DEPARTMENT OF AGRICULTURAL AND RESOURCE ECONOMICSUNIVERSITY OF CALIFORNIA, DAVIS

Dissertation Prospectus

Identifying farmers’ incentives to maintain cropgenetic diversity:

The case of traditional maize in Mexico

Aslıhan Arslan

June 16, 2005

Dissertation Committee

J. Edward Taylor Stephen R. Boucher Lovell S. Jarvis

1

Contents

1. Introduction 2

2. Objectives 4

2.1. Shadow Prices vs. Market Prices 5

2.2. Determinants of Shadow Price - Market Price Difference 5

2.3. Farmers’ Land Allocation Decision 6

2.4. Conservation of Maize Genetic Diversity 7

3. Theoretical Framework 8

4. Empirical Specification 11

4.1. Estimating Shadow Prices 11

4.2. Determinants of Shadow Prices 13

4.3. Explaining Land Allocation 13

4.4. Empirical Concerns 14

5. Data and Extensions 15

6. Conclusion 16

Appendix A: Karush-Kuhn-Tucker (KKT) Conditions for the Derivation of

Shadow Prices 17

Appendix B: A Model with Missing Product and Labor Markets 19

Appendix C: Maps 20

References 21

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1. Introduction

Economics, in theory and application, requires that prices reflect the true value

of goods and services. If the market price of a good is different than that good’s true

value to an individual (and/or society), that individual will choose the “incorrect”

amount of that good to provide or consume–as far as the market (and economics)

is concerned. A farmer who receives non-market benefits from his own crops may

not participate in the market because his (shadow) valuation is higher than the

market price. We need to account for non-market values to fully understand how

these “subsistence” farmers will respond to changes in economic conditions.

The literature on the adoption of new technologies has tried to explain why

farmers do not respond as expected to higher prices and yields promised by green

revolution technologies by simple economic analyses.1 Potential explanatory fac-

tors include risk, imperfections in insurance, credit, input or output markets, agro-

ecological and informational constraints, or “traditional values”, i.e., special pref-

erences for traditional crops (Feder, 1980; Bellon and Taylor, 1993; Smale et al.,

1994).2 Any crop that is valued by the farmer because it mitigates the effects of

these constraints will be undervalued by the market. Even if there are no such con-

straints, high transaction costs or farmers’ special preferences for their own crops,

can lead to resource allocation that cannot be explained by market prices (Dyer and

Yunez-Naude, 2003). In such cases, we can say that farmers’ decisions are governed

by household-specific shadow prices that differ from market prices (Becker, 1965;

De Janvry et al., 1991; Jacoby, 1993).

Market and shadow prices are more likely to to differ in centers of crop domestica-

tion, where native crops have an historical role in culture and nutrition. Moreover,

these centers are usually located in developing countries where the aforementioned

market imperfections are prevalent, making the difference between shadow and

market prices persistent.3 Native crop varieties have evolved with natural selection

1Green revolution technologies introduced improved crop varieties that have higher yields, andit was hoped that they would increase farmers’ income.

2See Feder et al. (1985); Feder and Umali (1993) for comprehensive surveys of the literatureon agricultural technology adoption.

3Some crops (center of domestication): Maize (Mexico), wheat and barley (Middle/Near Eastand North Africa), rice (Northern China) and potatoes (Peru). See http://veghome.ucdavis.

edu/classes/fall2003/plb12/cultiva.htm for more information.

3

and farmers’ choices to suit heterogenous soil and climate conditions, and meet cul-

tural, nutritional and economic needs. The resulting crop genetic diversity (CGD)

is an important material input to crop breeding research directed at improved yield

and resistance (Koo et al., 2003). Maintaining the flow of this input of crop breed-

ing research depends on the conservation of native crop varieties. While CGD

has traditionally been conserved in gene banks, crop breeders agree that on-farm

conservation (allowing crops to evolve in their natural environments) complements

conservation in gene banks (Brush, 1989; Bellon and Smale, 1998). Given that

on-farm conservation relies on farmers’ continued cultivation of native crops, it is

crucial to understand whether they respond to market or shadow prices.

