THE CASE OF TRADITIONAL MAIZE IN MEXICO 1 ... - Semantic Scholar

FARMERS’ SUBJECTIVE VALUATION OF SUBSISTENCE CROPS: THE CASE OF TRADITIONAL MAIZE IN MEXICO ASLIHAN ARSLAN Presented at the Mini-Symposium on Markets, Crop Diversity and Farm Welfare, 26th IAAE Conference, Australia, August 2006 Updated Draft: October 22, 2007 Abstract. Subsistence farmers may not respond to market incentives if their resource allocation decisions are based on shadow prices. This may lead to “puzzling” results from an economic point of view if shadow prices are not taken into account. Subsistence maize farmers in rural Mexico are an example with their non-response to decreasing maize prices after NAFTA. I analyze the true value measure of maize, hence famers’ real incentives to cultivate it, using nationally representative rural household data from Mexico. I develop an agricultural household model with an asymmetric missing market for a subsistence crop that arises from non-market values of this crop. I theoretically derive household-specific shadow prices of maize and estimate them for rural farmers in Mexico. Research results suggest that the value of traditional maize varieties to subsistence farmers is significantly higher than market prices for maize; the same is not true for modern maize varieties. I use estimated shadow prices to identify the key farm- and farmer-specific factors that are correlated with the farmers’ values of traditional maize. Use of irrigation and producing on land with high-quality soil are negatively correlated with shadow prices; male-headed households and those comprised of indigenous peoples have above-average shadow prices for traditional varieties of maize. The latter correlation is especially true in southern and southeastern Mexico indicating high de facto incentives to maintain traditional maize in these regions. On-farm conservation programs would be more effective if targeted to communities that have high shadow prices identified in this analysis. The method I use is flexible enough to be applied to guide conservation programs in other regions and with other crops.

1. Introduction Market prices reflect the true value of goods and services only for people who engage in trade given those prices. Understanding the value of goods for those who do not trade is more complicated for there is no observable, subjective value measure. The same complication is true for goods with missing markets. Individual behaviour may seem non-optimal from an economic point of view if we use inappropriate value measures, as did the behaviour of maize farmers in Mexico after NAFTA, when I thank to Edward Taylor and Steve Boucher for very useful comments and suggestions. All mistakes are mine. I also thank to Center on Rural Economies of the Americas and Pacific Rim (REAP) and Program for the Study of Economic Change and Sustainability in Rural Mexico (PRECESAM) for letting me use this unique data set. 1

SHADOW PRICES OF TRADITIONAL MAIZE

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they increased maize production in spite of decreasing prices. I develop an agricultural household model that combines a transaction cost (TC) model with an asymmetric market constraint to derive household-specific subjective values (i.e. “shadow prices”) of farmers’ crops. This market constraint extends on the “partly absent market” defined in Strauss (1986) as a source of non-separability in agricultural household models and conceptualizes the oft-mentioned non-market values of landraces for subsistence farmers – especially in centers of crop domestication and diversity. This model extends the agricultural household literature with missing markets and explains why subsistence farmers may allocate resources in ways that cannot be explained by conventional analyses using market prices. The theoretical model results in shadow prices that can be estimated econometrically. Empirical application of this model in the context of subsistence maize farmers in rural Mexico sheds light into their inelastic supply response to market incentives. Analysis of estimated shadow prices of traditional maize provides policy implications for conservation of maize landraces and makes a case for de facto conservation in Mexico – the center of domestication and diversity of maize.1 In the next section, I provide some background on the concept of shadow prices and its use in studying agricultural households with missing markets, and on the conservation of crop genetic diversity (CGD). In Section 3, I develop the theoretical model to derive household specific shadow prices of farmers’ subsistence crop. In Section 4, I describe data and estimate the shadow prices of traditional maize for subsistence farmers in Mexico. I also analyze the determinants of the difference between shadow and market prices to derive policy implications for on-farm conservation of traditional maize. I summarize the results and conclude in Section 5. 2. Background The concept of shadow price has been used by economists to represent the value of goods or services that are not traded in markets (Becker, 1965). Specifically, the shadow price of a crop arises from farmer’s resource allocation problem in the absence of perfect markets for that crop (i.e. he cannot buy or sell the crop). This results in the non-separability of farmer’s production decisions from consumption decisions, where the shadow price, rather than the market price, is the true value measure for the constrained crop (de Janvry et al., 1991; Taylor and Adelman, 2003). Conventional economic analyses may result in misleading expectations if they fail to represent the true value of these goods and services – as was the case when subsistence maize producers in Mexico “unexpectedly” increased their production in spite of decreasing prices after NAFTA. A thorough understanding of the structure and the determinants of shadow prices becomes particularly important when the non-marketed good in question is a crop that contains important genetic diversity whose conservation depends on farmers’ 1

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

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incentives to cultivate it (i.e. “shadow prices”), and on-farm conservation of crop genetic resources is an internationally accepted complement to conservation in gene banks. Using an agricultural household framework, I develop a theoretical model to derive household specific shadow prices for “non-tradable” crops. The shadow prices I derive may arise both because of transaction costs (TC) as in de Janvry et al. (1991), and imperfect substitutability of market purchased crops for the domestic crop. Based on the vast literature on the non-market values of maize for subsistence farmers in Mexico (most of whom are indigenous), I assume that domestic maize and market maize are two different goods that are imperfect substitutes in consumption (unlike in de Janvry et al. (1991)). I show how shadow prices may be the relevant value measure for farmer’s decisions if the private non-market values are significant even if the TC band is not binding. I also analyze theoretically how using shadow prices instead of market prices can improve our understanding of resource allocation by subsistence farmers.2 The standard agricultural household model acknowledges that farm households consume part or all of their products and provide part or all of their inputs (Chihiro, 1986). Early studies in the agricultural household literature assume perfect markets, but later studies allow for imperfect or missing markets, which are common in developing countries (Singh et al., 1986; Jacoby, 1993; Skoufias, 1994; de Janvry et al., 1991; Taylor and Adelman, 2003). While most of these studies use market prices to value agricultural output, both de Janvry et al. (1991) and Taylor and Adelman (2003) analyze farmer decisions under missing product markets and represent the value of the constrained food crop with a shadow price instead of market price. Missing markets in these models are farmer-specific and arise from TC that trap some farmers within the TC band where they cannot buy or sell their products. They assume perfect substitutability between domestic and market goods, therefore the household is indifferent between consuming either good as long as TC are not binding. I analyze how imperfect substitutability affects the results of earlier models and show that shadow prices may arise even in the absence of TC. Another characteristic of previous studies with missing markets is that the market constraints they analyze are symmetric, i.e. constrained farmers can neither buy nor sell their products/labor. The missing market discussed in this paper, however, is asymmetric (one-sided) such that it allows the farmer to sell the crop, but he has to produce it if he wants to consume it. This is because the domestic crop is characterized as a different consumption good due to its unobservable consumption characteristics and non-market values. As a result, the definition of missing market is farmer-and cropspecific, as opposed to the more general farmer-specific or market-specific definitions in the literature.

2

Throughout this text I use the term “subsistence farmer” to refer to small scale farmers who produce only for home consumption.

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There are no studies that analyze the effects of such an asymmetric market constraint on farmer behaviour. In light of recent developments in the study of farmers’ crop choices in centers of diversity, we can think of a crop as a bundle of multiple characteristics farmers pay attention to when choosing what to cultivate. These characteristics include production attributes, consumption attributes, subjective importance farmers place on their seed which may have provided subsistence to the family for decades, as well as other non-market benefits farmers get from farm production (Brush and Meng, 1998; Smale et al., 2001, 2003; Edmeades et al., 2004; Badstue et al., 2006; Dyer-Leal et al., 2002).3 All of these characteristics are convoluted for crops like maize (or wheat, rice, potatoes, etc.) where the seed is also the consumption good. The following discussion mainly refers to maize, but can be extended to other crops with similar characteristics. Although production attributes (e.g. plant strength, resistance to pests and disease, ear length, flowering time, adaptability to certain environments) are important in shaping farmers’ variety choices, I do not focus on them in this paper. Technology adoption literature covers a wide variety of production attributes that affect farmers’ variety selection, such as risk, agro-ecological conditions and information constraints (Feder, 1980; Just and Zilberman, 1983; Bellon and Taylor, 1993). How other production attributes mentioned above affect farmers’ decisions can be analyzed using the tools developed by this literature. I analyze how consumption attributes and non-market values affect subsistence farmers’ resource allocation decisions. Subsistence-oriented farmers in Mexico demand various consumption attributes of maize such as ease of shelling and processing, color, taste, softness of dough and suitability for certain dishes, which are found to be correlated with on-farm genetic diversity of maize landraces (Smale et al., 2003; Bellon, 1996; Bellon et al., 2006; Perales et al., 2003). Some of these attributes are unobservable and may create an imperfect market for crops with the specific bundle of traits demanded by the farmer. The difficulty in buying a crop with particular consumption traits may be compounded if different maize varieties are mixed in the market, where it is virtually impossible to observe some consumption attributes important to farmers. Unless every farmer’s maize is of identical quality, it is impossible for the farmer to recover the same quality of his own crop from the market – even if the quality difference is subjective.4 In this case, some farmers may prefer producing and consuming their own crop at higher costs, to ensure the supply of all the consumption traits they care about.

3

Small maize farmers in Mexico value maize for traditional, ceremonial, ritual values, as well as different tastes and cooking qualities (Salvador, 1997; Dyer-Leal, 2006; Berthaud and Gepts, 2004; Brush and Chauvet, 2004). 4 There could exist different silos for each maize quality, however, this would be very costly and in practice few farmers have access to such finely differentiated market for maize quality.

