FARMERS’ SUBJECTIVE VALUATION OF SUBSISTENCE CROPS:
THE CASE OF TRADITIONAL MAIZE IN MEXICO
ASLIHAN ARSLAN
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 they increased maize production in spite
of decreasing prices. I develop an agricultural household model to derive household specific subjective values (i.e. “shadow prices”) of non-marketed farm products that can be
estimated econometrically. 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. Empirical application of
the model in the context of subsistence farmers of traditional maize in Mexico provides policy
implications for conservation of maize landraces and makes a case for de-facto conservation
in their center of diversity.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’ non-marketed 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
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
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).
1
SHADOW PRICES OF TRADITIONAL MAIZE
2
policy implications for on-farm conservation of traditional maize. I summarize the results
and conclude in Section 5.
2. Background
The theoretical literature on shadow prices establishes that the value of goods and services
not traded in markets can be measured with their shadow prices, which result from internal
equilibria for each individual or household (Becker, 1974). For such goods, market prices
fail to represent value to guide individuals’ decisions. The agricultural household literature
with missing markets uses shadow prices to explain farmers’ responses – or the lack of it –
to changes in market conditions (Singh et al., 1986; Jacoby, 1993; Skoufias, 1994; de Janvry
et al., 1991; Taylor and Adelman, 2003). While most of these studies used 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. Although they define
the missing market as household specific, their simulation methods do not allow for the
estimation of household specific shadow prices.
Imperfect substitutability between household labor and hired labor, creates a missing
market for household labor and results in shadow wages that are higher than market wages.
Jacoby (1993) developed a method to econometrically estimate the resulting household
specific shadow wages. This method has been employed by a number of papers in the
literature on the labor supply of farm households (Skoufias, 1994; Barrett et al., 2005).
Although these papers improve our understanding of farm households’ labor supply under
missing markets, they do not consider the possibility of a missing market for some crops
and value farmers’ output at market prices.
The reason why market prices may not represent the true value of subsistence crops can
be a special type of missing market. In the 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 (e.g. plant strength, resistance to pests and disease,
ear length, flowering time, adaptability to certain environments), consumption attributes
(e.g. ease of shelling and processing, taste, color, suitability for certain dishes), subjective
importance farmers place on their seed which may have provided subsistence to the family
SHADOW PRICES OF TRADITIONAL MAIZE
3
for decades, as well as other non-market benefits farmers get from farm production (Brush
and Meng, 1998; Smale et al., 2001; Edmeades et al., 2004; Badstue et al., 2006; Dyer-Leal
et al., 2002). Empirical evidence suggests that, even if another farmer in the same village
has the same variety, the difficulty in trying to identify whether that farmer is going to
take good care of the crop, or whether that crop will satisfy all of the farmer’s different
needs imposes risks and transaction costs on the farmer (Badstue et al., 2006). Therefore,
the farmer values his own crops higher than those in the market, which creates a missing
market for what otherwise would be a perfect substitute for the farmer’s subsistence crop.
In this case, it is the household specific shadow price instead of market price that guides
farmer’s choices.
The endogenously determined shadow price captures the above mentioned non-market
values that define farmers’ incentives to cultivate a certain crop variety. 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, there are
no studies to explicitly account for household-specific shadow prices for subsistence 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 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).
SHADOW PRICES OF TRADITIONAL MAIZE
4
Whether farmers’ incentives are based on market prices or shadow prices is crucial for
understanding farmers’ responses to changes in economic environment and for improving
the efficiency of on-farm conservation programs.
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.2 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 farmer’s land, labor and input allocation
decisions across different crops (a subsistence crop and a cash crop) and activities (farm
production, off-farm work and leisure) to maximize his utility subject to a full income
constraint and a market constraint for the subsistence crop. This market constraint is such
that the farmer cannot buy the same product he produces; hence, the production of this
crop equals consumption and sales – if any. I assume that the unobserved quality of others’
crops and non-market benefits from farming one’s own crop discussed above translate into
imperfect substitutability of the market purchased crop for the farmer’s subsistence crop.3
The farmer produces two crops using labor, a purchased input and a given 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. There are no land markets, and he divides his land between
the subsistence crop and the cash crop. He also decides how to allocate resources like labor
and other inputs across different crops and activities to maximize utility.