My dissertation objective is to understand if, how and why the shadow and mar-

ket prices of traditional crop varieties differ. To do so, I will develop an agricultural

household model with multiple market constraints (i.e., agricultural output, labor,

insurance and credit markets) and derive estimable shadow prices for non-marketed

crops following the literature (Becker, 1965; Jacoby, 1993; Skoufias, 1994; Taylor

and Adelman, 2002). This theoretical model fills gaps in the economic literature

by accounting for the effects of multiple market failures on shadow prices and using

household-specific shadow prices to explain farmers’ land allocation.

For an empirical application of my theory, I will use nationally-representative

agricultural household data from rural Mexico, to estimate agricultural production

functions and derive subsistence farmers’ shadow prices for traditional maize.4 I

will use these shadow prices to econometrically identify the key determinants of the

value of traditional maize varieties to farmers (e.g., transaction costs, resistance to

shocks, culinary preferences, agro-ecological constraints). This identification will

improve the design and targeting of programs to conserve on-farm CGD of maize

in Mexico.

Mexico is the center of maize domestication, where the history of maize goes

as far back as 7000 BC (Dowswell et al., 1996). Since then farmers have selected

4The data set provides detailed information on household assets, income sources, agriculturalproduction, migration, market participation as well as the diversity of maize. See ENHRUM(Mexico National Rural Household Survey) http://precesam.colmex.mx for details.

4

and cross bred traditional maize varieties to meet their needs in heterogenous en-

vironments making Mexico the main host of maize genetic diversity in the world

(Turrent and Serratos-Hernandez, 2004). Moreover, current heterogeneous patterns

of market integration and migration makes Mexico an ideal place to econometrically

identify how economic incentives affect farmers’ valuation of native maize varieties

and the conservation of their genetic diversity.

Previous empirical studies on the CGD of maize and its conservation in Mexico

did not investigate the role of shadow prices in farmers’ resource allocation (Bellon

and Taylor, 1993; Van Dusen, 2000; Perales R. et al., 2003; Dyer and Yunez-Naude,

2003). My thesis will fill this gap and link the theory of agricultural household

production under imperfect markets to the literature on crop genetic resources to

derive policy implications for their conservation.

In what follows, I first discuss my research objectives in detail. Later, I present

my theoretical and empirical methods by placing them in the literature. I conclude

with a short discussion on the data and extensions to my research.

2. Objectives

My dissertation will answer the following questions:

(1) Do household-specific values (i.e., shadow prices) of traditional crop vari-

eties differ from market prices?

(2) What are the main determinants of the divergence between shadow prices

and market prices? Especially how are shadow prices affected by:

* better access to output markets,

* access to credit,

* uncertainty in production,

* domestic and international migration,

* farmer income, and

* demographic characteristics.

(3) Do shadow prices explain subsistence farmers’ land allocation decision bet-

ter than market prices?

5

(4) Can we improve the strategies and targeting of conservation programs for

traditional maize in Mexico?

2.1. Shadow Prices vs. Market Prices. Starting with Chayanov (1926) and

continuing with the agricultural household literature, shadow prices have been the

focus of economic studies on farm household behaviour under missing markets.

In the extreme Chayanovian view of the peasant economy, there are virtually no

markets, hence all inputs and outputs are valued at the shadow prices emerging

from the internal household equilibrium. Such extreme cases are increasingly hard

to find.

More realistic agricultural household models consider that not all markets are

missing in a typical peasant economy. The impacts of missing labor, land or credit

markets on agricultural supply elasticities have been analyzed both theoretically

and empirically (Singh et al., 1986; Chihiro, 1986). While these studies used mar-

ket prices to value agricultural output, De Janvry et al. (1991) analyzed missing

product market using shadow prices. However, their empirical model only allows

for one shadow price for everybody, which actually is unique to each household and

determines their incentives for maintaining non-market crops. Although Dyer and

Yunez-Naude (2003) acknowledge the need to use shadow prices instead of market

prices to value traditional crops with high non-market values, there are no studies

to explicitly account for household-specific shadow prices. My research will fill this

gap by estimating shadow prices, and testing whether and how they differ from

market prices for the case of traditional maize in Mexico. I hope to get the prices

“right” before attempting to explain farmers’ resource allocation decisions and the

implications for on-farm genetic diversity of maize in Mexico.