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Non-market values, such as ceremonial or ritual importance associated with cultivating and consuming the subsistence crop, leads farmers to treat this crop as a separate consumption good when making resource allocation decisions. An important non-market value of maize for indigenous maize farmers in Mexico is related to their identity as good farmers and members of community (Smale et al., 2003; Badstue et al., 2006; Perales et al., 2005).5 Another motivation for cultivating traditional maize in Mexico is to maintain the health of family seed that is important in the establishment and the survival of households. Therefore, we can expect that the marginal valuation of domestic maize to be higher for farmers for whom these non-market values are significant (i.e. a smaller degree of substitutability between domestic and market crop). Consequently, some farmers may not participate in the market, even if the observable TC (such as transportation costs) are not binding. Although the motivation of this model focuses on the case of traditional maize in Mexico, similar arguments about farmer preferences have been made for other countries and crops. Indigenous farmers in the Peruvian Andes prefer cultivating traditional potato varieties that are associated with various non-market benefits (Brush, 1992). Similarly, maize in Guatemala, wheat in Turkey or rice in Philippines have some consumption characteristics that make purchasing a close substitute in the market hard (Meng et al., 1998; Bellon et al., 1998; Isakson, 2007). Therefore, the model developed here provides intuition for farmers’ incentives for maintaining traditional crops in centers of diversity beyond subsistence farmers of maize in Mexico. The endogenously determined shadow price represents the money value of the utility the farmer receives by producing and consuming the “non-tradable” crop, i.e. the crop for which the asymmetric market constraint is binding. The household’s incentives for cultivating that crop, therefore, are represented by the shadow price. Therefore, shadow prices can be used to improve the efficiency of on-farm conservation programs by targeting areas where farmers have higher incentives to continue cultivating traditional crops. Although Dyer-Leal and Yunez-Naude (2003) acknowledge the need to use shadow prices instead of market prices to value traditional crops with high non-market values for subsistence farmers, there are no studies to explicitly account for household specific shadow prices for such crops. I fill this gap by estimating and analyzing the determinants of household specific shadow prices of traditional maize for subsistence farmers in rural Mexico. Understanding the determinants of farmers’ valuation of their crops in centers of crop domestication and diversity is particularly important for the conservation of traditional crop varieties. These varieties are the main sources of CGD because of millennia old processes of evolution and farmer selection to suit them to heterogenous soil and climate conditions, as well as to satisfy demand for various consumption characteristics (Liu et al., 2003; Berthaud and Gepts, 2004). Resulting genetic diversity is one of the 5

ADD Ref to The Story of Corn by Betty Fussell.

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most important material inputs of crop breeding research that improves yields and resistances of the world’s food crops (Koo et al., 2003). While conservation of CGD has traditionally been in the form of frozen conservation in gene banks, crop breeders increasingly agree that on-farm conservation that allows crops to continue their evolution in their natural environments is a complement to conservation in gene banks (Brush, 1989; Bellon and Smale, 1998). On-farm conservation relies on farmers’ incentives to continue cultivating these crops and these incentives are valuable in designing and targeting efficient conservation programs (Bellon and Smale, 1998). Whether farmers’ incentives are based on market prices or shadow prices is crucial for understanding their responses to changes in economic environment and for improving the efficiency of on-farm conservation programs. The contribution of such an understanding to models of farmer’s resource allocation is especially important if empirical focus is on rural economies where most farmers produce only for home-consumption and receive non-market benefits from their subsistence crop – as is the case with maize farmers (especially indigenous ones) in rural Mexico. I use a nationally representative agricultural household data from rural Mexico to estimate shadow prices of traditional maize and analyze their determinants. Mexico is the center of domestication of maize, where the history of maize goes as far back as 7000 BC (Dowswell et al., 1996). Farmers have been selecting and cross breeding native maize varieties since then to fit them to their needs and heterogenous agro-ecological conditions.6 Consequently, Mexico hosts the largest CGD of maize in the world with 59 different races that are valuable inputs for crop breeders to continue improving the worlds’ most widely used food grain (Yunez-Naude and Taylor; Berthaud and Gepts, 2004). The results of this research can be used to design and target effective conservation programs for this important crop. 3. Theoretical Model In this section, I develop a model to understand a farmer’s land and labor allocation decisions between different crops (a subsistence crop and a cash crop) and activities (farm production, offfarm work, leisure) in the presence of transaction costs and a market constraint for the subsistence crop. This market constraint arises from imperfect substitutability of market purchased crops for the domestic subsistence crop, hence the two goods enter into the utility function as separate consumption goods.7 Therefore, the market constraint for domestic crop is asymmetric, such that the farmer can 6

In an exhibition at the Museo de Culturas Populares in 1982, 600 different food preparations were documented, many of which require different types of maize (Brush and Chauvet, 2004). 7 In a series of informal interviews with maize farmers in 2 states (Puebla and Oaxaca) and 15 different communities in Mexico during July 2005, I have found that most farmers prefer the traditional maize they produce for consumption; do not like modern varieties (either because they do not have the perfect growing conditions for them, or they do not like the tortillas made with modern maize); think that maize production is not an income generating activity; and attach different consumption and production attributes to different varieties. These observations suggest two different categories of maize for farmers, home-produced maize that is mostly TV and purchased maize that is mostly MV.

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sell this crop, but cannot buy an identical crop in the market, which is similar to the “partly absent market” defined by Strauss (1986). The consumption of the domestic crop is equal to the production minus sales – if any. Suppose that a farmer produces a cash crop and a food crop using labor and a fixed amount of land (A). The markets for the cash crop and labor are perfect, hence the farmer can buy and sell these at market prices.8 There are no land markets and he divides his land between the subsistence crop and the cash crop (the cash crop is not a consumption good).9 He also decides how to allocate labor across different crops and activities to maximize his utility. Let Qi denote the quantity produced of the crop i, where i = s, c, identifying the subsistence crop and the cash crop respectively. Xm and Xl are, respectively, the amount of market goods and leisure consumed. He also consumes part or all of his subsistence crop denoted by Xsh , where the superscript h indicates that the only source of consumption of Xs is home production. He works on his farm, hires out his labor and can hire in as much labor as he likes at the market wage (w). Fi and HIi denote the amount of family labor and hired-in labor used in production of crop i, respectively. There are transaction costs to buy Xm and to sell the subsistence crop (tb and ts respectively) that create a transaction cost band around the market price as defined in de Janvry et al. (1991). Output is certain and the farmer’s decisions are: what proportion of land to cultivate with subsistence crop; how much labor to allocate to the production of each crop and off-farm work; how much of his subsistence crop to sell (Xss ); and how much to consume of all goods (i.e. Xsh , Xm , Xl ). Li is the total labor used in production of crop i, and θ is the proportion of land cultivated with the subsistence crop. The market good can be a crop similar to the domestic food crop. These two consumption goods can have different degrees of substitutability depending on how important the non-market values are for the farmer (i.e. Xm can be maize bought in the market for the case of Mexico). Z represents a vector of household characteristics (demand shifters), including indigenous identity, that are important in shaping preferences and therefore affect the marginal utilities from consumption. The farmer’s problem is given by: max

Xl ,Xm ,Xsh ,Xss ,θ,Fi

U (Xsh , Xm , Xl ; Z)

s.t.

They also support the asymmetric market constraint for home produced maize that is due to non-market values and unobserved consumption characteristics. 8For farmers in Mexico the cash crop can be fruits or vegetables produced mainly for the export market. 9Finan et al. (2005) find that land rental markets in rural Mexico are very inactive with only 5% of farmers participating in rental market using 1999 data from 25,000 households. This ratio is 7.6% of all plots in ENHRUM data used for the empirical analysis in this paper.

SHADOW PRICES OF TRADITIONAL MAIZE

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≤ ps (1 − ts )Xss + pc Qc + wHO + W

(1)

Qs

= g(Ls , Aθ)

(2)

Qc

= h(Lc , A(1 − θ))

(3)

= T¯

(4)

= Li , i = s, c

(5)

Xsh

≤ Qs − Xss

(6)

Xss

≥ 0

(7)

Xsh

≥ 0

(8)

Xm

≥ 0

(9)

0≤

θ

pm (1 + tb )Xm + w(HIa + HIc )

HO + Xl + Fs + Fc Fi + HIi

Ls

≤1

≥ 0

(10) (11)

where pj denotes the market prices of consumption goods and the cash crop identified with subscripts j = s, m, c; and W denotes exogenous transfers. U(.) is a continuously differentiable and strictly quasi-concave utility function and g(.) and h(.) are, respectively, production functions for subsistence crop and the cash crop that are quasi-convex. Equation 1 is the cash constraint, which indicates that the total expenditure on the consumption of market good and hired labor needs to be less than or equal to the value of marketed surplus plus labor income and exogenous transfers. Equation 4 is the time constraint, where T¯ is the household’s time endowment.10 The consumption of Xm can equal to zero if the TC for buying is prohibitively high (which depends on the degree of substitutability of market crops for domestic crop). The consumption of Xsh , can also equal to zero if the farmer does not cultivate this crop. I derive the conditions under which this would happen using the non-negativity constraint in equation 8. The other non-negativity constraints considered here (i.e. constraints 7, 10 and 11) are on the amount sold of, the proportion of land in, and the labor used for the subsistence crop to emphasize the corner solutions related to this crop that define shadow prices. Of special interest are Constraints 6 and 7, which together define the market constraint for the farmer’s subsistence crop (Qs ). Constraint 6 states that the consumption of the subsistence crop has to be less than or equal to the total amount produced minus sold, since he cannot buy it in the market. Constraint 7 states that the marketed surplus cannot be negative characterizing the one-sided missing market. Constraint 6 and the non-negativity constraints together determine the different regimes the 10I assume that the marginal utility of the first unit of leisure is very large (i.e. M U | l Xl =0 = ∞), hence we are not

concerned about a corner solution for Xl .

