, O15


AUTORES 6

(Recibido: Octubre 2011 / Aprobado: Febrero 2012)

* Instituto Tecnológico y de Estudios Superiores de Monterrey, Campus Ciudad de México. Electronic mail: <[email protected]>.

** El Colegio de México. Electronic mail: <[email protected]>. The authors would like to thank the Hewlett Foundation and the MacMillan Center at Yale University

for their fi nancial support to this work. We specially thank to professor Gustav Ranis for his eff orts coordinating the empirical studies prepared for the Global Citizen Project and the working group formed at the Economic Growth Center of Yale University for their valuable comments and observa-tions.

JOSÉ J. MORA / JESÚS ARELLANO

122

Abstract

In this work we present empirical evidence to test for the impact of remitt ances on expenditure patt erns in rural Mexican households located in poor areas. Using data from the Progresa-Oportunidades program from 1997 to 2000, we develop an econometric approach that deals with the selection mechanism aff ecting migration decisions, to estimate the impact that the probability of receiving remitt ances, internal and external, has on expenditure patt erns of rural poor households. Our fi ndings indicate that there are signifi cant eff ects on some expenditure categories. Household with higher probabilities of receiving internal and external remitt ances are more likely to spend in expenditure categories like physical and human investments. Keywords: migration, remitt ances, consumption, mexican households JEL Classifi cation: D12, O15

1. Introduction

International migration fl ows represent an essential component of the current process of globalization. International labor migration has tremendously increased and diversifi ed during the past few decades. According to the International Labor Organization, the number of international migrants increased from 81 million people in year 2000 to 191 million people in 2005 (ILO, 2006). Migratory movements around the world create an international labour market that generates important fl ow of monetary resources in the form of remitt ances transferred back to the origin countries. The total value of remitt ances send to developing countries has doubled over the last fi ve years and reached an estimated USD 167 billion in 2005. The value of remitt ances is twice as high as international offi cial development assistance (World Bank, 2006). Asia, Latin America and the Caribbean have been among the regions with the highest proportion of remitt ances received (UN, 2002).

Remitt ances sent to origin countries are an important fi nancial fl ow. An understanding of how these migrant and remitt ance fl ows aff ect migrants’ origin households is a core element in any assessment of how international migration aff ects source countries. This understanding is crucial to design

CONTENIDO 6

MIGRATION AND REMITTANCES EFFECTS ON CONSUMPTION OF THE POOREST: THE MEXICAN CASE

123

policies aiming to increase the potential of migration and remitt ances as development tools.

According to data provided by the Banco de México, international remitt ances transferred to Mexico in 1990 amounted to USD 2.50 billion. By 2008, this fi gure had grown to USD 25.14 billion. Until the end of the 1980s, international migration was mostly originated in few areas of Mexico. The states with the highest migratory tradition were located at the center-west of the country (Zacatecas, Michoacán, Jalisco and Guanajuato). However, from the beginning of the 1990s, emigration has become widespread throughout the country (INEGI, 2001) and is now a phenomenon aff ecting most of the municipios in Mexico. Due to its geographical vicinity, the United States has always been the main destination of Mexican migrants. Undoubtedly, migration and remitt ances fl ows have grown substantially in the last decades, generating a broad set of economic, political and social eff ects in both countries (see Unger, 2005).

Mexican emigration to the United States is a complex phenomenon with deep structural and historical roots on both sides of the border. Two of the main forces that have helped to structure the Mexico-US migratory system are: a) push factors related to the supply of Mexican laborers looking for employment and higher income options in the US; and b) pull factors associated with the labor force demand in the American agricultural, industrial and services sectors. Social and cultural factors are also important. Through a cumulative process, the latt er link the areas of origin and destination as migration increases and deepens over time. Migrant networks are decisive in reducing costs and risks associated with migratory movements, and in sustaining, recreating and perpetuating these movements (Massey et al., 1994; 1993).

The extraordinary growth of international migration and the monetary fl ows associated with this phenomenon has prompted social scientists to carry out studies on the diverse eff ects of migration in source and destination countries. A subject area that has received particular att ention is economic development.

The debate on the relationship between migration and development has changed in recent years. In the past, migration was seen as a failure caused by the lack of economic development, or even worse, as a contributor to the vicious circle that reinforced the problems of poverty and economic stagnation in migrant source countries. Recently, a diff erent view has


124

emerged: migration can contribute to development and may benefi t individual migrants and their families. In this approach, migration is taken as part of a virtuous circle in which development can be reinforced, not only in the country of destination but also in the country of origin (Taylor and Martin, 2001). Despite growing acceptance of this proposal, the exact relationship between migration and development remains to be established, both theoretically and empirically (Taylor, 1999; Unger, 2005).

In the Mexican case, there is a wide set of literature that explores possible eff ects of migration on various development indicators. Amuedo-Dorantes, et al. (2007) consider the impact on healthcare expenditures, Esquivel and Huerta-Pineda (2007) look at the impact on poverty, Hanson (2007) looks at labor force participation; Hanson and Woodruff (2003) analyze the impact on schooling, Hildebrandt and McKenzie (2005) and Kanaiupuni and Donato (1999) consider infant mortality, López Córdova (2005) analyzes the impact of remitt ances on schooling, infant mortality and poverty, Woodruff and Zenteno (2007) look at entrepreneurship.

Few studies have explored the particular case of migration and its eff ect on the poor. Data on Progresa-Oportunidades, the major antipoverty program in Mexico has been an important source of empirical fi ndings. For instance, Angelucci (2005) considers the impact of Progresa on the level of labor migration. She shows that the two types of tranfers have diff erent impacts on migration: in particular, unconditional cash transfers are associated with increased migration, while conditional cash transfers reduce migration levels of direct benefi ciaries, and, in some cases, of whole households. Azuara (2009) examines the sudden drop in the population size and gender composition of Mexican rural villages where the Progesa program was implemented between 1998 and 2005. He fi nds that the reduction of adult population of males is 6 times higher than for females, a clear sign of a signifi cant increase in the migration patt erns of this population. Stecklov et al., 2003 point out that public cash transfers reduce US migration but have litt le eff ect on domestic migration. Furthermore, they fi nd that the provision of cash transfers appears to reduce migration partly by reducing the relative deprivation levels of poor households. Shroff (2009) and Keskin (2009) look at the impact of remitt ances on poverty and income inequality respectively.

This paper off ers some empirical evidence on the eff ect of remitt ances (internal and external) on poor households’ expenditure patt erns. It represents a fi rst eff ort of approaching this relation in an integral manner.


125

No empirical evidence of possible eff ects on expenditure patt erns exists for the particular case of rural poor. In order to correctly look at migration and remitt ances impacts on expenditure patt erns, the econometric approach that we employ deals with selectivity on migration. The data to estimate the model comes from the evaluation data set of the Progresa-Oportunidades program.

The structure of the paper is as follows. Section two describes some empirical evidence regarding migration and expenditure decisions. Section three describes the data. Section four is devoted to present the empirical model. Section fi ve clarifi es some of the estimation issues mainly concerning variables included. Section six presents results on models estimated. Finally, the seventh section presents our conclusions.

2. Remitt ances and Expenditures in Rural Households

With regard to how remitt ances are spent and impact economic develop-ment, the literature contains three diff erent arguments. One view is based on remitt ance use surveys and argues that remitt ances can generate a com-plete and permanent dependence. In addition, remitt ances are often used for the acquisition of consumption goods instead of productive investment (Díaz-Briquets and Weintraub, 1991; Cornelius, 1990). The second point of view points out that the receipt of remitt ances can cause behavioral changes at the household level that may lower their development impact relative to the receipt of income from other sources (Barham and Boucher, 1998). Final-ly, there is a third recent view sustained by adherents of the New Econom-ics of Labor Migration arguing that remitt ances contribute to the develop-ment of rural communities increasing investments in human and physical capital (Stark, 1991; de Brauw and Giles, 2008).

The fi rst approach off ers often, a pessimistic view of the impact of migration on development in migrant-sending areas. Such studies conclude that remitt ances are not put into productive use and instead, they are conspicuously consumed (Chami et al., 2003; Taylor et al., 1996; Durand and Massey, 1992; and Papademetrious and Martin, 1991). It is possible that this research on remitt ance use off ers a partial and possibly distorted view of how remitt ances infl uence demand, due to the assumed fungibility of income. Moreover, it often rests on arbitrary defi nitions of what constitutes


126

productive investments: schooling, health and housing expenditures are often left out.

The general argument of the second approach is that a moral hazard problem arises between remitt ers and recipients. The dependency on these transfers induces recipients to use remitt ances as a substitute for other income sources. External shocks may lower income from other sources increasing the dependency on remitt ance transfers, and since they do not represent a capital fl ow, this may reduce economic activity and growth (Chami et al., 2003).

The third approach provides some evidence of productive uses of remitt ances in productive investments. Durand and Massey (1992) fi nd that in Mexico, the relative share of remitt ances spent on productive activities fl uctuated considerably from place to place and often reached substantial levels. Often, remitt ances are also used to overcome capital constraints in sending areas to fi nance public projects such as parks, churches, schools, electrifi cation, road construction, and sewers (Reichert, 1981; Massey et al., 1987; Goldring, 1990).

Other studies report that remitt ances have been critical to the capitalization of migrant-owned businesses (Escobar and Martinez, 1990; Massey et al., 1987; Cornelius, 1990). A number of studies from other world regions echo these fi ndings (for a detailed review, see Taylor, et al., 1996). Under the right circumstances, a signifi cant percentage of migrant remitt ances and savings may be devoted to productive enterprises. Durand and Massey (1992) conclude that, in Mexico “the highest levels of business formation and investment occur in urban communities, rural communities with access to urban markets, or rural communities with favorable agricultural conditions”.

Negative fi ndings on the productive impacts of remitt ances may be att ributable in part to poor research designs that do not consider the direct and indirect ways in which remitt ances may aff ect rural household expenditures. Recent empirical models have been designed to overcome this problem. These models have been based on econometric techniques that rigorously explore the eff ect of remitt ances on household expenditures, considering remitt ance income or migration as additional explanatory variables in household demand equations.