2.2. Determinants of Shadow Price - Market Price Difference. The differ-

ence between shadow and market prices may stem from missing product markets

(due to high transaction costs) or traditional and culinary characteristics that are

not represented in market prices (Sadoulet and De Janvry, 1995). Another factor

may be the value of crops’ risk mitigating characteristics when insurance is missing

6

(Dyer and Yunez-Naude, 2003). Even when traded in a market, crops that mit-

igate constraints on farmers’ decisions can have a market price that differs from

their true value for the farmer. Whether and how this difference is affected by

different factors needs to be investigated to understand farmers’ de facto incentives

to maintain CGD.5

After estimating household-specific shadow prices of traditional maize varieties,

I will analyze how the difference between shadow and market prices varies with

farmers’ participation in markets, geographical and socio-economic characteristics.

This will provide crucial information for identifying strategies for the conservation

of traditional maize varieties in Mexico. In cases where the key determinants of

de facto conservation are subject to change, we can predict the direction of change

in farmer incentives to maintain traditional varieties and allocate resources among

on-farm and off-farm conservation more efficiently.

2.3. Farmers’ Land Allocation Decision. After understanding the factors that

affect shadow prices, it is important to analyze how they affect farmers’ alloca-

tion of land among different crop varieties. This decision has been investigated in

the literature on adoption of new technologies. Early individual adoption mod-

els have emphasized the role of risk and uncertainty in the adoption decision and

demonstrated a tradeoff between yield mean and variance (Feder, 1980; Just and

Zilberman, 1983). Due to this tradeoff, farmers may chose to diversify their crop

portfolio with lower-yielding traditional crops instead of adopting new varieties on

a large scale.

Later studies identified other determinants of adoption such as agro-ecological

constraints, credit constraints, labor market constraints, safety-first considerations,

or traditional values (Bellon and Taylor, 1993; Smale et al., 1994; Zimmerer, 1991).

Farmer adoption will be constrained if soil quality or climate is not suitable for the

modern crops; if these crops require the use of modern inputs and cash-constrained

farmers cannot get credit; if a modern crop requires more labor and the labor market

is imperfect; if farmers are concerned with food safety hence allocate a portion of

5De facto conservation describes the cases where farmers maintain crop genetic diversity ontheir farms without outside intervention.

7

their resources to ensure food, regardless of market incentives; or if traditional crops

have cultural or religious significance.

The other side of the adoption coin missing from most of this literature is the

decrease in the area planted with genetically diverse traditional varieties. Zimmerer

(1991); Meng (1997); Dyer and Yunez-Naude (2003), and Van Dusen and Taylor

(2005) address the “tradeoff” between on-farm CGD and market integration (one of

the main determinants of adoption of modern varieties). These studies consider the

links between farmers’ integration with outside markets and diversity, but they use

market prices for farm inputs and outputs. My research will build on this literature

by using shadow prices for subsistence farmers of traditional crops and testing the

performance of shadow prices in explaining land allocation against that of market

prices.

2.4. Conservation of Maize Genetic Diversity. The Irish potato famine and

the southern leaf blight epidemic are only two examples of food crises caused by

wide-scale cultivation of genetically homogenous varieties. Even after these histor-

ical events, the importance of maintaining CGD only gained popular acceptance

when the spread of green revolution crops threatened the conservation of landraces

(Turrent and Serratos-Hernandez, 2004).6 Consequently, the Consultative Group

on International Agricultural Resources (CGIAR) initiated gene banks and research

centers for the most important food crops in their centers of domestication.7

The International Center for the Improvement of Maize and Wheat (CIMMYT)

in Mexico (one of the CGIAR centers) holds an extensive maize collection in gene

bank. Conservation in gene banks is increasingly complemented by on-farm conser-

vation, the feasibility of which has been investigated by a variety of studies (Doss,

2003; Bellon and Smale, 1998). Most of these studies emphasized the constraints

on the spread of adoption of new maize varieties and predicted a decline in diversity

as constraints were relaxed by market integration. However, these expectations did

6A landrace is a crop cultivar or animal breed that evolved with and has been geneticallyimproved by traditional agriculturalists but has not been influenced by modern breeding practices(Hoisington et al., 1999).

7Some CGIAR centers are: CIMMYT in Mexico (maize and wheat), CIP in Peru (potatoes),IRRI in Philippines (rice), ICARDA in Syria (ceraals, food legumes) and ICRISAT in India (cerealsof the semi-arid tropics). See http://www.cgiar.org/centers/index.html for more information.