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farmer may be in (e.g., all land in Qs and subsistence farmer; all land in Qs and commercial farmer; some land in Qs and subsistence farmer). This allows us to derive farmer-specific shadow prices of the subsistence crop and how it compares to the market prices for each case. By substituting Equations 2-5 into the budget constraint, we obtain the following Lagrangean: max

Xl ,Xm ,Xsh ,Xss ,θ,Li ,λ,µn

L = U (Xsh , Xm , Xl ; Z)

+λ[ps (1 − ts )Xss + pc h(Lc , A(1 − θ)) + W + w(T¯ − Xl − Ls − Lc ) − pm (1 + tb )Xm ] +µ1 [g(Ls , Aθ) − Xss − Xsh ] + µ2 Xss + µ3 Xsh + µ4 Xm + µ5 θ + µ6 (1 − θ) + µ7 Ls + µ8 Lc i = s, c n = 1, ..., 8 The first order conditions (FOC) are: F OCXl

:

M Ul = λw

(12)

F OCXm

:

M Um − λpm (1 + tb ) + µ4 = 0

(13)

F OCXsh

:

M Ush − µ1 + µ3 = 0

(14)

F OCXss

:

λps (1 − ts ) − µ1 + µ2 = 0

(15)

F OCθ

:

µ1 A(M P As ) − λpc A(M P Ac ) + µ5 − µ6 = 0

(16)

F OCLs

:

µ1 M P Ls − λw + µ7 = 0

(17)

F OCLc

:

λ(pc M P Lc − w) + µ8 = 0

(18)

Equations 13-18 are FOCs for variables that can take on zero values (i.e. corner solutions). We need to use the Karush-Kuhn-Tucker (KKT) conditions to obtain the optimality conditions for these variables.11 The KKT conditions are:12

11For the KKT conditions to be sufficient for a maximum, I assume that the utility function is pseudoconcave in addition to the quasi-concavity and quasi-convexity assumptions above. Pseudoconcavity also implies quasi-concavity because U(.) is pseudoconcave if and only if its gradient vanishes only at the global optimum and it is quasi-concave (Leo Simon, ARE 211 class notes: http://are.berkeley.edu/courses/ARE211/currentVersion/mathNPP2.pdf). 12 Note that Lc is automatically zero if θ = 1. The KKT conditions for Lc do not affect the following discussion on shadow prices. I discuss and interpret them in detail in Appendix A.

SHADOW PRICES OF TRADITIONAL MAIZE

∂L : M Um − λpm (1 + tb ) + µ4 ∂Xm ∂L : Xm ∂µ4 µ4 Xm ∂L : λps (1 − ts ) − µ1 + µ2 ∂Xss ∂L : Xss ∂µ2 µ2 Xss ∂L : M Ush − µ1 + µ3 ∂Xsh ∂L : Xsh ∂µ3 µ3 Xsh ∂L : µ1 A(M P As ) − λpc A(M P Ac ) + µ5 − µ6 ∂θ ∂L :θ ∂µ5 ∂L : (1 − θ) ∂µ6 µ5 θ = 0 ∂L : µ1 M P Ls − λw + µ7 ∂Ls ∂L : Ls ∂µ7 µ7 Ls

10

= 0

(19)

≥ 0

(20)

= 0

(21)

= 0

(22)

≥ 0

(23)

= 0

(24)

= 0

(25)

≥ 0

(26)

= 0

(27)

= 0

(28)

≥ 0

(29)

≥ 0

(30)

& µ6 (1 − θ) = 0

(31)

= 0

(32)

≥ 0

(33)

= 0

(34)

Equation 19 indicates that if a farmer is not buying the market good Xm , the monetized value of the marginal utility from consuming it must be less than or equal to the market price and TC (i.e.

M Um λ

= pm (1 + tb ) −

µ4 λ ).

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.

M Ui M Uj

=

pi pj ),

and the value of marginal product of land across crops (i.e. pi M P Ai = pj M P Aj ). However, these conditions take the following forms in the current model (by Equations 19, 25 and 28): M Ush M Um

=

pc M P Ac

=

µ1 − µ3 , λpm (1 + tb ) − µ4 µ1 M P As , when θ > 0. λ

(35) (36)

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For farmers who produce subsistence crop and consume positive amounts of Xsh and Xm , µ3 and µ4 are equal to zero, hence

µ1 λ

takes the place of ps in the conventional optimality conditions. Given

this optimization rule, I define the “shadow price” of Xsh as follows: ρ≡

µ1 , λ

where µ1 is the marginal utility of having one more unit of Qs , and λ is the marginal utility of income.13 We can observe from Equation 35 that, holding everything else constant, the higher a farmer’s marginal utility from consuming the subsistence crop, the higher its shadow price. Equation 36 means that the farmer equates the value of marginal product of land cultivated with the cash crop to the “shadow value of marginal product” of land cultivated with the subsistence crop. We can interpret ρ as the money value of having one more unit of Qs for the household (Heckman, 1974). Let us compare this interpretation with the interpretation of shadow wage in the labor supply literature. The shadow wage is defined as ω =

µ λ,

where µ is the shadow value of household’s time

constraint, and λ is the shadow value of income. It represents the monetized value to the household of a one unit increase in total time endowment. Similarly, the shadow price represents the amount of additional income that would increase the household’s utility by the same amount as one more unit of subsistence crop production (holding the technology and inputs constant). The shadow price is conceptually the same as the one in de Janvry et al. (1991), however, the conditions under which it arises are different. In the current model, some farmers may not participate in markets even if TC band is not binding, if the non-market benefits of the subsistence crop are significant for them. I discuss the different classes of farmers as defined by KKT conditions in detail in Appendix A. I show that if a farmer is not producing any subsistence crop (i.e. θ∗ = 0) it must be the case that the “shadow value of marginal product” of land from subsistence crop is less than the value of marginal product of land from the cash crop. The same is true for the value of marginal product of labor. For these farmers it is not worthwhile to allocate resources to subsistence crop production because they do not value it as much, and/or they can buy a close substitute for it in the market (indicating that unobserved characteristics and non-market values are not significant for such farmers). It is not the shadow price per se, but how it compares to the market prices including TC under different cases of market participation (i.e. Xss > 0 or Xss = 0), that determines whether the farmer is constrained by the missing market or not. For farmers who have θ∗ > 0 and sell part(all) of their subsistence crop, the shadow price is equal to(less than or equal to) the market price (i.e. ρ = (≤)ps (1 − ts )), and we can safely use the market price to represent the value of this crop to these types of farmers. If, however, the farmer is consuming all of Qs at home (i.e. Xss = 0), the shadow h 13We can derive the same shadow price using the FOC for leisure: M Us = µ1 −µ3 . M Ul λw

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price is greater than or equal to the selling price he would get in the market, i.e.:14 ρ=

µ1 µ1 − µ2 ≥ = ps (1 − ts ). λ λ

(37)

µ2 is the shadow value of the non-negativity constraint for Xss and represents how much the farmer’s utility would increase if we relaxed that constraint by one unit. Given that this is a non-negativity constraint, µ2 is the utility the farmer would get if he could sell a negative amount, i.e. if he could buy an identical product in the market. Therefore, farmers constrained by the non-negativity constraint for Xss value the subsistence crop more than the market.15 The results of this model differ from the TC band model in the literature in two ways. First, the upper limit of the TC band depends on how costly it is for the farmer to find a close substitute for his domestic crop in the market (i.e. how substitutable market crop is for his own). Second, the lower limit of the TC band is higher for farmers who value their domestic crops highly (i.e. representing a smaller degree of substitutability due to non-market values of the domestic crop). Figure 1 on the next page demonstrates how allowing for imperfect substitution affects the traditional TC band model using the graphical presentation in Taylor and Adelman (2003). I use indigenous identity (I) as an indicator for non-market values attached to domestic (subsistence) crop, that is one of the demand shifters in the utility function. I assume that the degree of substitutability between domestic crop and market crop is lower for farmers with I = 1. This is manifested in higher transaction costs for buying a substitute for the domestic crop in the market. In the upper panel, a farmer with I = 0 will produce Qs and buy maize equal to the difference between demand and supply of domestic maize (i.e. Xs − Qs ) at the market price pm and the unit transaction cost tb . However, a farmer with I = 1 will not buy at the given prices if the transaction costs associated with finding a good substitute for domestic good are higher. This is represented by the wider TC band with the bold dashed upper limit. Holding the observable TC constant, we may observe that some farmers (I = 1) do not buy this crop in the market even though it seems like they face the same TC as others who buy in the same community. Farmers who have higher unobserved TC will start buying in the market only if the market price and/or observable TC were lower than p0m (1 + tb ), corresponding to a lower market price p0m . Therefore, the “inelastic response” of farmers to market signals may be observed more than what the traditional TC band model would suggest.