For instance, Adams (2005) fi nds evidence that the spending behavior of rural Guatemalan households with remitt ances was signifi cantly diff erent from that of households without remitt ances. Specifi cally, households with remitt ance income spent less on consumption goods and more on human


127

and physical capital investments than otherwise similar households without remitt ance income. Hanson and Woodruff (2003), Borraz (2005), Suarez and Avellaneda (2007), Alcaraz and Chiquiar (2007), Pederzini and Meza (2008) and Cuecuecha (2008) have analyzed the eff ects of migration and remitt ances on schooling in Mexico. The general fi nding is that schooling investments are positively aff ected. Hildebrandt and Mckenzie (2005) obtain similar results concerning health (see also Alderman, 1996; Edwards and Ureta, 2003; Adams, 2005 and 1998; Yang, 2005; López Córdova, 2004; and Adams et al., 2008).

However, expenditure decisions at the household level are not independent. When a household is deciding whether to allocate or not part of total income to certain market or good it is also taking in account the opportunity cost incurred by not allocating this money to any other alternative. Instead of analyzing possible eff ects of migration in a particular expenditure category, we built a system of demands that take in account the totality of expenditures decisions inside the household. Specifi cally, total expenditure is classifi ed and a system of demands that takes in account selection on migration and consumption is estimated. This empirical exercise is made for the particular case of rural poor in Mexico.

The data and empirical modeling approach designed to explore the possible eff ects of remitt ances on household expenditure patt erns in rural Mexico are described below.

3. The Progresa-Oportunidades Evaluation Data Set

Progresa (currently known as Oportunidades) is the major cash-transfer public program that the Mexican government has undertaken to enhance human capital of poor households. Its objective is to alleviate current poverty through monetary benefi ts conditioning the transfers to certain human-capital-investments rules. Basically, children in selected households must att end school on a regular basis and visit health centers for inoculations and constant health care. This two components aim to reduce future poverty levels by breaking the vicious circle of poverty in which poor household remain poor because their level of human capital is low. Nowadays, Progresa-Oportunidades covers all municipios in Mexico, benefi ciates around 5 million households and has a budget of 40.5 billion pesos in 2009.


128

This paper uses the dataset collected during years 1997-2000 for evaluating the impact of Progresa on initial benefi ciary households.

The early design of Progresa involved the identifi cation of the poorest villages in Mexico. For evaluating purposes a set of 506 rural villages was fi rst identifi ed among seven states in Mexico. These villages were located in extremely poor areas. In 1997 the Mexican government carried out a census of all households in these villages (Encuesta de Características Socioeconómicas de los Hogares, ENCASEH) collecting information on household demographic composition, income and assets to identify poor households. Ultimately, this information was used to calculate per capita incomes to be compared with certain poverty threshold. Households eligible to receive Progresa transfers would be those below this poverty line. Then, 320 villages were randomly selected to receive Progresa transfers during the fi rst two years of the program (summer 1998 - summer 2000) and were assigned to the “treatment group”. The remaining 186 villages were assigned to the “control group” and would receive transfers starting in the fall of 2000.

This “quasi experimental” design was necessary to properly evaluate the impact of the program since it was possible to fi nd a comparison group similar (in observables and non observables) to the benefi ciary households in all aspects but that do not receive the program. The panel data collected information for about 24 thousand households during this implementation and evaluation process. The resulting experimental data has been used to evaluate program impacts regarding outcomes related to education and health (see Skoufi as and Parker, 2001; Schultz , 2001; Buddelmeyer and Skoufi as, 2003; Parker et al., 2006; Todd and Wolpin, 2006). The potential selection bias present in treatment and comparison groups is presumably corrected with this randomized design.

A total of six evaluation surveys (Encuestas de Evaluación de Hogares, ENCEL) were carried out from 1998 to 2000, two in each year. They collected information on income, labor, schooling, health, women empowerment, consumption and assets. Though not originally designed to study the migration phenomenon, questionnaires in the October/November surveys collected a very complete data set on migrant characteristics which include demographics such as age, education, marital status, place of residence, date of migration, reason for leaving, job characteristics and whether or not they sent remitt ances to the origin household. This information allows us to deal with the selection bias aff ecting the decision to migrate and remit.


129

Migrants and remitt ances can be classifi ed into internal and external depending on the place of residence. An individual living in another state in Mexico is classifi ed as internal. Unfortunately, external migrants are those living in another country without a way of knowing which country this is. Since we are focusing in the poorer rural households and given the strength of the traditional Mexico-US migration phenomenon, it is very likely that transfers sent by these individuals are coming from the United States.

When analyzing the eff ect of remitt ances on expenditure patt erns we must recall that rural households contained in the Progresa dataset are not representative of all rural Mexico. They represent population at the lowest level of the income distribution in Mexico. Generalizing results to the entire rural population would be mistaken. However the availability of this dataset together with the very rich information on migration that it contains represents a valuable opportunity to study the possible eff ects of this phenomenon on the particular case of expenditure patt erns of poor rural households. Migration linkages of poor households can modify in diff erent ways consumption priorities compared to non-poor households. Since they are poor, the extra money at hand represented by a remitt ance could be used to fi rst satisfy basic needs (or current consumption) instead of devoting this money to certain physical or human capital investment. Since our sample is poor-dominated, this fi nding would not be a surprise.

We take the annualized values of income and expenditures provided by the ENCEL surveys. We decided to use the second survey of each year (October/November) because it is in these rounds that information of migrant characteristics was collected. Income and expenditure records were adjusted to 2002 prices and divided by the household size to obtain yearly measures in per capita terms. Unfortunately, we could not use data from the ENCASEH census since it did not contain information on household expenditures. We also dropped observations with important missing information. The fi nal sample consists of 63 771 household observations in all of the years.

Table 1 presents some summary statistics for the sample, with households divided by their type-of-migrant condition. 8 313 households (13.0%) reported to have at least one internal migrant while 1 519 (2.4%) had at least one external migrant. 497 households (0.8%) had at least one of each type. It is not surprising that the external migration phenomenon is barely present in this sample. Placing family members in a migrant labor market is, under the view of the New Economics of Labor Migration


130

(Taylor et al., 2001), a strategy of the households to maximize future income fl ows. However, households must incur the cost of sending and supporting migrants initially. Poor households are very unlikely to have enough monetary resources to fi nance such enterprise. In fact, only 33.4% of households having at least one external migrant were receiving Progresa transfers. Clearly, the majority of external migrant households (EMH) are not poor.

Having a migrant is not a suffi cient condition for a household to receive remitt ances. It will depend on the social arrangement that exist between household and migrants. It will also depend on migrant and household characteristics. Actually, only 19% of internal migrant household (IMH) receive remitt ances. In contrast, 60% of EMH receive external remitt ances. A similar situation is present for the both migrant households (BMH) group. It seems that external migrants have stronger motivations to remit.

Families tend to be numerous in this sample. The average for non migrant households (NMH) is 5.8; migrant household’s average is always above 6 members. They also seem to be long lasting households since the average of kids below 15 years old is always close to 2, meaning that they are likely to be composed by a majority of adult members.

All schooling indicators are low. Household heads have on average no more than 3 years of schooling. Adult household members have on average no more than 4 years of schooling, not even enough to have completed primary education (6 years). In all cases, adult males are slightly bett er educated than adult females. Literacy, a very basic skill, is not totally adopted as well. Only around 70% of household heads and household members are literate. As expected, a higher proportion of households (14%) are headed by a female in the EMH and BMH categories. This proportion is lower in the NMH and IMH categories.

It is also evident that the indigenous background dominates the sample. In the case of NMH, on average only 32% of household heads and 23% of household members speak Spanish. Interestingly, the lowest percentage is seen in the EMH group with only 7% of household heads and 5% of household members speaking Spanish.

Averages of house and assets variables are also very low. For the case of the NMH category, 7% of households have drainage, 73% have electricity, 62% have farm lands, only 14% have their roof made of concrete, have on average less than 2 rooms and very few have a vehicle of their own. In general, for


131

Table 1Summary Statistics of Non-Migrants and Migrant Households

Mean-difference t-test

Not migrants

Internal migrants

External migrants

Both migrants

Not migrants vs

Internal migrants

Not migrants vs

External migrants

Not migrants vs

Both migrants

Hh receive external remittances (1=yes, 0=No)

0.60

(0.49) 0.41

(0.49)

Hh receive internal remittances (1=yes, 0=No)

0.19

(0.39)

0.16 (0.37)

Hh receive Progresa Transfers (1=yes, 0=No)

0.44 (0.50)

0.40 (0.49)

0.33 (0.47)

0.35 (0.48)

5.27*** 8.62*** 4.16***

Hh size 5.77

(2.81) 7.01

(3.06) 6.30

(2.97) 7.91

(3.22) -34.57*** -6.84*** -14.72***

Numbers of kids below 15 years old

2.34 (2.03)

2.20 (2.05)

1.97 (1.98)

2.33 (2.18)

5.54*** 7.20*** 0.09

Hh head’s schooling 2.92

(3.06) 2.11

(2.37) 2.18

(2.43) 1.84

(2.21) 27.49*** 11.50*** 10.75***

Hh head’s age 48.00

(16.20) 53.09

(12.67) 53.58

(13.29) 55.22

(11.10) -32.78*** -16.03*** -14.36***

Hh average education of adult females

3.32 (2.85)

3.27 (2.55)

3.43 (2.53)

3.75 (2.25)

1.48 -1.66* -4.22***

Hh average education of adult males

3.90 (2.99)

3.87 (2.64)

3.81 (2.55)

4.05 (2.51)

0.92 1.29 -1.35

Hh head’s sex (1=male, 0=female)

0.90 (0.30)

0.88 (0.33)

0.86 (0.35)

0.86 (0.34)

5.58*** 4.38*** 2.29**

Hh head speaks spanish (1=yes, 0=No)

0.32 (0.47)

0.29 (0.46)

0.07 (0.26)