8

not materialize, due to de facto conservation of landraces among farmers (Dyer

and Yunez-Naude, 2003). This created hopes for decreasing the costs of on-farm

conservation by targeting farmers with higher likelihood of de facto conservation

(Bellon and Smale, 1998; Brush et al., 1992; Brush and Taylor, 1992).

De facto conservation implies that the shadow price of traditional maize is higher

than market prices due to market constraints or farmer preferences (Dyer and

Yunez-Naude, 2003). How these shadow prices are determined and how they can be

used to devise efficient conservation programs across regions with different shadow

prices have not yet been studied economically. One of the goals of my thesis is filling

this gap using a nationally-representative data set to guide conservation programs

for maize landraces in Mexico. 8

3. Theoretical Framework

The standard model of agricultural household behaviour accounts for the fact

that farm households consume part or all of their products and provide part or all

of their inputs (Chihiro, 1986). Whereas early studies in the agricultural household

literature assumed perfect markets, later studies allowed for the missing markets

which are common in developing countries (Singh et al., 1986; Taylor and Adelman,

2002; Van Dusen and Taylor, 2005).9

I will first describe a stylized agricultural household model with a potential

missing market for the traditional crop to derive its shadow price. (I discuss another

model with missing labor markets in Appendix B.) In this simple model, a farmer

produces only one crop (Xa) using labor (L) and fixed land (A). He consumes

part or all of his product at home (Xha ), purchases market goods (Xm) and enjoys

leisure (Xl). He works on his farm (F ), hires out his labor (HO) and can hire in

as much labor as he likes (HI) for production at the market wage (w). There are

no shocks to production, land is homogenous, and there is no land market, so the

farmer only decides how much labor to allocate to on-farm and off-farm work, how

much of his product to sell (Xsa) and how much to consume of all three goods (i.e.

8See Appendix C for maps of the distribution of landraces and the areas covered by ENHRUMsurvey in Mexico.

9For a comprehensive review of the agricultural household literature, see my orals essay athttp://tinyurl.com/6q85m

9

Xha , Xm, Xl). The farmer’s problem is given by:

maxXs

a,Xha ,Xm,Xl,L,F

U(Xha , Xm, Xl; Z) s.t.

pmXm ≤ paXsa + w(HO −HI)(1)

Qa = Qa(L, A)(2)

HO + Xl + F = T(3)

F + HI = L(4)

Xsa + Xh

a ≤ Qa(L, A)(5)

Xsa ≥ 0 and Xh

a ≥ 0(6)

where household and market goods are imperfect substitutes in consumption and

their prices are pa and pm respectively. Z is a vector of household characteristics,

L and A are, respectively, labor and land used in production.

The first constraint is the cash constraint, which indicates that the expenditure

on the market good needs to be less than or equal to the value of marketable surplus

plus net labor income. Equation (2) is the production function for Qa which is

concave in labor (L) and fixed land (A). Equation (3) is the time constraint where

T is the household’s time endowment. Of special interest is constraint (5), which

–along with non-negativity constraints (6)– determines the different regimes the

farmer may be in (subsistence farmer or commercial farmer), allowing us to derive

shadow prices for Qa.

By substituting (3) and (4) into the budget constraint, we obtain the following

Lagrangean:

maxXs

a,Xha ,Xm,Xl,λ,µ1,µ2,µ3

L = U(Xha , Xm, Xl, Z)+λ[paXs

a +wT − pmXm−wXl−wL]

+µ1[Qa(L, A)−Xsa −Xh

a ] + µ2Xsa + µ3X

ha

The FOCs for Xm, Xl and L are:

MUm = λpm(7)

MUl = λw(8)

µ1MPL = λw(9)

10

Karush-Kuhn-Tucker (KKT) conditions for optimal choices of Xsa and Xh

a are:

∂L

∂µ2= Xs

a ≥ 0(10)

∂L

∂Xsa

= λpa − µ1 + µ2 = 0(11)

µ2Xsa = 0(12)

∂L

∂µ3= Xh

a ≥ 0(13)

∂L

∂Xha

= MUha − µ1 + µ3 = 0(14)

µ3Xha = 0(15)

Qa(L, A)−Xsa −Xh

a ≥ 0(16)

µ1[Qa(L, A)−Xsa −Xh

a ] = 0(17)

In an agricultural household model with perfect markets, the farmer equalizes the

ratio of marginal utilities of each good to the ratio of market prices (i.e., MUi

MUj= pi

pj).