14For this group of farmers µ ≥ 0 and µ = 0. See Appendix A for details. 2 3 15Rewriting the Equation 15 on page 9 as µ2 = µ1 − p (1 − t ) provides more intuition about this constraint (all s s λ λ

terms in this equation are monetized). The monetized value of relaxing the non-negativity constraint by one unit is equal to the subjective value of one more unit of production using the same inputs minus the market value of that crop. Hence the conclusion that the shadow price is greater than or equal to the market price for farmers who do not sell any subsistence crop given market prices and TC.

SHADOW PRICES OF TRADITIONAL MAIZE

13

$ Maize Supply pm(1+tb) (I=1) pm'(1+tb) (I=1) pm(1+tb) (I=0) Buy if I=0 pm' ps(1-ts)

Maize Demand Qs

Xs

Xs

$ Maize Supply

pm(1+tb)

ps'(1-ts) (I=1) ps(1-ts) (I=0)

Sell if I=0

Maize Demand (I=1) Maize Demand (I=0) Xs

Qs

Xs

Figure 1. Transaction cost band and imperfect substitutability in consumption due to nonmarket values of domestic crop. First panel shows the wider TC band for I = 1 as opposed to the TC band for I = 0. Second panel shows the higher selling price required to enter the market by farmers with I = 1.

The lower panel of Figure 1 depicts the demand for maize by two farmers, one with I = 0 and the other with I = 1. The higher valuation of subsistence crop by the indigenous farmer is represented by the higher willingness to pay for the same amount of domestic maize. Given the market price ps and transaction costs for selling in the market (ts ), the farmer with I = 0 will produce Qs and sell the difference between Qs and Xs . Even though the indigenous farmer is facing the same transaction

SHADOW PRICES OF TRADITIONAL MAIZE

14

costs, he will not sell at these prices because his subjective valuation is higher than the market price. He will start selling only if the selling price minus TC is above p0s (1 − ts ). For farmers within the TC band defined as above, production decisions are affected by µ1 and λ, which depend on household characteristics that would not affect production under perfect markets. We can interpret the decision criteria for optimal labor allocation of a farmer who produces some subsistence crop (i.e. µ5 = µ6 = 0) using the Equation 17: µ1 M P Ls = λw

(38)

The left hand side of Equation 38 represents the marginal benefit the farmer receives (in utility terms) from allocating the last unit of labor into the production of subsistence crop. The right hand side represents the marginal cost of that last unit of labor in utility terms.16 Although µ1 and λ are not observable, we can define an estimable expression for ρ as follows: ρ≡

w µ1 = . λ M P Ls

(39)

As we can see from Equation 36 and Figure 2 on the following page, the land allocated to the subsistence crop by a subsistence farmer depends on (and increases with) its shadow price. Ignoring shadow prices and using market prices to value the subsistence crop would make farmers seem to allocate “irrationally” high amounts of land to this crop. However, by capturing the non-market values associated with subsistence crop, shadow prices can explain the rationality of farmers’ behaviour. Therefore, using estimated shadow prices in econometric analysis is likely to improve our models of land allocation by subsistence farmers. Given the Equation 39 and using an empirical method similar to Jacoby (1993) and Skoufias (1994), we can econometrically estimate household-specific shadow prices by estimating the production function to derive the marginal product of labor for each household. We can also test whether shadow prices are statistically different from market prices and empirically analyze the determinants of this difference. Moreover, using shadow prices instead of market prices for non-market producers can improve our analyses of farmers’ crop choice and land allocation decisions, as well as help us explore farmers’ incentives to cultivate traditional crops associated with on-farm conservation of genetic diversity. In the next section, I estimate production functions and calculate the household specific shadow prices using the estimated marginal product of labor. I test whether the estimated shadow prices are statistically different from market prices, using the test for separability in Jacoby (1993) and conclude that shadow prices are significantly higher from market prices for subsistence farmers of traditional 16λ is the marginal utility of income and it is multiplied with the wage the farmer pays for labor.

SHADOW PRICES OF TRADITIONAL MAIZE

VMPA s

15

VMPA c VMPA s = *MPA s

VMPA c = p c *MPA c

VMPA s = p s *MPA s

0


*


0

A=1

Figure 2. Optimal land allocation using market prices vs. shadow prices for subsistence crop. θ ∗ is the proportion of land that would be allocated to Qs using the market price (ps ) and θ0 is the proportion of land that is allocated to Qs using the shadow price (ρ).

maize. Then, I proceed with the analysis to identify regional patterns for shadow prices of traditional maize and the determinants of the difference between shadow and market prices in rural Mexico.

4. Estimation and Decomposition of Shadow Prices 4.1. The Data. I use agricultural household data from the Mexican National Rural Household Survey (ENHRUM) that was collected in January-February 2003. This data set covers 1782 households in 16 villages of each of the 5 geographic regions in Mexico, and it is designed by the National Institute of Statistics, Geography and Informatics (INEGI) to be nationally representative of rural Mexico.17 The following is a non-exhaustive list of the variables included in the survey: household demographics; plot level information on land, labor, fertilizer, animals and machinery used for agricultural production in 2002; total production; marketing and consumption of products; maize diversity; migration history; off-farm income sources; credit market participation and other assets.18 The survey covers all agricultural activities in two crop cycles (Spring-Summer and AutumnWinter) during 2002. There are 573 households who cultivated at least some maize on 897 plot-cycles, 73% of which are in the South-Southeast and Central regions. The input data is collected at the plot level, which makes the estimation of a production function for maize difficult for plots with multiple crops. Therefore, in what follows I use a subsample of the plots that are cultivated only with 17

See Appendix B for geographical distribution of the ENHRUM sample and maize landraces in Mexico. For more details on the ENHRUM data see: http://precesam.colmex.mx.

18

SHADOW PRICES OF TRADITIONAL MAIZE

16

maize, which constitutes 25% of all plots, 63% of all maize plots and 67% of maize growing households in the sample.19 86% of the plots used in this subsample are cultivated with traditional maize (Table 1).20 The differences across regions in terms of traditional maize cultivation are informative. South-Southeast Region includes the poorest states in Mexico with high indigenous population and 92% of the plots in this region are cultivated with traditional varieties. On the other hand, Northwest Region includes states with higher GDP per capita, large scale farming and industrial production (Chiquiar, 2005), where only 15% of plots are cultivated with traditional maize. Table 1. Percentage of plots under different maize types by region

% of Maize types Region MV TV South-Southeast 8 92 Central 7 93 Western Cent. 22 78 Northwest 85 15 Northeast 20 80 Total 14 86 Table 2 on the next page demonstrates the differences between regions using some variables related to households’ socio-economic status. We can see that households in the South-Southeast and Central Regions have lower wealth indices, own less land that is mostly not irrigated and are more likely to belong to an indigenous community.21 They also have less farm income and sell only very small percentages of their total maize production. In the whole sample, 74% of households did not sell any maize in the market, and this proportion increases to 80% for households that grow traditional maize. Given that maize production is seen as a traditional subsistence activity rather than a business among small scale farmers, market prices are likely to fail to represent the value of maize to them. We can expect that the household specific shadow prices of TVs would be higher than market prices capturing the non-market benefits farmers receive from them. If this is true, identifying the observable characteristics of farmers with higher likelihoods to maintain TVs will prove useful in targeting onfarm conservation programs. In the next section, I estimate production functions for TVs and MVs to 19

I test whether some key variables that affect households’ production and preferences differ significantly between the sub-sample and the whole sample in my dissertation. I conclude that the subsample I use in the empirical analysis is not statistically significantly different from the whole sample. 20 Classification of maize into distinct varieties is problematic due to the open pollinated nature of maize (Bellon et al., 2006). I use farmer definitions to classify maize into traditional and improved varieties. I use traditional maize (TV) to refer to maize identified as “criollo” by the farmer. I use the term modern maize (MV) to refer to maize identified as “h´ıbrido.” 21Wealth index is a variable created using Principal Component Analysis based on the characteristics of households’ primary residence, access to utilities, and ownership of a television and refrigerator. I report the quintiles of the wealth index to give an idea of the distribution of wealth in the sample.

SHADOW PRICES OF TRADITIONAL MAIZE

17

Table 2. Means of household characteristics by region

South-Southeast Central Western Cent. Northwest Northeast Total

Wealth Index (q-tile)

Education (years)

1.63 2.03 3.46 4.85 2.95 2.28

3.72 3.43 2.7 4.54 4.65 3.6

Total land owned (ha.) 6.71 1.74 8.37 21.43 61.73 10.93

Irrigated land (%) 9.57 21.06 17.21 61.54 7.09 15.85

Indigenous % 0.74 0.29 0.02 0 0.03 0.4

Total farm inc. ($MX) 2,105 7,572 12,705 124,596 8,260 9066.55

Maize sold (%) 0.09 0.07 0.31 0.83 0.13 0.14

derive shadow prices, test whether they are different from market prices for these two types of maize and investigate socio-economic and agro-ecological variables correlated with shadow prices. 4.2. Estimating production functions and shadow prices of maize. The production technologies of MVs and TVs are different. MVs require irrigation and regular application of fertilizers and pesticides, whereas TVs are usually grown on rain-fed land with little or no fertilizers. TVs are seen as more resistant to pests and diseases during storage, which makes them preferable for subsistence farmers who save their own seed (Bellon et al., 2006). Some of these differences can be observed in Table 3 on the following page. There is a three-fold difference between the yields of the two types of maize. TVs are produced on smaller plots, with more labor, less fertilizer and less investment. 69% of traditional maize plots are cultivated with saved seed, as opposed to 13% of modern maize plots. Estimating production functions for TVs and MVs can cause selection bias if there are some unobservable variables that affect both farmers’ crop choice and productivity (Vella, 1998). I check whether there is selection bias using the two step Heckman procedure and conclude that selection is not significant for either maize variety. Therefore, I report the results that do not control for selection. Farmers who produce maize exclusively for home consumption and those who produce it commercially may differ in terms of their production practices. I define commercially oriented farmers as those who sold more than 30% of their maize in the survey year (% 27 of maize farmers). A quick look at the differences between commercial and non-commercial farmers in terms of main inputs shows that the differences in their use of labor, animal traction and the slope of their plots are statistically significant (Table 4). Given this difference, we may consider using a dummy variable to identify commercial farmers in our production function estimations. However, if there are any unobserved variables that are correlated with this dummy and the yield per hectare, we may have endogeneity bias in our regressions. For example, farmers who are open to innovation (an unobserved variable) may be more likely to be commercially oriented and they may also be more likely to engage in different management practices