0.08 (0.27)

4.18*** 34.46*** 19.46***

Hh head is literate (1=yes, 0=No)

0.69 (0.46)

0.64 (0.48)

0.69 (0.46)

0.67 (0.47)

8.97*** 0.44 0.91

Percentage of hh members literate

0.59 (0.29)

0.67 (0.26)

0.71 (0.25)

0.75 (0.22)

-22.77*** -17.36*** -15.26***

Percentage of hh members that speak spanish

0.23 (0.36)

0.23 (0.36)

0.05 (0.19)

0.06 (0.22)

0.83 36.83*** 17.37***

Hh has plumbing (1=yes, 0=No)

0.07 (0.25)

0.07 (0.26)

0.11 (0.32)

0.11 (0.31)

-1.92* -5.50*** -2.77***

Hh has electricity (1=yes, 0=No)

0.73 (0.44)

0.76 (0.43)

0.87 (0.34)

0.86 (0.34)

-5.17*** -15.86*** -8.61***

Hh owns house (1=yes, 0=No)

0.94 (0.24)

0.97 (0.18)

0.97 (0.18)

0.97 (0.18)

-12.13*** -5.43*** -3.39***

Hh owns farm lands (1=yes, 0=No)

0.62 (0.48)

0.72 (0.45)

0.66 (0.48)

0.73 (0.44)

-18.20*** -2.69*** -5.58***

Average vehicles 0.09

(0.31) 0.10

(0.33) 0.24

(0.45) 0.24

(0.48) -2.63*** -12.51*** -7.06***

Roof of concrete (1=yes, 0=No)

0.14 (0.34)

0.13 (0.34)

0.21 (0.41)

0.17 (0.38)

2.10** -6.62*** -1.96**

Roof of asbestos lamina(1=yes, 0=No)

0.12 (0.33)

0.15 (0.36)

0.16 (0.37)

0.20 (0.40)

-6.84*** -3.68*** -3.96***

Roof of bricks(1=yes, 0=No)

0.11 (0.31)

0.11 (0.31)

0.18 (0.38)

0.15 (0.36)

-1.46 -7.09*** -2.73***

Note: ***, ** and * indicate signifi cance of parameters at 0.01, 0.05 and 0.1, respectively.Source: own elaboration.


132

Table 1Summary Statistics of Non-Migrants and Migrant Households

(Continued)

Mean-difference t-test

Not migrants

Internal migrants

External migrants

Both migrants

Not migrants vs

Internal migrants

Not migrants vs

External migrants

Not migrants vs

Both migrants

Roof of palm (1=yes, 0=No)

0.13 (0.34)

0.12 (0.32)

0.05 (0.23)

0.06 (0.24)

4.31*** 13.27*** 6.38***

Average rooms 1.80

(1.12) 2.02

(1.17) 2.23

(1.25) 2.38

(1.19) -15.81*** -13.27*** -10.87***

Lost crop because of some shock (1=yes, 0=No)

0.32 (0.47)

0.39 (0.49)

0.24 (0.43)

0.25 (0.43)

-11.68*** 7.02*** 3.91***

Lost farmable land because of some shock (1=yes, 0=No)

0.10 (0.30)

0.12 (0.33)

0.08 (0.27)

0.07 (0.26)

-5.07*** 3.43*** 2.30**

Male external migrants 1.12

(0.76) 1.13

(0.77)

Female external migrants 0.37

(0.69) 0.41

(0.68)

Husband migrated externally (1=yes, 0=No)

0.10

(0.30) 0.05

(0.22)

Wife migrated externally (1=yes, 0=No)

0.01

(0.08) 0.002 (0.04)

Mean age of external migrants

22.65 (8.12)

21.82 (7.30)

Mean schooling of external migrants

6.24

(2.07) 6.21

(2.03)

Maximum time that a hh member migrated externally

2.28

(2.50) 2.41

(2.63)

Male internal migrants 0.92

(0.97)

0.71 (0.89)

Female internal migrants 1.01

(1.00)

1.14 (1.02)

Husband migrated internally (1=yes, 0=No)

0.02

(0.14)

0.01 (0.11)

Wife migrated internally (1=yes, 0=No)

0.01

(0.10)

0.01 (0.09)

Mean age of internal migrants

21.10

(10.21)

19.87 (9.05)

Mean schooling of internal migrants

6.06

(2.15)

6.21 (2.19)

Maximum time that a hh member migrated internally

2.72

(4.29)

2.91 (4.32)

Observations 53,442 8,313 1,519 497



133

these variables there is statically signifi cant evidence that migrant households have slightly bett er average values than non-migrant households.

Rural households, mainly those devoted to agricultural production, are often aff ected by external shocks that make their income fl ows unstable. Shocks like droughts, fl oods, frosts, fi res and plagues are actually very common events that may cause important losses in terms of income or assets. As can be seen in Table 1, losing the crop because of some shock is very common: 32% of NMH, 39% of IMH, 24% of EMH and 25% of BMH suff ered this loss. Also, nearly 10% of households in all groups were not able to farm because of the appearance of some of these shocks. Households make adjustments to face these events. It will be interesting to evaluate how these losses aff ect migration and expenditure decisions.

It also seems that gender characteristics are diff erent for each type of migration. External migrants are mainly males while internal migration seems to be a female phenomenon. Though the averages indicate this, it is also evident that the number of migrants that a household decide to send is not high in these sample. Husbands are more likely to migrate externally while wifes are very unlikely to migrate. Age and schooling are very similar between internal and external migrants. Interestingly, the average schooling is higher for migrant individuals than current adult members of the household. The former have enough years of schooling to have completed primary education. This agrees with the NELM (Taylor et al., 2001) which posits that, among household members, bett er educated people fi nd a higher reward in migrant labor markets and thus are more likely to migrate.

Yearly income and remitt ance fi gures by household categories are summarized in Table 2. EMH seem to be moderately dependent on monetary resources coming from abroad, with external remitt ances representing on average 18.4% of their total income, receiving 1 025.8 pesos per capita per year. IMH are dependent on internal remitt ances for 4.9% of their total income and receive on average 332.8 pesos per capita. BMH seem to diversify dependence with their share of external remitt ances in total income is slightly higher, representing 10.4% versus 2.3% of internal remitt ances. These dependency fi gures are low compared to other rural household samples. The Encuesta Nacional de Ingresos y Gastos de los Hogares (ENIGH), a representative nation-wide survey at the national and rural/urban levels, reports a 40% and a 25% dependency of external and internal remitt ances respectively (see Mora and Arellano, 2009).


134

Table 2Income and Remitt ances Data of Non-Migrant and Migrant Households (pesos)

Non Migrants Internal Migrants External Migrants

Total Income Total

Income Remittances % Total

Income Remittances %

1998 4,373.7 4,435.3 638.3 8.8 7,303.3 895.1 22.5

1999 3,678.6 3,284.9 215.2 3.3 6,109.0 1,022.4 16.0

2000 4,445.0 3,698.7 68.6 2.2 7,088.5 1,152.9 16.7

All years 4,171.9 3,817.6 332.8 4.9 6,857.7 1,025.8 18.4

Obs. 53,442 8,313 1,519

(Continued)

Both Migrants

Total Income

External Remittances

Internal Remittances

% Ext. % Int. % Total

1998 7,418.6 421.6 110.5 15.2 4.4 19.6

1999 4,670.6 330.2 47.9 8.5 2.0 10.5

2000 3,566.3 383.1 36.4 8.4 1.2 9.6 All years 4,979.0 381.4 61.2 10.4 2.3 12.7

Obs. 497

Source: own elaboration.

Interestingly, every year the EMH group had the highest level of total income. This also agrees with the NELM (Taylor et al., 2001) since it means that external migrant households are not those at the bott om of the income distribution. There is a downward trend on the share of remitt ances on total income over the years. However the period analyzed is too short to draw conclusions.

Household expenditures were divided in eight categories: Food, Health (medical services, medicines), Education (tuition, materials), Durable Goods (furniture, household equipment and vehicles), Non Durable Goods (household cleaning items, personal care items and clothing), Patrimony (additional constructions/renovations), Farm Animals (cows, goats, pigs, horses, chickens, donkeys, rabbits). This expenditure category is intended


135

to capture productive investments. The rest of household expenditures are lumped in an Other category, (transportation, fuels, other expenditures, etc.).

Table 3 presents average budget shares for each of the expenditure categories defi ned. Food, the primary need, occupies the highest proportion of total expenditure for all of the household categories, always above 70%. This means that it remains less than one third of all monetary resources to satisfy the rest of needs that a household has. In fact, the Non Durable Good category represents around 9% of total expenditure. Let us recall that this expenditure category includes another basic need: clothing. When we add Health and Education, it remains less that 10% of total expenditure available to be devoted to capital and productive investments. In fact, the Durable Goods, Patrimony and Farm Animals categories do not represent more than 3% of total expenditure.

Table 3Average Budget Shares of Expenditure Categories by

Non-Migrant and Migrant Households(percentages)

Not Migrants

Internal Migrants

Only

External Migrants

Only

Both Migrants

Not Migrants vs Internal Migrants

Not Migrants vs External Migrants

Not Migrants vs Both

Migrants Food 78.86 77.68 73.15 72.98 5.59*** 10.91*** 6.47*** Health 2.44 2.86 4.20 4.10 -3.82*** -6.17*** -3.45*** Education 1.52 1.59 1.44 1.30 -1.42 0.73 1.14 Durable Goods 0.50 0.48 1.17 1.29 0.60 -3.63*** -2.48** Non Durable Goods 9.34 9.28 8.98 9.32 0.56 1.72* 0.04 Patrimony 0.96 1.01 2.63 2.01 -0.58 -5.87*** -2.47** Farm animals 0.15 0.24 0.30 0.20 -3.16*** -1.54 -0.60 Other 6.23 6.88 8.13 8.80 -5.08*** -6.36*** -4.57*** Obs. 53,442 8,313 1,519 497

Note: ***, ** and * indicate signifi cance of parameters at 0.01, 0.05 and 0.1, respectively. Source: own elaboration.