Let Qi denote the quantity produced of the crop i, where i = a, c, and a identifies the
subsistence crop and c identifies the cash crop. Xc , Xm and Xl are respectively the amount
2
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).
3
22 out of 30 farmers I interviewed in 2 states and 15 different communities in Mexico during July 2005 said
that the quality of the maize they buy in the market is not as good as their own maize, and they use the
two different maize varieties for different purposes.
SHADOW PRICES OF TRADITIONAL MAIZE
5
of cash crop, market goods and leisure consumed. He also consumes part or all of his
subsistence crop denoted by Xah , where the superscript h indicates that the only source of
consumption of Xa is household’s own 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 , HIi and Ii
denote, respectively, the amount of family labor, hired in labor and purchased input used
in production of crop i. 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 purchased input to use; how much of his subsistence
crop to sell (Xas ); and how much to consume of all four goods (i.e. Xah , Xc , Xm , Xl ). Li
is the total labor used in production of crop i, θ is the proportion of land cultivated with
the subsistence crop and Z is a vector of household characteristics. The farmer’s problem
is given by:
max
Xah ,Xc ,Xm ,Xl ,Xas ,θ,Fi ,Ii
pc Xc + pm Xm + pI (Ia + Ic ) ≤
U (Xah , Xc , Xm , Xl ; Z) s.t.
pa Xas + pc Qc + w(HO − HIa − HIc ) + W
(1)
Qa
=
θqa (La , Ia )
(2)
Qc
=
(1 − θ)qc (Lc , Ic )
(3)
HO + Xl + Fa + Fc
=
T̄
(4)
Fi + HIi
=
Li , i = a, c
(5)
Xas + Xah
≤
Qa
(6)
Xas
≥
0
(7)
0≤
θ
≤1
(8)
where pj denotes the market prices of consumption goods and purchased input identified
with subscripts j = a, c, m, I; and W denotes exogenous transfers.
Equation 1 is the cash constraint, which indicates that the total expenditure on the
consumption of cash crop, market good and purchased input needs to be less than or equal
to the value of marketed surplus plus net labor income and exogenous transfers. Equations
2 and 3 are production functions for Qa and Qc , where the land endowment is normalized
such that A = 1, and qa and qc are the per hectare production functions that are concave in
labor and purchased input. Equation 4 is the time constraint, where T̄ is the household’s
SHADOW PRICES OF TRADITIONAL MAIZE
6
time endowment. I assume that the marginal utility from the first unit of consumption of
all goods is very large (i.e. M Uk |Xk =0 = ∞, k = a, c, m, l), hence the household has to
consume positive amounts of all consumption goods, and we are not concerned about the
corner solutions for these goods. The only non-negativity constraints considered here (i.e.
constraints 7 and 8) are on the amount of subsistence crop sold and the proportion of land in
subsistence crop, to emphasize the corner solutions related to this crop that define shadow
prices. Of special interest is Constraint 6, which is the market constraint for the farmer’s
subsistence crop (Qa ). Constraint 6 and the non-negativity constraints together determine
the different regimes the farmer may be in (e.g. all land in Qa and subsistence farmer; all
land in Qa and commercial farmer; some land in Qa and subsistence farmer...etc.), allowing
us to derive farmer specific shadow prices of Qa for each case.
By substituting Equations 4 and 5 into the budget constraint, we obtain the following
Lagrangean:
max
Xas ,Xah ,Xc ,Xm ,Xl ,θ,Li ,Ii ,λ,µn
L = U (Xah , Xc , Xm , Xl ; Z)
+λ[pa Xas + pc (1 − θ)qc (Lc , Ic ) + W + w(T̄ − Xl − La − Lc ) − pc Xc + pm Xm + pI (Ia + Ic )]
+µ1 [θqa (La , Ia ) − Xas − Xah ] + µ2 Xas + µ3 θ + µ4 (1 − θ) + µ5 Lc + µ6 Ic
n = 1, 2, 3, 4, 5, 6
The first order conditions (FOC) for Xah , Xc , Xm , Xl , La and Ia are:
F OCXah
: M Uah = µ1
(9)
F OCXc
: M Uc = λpc
(10)
F OCXm
: M Um = λpm
(11)
F OCXl
: M Ul = λw
(12)
F OCLa
: µ1 θM P La = λw
(13)
F OCIa
: µ1 θM P Ia = λpI
(14)
Note that θ cannot be equal to zero, because that would require that the consumption of the subsistence crop – for which there is no perfect substitute – equaled to zero.