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Table 3. Summary statistics for plots cultivated with TV and MV Variable name yieldpha noryieldpha land seedpha irrigD soilq slope droughtD m1400 walktime famlabpha hirelabpha totlabpha machpha animpha fertpha pestpha inpcostpha investpha ownseedD N

Definition TV MV Yield (kg./ha.) 875.71 2821.24 Yield in a normal year 1471.31 3914.08 Plot area (ha.) 1.94 3.41 Seed amount/ha. 19.36 21.77 Irrigation dummy 0.11 0.37 Soil quality (1: Bad, 2: Regular, 3: Good) 2.33 2.20 Slope (1: Plain, 2: Sloped, 3: Very steep) 1.55 1.41 Drought dummy 0.33 0.39 Plot is > 1400 masl. 0.76 0.63 Walking time from the parcel to the community 39.04 38.41 center (mins.) Total family labor (days/ha.) 49.53 34.43 Total hired labor (days/ha.) 9.29 4.65 Total labor (days/ha.) 58.93 39.08 Total machinery hours/ha. 6.42 25.03 Total animal hours/ha. 15.62 7.53 Fertilizer cost/ha. 354.67 497.83 Pesticide cost/ha. 119.40 997.63 Total input cost/ha. 474.83 642.25 Total investment in plot ($MX/ha.) 73.84 365.94 Used own seed (%) 0.69 0.13 Number of observations 476 75

Table 4. Differences in input uses between commercial and non-commercial farmers

Sold more Labor than days/ha 30%? No 62.33 Yes 24.80 Difference 37.53∗

Seed kg/ha

Machinery hrs/ha

Animal hrs/ha

Soil quality

Slope

19.89 18.68 1.21

4.39 4.84 -0.45

16.36 5.18 11.18∗

2.31 2.31 0

1.57 1.33 0.24∗

∗

Indicates that the difference between the means of two groups is statistically significant at %10 level using a t-test.

that affect their yield. In this case the unobserved “innovativeness” variable will result in bias in the estimated coefficients. Therefore, I estimate production functions controlling for the possible endogeneity of the commercial farmer dummy. I use two different methods to control for endogeneity: two-stage least squares (2SLS) regressions with instrumental variables (IV) and two-step IV regressions with a probit model in the first step. Two-stage least squares estimation uses a linear probability model with instruments in the first step. The predicted values of the endogenous variable are then used to estimate the second stage regression. Because the first step in our model is a binary variable, we can also use a two-step IV estimation that uses a probit model in the first step. Although using a probit model for the first step may seem more

SHADOW PRICES OF TRADITIONAL MAIZE

19

intuitive when the endogenous variable is binary, this model depends on the normality assumption that may not be true in reality. Angrist (2000) shows that linear probability model is consistent regardless of whether the first stage is linear or not, and claims that “it is safer to use a linear first stage.” I use both methods to compare the results and check the robustness of the production function estimations (Table 5). The regression standard errors are clustered at the Rural Development District (DDR) level to correct for potential error correlation due to unobserved characteristics that are common to all households within a DDR.22 Because households have different number of plots in the data set, I weighted the observations using the reciprocal of the square root of the number of plots for each household, to ensure equal representation. Table 5. Production functions controlling for the endogenous dummy for commercial maize producers (Dep. var: ln(yieldpha)) IV(2SLS+Linear Prob.)†† Variables TV MV ∗∗∗ ln(land) -0.307 -0.17 ln(totlabpha) 0.178∗ 0.232∗ ln(seedpha) 0.194∗∗ 0.676∗∗ ln(inpcostpha) 0.121∗∗∗ 0.075 ln(machpha) 0.15 0.655∗∗ ln(animpha) 0.029 0.062 droughtD -0.084 -0.755∗ soilq† 0.300∗∗∗ 0.218 slope† 0.051 -0.617∗∗ irrigD 0.425 0.525∗∗∗ m1400 -0.036 -1.026∗∗∗ age -0.008 -0.030∗ educ -0.043 -0.05 South-Southeast -0.737 -0.401 Central -0.559 -1.287∗∗ Western Central -0.443 -0.422 sold30 0.727 0.304 Constant 5.452∗∗∗ 5.684∗∗∗ Observations 425 66

IV(probit)†† TV MV ∗∗∗ -0.317 -0.180 0.189∗ 0.215 0.196∗∗ 0.661∗∗ 0.117∗∗∗ 0.071 0.162∗ 0.650∗∗ 0.033 0.053 -0.079 -0.750∗ 0.298∗∗∗ 0.227 0.062 -0.624∗∗ 0.405 0.530∗∗∗ -0.044 -1.026∗∗∗ -0.008 -0.030∗ -0.044 -0.050 -0.739 -0.390 -0.58 -1.240∗∗∗ -0.487 0.430 0.931 0.333 5.427∗∗∗ 5.755∗∗∗ 425 66

Significance levels: ∗ : 10% ∗∗ : 5% ∗ ∗ ∗ : 1% † Soil quality and slope variables are rescaled to (-1,0,1) to prevent unnecessary imposition of a cardinal meaning to categorical variables. †† The

following instruments are used in the first step: the percentage of village maize production sold, the time it takes to go to the community center, dummy variables that identify whether the farmer had any off-farm income from Mexico or US in 1980.

22Rural Development Districts are districts defined by SAGARPA (Secretary of Agriculture, Ranching, Rural Devel-

opment, Fisheries, and Food Supply) that have similar production potentials. See http://www.cem.itesm.mx/derecho/ nlegislacion/federal/35/index.html, Capitulo 6, 7 and 8.

SHADOW PRICES OF TRADITIONAL MAIZE

20

The percentage of village maize production sold in the market may affect whether a farmer is commercially oriented through network effects or through its effect on the village market structure. However, this variable should not effect productivity except through its effect on the commercial farmer dummy. Community centers are usually where markets are, hence the time it takes to go there may be correlated with the commercial farmer dummy, but it should not effect productivity directly. Even if there is no market at the community center, this variable can instrument for access to information about marketing opportunities that may be correlated with the commercial farmer dummy. Historical off-farm income and migration variables may be correlated with the commercial farmer dummy if living in a village where a lot of households have off-farm employment and/or temporary migrants to the US affect farmers’ attitudes towards selling their maize or their ability to do so. However, these variables are far enough back in time that they are predetermined and should not affect the current productivity. I test the validity of these instruments using a number of tests reported by Stata’s ivreg2 command (Table 6). Table 6. Tests for the validity of instrumental variables used in the IV-2SLS model (p-values reported) Tests TV MV Underid. test: H0 =Eqn. is underidentified Anderson canonical correlation 0.009 0 Overid. tests: H0 =Overid. restrictions are valid Hansen J Statistic 0.41 0.25 Anderson-Rubin F-test 0.27 0.69 Anderson Canonical Correlations test strongly rejects the hypothesis that the equation is underidentified.23 Overidentification tests fail to reject the hypothesis that the instruments are valid, i.e., uncorrelated with the error term and correctly excluded from the production function equation.24 Therefore, I conclude that the instruments are valid. All of the estimated input elasticities are positive as expected. There are some notable differences between the production functions for TVs and MVs. There are significant decreasing returns to scale to land for TVs but not the MVs. Drought, slope and elevation are correlated significantly and negatively with per hectare productivity of MVs, but the correlation is not significant for TVs. This suggests that, holding everything else constant, TVs are more resilient to sub-optimal growing conditions. 23The Anderson canonical correlations test is a likelihood-ratio test of whether the equation is identified, i.e., that the

excluded instruments are “relevant,” meaning correlated with the endogenous regressors. 24Hansen J statistic tests the joint null hypothesis is that the instruments are valid instruments, i.e., uncorrelated with the error term, and that the excluded instruments are correctly excluded from the estimated equation. Under the null, the test statistic is distributed as chi-squared in the number of overidentifying restrictions. Anderson-Rubin statistic is a Wald test that is distributed as chi-squared with L2 degrees of freedom, where L2 is the number of excluded instruments.