There are interesting diff erences in budget shares across household categories. EMH and BMH devote signifi cantly more of their total expenditure to health care (slightly above 4%) than NMH. There are no signifi cant diff erences between groups, compared to NMH, regarding expenditures on education.


136

All migrant household categories expend signifi cantly less on food than NMH while external migrant households (EMH and BMH) expend signifi cantly more on durable goods and patrimony. EMH devote a signifi cantly lower share of their total expenditure (8.98%) to Non Durable Goods compared to NMH (9.34%). Finally, only IMH seem to spend signifi cantly more than NMH in farm animals (0.24% vs 0.15%).

Though the diff erences are not remarkable, migration may have something to do with the way households decide how to spend their monetary resources. The empirical models applied to explore this possibility are next explained.

4. Empirical Model

One of the hypotheses of the NELM theory is that households decide to send a household member to work abroad (internally or externally) because this represents their best strategy to overcome current monetary constraints and increase future income fl ows. Remitt ance perceptions may allow recipient households to devote monetary resources to certain markets that otherwise would remain out of their budget.

The previous paragraph implies three decision processes. First, a household must decide, given household characteristics, whether to send or not household members to work abroad. Second, migrant members must decide whether to send or not remitt ances. This outcome will depend a lot on the type of social arrangement previously established between migrants and households and on migrant characteristics. Third, once the household have received remitt ances, it must decide the way in which they will be used. This decision will depend again on household profi les. Summarizing, households fi rst select into migration looking for additional income: remitt ances. If successful, households receive remitt ances and spend them accordingly to what they consider their priorities.

This context implies a causality relation to take in account in order to obtain a genuine eff ect of migration and remitt ances on expenditure patt erns: remitt ances perception could not be observed if there are no migrants associated to the household. Also, households selecting into migration can be diff erent, in observables and unobservables, from households not participating in migration processes. The econometric approach that we


137

adopt in order to eff ectively correct this selection bias problem follows closely the ideas of Taylor et al. (2003) and Meza and Pederzini (2009).

The decision of household j to allocate family members to labor migration M will depend on household (H) and village characteristics (V). This last set of variables is intended to capture migration linkages diff erentiated by regional areas in Mexico. This relation can be represented by:

*0 1 2j j j jM H V u (1)

where

0jM if * 0jM ; household has no migrants

1jM if * 0jM ; household has at least one migrant

M * is the latent variable governing the decision of a household participating in labor migration. Once self selected, a household sees the outcome of perceiving remitt ances or not. The decision of a migrant to send remitt ances to their families depends on migrant (Z) and household characteristics (H) and is represented by:

*0 1 2j j j jR Z H e (2)

where

0jR if * 0jR ; household doesn’t receive remitt ances

1jR if * 0jR ; household receive remitt ances

Equation (2) is only seen when 1jM . These two relationships represent a Probit model with sample selection (Van de Ven and Van Pragg, 1981) that can be solved in two steps:

1. Obtain maximum likelihood estimates of from the Probit model depicted in equation (1). For each observation in the sample we calculate the Inverse Mill Ratio ' / 'j j j X X , where jX is a vector containing jH and jV .


138

2. Estimate equation (2) with j included as an additional regressor to

correct for self-selection on migration as follows:

*0 1 2j j j j jR Z H e for 1jM (3)

From equation (3), we obtain the selection-corrected probability of a household to get remitt ances. The probability of gett ing remitt ances for household not having migrants is set to zero. This heckprob procedure solves the potential endogeneaity of migration and remitt ances and the selectivity bias caused by the fact that not all migrant households receive remitt ances. Equations (1) and (3) are estimated for internal and external migration independently.

Since they summarize migration and remitt ances eff ects, the selection-corrected probabilities from equation (3) for both, receiving internal and external remitt ances, are our key variables to develop the demand system that will explore possible eff ects of internal and external migration on expenditure patt erns.

A common problem when dealing with consumption data, and especially with disaggregated expenditure categories, is the existence of a large number of zeros in the dependent variable. The reasons for the presence of zeros (see Garcia and Labeaga, 1996) could be a simple infrequency of purchase, a voluntary abstention (selection) and a budged-constrained corner solution.

How to eff ectively deal with censored expenditure data becomes more complex in a context of several expenditure categories to be modeled. Since censorship is generated by the same dataset and all expenditure categories share several explanatory variables, censored regressions have correlated error terms. Estimating each equation separately leads to ineffi cient estimators since it fails to take in account the interrelations across equations. Besides, the selection mechanism is not addressed. In a context of a system of equations with limited dependent variables the modeling of the data must be diff erent.

We develop the censored system of demands proposed by Shonkwiler and Yen (1999) (see also Heien and Wessells, 1990; Perali and Chavas, 2000; Lazaridis, 2003 and Jabarin, 2005). The intrinsic assumption is that a selection mechanism takes place when a household is deciding whether to participate in a given market or purchase a given good.

This approach involves a system of equations in which the dependent variables, household expenditure shares, are censored by unobserved latent


139

variables infl uencing the decision to spend income on certain consumption categories. In the system, expenditure by household h in market i, ehi is observed only if the household’s total desired expenditure on the item exceeds some threshold (i.e., 0hie ). This threshold will depend on the lumpiness of the good as well as opportunity cost that the household is incurring by not expending on some other market. Of course, household priorities also matt er. Poor households would prefer to fi rst satisfy basic needs, such as food or current consumption and then, if the budget constraint is not binding, spend on durable goods or physical investments.

Assuming that the stochastic errors are approximately normal with zero means and a fi nite variance-covariance matrix that is constant over all observations —that is, iid— the system of expenditure equations can be estimated with Lee’s (1978) multivariate generalization of Amemiya’s (1974) two-step estimator.

In a fi rst stage, a probit is independently estimated for participation in each expenditure category.

* ''ji j jiP f X u i = 1,2,3,…,8 (4)

where

0jiP if * * / 0ji ji jP e E

1jiP if * * / 0 0ji ji jP e E

In equation (4), Pji is the latent variable governing the decision of household j to participate in market i and Ej represents total expenditure of the household. Thus, the dependent variable in each probit is equal to 1 if 0jie and zero otherwise. jX is a vector containing household and village characteristics and is a vector of parameters to be estimated. Parameter estimates obtained in this fi rst stage are used to calculate ' jX and ' jX which denotes the standard normal density function and the normal cumulative distribution function respectively.

In a second stage, functions and are used to generate selection-corrected variables to be included in a system of equations as follows:

/ ' ' 'ji j j j i j jie E X f W X i = 1,2,3,…,8 (5)


140

Where Wj is a vector of household characteristics and ' is a vector of parameters to be estimated. In practice ' jf W takes a linear form. The set of eight equations depicted in (5) was estimated using the seemingly unrelated regression (SUR) technique as proposed in Shonkwiler and Yen (1999).

Following this approach, the share of each household expenditure category in total expenditure is regressed, against household characteristics and the selection-corrected probabilities from equation (3) for both, receiving internal and external remitt ances.

5. Estimation Issues

The list of household, individual migrant and village variables used across equations (1) to (5) can be found in Table 4. Household variables are mainly designed to capture human and physical capital assets trough educational, ethnic, wealth and house characteristics.

Since Progresa is the main motivation driving this data, it would be of particular interest to analyze if receiving Progresa transfers has anything to do with migration and expenditure decisions. Thus, this variable is included as part of the household characteristics set in all equations.

As mentioned earlier, rural households are often aff ected by unpredictable shocks that make their income fl ows unstable. In agriculture, producers often see their crops lost because of a fl ood, a drought or a plague. Sometimes, they are not even to farm because of the appearance of some of these external shocks. It would also be interesting to evaluate if these events infl uence migration and expenditure decisions as well. A couple of variables measuring this are included as part of the household characteristics set.

Motivations to remit are complex. They are obviously driven by migrant and household characteristics. Data availability of migrant’s age, schooling, gender, parental relation and migration experience allowed us to explore how these migrant characteristics may infl uence the decision of a migrant to remit once the household has self-selected into labor migration. Eff ects might be diff erent for internal and external migration.

Village variables are mainly intended to capture location eff ects. In addition to household characteristics, migration is also a function of migration networks or contacts with people who have previously migrated.


141

Table 4List of the variables used

Household variables Logarithm of hh size: lnhsize Hh receives progresa: progresa (1=yes, 0=no) Numbers of kids below 15 years old: nkids Hh head’s schooling: schoolinghead Hh head’s age: agehead Hh head’s age squared: agehead2 Hh head’s sex: sexhead (1=yes, 0=female) Hh speaks spanish: headspanish (1=yes, 0=no) Proportion of hh members that are literate: prcliterate Hh has plumbing: hasplumbing Hh has electricity: haselectricity Hh owns the house: ownshouse (1=yes, 0=no) Hh owns lands: ownslands (1=yes, 0=no) House’s roof made of concrete : roofconcrete (1=yes, 0=no) House’s roof made of asbestos lamina: rooflamasb (1=yes, 0=no) House’s roof made of teja: roofteja (1=yes, 0=no) House’s roof made of palm : roofpalm (1=yes, 0=no) Hh lost crop because of some shock: sl_crop (1=yes, 0=no) Hh lost farmable land because of some shock: sl_land (1=yes, 0=no) Probability of receiving external remittances: prextremit Probability of receiving internal remittances: printremit Logarithm of total per capita expenditure: lntotalexppc

Migrant variables Number of male migrants (internal or external): malemigrants Number of female migrants (internal or external): femalemigrants Husband migrated (internally or externally): husbandleft Wife migrated (internally or externally): wifeleft Mean age of migrants (internal or external): meanagemig Mean schooling of migrants (internal or external): meanschoolmig Maximum years that the hh member left (internally or externally): maxtimeleftmig

Village variables 2000 Migration Index (municipio): migrationindex2000 2000 Nutrition Index (municipio):nutritionindex2000 Mean annual temperature: meanannualtemp Mean annual precipitation: meanannualprec Village was randomly selected to receive progresa transfers: vtreatment

Time variables Dummy for Year=1998: year98 Dummy for Year=1999: year99 Dummy for Year=2000: year00

Source: own elaboration.