However, due to the constraint on agricultural output market and the nonnegativity

constraints, this ratio takes the following form in the current model (by (7) and

(14)):

MUha

MUm=

µ1 − µ3

λpm

Given this optimization rule, I define the shadow price of Xha as follows:

ρa ≡ µ1 − µ3

λ

This definition of shadow price takes on different values for different cases pos-

sible by KKT conditions (discussed in detail in Appendix A). For farmers who sell

part (all) of their product, shadow price equals (is less than) market price. If,

however, the farmer is consuming all of his product at home, the shadow price is

greater than the market price:

ρa =µ1

λ>

µ1 − µ2

λ= pa(18)

where µ1 is marginal utility of having one more unit of Qa and λ is marginal utility

of income. We can also interpret ρa as the money value of having one more unit of

Qa for the household (Heckman, 1974). The fact that µ1 and λ depend on house-

hold characteristics is the reason why under missing markets farmers’ production

11

decisions depend on consumption side parameters, which otherwise would not af-

fect production decisions. Although µ1 and λ are not observable, we can define an

estimable expression for ρa by combining (9) and (18):

ρa ≡ µ1

λ=

w

ˆMPL(19)

Given this specification, we can econometrically estimate household-specific shadow

prices by first estimating the production function and ˆMPL for each household. We

can also test whether shadow prices are statistically different from market prices,

and build empirical models to analyze the determinants of this difference and farm-

ers’ land allocation decisions. This basic model does not consider the uncertainty

farmers face in their production decisions (Just, 2000). I hope to incorporate pro-

duction uncertainty into this model, which will also allow me to identify the risk-

mitigating characteristics of traditional crops valued by farmers (Bellon and Taylor,

1993). In the following section, I discuss the empirical specifications for the basic

model.

4. Empirical Specification

4.1. Estimating Shadow Prices. Although the theory on internal equilibrium

and shadow prices of farm households is well established, empirical studies rarely

focused on the estimation of shadow values emerging from these models (Becker,

1965; Singh et al., 1986; Chihiro, 1986; Taylor and Adelman, 2002). These stud-

ies simulate the farmer’s problem and policy changes of interest to show how the

interdependence of consumption and production decisions can create unexpected

supply responses (De Janvry et al., 1991; Singh et al., 1986; Taylor and Adelman,

2002). Even though such simulation analyses generate shadow prices for each bind-

ing constraint, they cannot account for the fact that each subsistence household

has a unique shadow price that depends on its socio-economic and agro-ecological

characteristics. This individual-level variation can be exploited with econometric

estimation of shadow prices.

Existing studies that estimate shadow values econometrically are concerned with

labor market imperfections and shadow wages (Jacoby, 1993; Skoufias, 1994). I will

12

extend this literature by allowing for imperfect agricultural output markets and

production risk.

According to the discussion in the previous section the shadow price of the non-

marketed crop is given by:

ρa ≡ w

MPL

Traditional maize is usually produced for home consumption in rural Mexico:

around three quarters of traditional maize farmers in the sample did not sell maize

in the market, therefore do not have market prices to represent their valuation

of traditional maize. I will use this expression to represent the shadow prices of

traditional maize that is not marketed. We can estimate household-specific shadow

prices by estimating a production function for the agricultural product following

the methodology in Jacoby (1993) and Skoufias (1994). An estimate for shadow

prices is then obtained by using the market wage for agricultural labor (if the

labor market is perfect) and the estimated marginal product of labor evaluated at

farmers’ optimum (i.e., ρa = wˆMPL

).10 To test whether the estimated shadow prices

are statistically different from market prices, I adopt the test for separability used

by Jacoby (1993). We first need to run the following regression:

ρa = α + βpa + u

and test the null hypothesis of:

H0 : α = 0, β = 1

Rejection of this hypothesis allows us to conclude that subsistence farmers’ shadow

prices are significantly different from market prices and explains why some farmers

may not respond to changes in market prices. Getting a true measure of farmer

valuation of non-market crop varieties is an important step in understanding how

these values are determined. I will discuss how we can decompose the shadow price

into its determinants in the next section.