SHADOW PRICES OF TRADITIONAL MAIZE

21

Given Angrist’s suggestions (Angrist, 2000) and the fact that the coefficients do not differ across specifications, I use the labor elasticities estimated by the 2SLS method to calculate the marginal product of labor (MPL).25 Using the estimated marginal product of labor and wages in the formula for shadow prices (i.e. ρˆa =

w ), Mˆ PL

I calculate the shadow prices of traditional maize for each farmer.26

Table 7 summarizes shadow prices for sellers and non-sellers of maize by different varieties. Table 7. Summary statistics for estimated shadow prices and observed market prices

Variable TV MV Shadow price for full sample 48.34 13.77 Shadow price for sellers 20.50 5.19 Shadow price for non-sellers 58.18 25.53 Observed market price/kg. 1.98 1.57 As we can see from Table 7, estimated shadow prices for TVs are higher than those for MVs, and they are higher for non-sellers for both varieties. We can also observe that the average village level market price is lower than the shadow prices for all groups. The difference between market prices and estimated shadow prices is very big, which essentially stems from the fact that farmers are using too much labor as compared to the optimal level that can be justified by market prices. Very high shadow prices indicate that the marginal value of using one more hour of labor for maize production exceeds the marginal value of leisure (or of other uses of labor) at the optimal point implied by market prices. Therefore, farmer uses labor until its value of marginal product equals the wage rate. It could be argued that because production is uncertain and farmers are risk averse, they apply more labor to production to hedge against down-side risk. If this is the case, we would observe the estimated difference between the shadow prices of TVs and MVs only if TVs were more risky. However, in this case farmers would adjust their portfolio and switch to MVs if TVs were not valued more. Therefore, the high levels of observed labor use can be attributed to higher subjective valuation of landraces by farmers – especially for non-sellers. Smale (2005) also argues that labor to land ratios explain where landraces are still grown and will continue to be grown. A high labor to land ratio corresponds to a high shadow price in the current model confirming this statement. To test whether the estimated shadow prices are statistically significantly different from market prices, I use the method in Jacoby (1993) and Skoufias (1994). I run the following regression for sellers 25The coefficients of the production function are input elasticities given by β ˆ = ∂Q L . The MPL of labor is then ∂L Q

calculated by M P L = βˆ Q as in Jacoby (1993) and Skoufias (1994). L

26This formula essentially assumes that the labor market is perfect for the households in the sample, because it uses

market wages to value their time. I have tested this assumption by estimating production functions with family labor and hired labor separated. I calculated the shadow wages for family labor and ran the test of separability as in Jacoby (1993) for farmers who sold some of their product in the market. I fail to reject the separability hypothesis and conclude that shadow wages are not significantly different from market wages, hence use the market wage to value households’ time.

SHADOW PRICES OF TRADITIONAL MAIZE

22

and non-sellers of both TVs and MVs: ρˆ = α + βp + u, to test the null hypothesis of α = 0,

(40)

β = 1. Under the null, the market prices reflect the value

of marginal product of labor to farmers, hence we can use the market prices to value farmer’s product. Rejection of H0 indicates that market prices do not reflect the subjective value of that crop to farmers and one should use estimated shadow prices to better understand farmer behavior. I estimate Equation 40 using weighted least squares estimation using the same weights as in production function estimations. I also use village level clusters to control for possible error correlation between the farmers in the same village. Table 8 summarizes the results of F-tests and t-tests to test the null hypothesis. Table 8. Summary of test results: Are estimated shadow prices equal to observed market prices?

Seller F-test t-tests Non-seller F-test t-tests

MV α ˆ βˆ -1.94 5.22 (0.17) (0.83) (0.44) -15.03 40.10 (0.17) (0.77) (0.41)

TV α ˆ βˆ 21.08 0.70 (0.00) (0.38) (0.97) 52.95 2.62 (0.00) (0.06) (0.89)

(p-values in parentheses)

For MVs, we fail to reject the null hypothesis of equality of shadow and market prices with both tests regardless of whether the farmer sold maize or not. This may be explained by the fact that MVs lack the non-market values attached to maize landraces. Maize seed that has been bought “in a bag” does not possess the attributes of landraces that have been evolving with farmer selection and are intertwined with their culture. For sellers of TVs, the F-test rejects the joint hypothesis, however, the individual t-tests fail to reject the equality of shadow and market prices. We can conclude that although the average estimated shadow price for sellers of TVs is higher than market prices, this difference is not statistically significant, hence we can use market prices to represent the value of domestic maize to a farmer who is selling it in the market. For non-sellers of TVs, however, both F-test and t-tests reject the hypothesis that the estimated shadow prices are not different from market prices. The estimated shadow prices are statistically significantly higher than market prices as indicated by α ˆ that is significantly different from zero at 6% level. Using market prices to understand the cropping decisions of subsistence farmers, therefore, may

SHADOW PRICES OF TRADITIONAL MAIZE

23

lead to “puzzling” results where these farmers seem to act “irrationally” by allocating more resources to maize production than can be justified by market prices. Moreover, subsistence farmers are isolated from market price shocks because their decisions are based on shadow prices, hence may exhibit an inelastic supply response. Given that we concluded that the wedge between farmer-specific shadow prices of TVs and market prices is statistically significant, next step is to understand which socio-economic and agro-ecological variables are correlated with this wedge. This will provide important policy implications for conservation of the genetic diversity embedded in TVs. Conservation programs can concentrate on the key variables that are correlated with the wedge between market and shadow prices to more efficiently allocate resources to on-farm and off-farm conservation. We can also better understand how different groups of farmers may/may not respond to changes in market prices. I analyze farmer- and farm-specific characteristics that may be correlated with estimated shadow prices in the following section. 4.3. What predicts high shadow prices? The theoretical model developed in Section 3 shows that the shadow price depends on household characteristics (though preferences and endowments), plot characteristics and indicators of market access. Table 9 summarizes the estimated shadow prices and sample means of some socio-economic and market access variables for the non-sellers of TVs by region. South-Southeast region has the highest estimated shadow prices and highest percentage of indigenous farmers. This region also has lowest levels of wealth and off-farm income as compared to other regions. Most farmers in Northwest and Northeast regions have some kind of off-farm income and they have the smallest shadow prices for TVs. There seems to be a negative correlation between wealth, off-farm income and the farmers’ subjective valuation of TVs according to unconditional means. Table 9. Sample means of socio-economic and market access variables by region

Region South-Southeast Central Western Cent. Northwest Northeast Total

ρˆ wqtile indig. totown offarmD ownseed TC/kg 84.95 1.50 0.72 6.51 0.38 0.69 0.00 34.25 2.06 0.26 1.70 0.50 0.75 0.02 56.72 2.95 0.02 9.21 0.47 0.36 0.00 0.18 4.75 0.00 8.88 0.75 0.25 0.00 20.05 2.88 0.00 72.81 0.63 0.40 0.01 58.18 2.07 0.38 11.9 0.46 0.63 0.01

More farmers in the Southern and Central regions use their own seed, which seems to be correlated with high shadow prices. It is not surprising that if a farmer is diligent in saving and taking care of his seed, he would attach non-market values to his maize that would set own-produced maize apart from

SHADOW PRICES OF TRADITIONAL MAIZE

24

purchased maize as indicated by high shadow prices. The last column summarizes the transportation costs per kilogram paid by farmers to buy/sell maize. These costs are very small and cannot justify the high estimated shadow prices. Table 9 may provide some intuition into the relationships between shadow prices and the variables considered. However, this table demonstrates only unconditional means without controlling for other variables, hence is just descriptive. I use the difference between shadow and market prices to econometrically analyze the key factors that are correlated with shadow prices. There is one issue one needs to consider before running regressions of estimated shadow prices on various explanatory variables. The fact that ρˆ is not observed directly but estimated with error introduces an additional source of variance to standard errors of the estimation with ρˆ as a regressand. The test statistics will not be valid unless the standard errors are corrected (Dumont et al., 2005). I use bootstrapping method to correct for this bias (Cameron and Trivedi, 2005). The theoretical model in Section 3 indicates that shadow prices depend on variables that affect farmers’ production and preference shifters in their utility functions. Using the Equation 39 on page 14 we can express the estimating equation for shadow price decomposition as follows: ρˆn = f (Pp , Zn ) + un . P is a vector of plot characteristics that affect production, Z is a vector of preference shifters, and p and n are indices for plots and farmers respectively. These vectors also include some market access variables that may affect production practices or preferences. I use the variables from previous studies that are shown to affect farmers’ crop choice decisions and their valuation of traditional crops (Bellon and Smale, 1998; Van Dusen, 2000; Meng, 1997; Brush and Meng, 1998; Smale, 2006). These variables are: wealth, gender, age, education, land size, animals owned, the share of maize area, migration, off-farm income, credit access, time to community center, government transfers, soil quality, slope, altitude, irrigation and regional controls. All of these variables have different correlations with on farm diversity in different settings as summarized in Smale (2006). One other variable often discussed in the literature that is correlated with cultivating traditional crops is indigenous identity. However, this variable is usually discussed in qualitative or descriptive studies but not used in econometric analyses (Brush and Perales, 2007; Perales et al., 2005; Preibisch et al., 2002). It is often mentioned that indigenous farmers attach various non-market values to maize (especially traditional varieties), which is one of the reasons why they continue cultivating it despite disincentives based on market prices. I include indigenous identity dummy as a preference shifter and test the following hypothesis implied by these previous studies:

SHADOW PRICES OF TRADITIONAL MAIZE

25

∂ ρˆ > 0, I = 1 if farmer speaks an indigenous language ∂I Regression results are given in Table 10, where standard errors are clustered by household and village to control for possible error correlation across different plots of a household, and across households in the same village. I use three different specifications: Column (1) uses only socio-economic variables that shape farmers’ preferences, Column (2) includes variables related to farmers’ market access in addition to socio-economic variables, and Column (3) includes an interaction variable between indigenous language dummy and South-Southeast region. This interaction variable controls for the fact that most of the indigenous farmers live in this region and the indigenous dummy may have a different effect there. Table 10. Bootstrapped results: Dep.var: (ˆ ρ − p) using ρˆ from IV-2SLS model (1) Variable Coef. (p) wqtile -2.99 (0.64) gender 35.47∗∗ (0.02) age -0.26 (0.68) educ -1.48 (0.63) totown -0.05 (0.97) totanimals 0.43 (0.25) maizareash 23.76 (0.31) bracerohh -16.11 (0.50) indiglang 25.76∗ (0.06) indigR1 othersoffD otherscredit walktime govprogs soilq slope m1400 irrigD South-Southeast 41.98 (0.15) Central -1.46 (0.96) Western Cent. 44.81 (0.12) Northwest 18.72 (0.52) Constant -10.8 (0.87) N 314 Significance levels:

∗ : 10%

∗∗ : 5%

(2) Coef. -2.83 35.73∗∗ -0.17 -1.1 -0.09 0.39 17.53 -17.62 26.57∗ 35.91 -18.99 0.34∗ 0.83 -33.52∗∗ -4.42 -22.06 -39.77∗∗∗ 50.33 15.73 51.89∗ 71.81 -13.66 314

(p) (0.66) (0.02) (0.76) (0.71) (0.94) (0.30) (0.46) (0.40) (0.06) (0.18) (0.53) (0.07) (0.95) (0.01) (0.68) (0.20) (0.01) (0.11) (0.62) (0.09) (0.13) (0.84)

(3) Coef. -2.91 28.37∗∗ -0.19 -0.75 -0.08 0.38 11.41 -20.14 -7.24 77.20∗∗∗ 31.57 -22.01 0.27

(p) (0.63) (0.04) (0.73) (0.80) (0.94) (0.30) (0.63) (0.33) (0.54) (0.00) (0.23) (0.47) (0.17)

-33.05∗∗ (0.01) -9.73 (0.38) -24.72 (0.13) -33.05∗∗ (0.01) 16.66 (0.57) 23.23 (0.46) 50.45∗ (0.10) 51.68 (0.21) 6.46 (0.92) 314

∗ ∗ ∗ : 1%

Previous empirical studies find that wealth, household head’s education and household size are positively correlated with on farm diversity (cultivation of landraces) (Smale, 2006). Bellon and Taylor (1993) find that household wealth and household head’s age are negatively correlated with maize

SHADOW PRICES OF TRADITIONAL MAIZE

26

landrace cultivation. However, holding everything else constant, these variables are not significantly correlated with farmer-specific shadow prices of maize landraces in the current sample. In all three specifications, male farmers value TVs higher than females. This suggests that among the non-market values, the value of being a good farmer and preserving the family seed may be more important than the consumption characteristics (e.g. culinary superiority) women tend to care more about. In addition to wealth, two other variables related to farmers’ endowments are total area and number of animals owned. Both of these variables have no significant correlation with shadow prices. The percentage of total land area that is cultivated with TVs may indicate preferences towards TVs, hence high shadow prices. Controlling for other variables, however, maize area share is not correlated with shadow prices. It has been argued that migration to US is a detriment to on farm conservation of maize landraces in Mexico (Nadal, 2000; Turrent and Serratos-Hernandez, 2004). The bracero variable identifies households that have at least one member who participated in the Bracero Program in the past.27 If migration affects households’ preferences by shifting preferences towards market goods, we might expect that households with migration histories will have a lower valuation for TVs. Although the bracero variable has a negative coefficient, it is not significant in any of the specifications. Another variable often found to affect farmer’s likelihood of cultivating landraces in the literature is belonging to an indigenous group (Turrent and Serratos-Hernandez, 2004; Perales et al., 2005; Brush and Perales, 2007). The coefficient on the indigenous language dummy is significant and positive in the first two specifications. This indicates that non-market values of TVs captured in shadow prices are higher for indigenous farmers, which underlines their role as stewards of genetic diversity. Given that 78% of indigenous farmers in the current sample (i.e. non-sellers of TVs) are in the South-Southeast region, we may wonder whether the coefficient of indigenous language dummy is picking up the effect of the South-Southeast regional dummy. To test whether being indigenous has a different effect in this region, I include an interaction variable between indigenous language dummy and South-Southeast region in column 3. The coefficient of this interaction term is very big and significant, and the indigenous language dummy loses its significance after its inclusion. This suggests that, controlling for other variables, being indigenous does not have an effect on shadow prices in other regions. However, it has a very strong and significant effect on farmers’ valuation of maize landraces in South-Southeast region. Four variables represent market access: the percentage of farmers in the village that have-off farm income, the percentage of farmers in the village that have some kind of credit, the time it takes for the farmer to go to the community center and a dummy variable indicating whether the farmer receives any

27The Bracero Program was created by the governments of Mexico and the US to bring legal agricultural workers to

the US. The program started in 1942 and lasted until 1964 which brought around 4 million “braceros” to the US.

SHADOW PRICES OF TRADITIONAL MAIZE

27

government transfers.28 Government transfers could potentially alleviate the effect of credit market imperfections by relaxing farmers’ liquidity constraint. Neither this variable, nor the credit market and off-farm income variables are significantly correlated with shadow prices. The results indicate that farmer valuation of TVs does not decrease with improved access to off-farm labor, credit and other markets, which restores hopes for de facto conservation of maize landraces in the face of improved market access. Previous studies mostly find that the transaction cost of going to the nearest market is negatively correlated with on-farm diversity (Bellon and Taylor, 1993; Meng, 1997; Van Dusen, 2000; Smale et al., 1994). Time it takes for the farmer to go from his/her plot to the community center is a proxy for transaction costs. This variable is significantly correlated to shadow prices only in one specification (column 2), however its significance disappears when we include the interaction term (column 3). This indicates that indigenous farmers in South-Southeast region farm in more isolated places, therefore controlling for this group of farmers makes the time to community center variable insignificant.29 For the rest of the farmers, shadow price is independent of how far away from community center their plots are. ENHRUM data includes farmer reported costs of transportation incurred to buy and/or sell maize in the market. The average transportation costs paid by farmers in the sample is negligible (0.01 Pesos per kilogram of maize) and they cannot justify high shadow prices observed. This confirms the theoretical point that if some farmers have different preferences toward domestic maize and market purchased maize, they may make decisions based on shadow prices rather than market prices even if observable TC do not constrain them. Soil quality, slope, irrigation and altitude are agro-ecological variables that affect growing conditions and productivity of both TVs and MVs. Bellon and Taylor (1993) find that cultivation of TVs in Mexico is negatively correlated with high soil quality. I find that soil quality is negatively and significantly correlated with farmers’ subjective valuation of TVs confirming their finding. Similarly, irrigation is negatively and significantly correlated with shadow prices, indicating that farmers who have better growing conditions value TVs less. Perales et al. (2003) finds that altitude is positively correlated with the cultivation of maize landraces in Mexico. Even if it is not significant in the current model, this does not necessarily contradict Perales et al. (2003). Altitude may make a farmer more likely to cultivate TVs, but given that a subsistence farmer is already cultivating them, his subjective valuation (i.e. incentives to cultivate TVs) does not depend on altitude.

28The first two variables exclude the farmer himself/herself to remove potential endogeneity of these variables. 29The difference in walktime variable between the indigenous farmers in this region and the rest of the farmers is

statistically significant at 1% level using a t-test.

SHADOW PRICES OF TRADITIONAL MAIZE

28

In summary, four variables are significantly correlated with farmer-specific shadow prices of TVs that are over and above observed market prices. Farmers who have plots with good soil quality and irrigation have lower shadow prices, whereas male farmers have higher shadow prices. The most important indicator of high shadow prices is being an indigenous farmer in the South-Southeast region. Controlling for other farmer and farm variables, indigenous identity increases the demand for TVs causing higher de facto incentives for their continued cultivation. There are important policy implications of these results. Programs for on-farm conservation of genetic diversity of maize in Mexico will be more cost effective if targeted at communities with indigenous populations where de facto conservation is more likely. These areas represent least-cost conservation opportunities as defined by Bellon and Smale (1998) where both the public value of diversity and the private incentives to conserve them are high. These results agree with previous research that emphasizes the preservation of traditional agroecosystems to ensure the on-farm conservation of traditional crop varieties (Altieri, 2004; Louette et al., 1997; Peterson, 2000). Rural development policies in areas where indigenous identity is strong could be accompanied with programs to raise awareness such as diversity fairs to strengthen the incentives to maintain traditional varieties. More resources may be needed to maintain TVs on-farm in regions where the indigenous identity is not strong, irrigation projects are being developed or programs to improve soil quality exist. The potential negative effects of such projects on traditional maize cultivation in areas of diversity can be counteracted with additional programs to increase farmers’ incentives to maintain traditional varieties, such as conservation payments, or programs to create niche markets to increase the market value of traditional maize varieties. These policies may also improve farmers incentives in areas where de facto incentives to maintain TVs are low. However, a more effective way of allocating conservation budgets in such low-incentive areas may be prioritizing off-farm conservation rather than on-farm conservation. Most previous research finds a positive correlation between on farm diversity of landraces and household wealth (Smale, 2006). These findings suggest that conservation policies should target wealthier households to have better results. However, there is no correlation between households’ wealth and their shadow prices for TVs in the current analysis. Given that there is no tradeoff between wealth and shadow prices of TVs in rural Mexico, conservation policies should not be targeted based on wealth but should consider the non-market values of TVs for indigenous people in marginal growing environments. This finding does not necessarily contradict with previous studies. It can be the case that, controlling for other variables – especially indigenous identity – wealth does not affect subjective valuation of landraces in general, but the number of varieties cultivated may be correlated with wealth given a household already cultivates landraces. Even though wealthier farmers may be associated with