142

In theoretical and empirical works, these networks have appeared among the most important variables driving migration (Taylor et al., 1996). Thus, households in villages where migration histories are traditionally strong are more likely to send migrants. Since there is no such information on the Progresa data set to proxy this, we have used the Migration Index for 2000 calculated at the municipio1 level by the Consejo Nacional de Población (CONAPO, 2002) which condensates in one single measure several aspects of the Mexico-US migration phenomenon such as the percentage of households with migrants and remitt ances. The higher the Index the higher the intensity of the migration phenomenon in that municipio. Migrant remitt ances may also be infl uenced by village norms to remit. Thus, the Migration Index is also included in the remitt ance probit equation.

Not only migration intensities diff erences across villages may matt er. We already know that villages in this sample are the poorest in Mexico. In this aspect, they are not systematically diff erent. However, poverty has diff erent faces. Trying to identify an accurate variable to capture diff erences in wellbeing across villages, we used the Nutritional Risk Index 2000 calculated by the Instituto Nacional de Ciencias Médicas y Nutrición Salvador Zubirán (INCNMNSZ, 2003). This is also a measure that summarizes several demographic and health variables at the household level and it refl ects the nutritional situation of the population at a particular municipio. The higher the Index, the higher the nutritional defi ciencies of the population.

Mean annual temperatures and mean annual precipitations calculated from period 1971-2000 are also included (Mendelshon et al., 2008) to capture location eff ects. Finally, we identify villages originally selected to receive Progresa transfers during this evaluation period looking for possible spillovers on migration and expenditure behavior caused by the presence of this Federal program.

The selection-corrected probabilities of receiving remitt ances obtained from equation (3) and included in equation (5) are already summarizing all possible eff ects of migration processes. They are our key variables to evaluate possible eff ects on expenditure patt erns. Since the selection bias has been corrected and the endogeneity between migrants and remitt ances has

1 The municipio is the lowest level of political administration in Mexico. It is under the state level and comprises several villages.


143

been solved, results on these particular variables can be interpreted as net exogenous eff ects of migration and remitt ances on expenditure patt erns.

6. Results

a. Probit Selection Model

Table 5 presents results from the Probit Selection Model estimated with equations (1) and (3). Panel a displays results for the probability of a household having a migrant. Equations for the probability of having external or internal migrants are estimated independently. Several household variables are signifi cant. The logarithm of the household size has a signifi cant positive eff ect on the probability of having an external or internal migrant with an increase of 0.01 and 0.15 respectively. The higher the number of potential migrants the higher the probability and the economic reward of placing at least one into labor migration.

Interestingly, the fact of receiving Progresa transfers seems to discourage external migration, it signifi cantly decreases the probability of having an external migrant by -0.002. In contrast, the marginal eff ect of this variable is not signifi cant in the case of internal migrants. Since Progresa transfers represent additional income they can be viewed as a substitute of external remitt ances. Therefore, the household will have no need of placing members in external labor markets.

Having kids below 15 is also a deterrent for migration. A one-member increase in the number of kids below 15 decreases the probability of having and external and an internal migrant by -0.002 and 0.02 respectively. Since migrants are mainly adults, taking care of children before participating in labor migration could be preferred. Households where the head is a male, speaks Spanish and has more years of schooling are less likely to have migrants, internal or external. As we have seen in the summary statistics, households in the sample are mainly indigenous. These results confi rm that among all household those more likely to migrate are also indigenous. The older the household head the higher the probability of having an internal or external migrant. This last result has sense if the main motive of migrants is altruism towards elderly parents staying behind. This might be indicating the existence of an explicit social arrangement between parents and potential


144

migrants at this stage of the deciding process. An increase in the percentage of household members that are literate signifi cantly increases the probability of having internal and external migrants. This eff ect is higher in the case of internal migration. Since most of internal migration is urban driven, it is possible to think about higher returns to human capital in urban jobs. Thus, a household with higher levels of human capital will have bett er chances of success allocating a member in urban labor markets.

Having farm lands encourages internal migration with a signifi cant increase of 0.006 in the probability. Few of the house characteristics result signifi cant. In particular, having the roof made of palm decreases the probability of having internal or external migrants while households with their roofs made of asbestos lamina are more likely to migrate. This confi rms that idea that migrant household are those at the bott om of the income distribution (if we use the material roof as a proxy of house wealthiness).

Results regarding the eff ects of external shocks in migration decisions are of particular interest. For the case of external migration it seems that neither losing farmable land nor losing the crop stimulates migration. Instead, it signifi cantly decreases the probability of having an external migrant. As we have mentioned, to place a migrant in external labor markets households must bear the monetary cost of such process. It is possible that not being able to farm or losing planned income aff ects the availably of monetary resources that could have been used to fi nance migration. It is also possible that in this particular situation, the best choice of the household is placing family members in local labor markets (included family production) to alleviate the external shock that income has suff ered because the perception of remitt ances would not be as immediate as the perception of local wages.

Several village characteristics are also signifi cant. As expected the Migration Index is higly signifi cant in the case of external migration. Households in villages where migration linkages are well consolidated are more likely to have external migrants. Since the Migration Index does not capture internal processes it is not surprising that it does not have any eff ect on internal migration.

Households in villages whit high levels of nutritional risk are also less likely to migrate externally. On the opposite, high nutritional risks stimulate internal migration. High nutritional defi ciencies must be associated with lower levels of economic position, even among poor households. So, for households in municipios with high levels of nutritional risk the cost of


145

bearing external migration might be higher compared to the one needed to fi nance internal migration. Location eff ects such as being in a treatment village and climate variables are also signifi cant in some cases, especially for external migration.

Once households select into migration, migrants select into sending remitt ances. Results of this second stage on our Probit selection model are shown in Panel b of Table 5. Again, several household characteristics result signifi cant. The higher the numbers of household members the lower the probability of sending remitt ances. This is true for both internal and external migrants. A numerous family might represent several potential income sources as local employees or participants in family production. Household members living abroad may conclude that additional income for the household is not necessary.

Receiving Progresa is not a factor that migrants take in account when deciding whether to send or not remitt ances. A negative and signifi cant eff ect would have mean that remitt ances are eff ectively view as a substitute for remitt ances from the migrants’ perspective. A one-member increase in the number of kids below 15 signifi cantly increases the probability of sending external and internal remitt ances by 0.02 in both cases. Thus, once self selected into migration, migrants that probably left children behind are more likely to send remitt ances. The schooling of the household head signifi cantly increases the probability of sending remitt ances but just for internal migrants. The age of the household head is negatively associated with the probability of sending internal remitt ances. Households headed by a male are also more likely to receive internal remitt ances. Apparently, household head’s human capital indicators are only considered by internal migrants. This can be an indicator of diff erences in the way altruism is determined in each migration process.

As we have seen in the fi rst stage indigenous household are more likely to migrate. Results on this second stage indicate that they are also more likely to receive external remitt ances. A household where the head speaks Spanish is less likely to receive internal remitt ances with a signifi cant decrease in the probability of -0.13. Interestingly, the opposite happens for internal remitt ances with a signifi cant increase of 0.01. Ethnic origins seem to motivate diff erently internal and external migrants when deciding whether to send or not remitt ances.

One might also think that external shocks to household income might also motivate migrants to send remitt ances. This is true when a household loses


146

Tabla 5Probit Selection Model for Internal and External Migration

Panel a. Selection on Migration

Hh has external migrant (1=yes, 0 otherwise)

Hh has internal migrant (1=yes, 0 otherwise)

Parameter Estimates

Marginal effect Parameter Estimates

Marginal effect

lnhsize 0.361 ***11.88 0.011 ***11.37 0.763 ***39.71 0.146 ***40.19

treated -0.109 ***-3.48 -0.003 ***-3.51 0.027 *1.70 0.0004 0.10

nkids -0.051 ***-6.16 -0.002 ***-6.06 -0.120 ***-24.39 -0.023 ***-24.04

schoolinghead -0.022 ***-4.12 -0.001 ***-4.08 -0.029 ***-9.48 -0.006 ***-9.54

agehead 0.058 ***10.16 0.002 ***10.15 0.069 ***21.96 0.013 ***22.31

agehead2 -0.0005 ***-9.46 -0.00002 ***-9.44 -0.001 ***-19.48 -0.0001 ***-19.73

sexhead -0.144 ***-4.21 -0.005 ***-3.71 -0.200 ***-9.44 -0.042 ***-8.68

headspanish -0.430 ***-11.73 -0.012 ***-13.62 -0.054 ***-3.43 -0.010 ***-3.38

prcliterate 0.370 ***7.56 0.012 ***7.48 0.261 ***9.28 0.050 ***9.21

hasplumbing 0.055 1.47 0.002 1.39 -0.001 -0.02 -0.001 -0.10

ownshouse 0.087 1.50 0.003 *1.64 0.032 0.92 0.006 0.92

ownslands 0.024 0.94 0.001 0.94 0.031 **2.04 0.006 *1.95

rooflamasb 0.075 **2.39 0.003 **2.25 0.086 ***4.44 0.017 ***4.35

roofteja 0.141 ***4.27 0.005 ***3.78 -0.019 -0.87 -0.004 -0.89

roofpalma -0.238 ***-5.20 -0.006 ***-6.30 -0.043 **-2.03 -0.007 *-1.78

sl_crop -0.120 ***-4.40 -0.004 ***-4.57 0.031 **2.04 0.006 **2.07

sl_land -0.125 ***-3.00 -0.004 ***-3.36 -0.011 -0.48 -0.001 -0.35

vtreatment 0.051 *1.72 0.002 *1.73 -0.011 -0.99 -0.006 0.67

migrationindex2000 0.237 ***19.76 0.007 ***17.16 -0.010 -1.36 -0.001 -0.60

nutritionindex2000 -0.014 ***-6.28 -0.0004 ***-6.34 0.003 ***3.63 0.001 **2.21

meanannualtemp 0.067 ***17.77 0.002 ***16.39 -0.0001 -0.08 -0.0001 -0.35

meanannualprec -0.001 ***-13.97 -0.00004 ***-14.10 -0.0001 ***-3.36 0.00001 ***-2.84

year99 0.001 0.03 0.00002 0.03 -0.063 ***-3.83 -0.011 ***-3.60

year00 0.084 ***3.02 0.003 ***2.91 -0.234 ***-13.72 -0.042 ***-14.10

Constant -4.988 ***-28.67 -3.944 ***-43.13

Observations 63,771 63,771

Note: ***, ** and * indicate signifi cance of parameters at 0.01, 0.05 and 0.1, respectively. Log likelihood for Internal Migration: -8, 558.0. Log likelihood for external migration: -27,016.8.Source: own elaboration.