10See Appendix B for a model where labor market imperfection is also considered.

13

4.2. Determinants of Shadow Prices. Shadow prices are determined internally

at the household level, hence they depend on household characteristics and house-

hold specific indicators of market participation. Previous studies on maize in Mex-

ico identify factors such as lack of insurance, employment of family labor, culinary

superiority and cultural significance of maize to explain cultivation of landraces de-

spite small profits (Dyer and Yunez-Naude, 2003). Specifically, I will use variables

such as transaction costs (e.g. costs of transporting farm products to the nearest

market or buying seeds from market), plot characteristics (e.g. soil quality, irri-

gation, slope), percentage of crops consumed at home, access to credit, household

income and assets, migration status, tenure status (private or communal), farmer’s

age, education, and ethnicity as explanatory variables for the difference between

shadow prices and market prices.11

Identifying the correlation between income and shadow prices is challenging be-

cause of possible endogeneity. If there are omitted variables that both affect income

and shadow prices, the estimated coefficient of income will be biased. I will use an

instrumental variable for income to address this problem.

Whereas the difference between shadow and market prices may be driven by

market parameters in one region, it may depend on agro-ecological conditions of

farmers’ plots in the other (Perales R. et al., 2003). Understanding such differences

between different localities will help planning and targeting conservation programs.

4.3. Explaining Land Allocation. The opening of maize trade between Mexico,

United States and Canada after NAFTA was followed by a decline in maize prices.

Farmers were expected to decrease the proportion of land allocated to traditional

maize varieties, threatening the on-farm conservation of traditional maize. These

expectations did not materialize and subsistence farmers increased their land al-

located to maize landraces (Dyer et al.). This suggests that their land allocation

decision was not purely based on market prices, and there is hope for continued

on-farm conservation of maize in Mexico. This example illustrates the importance

11There are 84 ethnic groups in Mexico, which are considered as the long-term stewards of the59 races of maize (Turrent and Serratos-Hernandez, 2004).

14

of understanding how farmers allocate their land among different varieties for the

conservation of CGD.

Although the simple model presented here does not include land allocation as

a choice variable, it is possible to extend it to include land allocation. In my

dissertation, I will extend this model to analyze the links between shadow prices

and the proportion of land allocated into traditional maize. After estimating the

shadow prices for subsistence farmers in such an extended model, we will be in a

position to explain farmers’ land allocation better than simple models of agricultural

household that take prices as given. I will develop an empirical model of farmers’

land allocation decision and compare the performance of shadow prices and market

prices in explaining how and why farmers’ may not respond to market incentives

as expected.

Using shadow prices as an explanatory variable in an empirical land allocation

model is challenging because they are determined simultaneously with labor and

land allocation. To overcome a similar problem due to sequential estimation, Jacoby

(1993) used instrumental variables approach to estimate farmers’ labor supply using

shadow wages. I will use a similar econometric method to estimate the proportion

of land allocated to traditional maize in Mexico.

4.4. Empirical Concerns. The previous discussion relies on a primal model of

agricultural production where an agricultural production function is estimated.

However, there are some problems in estimating primal production functions (es-

pecially for agriculture), which are well-recognized in the empirical production re-

search literature (Just, 2000; Mundlak, 2000). One of the important problems is

the endogeneity of variable input choices and the resulting bias in the estimated

parameters of the production functions. This is the main motivation for the use

of duality in empirical production literature (Mundlak, 2001). Dual models do not

suffer from endogeneity since they consist of cost or profit function estimation using

market prices that are exogenous under perfect competition. Therefore dual models

have dominated the empirical production literature since the 1970s.

Duality theory was only recently applied to agricultural household models where

some prices may be endogenous until more recently. Whereas Lopez (1984); Coyle

15

(1994) and Sadoulet and De Janvry (1995) all use agricultural household models and

a dual approach to agricultural production, they derive output supply and factor

demand equations as systems where it is impossible to estimate shadow prices. I

hope to extend the duality approach to agricultural household models such that

it is possible to estimate shadow prices without relying on production function

estimates. If I can develop a theoretical model based on duality theory, I would like

to compare the shadow prices under primal and dual models to test the robustness

of my proposed model.