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29

greater on-farm diversity, we cannot really say anything about their incentives to maintain those varieties without understanding the shadow prices if non-market values of some of those varieties are significant. Ideally one should calculate shadow prices for each variety to better understand nonmarket values attached to each variety. However, the ENHRUM data set does not allow this due to its structure because the production data is not differentiated between varieties. Future studies should combine shadow prices for each variety and diversity indices to better understand which varieties are most likely to be maintained and how shadow prices relate to diversity. 5. Summary and Conclusions In this paper, I model the decision making of an agricultural household that is subject to an asymmetric market constraint for the subsistence crop to derive its shadow prices. I show theoretically that market prices may fail to represent the value of crops with significant non-market values to subsistence farmers and that we can better understand land allocation decisions using shadow prices rather than market prices for such farmers. This model allows us to econometrically analyze the determinants of shadow prices, which reflects farmers’ incentives for growing subsistence crops that have non-market values. Understanding the factors that make farmers value traditional crops more than market prices has important policy implications for the conservation of genetic diversity in landraces. Using a nationally representative household data from rural Mexico, I have estimated shadow prices of traditional maize varieties for farmers. Shadow prices are significantly higher than market prices for subsistence farmers of traditional maize in the sample. Among the significant determinants of this difference are being gender, ethnic identity, isolation, access to irrigation, and soil quality. These determinants can be used as guides to efficiently allocate public and private funds for the conservation of traditional maize varieties in Mexico. The method I use is flexible enough to be applied in other regions and with other crops.

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30

Appendix A: KKT Conditions The Lagrangean for the basic model is: max

Xl ,Xm ,Xsh ,Xss ,θ,Li ,λ,µn

L = U (Xsh , Xm , Xl ; Z)

+λ[ps (1 − ts )Xss + pc h(Lc , Ic , A(1 − θ)) + W + w(T¯ − Xl − Ls − Lc ) − pm (1 + tb )Xm ] +µ1 [g(Ls , Is , Aθ) − Xss − Xsh ] + µ2 Xss + µ3 Xsh + µ4 Xm + µ5 θ + µ6 (1 − θ) + µ7 Ls + µ8 Lc i = s, c, n = 1, ..., 8. Leisure cannot be zero by assumption, hence we can use the FOC to get the optimal condition: M Ul = λw. Farmer equates the money value of his marginal utility of leisure to wage rate at the optimum. We need to use the KKT conditions for optimal choices of Xm , Xss , Xsh , θ and Li where (i = s, c) because of the possibility of corner solutions for these variables: ∂L : M Um − λpm (1 + tb ) + µ4 ∂Xm ∂L : Xm ∂µ4 µ4 Xm ∂L : M Ush − µ1 + µ3 ∂Xsh ∂L : Xsh ∂µ3 µ3 Xsh ∂L : λps (1 − ts ) − µ1 + µ2 ∂Xss ∂L : Xss ∂µ2 µ2 Xss ∂L : µ1 A(M P As ) − λpc A(M P Ac ) + µ5 − µ6 ∂θ ∂L :θ ∂µ5 ∂L : (1 − θ) ∂µ6 µ5 θ = 0 ∂L : µ1 M P Ls − λw + µ7 ∂Ls

= 0

(41)

≥ 0

(42)

= 0

(43)

= 0

(44)

≥ 0

(45)

= 0

(46)

= 0

(47)

≥ 0

(48)

= 0

(49)

= 0

(50)

≥ 0

(51)

≥ 0

(52)

& µ6 (1 − θ) = 0

(53)

= 0

(54)

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31

∂L : Ls ∂µ7

≥

0

(55)

µ7 Ls

=

0

(56)

=

0

(57)

≥

0

(58)

=

0.

(59)

∂L = λ(pc M P Lc − w) + µ8 ∂Lc ∂L = Lc ∂µ8 µ8 Lc

The Equation 41 indicates that if a farmer is not buying the market good Xm the monetized value of the marginal utility from consuming it must be less than or equal to the market price and TC. Although the decision to buy Xm or not may provide intuition into the substitutability of market good for domestic good, the shadow price of domestic good is determined independently. This is because Xs is a different consumption good, and the production decisions depend on the tradeoffs between the cash crop and the domestic crop. In what follows, I assume interior solution for Xm , hence µ4 = 0. Let us interpret the different cases implied by the KKT conditions related to Xs : ¯ − Xss − Xsh > 0, 0 < θ < 1, µ1−8 = 0. Case 1: Xss > 0, Xsh > 0, Qa (L, A) If the sum of home consumption and sales of Xs is less than the total production market price has to be equal to zero by 47 on the preceding page. Therefore there will never be waste since market prices are strictly positive. For the following cases I assume there is no waste and hence µ1 > 0. Case 2: Xss > 0, Xsh > 0, θ = 0, µ5 ≥ 0, µ2,3,6,7,8 = 0. This case is impossible, since the farmer has to have θ > 0 to be able to sell any Qa . For θ = 0, we can similarly rule out the cases where Xss > 0, Xsh = 0 and Xss = 0, Xsh > 0. Case 3: Xss = Xsh = 0, θ = 0, µ4 ≥ 0, µ6 = 0, µ2,3,5,7,8 ≥ 0. This case represents farmers who only grow cash crop. We can rewrite the Equation 50 to get: µ1 µ5 M P As = pc M P Ac − . λ λA This condition indicates that the marginal (monetized) value of an extra unit of subsistence crop is worth less than the value of marginal product of land allocated to cash crop. For farmers in this group the non-market benefits and the unobservable characteristics of subsistence crop are not important. Therefore it is not worth to allocate any resources to subsistence crop production. Case 4: Xss > 0, Xsh > 0, 0 < θ < 1, Lc > 0, µ2−8 = 0. This case characterizes the farmer who sells part of Xs in the market. For this group of farmers market price equals shadow price, i.e. ρ = ps (1 − ts ) =

µ1 λ

and we can safely use market price

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to represent farmers’ valuation of the subsistence crop. Therefore, the optimality conditions for allocation of land, labor and input are the conventional conditions where farmer equates the value of marginal products across crops, i.e.: ps (1 − ts )M P As = pc M P Ac , pi M P Li = w, i = s, c. Case 5: Xss > 0, Xsh = 0, 0 < θ < 1, µ3 ≥ 0, µ2,5−8 = 0. Farmer is selling all his product at the market price, which is greater than or equal to the shadow price, i.e. ρ=

µ1 − µ3 µ1 ≤ = ps (1 − ts ) λ λ

This case is similar to Case 3 and we can use market prices. The case where both Xsh and Xss are equal to zero when 0 < θ < 1 is not likely to occur (given the “no-waste” assumption in Case 1), hence will not be considered here. Case 6: Xss > 0, Xsh > 0, θ = 1, Lc = 0, µ2−5 = 0, µ6−8 ≥ 0. In this case, farmer only cultivates the subsistence crop and sells part of it (hence ps (1 − ts ) = µ1 λ ).

The optimality conditions for resource allocation are: µ6 = pc M P Ac , λA µ8 pc M P Lc = w − . λ

ps (1 − ts )M P As −

According to the first condition, if the farmer allocated one unit of land to the cash crop, its value would be less than the value of marginal product of land allocated to the subsistence crop. Accordingly, the value of marginal products of the first unit of labor and purchased input to be used for the cash crop would be less than the market prices of these inputs. Therefore, the farmer does not allocate any land to the cash crop at the optimum. When θ = 1, the case of Xss > 0, Xsh = 0 is similar to Case 5, and the case of Xss = 0, Xsh = 0 is ruled out in Case 1. Case 7: Xss = 0, Xsh > 0, 0 < θ < 1, µ2 ≥ 0, µ3−8 = 0. This case characterizes subsistence farmers, who consume all of their subsistence crop at home. The market price is less than or equal to farmers’ shadow price as given by 47 on page 30: ps (1 − ts ) =

µ1 − µ2 µ1 ≤ =ρ λ λ

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Farmer is not selling Qa since he values it more than the market. The optimality condition for land allocation is different from the conventional condition in Case 3 above. Here the farmer equates the value of marginal product of land allocated to cash crop to the “shadow value of marginal product” of land allocated to subsistence crop, i.e.: µ1 M P As = pc M P Ac . λ The conditions for labor and purchased input for the subsistence crop set the “shadow value of marginal product” of inputs equal to market prices of these inputs: µ1 M P Ls = w λ For this group of farmers we need to estimate shadow prices to understand how they value their subsistence crop, and how they make resource allocation decisions. Case 8: Xss = 0, Xsh > 0, θ = 1, µ3−7 = 0, µ2,6,8 ≥ 0. In this case, farmer only cultivates the subsistence crop and consumes all of it at home. The optimality condition for land allocation is: ρM P As −

µ6 M P As = pc M P Ac , λ

which means that if he allocated one unit of land to the cash crop, its value would be less than the “shadow value of marginal product” of land allocated the subsistence crop. The conditions for labor and purchased input are the same as in the Case 6 above, and similarly shadow prices rather than market prices should be used to understand the subjective valuation of farmers in this group.

SHADOW PRICES OF TRADITIONAL MAIZE

Appendix B: Maps

Figure 3. Regional Distribution of the communities in the Mexican National Rural Household Survey (ENHRUM 2003)

Figure 4. Regional Distribution of Maize Landraces in Mexico (Turrent 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 yellow and orange areas. Dark green dots represent maize, and red dots represent teosinte (the ancestor of maize) populations.

34

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35

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