147

Tabla 5Probit Selection Model for Internal and External Migration

(Continued)Panel b. Selection on the decision to remit

Hh receives external remittances (1=yes, 0 otherwise)

Hh receives internal remittances (1=yes, 0 otherwise)

Parameter estimates

Marginal effect Parameter estimates Marginal effect

lnhsize -0.317 ***-3.24 -0.119 ***-2.56 -0.845 ***-36.27 -0.142 ***-25.90

treated -0.009 -0.14 -0.003 -0.14 -0.006 -0.36 -0.001 -0.36

nkids 0.047 **2.10 0.018 *1.88 0.135 ***23.89 0.023 ***19.66

schoolinghead 0.007 0.44 0.002 0.43 0.022 ***6.28 0.004 **6.43

agehead -0.007 -0.38 -0.003 -0.37 -0.061 ***-16.36 -0.010 ***-17.72

agehead2 0.0001 0.41 0.00002 0.40 0.0005 ***15.15 0.0001 ***16.00

sexhead -0.003 -0.03 -0.001 -0.03 0.153 ***6.39 0.028 ***6.04

headspanish -0.376 ***-2.91 -0.137 ***-3.61 0.060 ***3.49 0.010 ***3.51

prcliterate -0.151 -1.02 -0.057 -0.96 -0.209 ***-6.54 -0.035 ***-6.65

hasplumbing -0.166 *-1.74 -0.061 -1.62 -0.014 -0.50 -0.002 -0.49

ownshouse 0.205 1.22 0.074 1.27 -0.005 -0.12 -0.001 -0.12

ownslands 0.093 1.41 0.035 1.41 -0.015 -0.89 -0.002 -0.89

rooflamasb 0.159 *1.93 0.061 *1.89 -0.096 ***-4.52 -0.017 ***-4.29

roofteja -0.037 -0.43 -0.014 -0.42 -0.015 -0.62 -0.003 -0.62

roofpalma -0.079 -0.60 -0.029 -0.61 0.034 1.47 0.006 1.50

sl_crop 0.145 *1.92 0.055 *1.74 -0.018 -1.11 -0.003 -1.11

sl_land -0.360 ***-3.08 -0.127 ***-3.02 -0.017 -0.69 -0.003 -0.68

malemigrants 0.216 ***5.37 0.081 ***4.43 0.039 ***6.54 0.006 ***6.04

femalemigrants -0.142 ***-3.16 -0.053 ***-2.75 0.006 1.45 0.001 1.44

husbandleft 0.658 ***4.55 0.247 ***3.84 0.200 ***5.32 0.033 ***5.02

wifeleft 0.178 0.44 0.067 0.44 -0.074 *-1.69 -0.012 *-1.67

meanagemig 0.018 ***4.21 0.007 ***3.58 -0.0001 -0.31 -0.00002 -0.31

meanschoolmig 0.023 1.53 0.008 1.50 0.020 ***6.52 0.003 ***5.94

maxtimeleftmig 0.016 1.27 0.006 1.25 0.004 ***3.05 0.001 ***3.07

year99 -0.212 ***-2.74 -0.078 **-2.51 -0.025 -1.24 -0.004 -1.22

year00 -0.217 ***-2.82 -0.080 **-2.47 0.106 ***4.37 0.017 ***4.74

migrationindex2000 0.088 *1.66 0.033 **2.01 0.013 1.62 0.002 1.61

Constant -0.329 -0.40 3.826 ***33.17

Observations 2,016 8,810

Note: ***, ** and * indicate signifi cance of parameters at 0.01, 0.05 and 0.1, respectively. Log likelihood for Internal Migration: -8, 558.0. Log likelihood for external migration: -27,016.8.Source: own elaboration.


148

its crops because of some shock since the probability of sending remitt ances signifi cantly increases by 0.05. However, this result is diff erent when the household could not farm because of some shock with a signifi cant decrease of -0.13. The diff erence between these results can be due to the fact that when a household loses the crop, it has already incurred in some investments necessary to farm. The crop represents the future income infl ow obtained with these investments. When it fails to be materialized this beforehand-projected income does not reach the household unbalancing the monetary resources necessary to satisfy planned expenditures. Here, migrants take the decision of sending remitt ances to fulfi ll the missing income caused by unplanned shocks. When the household has not farmed yet, it is still on time to make adjustments and possibly fi nd alternative income sources. Adjustments are easier since investments have not been made. In this case remitt ances are not as necessary.

Migrant characteristics are also very important determinants when deciding whether to send or not remitt ances. A one-migrant increase in the number of male migrants increases the probability of sending external and internal remitt ances by 0.08 and 0.01 respectively. The number of female migrants is associated with a signifi cant decrease in the probability of sending external remitt ances of -0.05. Male migrants obviously have strong motivations to remit. If the migrant turns out to be the husband, it signifi cantly increases the probability of sending external and internal remitt ances by 0.24 and 0.03 respectively. Evidently, husbands have at the origin households enough reasons to care about, a wife, children, or even mother and father. This result is not surprising and it is interesting to note that the eff ect is stronger for the case of external remitt ances. In contrast, when the wife leaves the household, the probability of sending internal remitt ances signifi cantly decreases by -0.01. Seeing a wife migrating, especially internally could also be and indicator of an entire family migrating. Thus, strings att ached to origin households could be less important as to send remitt ances.

The average age of migrants has only a positive signifi cant eff ect in the case of external remitt ances while the average schooling has it in the case of internal remitt ances. Finally, migration experience is only important in the case of internal migration. A one-year increase in the maximum years that a migrant has been away signifi cantly increases the probability of sending internal remitt ances by 0.001.


149

Results of this second stage are used to calculate the selection-corrected probabilities of perceiving external and internal remitt ances to be included in our analysis of expenditures patt erns described next.

b. Eff ects on Household Expenditure Patt erns

Table 6 presents results for equation (4) where the probability of a household participating in each of the eight expenditure categories is modeled. It is interesting to note the eff ect that the selection corrected probabilities have on this fi rst stage of estimation. The probability of receiving internal or external remitt ances has a positive and signifi cant eff ect on the probability of spending in Health, Durable Goods, Non Durable Goods and Patrimony. Besides, the probability of receiving internal remitt ances has a positive eff ect in the probability of spending in Farm Animals. So, this fi rst stage reveals that migration and remitt ance eff ects indeed change expenditure decisions. Households linked to these phenomenons are more likely to spend in physical capital categories such as Durable Goods, Patrimony and Farm Animals. Health, a very important human capital component is also benefi ciated. As expected, the probability of satisfying current consumption (Non Durable Goods) is also increased meaning that receiving remitt ances might indeed help households to drop monetary barriers that would otherwise keep them in poverty. Since virtually every household participates in the Food market it is comprehensive that remitt ances have no eff ect on this category. Finally, there is no evidence of remitt ance eff ects in the probability of spending in Education.

Several household characteristics turned out to be signifi cant. Most of these eff ects are maintained and consistent in the second stage of the censored system of demands. It rests to evaluate in this second stage the fi nal balance in terms of allocations once the eff ect of selection on consumption has been taken in account.

Let us fi rst start analyzing some results on household characteristics. Of particular interest are results on the variable indicating if the household receives Progresa transfers or not. It signifi cantly increases the share devoted to Food (0.82%), Non Durable Goods (0.68%) and Durable Goods (5.59%). It seems that Progresa eff ectively helps households to alleviate the three types of poverty offi cially defi ned by the Secretaria de Desarrollo Social (SEDESOL, 2002): Nutritional Poverty, Capabilities Poverty and Patrimony Poverty.


150

Table 6Probit Models for Selection on Consumption

Food Health Education Durable Goods

Coef. t Coef. t Coef. t Coef. t

lnhsize 1.163 ***13.85 0.515 ***25.22 0.843 ***43.41 0.502 ***16.76

progresa -0.089 -0.80 -0.088 ***-4.51 0.178 ***10.43 -0.143 ***-5.21

nkids -0.043 -1.45 -0.013 **-2.44 0.131 ***29.89 0.009 1.34

schoolinghead -0.008 -0.50 0.012 ***4.66 0.019 ***8.57 -0.013 ***-3.37

agehead -0.001 -0.07 -0.017 ***-6.17 0.031 ***12.48 -0.018 ***-4.43

agehead2 -0.00002 -0.15 0.0002 ***7.89 -0.0004 ***-16.49 0.0001 ***2.70

sexhead -0.231 **-2.22 0.023 0.98 -0.054 ***-2.70 0.011 0.33

headspanish 0.231 **2.53 -0.126 ***-7.31 0.158 ***11.64 -0.008 -0.34

prcliterate -0.168 -1.44 -0.073 ***-2.61 0.389 ***15.68 0.076 *1.87

hasplumbing -0.157 -1.24 0.014 0.56 -0.061 ***-2.80 0.034 0.97

haselectricity -0.063 -0.74 0.082 ***4.80 0.118 ***8.62 -0.008 -0.35

ownshouse 0.067 0.49 -0.063 **-2.17 0.035 1.43 0.068 1.57

ownslands 0.072 0.92 0.008 0.50 -0.041 ***-3.32 0.059 ***2.79

roofconcrete -0.107 -0.93 0.018 0.89 0.073 ***4.27 -0.020 -0.72

rooflamasb 0.193 1.51 0.002 0.08 -0.011 -0.62 -0.037 -1.25

roofpalma 0.121 1.06 -0.084 ***-3.60 -0.032 *-1.75 -0.041 -1.27

sl_crop -0.011 -0.13 0.062 ***4.05 0.150 ***11.63 -0.028 -1.23

sl_land -0.115 -0.86 -0.001 -0.04 0.063 ***3.31 -0.174 ***-4.63

prextremit 0.003 0.61 0.002 ***2.61 -0.0002 -0.30 0.002 ***2.64

printremit 0.0002 0.13 0.001 ***4.06 -0.0002 -1.24 0.001 ***4.36

lntotalexppc 1.035 ***27.16 0.633 ***55.33 0.382 ***39.67 0.613 ***40.32

year99 0.455 ***4.62 -0.225 ***-13.83 0.120 ***8.48 n.a. n.a.