5. Data and Extensions

The ENHRUM (Mexico National Rural Household Survey) data I will use were

collected in 2003 by PRECESAM (Program for Studies on Economic Change and

Agricultural Sustainability in Mexico), an NGO funded by researchers at the Col-

lege of Mexico and University of California, Davis. The sample was selected by

INEGI (National Institute for Statistics, Geography and Informatics) to be rep-

resentative of rural Mexico and covers 1,778 households in 16 villages of the 5

geographic regions.

Some of the variables included in the survey are: household demographics, plot-

level information on land, labor, fertilizer, animals and machinery used for agricul-

tural production in 2002 (specific to different phases of production), total produc-

tion, marketing and consumption of products, maize diversity (number and names

of the maize varieties cultivated), migration history, off-farm income sources, credit

market participation, and other assets. In addition to the survey data, a maize

sample was collected from farmers, which is being analyzed in the lab for contam-

ination of traditional maize by genetically modified maize. I will examine the test

results once they are available to see whether I can use some of the information to

link the shadow prices to a scientific measure of genetic diversity of maize.

ENHRUM data provide sufficient plot level information and heterogeneity to es-

timate the production functions, shadow prices and farmer land allocation decisions

proposed here. 87 percent of total maize plots (885 plots) were cultivated with tra-

ditional maize in 2002 (this share was 37 percent in the Northwest region and 92

16

percent in the South-Southeast region). Around three quarters of traditional maize

farmers in the sample did not sell any traditional maize in the market, hence we do

not have market prices to represent their valuation of traditional maize. One short-

coming of the data may be the difficulty in separating the inputs for multiple crops

on the same plot, which is a typical problem for agricultural survey data. Although

the survey was designed to overcome this, I will exclude plots with multiple crops

and high levels of inputs (after carefully examining the survey questionnaires) to

minimize the potential effects of this issue on shadow price estimates.

In addition to my quantitative analysis, I will do qualitative field research in

the survey regions this summer. I will conduct focus group meetings with one

group of farmers in each region to improve my understanding of farmers’ attitudes

towards traditional maize varieties, the constraints they face in production, and

their motives in deciding which crops to cultivate. Although focus groups cannot

generate representative information, the qualitative richness of the information I

will gain will complement my quantitative analysis and serve as a reality check for

my research.

6. Conclusion

My dissertation will extend the existing agricultural household literature under

market imperfections by allowing explicit consideration of shadow prices of farm

product. It will also build upon the existing literature on conservation of crop

genetic diversity by analyzing the determinants of the “true” value of these resources

for farmers.

Maize is the cereal with the largest total production in the world, and Mexico

hosts its main genetic diversity (Turrent and Serratos-Hernandez, 2004). I hope to

contribute to the understanding of farmers’ valuation of traditional maize varieties

in their center of diversity. The answer to the question of “what are farmers’ incen-

tives to maintain the on-farm crop genetic diversity?” will have policy implications

for the conservation of genetic diversity of this important food crop in Mexico in

particular and guide future research on crop genetic diversity in different settings

in general.

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Appendix A: Karush-Kuhn-Tucker (KKT) Conditions for the Derivation ofShadow Prices

Given the Lagrangean:

maxXs

a,Xha ,Xm,Xl,λ,µ1,µ2,µ3

L = U(Xha , Xm, Xl, Z) + λ[paXs

a + wT − pmXm − wXl − wL]

+µ1[Qa(L, A)−Xsa −Xh

a ] + µ2Xsa + µ3X

ha

and the FOCs for Xm, Xl and L:

MUm = λpm(20)

MUl = λw(21)

µ1MPL = λw(22)

We need to use the KKT conditions for optimal choices of Xsa and Xh

a because of thepossibility of a corner solution for market sales of Xa.