year00 0.333 ***3.82 -0.478 ***-26.83 0.036 ***2.51 0.482 ***23.71

vtreatment 0.158 1.56 0.001 0.06 -0.113 ***-6.77 0.081 ***3.03

migrationindex2000 -0.141 ***-3.28 0.025 ***2.93 -0.065 ***-8.83 -0.057 ***-4.63

nutritionindex2000 0.011 *1.73 0.001 0.89 -0.006 ***-5.65 0.008 ***4.32

meanannualtemp -0.008 -0.69 -0.006 ***-2.79 -0.014 ***-7.25 0.006 *1.95

meanannualprec -0.0001 -0.52 0.0001 **2.26 0.001 ***12.96 -0.0002 **-2.19

constant -5.454 ***-10.85 -5.912 ***-47.86 -5.606 ***-52.23 -6.792 ***-39.60

Log likelihood -671.92 -22,535.1 -35,278.7 -10,416.3

R2 0.51 0.12 0.19 0.11

Obs. 63,771 63,771 63,771 63,771



151

Table 6Probit Models for Selection on Consumption

(Continued)

Non Durable Goods Patrimony Farm animals Other


lnhsize 0.538 ***25.04 0.528 ***17.82 0.219 ***5.42 0.632 ***38.92

progresa 0.115 ***5.00 -0.104 ***-3.83 -0.360 ***-9.98 -0.003 -0.18

nkids 0.016 ***2.67 0.036 ***5.08 0.061 ***6.08 -0.019 ***-4.75

schoolinghead 0.008 **2.14 0.0001 0.02 -0.022 ***-3.97 0.006 **2.56

agehead -0.0002 -0.07 -0.009 **-2.15 -0.020 ***-3.82 0.011 ***5.20

agehead2 -0.0001 **-2.01 0.00004 1.00 0.0002 ***3.22 -0.0001 ***-5.60

sexhead 0.026 1.07 0.041 1.18 0.062 1.32 0.033 *1.82

headspanish -0.021 -1.09 0.063 ***2.69 -0.074 **-2.28 0.026 **2.01

prcliterate 0.228 ***7.67 0.205 ***4.99 0.004 0.08 0.079 ***3.61

hasplumbing -0.027 -0.88 -0.038 -1.06 0.062 1.31 0.066 ***3.20

haselectricity 0.050 ***2.65 -0.015 -0.65 0.0001 0.00 0.135 ***10.38

ownshouse 0.011 0.31 0.192 ***4.09 0.086 1.37 -0.076 ***-3.25

ownslands 0.018 1.06 0.063 ***3.01 0.001 0.03 0.011 0.93

roofconcrete 0.081 ***3.10 -0.076 ***-2.67 -0.050 -1.25 0.035 **2.12

rooflamasb 0.033 1.36 0.025 0.89 0.098 **2.56 0.170 ***10.45

roofpalma -0.005 -0.22 0.020 0.64 -0.096 **-2.02 0.057 ***3.31

sl_crop 0.091 ***4.92 0.060 ***2.76 0.091 ***3.19 0.003 0.22

sl_land -0.020 -0.68 -0.306 ***-8.07 -0.113 **-2.40 -0.056 ***-3.09

prextremit 0.003 ***3.54 0.003 ***3.26 -0.001 -0.86 -0.001 -1.38

printremit 0.0005 *1.80 0.001 ***4.71 0.003 ***6.87 0.001 ***5.07

lntotalexppc 0.510 ***40.94 0.800 ***51.29 0.448 ***22.54 0.661 ***69.49

year99 0.557 ***26.92 n.a. n.a. n.a. n.a. 0.267 ***19.79

year00 0.433 ***22.23 0.297 ***14.31 n.a. n.a. 0.227 ***16.59

vtreatment -0.003 -0.15 0.059 **2.24 0.242 ***7.09 -0.066 ***-4.27

migrationindex2000 -0.095 ***-9.53 -0.064 ***-5.24 0.003 0.19 -0.039 ***-5.62

nutritionindex2000 0.008 ***5.39 0.005 ***2.81 0.014 ***5.30 -0.015 ***-13.77

meanannualtemp -0.013 ***-4.97 0.008 **2.51 -0.002 -0.57 -0.001 -0.54

meanannualprec 0.0001 1.54 -0.0002 ***-3.21 0.0002 **2.30 -0.0003 ***-6.75

constant -3.318 ***-24.31 -8.755 ***-49.17 -5.557 ***-24.24 -6.253 ***-61.57

Log likelihood -15,982.4 -10,553.3 -4,980.9 -39,252.1

R2 0.12 0.15 0.07 0.10

Obs. 63,771 63,771 63,771 63,771



152

Results on Health and Education are tricky and must be interpreted carefully: the expenditure shares devoted to health and education signifi cantly decrease if the household receives Progresa by -0.96% and -0.36% respectively. Since Progresa is aimed to increase healthiness of household members, it is then comprehensive that families receiving Progresa will suff er fewer diseases and thus, expend less in medicines and health care. Medical att ention that they already have with Progresa has actually no cost. So, they will devote a lower share of their total expenditure to health compared to non-progresa households. Progresa also grants scholarships to children. This also has the general eff ect of decreasing the share devoted to Education compared to Non-Progresa households.2

Other household characteristics agree in general to expectations. For instance, a one-year increase of a household head’s schooling decreases the share devoted to food by -0.312% and increases that devoted to education by 0.07%. A one-percent increase in the percentage of literate household members also increases the share devoted to Education (1.83%). A household head being male decreases the share devoted to Education (-0.26%) and Patrimony respectively and increases that devoted to Durable Goods (2.38%), Health (1.13%) and Food (0.5%). Obviously, the higher the level of total household expenditure, the higher the probability of a household participating in each category defi ned.

Several house characteristics also appear signifi cant. For instance, households with their roofs made of concrete (presumably those with bett er house conditions) spend signifi cantly more in Health (1.55%), Education (0.04%), Durable Goods (2.29%), Non Durable Goods (0.94%) and Patrimony (1.50%) than otherwise. Having farmable lands has a signifi cant and positive eff ect of the share devotes to Farm Animal (one of our productive investments categories) with an increase of 2.97%.

External shocks also aff ect household expenditure allocations. The Patrimony category is the most aff ected by both, losing the crops and being

2 Think about a school that charges 100 of tuition (or transportation cost or materials) and also about two children, one that has a Progresa scholarship that reaches a coverage of 80 of tuition and one that has no scholarship. The Progresa child has to devote just 20 of his income (household income) to pay for tuition, while the Non-Progresa child needs to pay 100. Both households have a total budget of 200. If we take Progresa transfers as part of household income, then the Progresa household will have 280. As a share, the Progresa household is devoting 7% of their total income to Education while the Non-Progresa household devotes 36%.


153

unable to farm because of some shock with signifi cant decreases of -5.2% and -4.5%. Interestingly, this causes an allocation where the Farm Animals category is the most benefi ciated with signifi cant increases of 3.37% and 6.03%. Apparently, households focus resources on animal production when agricultural production is not possible.

Moving to our results with respect to the central issue of migration and remitt ances, we fi nd that a 1% increase in the probability of receiving internal remitt ances signifi cantly decreases the share devoted to Food (-0.01%), Durable Goods (-0.04%) and Non Durable Goods (-0.003%). However, we fi nd no evidence of positive eff ects on any of the expenditure categories but other. An increase in the probability of receiving external remitt ances by 1% signifi cantly decreases the share devoted to Food (-0.02%) and Education (-0.01%) and increases the share expended on Patrimony (0.04%) and Farm Animals (0.09%).

These results contrast with Mora and Arellano (2009) who found, using a similar approach, evidence of signifi cant eff ects in most of expenditure categories defi ned. Their general result is that internal remitt ances seem to stimulate more categories related to human development investments, health and education, while external remitt ances aff ect positively physical capital investments. However, results of the present study seem to indicate that internal remitt ances have no positive relation with neither human capital nor physical capital investments. External remitt ances do have a positive eff ect on physical capital investments (Patrimony and Farm Animals) but appear with a negative and signifi cant eff ect on Education.

To understand these results an integral analysis must be made. The fi rst stage has revealed that households receiving remitt ances are more likely to spend in certain categories. In particular, households receiving internal remitt ances are more likely to spend in health, a human capital category, and all physical capital categories defi ned (durable goods, patrimony and farm animals). External remitt ances also motivate health expenditures and physical capital investments (durable goods and patrimony).

However, the second stage indicates that the fi nal allocation of monetary resources between expenditure categories, with remitt ances at hand and once selected into consumption is almost not aff ected. Let us recall that households still have a fi xed budget, even taking in account remitt ances received. Let us also recall that their income profi le is low and additionally, some of them are being subject of conditional cash transfers that also alter


154

expenditure decisions, especially those of health and education. All these factor combined may cause diff erent allocations that may end up with expenditure mixtures (shares) unchanged or even decreased but these doesn’t indicate that their well being is worsen off or unaff ected by the remitt ance perception. A household receiving external remitt ances can be spending more in certain category but the share of total expenditure devoted to it can remain unaff ected.