∂L

∂µ2= Xs

a ≥ 0(23)

∂L

∂Xsa

= λpa − µ1 + µ2 = 0(24)

µ2Xsa = 0(25)

∂L

∂µ3= Xh

a ≥ 0(26)

∂L

∂Xha

= MUha − µ1 + µ3 = 0(27)

µ3Xha = 0(28)

Qa(L, A)−Xsa −Xh

a ≥ 0(29)

µ1[Qa(L, A)−Xsa −Xh

a ] = 0(30)

Equations (19) and (26) imply that

ρa =µ1 − µ3

λ(31)

To derive the shadow price of Xa we need to consider different cases implied by KKTconditions:

Case 1: Xsa > 0, Xh

a > 0, Qa(L, A)−Xsa −Xh

a > 0, µ1 = 0, µ2 = 0, µ3 = 0If the sum of home consumption and sales of Xa is less than the total productionmarket price has to be equal to zero by (23). Therefore there will never be wastesince market prices are strictly positive. For the following cases I assume there isno waste and hence µ1 > 0.

Case 2: Xsa > 0, Xh

a > 0, µ1 > 0, µ2 = 0, µ3 = 0This case characterizes the farmer who sells part of Xa in the market. For thisgroup of farmers market price equals shadow price, i.e. ρa = pa = µ1

λand we

can safely use market price to represent farmers’ valuation of the agriculturalproduct.

Case 3: Xsa > 0, Xh

a = 0, µ1 > 0, µ2 = 0, µ3 > 0Farmer is selling all his product at the market price since market price is higherthan shadow price, i.e.

pa =µ1

λ> ρa =

µ1 − µ3

λ

The case where both Xha and Xs

a are equal to zero is not likely to occur hencewill not be considered here.

18

Case 4: Xsa = 0, Xh

a > 0, µ1 > 0, µ2 > 0, µ3 = 0This case characterizes subsistence farmers, who consume all their product athome. The market price is less than farmers’ shadow price as given by (23) and(30):

pa =µ1 − µ2

λ< ρa =

µ1

λFarmer is not selling his product since he values his product more than the mar-ket.For this group we need to estimate shadow prices to understand how farmers’value their crops. Combining (21) and (30) we can derive an estimable expressionfor shadow prices:

ρa =µ1

λ=

w

MPL

19

Appendix B: A Model with Missing Product and Labor Markets

This model allows for the possibility of missing labor markets in addition to the missingproduct markets discussed in the text. In this model farmer is producing one more crop Xc

for which there is a perfect market, so farmer decides how to allocate his labor among twoproducts (La, Lc). In addition to product markets for agricultural good, if the labor marketis also missing for the farmer, then we have another constraint in optimization. Here Iexplicitly model the subsistence farmers of Qa without considering KKT conditions. Inaddition to the model in text there is one more constraint on labor use (i.e. La +Lc +Xl =T ). The Lagrangean for this problem is:

maxXa,Xc,Xm,Xl,λ,µ1,µ2

L = U(Xa, Xc, Xm, Xl; Z) + λ[pcQc(Lc, Ac)− pmXm − pcXc]

+µ1[Qa(La, Aa)−Xa] + µ2[T −Xl − La − Lc]

The FOC are:

MUa = µ1(32)

MUc = λpc(33)

MUm = λpm(34)

MUl = µ2(35)

µ1MPLa = µ2(36)

λpcMPLc = µ2(37)

FOC’s (31)-(32) imply ρa = µ1λ

, and (35)-(36) imply MPLcMPLa

= µ1λpc

. Combining these two

conditions we get the following expression for the shadow price of non-marketable productin the absence of labor markets:

ρa = pcMPLc

MPLa

It is possible to test whether we should use market wages in estimating shadow prices byemploying the approach in Jacoby (1993) and Skoufias (1994). If labor market is perfectfarmer will equalize the wage rate to marginal productivity of labor across all activities.To test this, we can run the following regression:

ˆMPLc = γ + θw + u

The null hypothesis in this case will be:

H0 : γ = 0, θ = 1

Rejection of this hypothesis means that market wage does not reflect the true value ofhousehold labor, hence we need to use shadow wages instead of market wages in deter-mining shadow prices of non-marketable variety.

20

Appendix C: Maps

Figure 1. Regional Distribution of Mexico National Household Survey(ENHRUM 2002)

Figure 2. Regional Distribution of Maize Landraces in Mexico (Tur-rent et al. 2004): Low-land maize is distributed in blue and purple areas,mid-elevation maize in green and brown areas and highland maize in yel-low and orange areas. Dark green dots represent maize, and red dotsrepresent teosinte (the ancestor of maize) populations.

21

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