Consequently, our results suggest that remitt ances increase the probability of households participating in several human and physical capital variables. Internal remitt ances motivates a more active participation in health and all human and physical categories. External remitt ances motivate participation in health, durable goods and farm animals. In all cases, the eff ect of external remitt ances is higher than that of internal remitt ances. Evidently, remitt ance perceptions allows recipient households to devote monetary resources to certain markets that otherwise would probably remain out of their budget.

Despite this obvious increase in well being of households, the fi nal balance obtained in this exercise indicates that, all factors combined, the eff ect of internal and external migration and remitt ances is strong enough to have signifi cant eff ects only in few expenditure categories.

7. Conclusions

In this work we develop an empirical exercise that explores possible eff ects of migration and remitt ances on expenditure patt erns of households located in the poorest villages of Mexico. Several att empts of establishing the relation between these phenomenons and the way through which they aff ect expenditure decisions have been made. However, most of the time an independent approach is used and a single part of the complete history is analyzed. We adopted and integral approach that divides total expenditure in categories of interests looking not just for signifi cant eff ects on current consumption but also on concepts strongly related to human and economic development.

The evaluation data set for Progresa-Oportunidades represented a great opportunity to look for these eff ects since no att empts have been undertaken to analyze the particular case of poor households. The econometric approach we used allowed controlling for the potential selection biases arising from


155

Table 7Censored System of Demands, Seemingly Unrelated Regressions

Food Health Education Durable Goods


lnhsize -7.143 ***-48.98 -1.318 ***-3.26 -0.381 ***-3.02 3.215 ***4.71

progresa 0.823 ***8.51 -0.964 ***-2.85 -0.358 ***-5.92 5.590 ***11.70

nkids 0.076 **2.14 -0.304 ***-2.75 0.186 ***7.79 -1.501 ***-9.46

schoolinghead -0.117 ***-6.04 0.150 ***3.13 0.073 ***6.8 -0.149 *-1.77

agehead 0.198 ***11.53 0.078 1.42 0.103 ***6.83 -0.253 **-2.47

agehead2 -0.001 ***-8.90 0.001 1.35 -0.001 ***-7.03 0.003 ***3.54

sexhead 0.504 ***3.38 1.129 **2.39 -0.261 **-2.18 2.386 ***2.86

headspanish 0.667 ***6.41 -2.050 ***-5.36 0.077 1.18 -7.044 ***-12.90

prcliterate -1.775 ***-9.79 -1.077 *-1.87 1.831 ***12.19 8.421 ***8.37

hasplumbing -1.515 ***-8.14 2.134 ***4.51 0.363 ***3.08 -3.426 ***-4.37

haselectricty -2.219 ***-20.15 2.824 ***7.25 0.607 ***8.30 5.603 ***10.18

ownshouse 1.392 ***6.69 -1.325 **-2.11 -0.400 ***-2.94 -1.336 -1.16

ownslands -0.791 ***-7.78 -1.313 ***-4.15 -0.136 **-2.10 -2.210 ***-4.38

roofconcrete -1.825 ***-12.32 1.551 ***4.21 0.411 ***4.80 2.290 ***3.81

rooflamasb -2.462 ***-16.93 2.011 ***4.72 0.141 1.57 5.034 ***6.73

roofpalma 1.526 ***10.86 -1.476 ***-2.58 -0.367 ***-3.89 6.597 ***8.52

sl_crop -1.057 ***-9.93 2.774 ***8.83 0.477 ***7.23 -0.189 -0.33

sl_land 0.226 1.40 1.871 ***3.72 0.204 **2.16 11.917 ***10.62

prextremit -0.019 ***-3.44 0.005 0.45 -0.014 ***-4.18 0.006 0.35

printremit -0.011 ***-6.87 0.006 1.36 -0.001 -1.01 -0.041 ***-5.59

lntotalexppc -6.095 ***-68.97 -1.702 ***-12.21 -0.211 ***-5.89 0.861 ***4.13

year99 -2.241 ***-13.84 0.299 ***3.41 0.040 1.06 -0.462 ***-11.6

year00 -4.058 ***-24.81 0.788 ***8.17 0.034 0.91 -0.185 ***-4.23 )X( j'

-65.926 ***-50.71 28.712 ***49.49 2.747 ***14.55 1.005 1.47

_cons 131.889 ***168.65 -2.303 ***-20.36 -0.188 ***-3.76 -0.045 -1.19

R2 0.12 0.06 0.06 0.09

Obs. 63,771 63,771 63,771 63,771



156

Table 7Censored System of Demands, Seemingly Unrelated Regressions

(Continued)

Non Durable Goods Patrimony Farm animals Other


lnhsize 0.482 ***3.95 5.626 ***8.08 -0.443 -0.44 0.994 ***4.40

progresa 0.689 ***8.77 -4.689 ***-9.04 -0.497 -0.57 -0.865 ***-5.49

nkids 0.097 ***3.40 0.560 ***3.20 -0.536 **-2.13 -0.490 ***-8.68

schoolinghead -0.012 -0.83 -0.301 ***-3.76 0.379 ***2.64 0.098 ***3.50

agehead -0.113 ***-7.69 -0.404 ***-3.77 0.147 1.02 0.036 1.18

agehead2 0.0004 ***3.09 0.003 ***3.34 -0.002 -1.17 -0.0003 -1.11

sexhead -0.176 -1.37 -3.079 ***-3.48 0.924 0.72 -0.893 ***-3.43

headspanish -0.033 -0.39 1.431 **2.48 -3.074 ***-3.61 0.174 0.97

prcliterate 1.272 ***8.21 -11.356 ***-10.7 -8.687 ***-6.21 0.490 1.52

hasplumbing 0.852 ***5.86 -1.849 **-2.09 4.286 ***3.97 0.654 **2.50

haselectricty 0.406 ***4.52 -2.844 ***-4.73 -1.587 *-1.85 1.290 ***6.37

ownshouse -0.118 -0.72 -4.460 ***-3.18 1.963 0.99 -1.529 ***-4.73

ownslands 0.802 ***9.71 1.184 **2.19 2.986 ***3.87 -0.100 -0.61

roofconcrete 0.939 ***8.40 1.499 **2.30 0.419 0.43 0.806 ***3.77

rooflamasb 0.772 ***6.79 -2.894 ***-3.89 0.822 0.87 1.874 ***8.66

roofpalma -1.353 ***-11.67 -4.632 ***-5.84 -2.255 -1.49 0.214 0.87

sl_crop 0.147 *1.70 -5.215 ***-9.56 3.366 ***4.57 0.020 0.12

sl_land -0.489 ***-3.86 -4.511 ***-3.79 6.028 ***4.19 0.834 ***3.27

prextremit 0.001 0.29 0.036 **2.10 0.09 ***2.72 -0.003 -0.33

printremit -0.003 **-2.27 -0.007 -0.93 0.015 1.52 0.006 **2.48

lntotalexppc -1.437 ***-22.01 6.371 ***27.2 -1.820 ***-6.06 0.454 ***5.53

year99 3.497 ***34.88 -0.934 ***-16.4 -0.441 ***-20.6 0.587 ***5.65

year00 3.105 ***32.37 -0.136 **-2.36 -0.389 ***-17.8 0.938 ***9.03 )X( j' -5.474 ***-6.38 -3.357 ***-5.10 10.638 ***9.34 19.388 ***45.82

_cons 18.829 ***28.58 0.302 ***6.01 0.226 ***9.79 -2.863 ***-17.9

R2 0.07 0.20 0.02 0.04

Obs. 63,771 63,771 63,771 63,771



157

migration and consumption. In addition, a censored system of demands is estimated where the fact that expenditure decisions are not isolated is also taken in account.

Results indicate that household, village and migrant characteristics are important factors driving the decision of a household to allocate member in labor migration markets, internal or external, as well as the decision of migrants in sending money back home. Once selection into migration is accounted for, the probability for a household to participate in several expenditures categories is signifi cantly aff ected by our key variables summarizing migration and remitt ances eff ects: the probability of receiving internal and external remitt ances.

In particular, household with higher probabilities of receiving internal and external remitt ances are more likely to participate in the Non Durable Goods category (partially capturing current consumption) and several human and physical capital investments. Specifi cally, internal remitt ances signifi cantly encourage participation in health and all physical capital categories defi ned (Durable Goods, Patrimony and Farm Animals). External remitt ances also encourage expenditures in Health, Durable Goods and Farm Animals. When compared, the eff ect of external remitt ances is higher than that of internal remitt ances. In contrast with results of Mora and Arellano (2009), the case of poor households seems to indicate that there are no diff erentiated eff ects of internal and external remitt ances. For their particular context, external remitt ances have stronger eff ects on both human and physical capital investments.

These fi ndings do not support the view that households receiving remitt ances disproportionately spend their income on “current consumption”. Besides evidence of positive eff ects on current consumption our fi ndings reveal that remitt ances infl uence investments on human and physical capital categories and that a productive use encouraging development is indeed possible.

Besides this fi rst sign of increased well being of households, results also indicate that the eff ect of internal and external migration and remitt ances is signifi cant in the fi nal allocation of some expenditure categories. The probability of receiving internal remitt ances decreases the share devoted to Food, Durable Goods and Non Durable Goods, while the probability of receiving external remitt ances decreases the share devoted to Food, Education and increases the share expended on Patrimony and Farm Animals.


158

Several factors might be driving fi nal allocations of expenditures, but we do not consider that the lack of a signifi cant eff ect or the appearance of a negative one means that households linked with migration processes are worse off . As indicated previously, household receiving remitt ances are more likely to spend and can be spending more in certain category but at the end the share of total expenditure devoted to it can remain unaff ected. This can be comprehensive since their poverty condition implies a budget constraint that might be still binding. This also proofs that rural poor have a diff erent context that must be properly understood to correctly interpret results.

Our fi ndings indicate that internal and external remitt ances aff ect household expenditure patt erns. These income sources are not fungible and reshape household demands in ways that are independent of total income. They allow households to devote monetary resources in markets or goods that otherwise would remain out of their budget, an important fi nding, especially for poor rural Mexican households.

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