That,nevertheless, is ruled out above with the assumption that marginal utility of consumption goods evaluated at zero is very large. However, θ can be equal to one, where the farmer
SHADOW PRICES OF TRADITIONAL MAIZE
7
does not cultivate any cash crop, in which case Lc and Ic will automatically be zero.4 To
obtain the optimality conditions for Xas and θ including corner solutions, we need to use the
Karush-Kuhn-Tucker (KKT) conditions:5
∂L
: Xas
∂µ2
≥ 0
(15)
= 0
(16)
≥ 0
(17)
≥ 0
(18)
∂L
: µ1 qa (La , Ia ) − λpc qc (Lc , Ic ) + µ3 − µ4
∂θ
= 0
(19)
µ2 Xas
= 0
(20)
µ3 θ
= 0
(21)
=
(22)
∂L
: λpa − µ1 + µ2
∂Xas
∂L
:θ
∂µ3
∂L
: (1 − θ)
∂µ4
µ4 (1 − θ)
0
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 9, 10 and 19):
M Uah
M Uc
=
µ1
qa (La , Ia ) =
λ
where
µ1
λ
µ1
,
λpc
(23)
pc qc (Lc , Ic ), when θ > 0,
(24)
takes the place of pa in the conventional optimality conditions. Given this opti-
mization rule, I define the “shadow price” of Xah as follows:
ρa ≡
µ1
,
λ
where µ1 is the marginal utility of having one more unit of Qa , and λ is the marginal utility
of income. We can interpret ρa as the money value of having one more unit of Qa for the
household (Heckman, 1974).
4Note that the farmer still can have positive levels of consumption of cash crop that he can buy in the
market.
5The KKT conditions for L and I do not affect the discussion on shadow prices that follows. I discuss
c
c
and interpret them in detail in Appendix.
SHADOW PRICES OF TRADITIONAL MAIZE
8
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. Their ratio (i.e. shadow
wage) 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 an amount equal to one more unit of subsistence
crop production.
I discuss the different classes of farmers as defined by KKT conditions in detail in the
Appendix. For farmers who have θ > 0 and sell part of their subsistence crop, the shadow
price equals the market price, i.e. ρa = pa =
µ1
λ ,
and we can safely use the market price to
represent the value of the this crop to farmers. If, however, the farmer is consuming all of
Qa at home, the shadow price is greater than the market price, i.e.:6
ρa =
µ1
µ1 − µ2
>
= pa
λ
λ
(25)
Production decisions are affected by µ1 and λ, which depend on household characteristics that would not affect production under perfect markets. Although µ1 and λ are not
observable, we can define an estimable expression for ρa by using Equations 13 and 14:
ρ̂a ≡
µ1
w
pI
=
=
.
ˆ
λ
θ M P La
θMˆP I a
(26)
The model developed here is similar to the one in de Janvry et al. (1991) in that it is
concerned with the shadow price of a “non-tradable” farm product. However, they assume
perfect substitutability between farmer’s product and the market product; therefore, the
shadow price equals the market price whenever transaction costs do not constrain farmer’s
access to markets. The shadow price is implicit in their simulation and cannot be estimated
econometrically for each household. The discussion in Dyer-Leal et al. (2002) sets the stage
for the model developed here with its explicit emphasis on shadow prices for subsistence
farmers, but they do not derive shadow prices analytically, and the village-wide general
equilibrium model used in the empirical application does not allow for empirical estimation
of shadow prices in large samples.
Given Equation 26 and using an empirical method similar to Jacoby (1993) and Skoufias
(1994), we can econometrically estimate household-specific shadow prices by estimating the
6For this group of farmers µ > 0. See Appendix for details.
2
SHADOW PRICES OF TRADITIONAL MAIZE
9
production function to derive the marginal product of labor or the purchased input 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 to explore
farmers’ incentives to cultivate traditional crops associated with on-farm conservation.
In the next section, I estimate a production function for subsistence farmers 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 used by Jacoby (1993) and conclude that shadow prices are significantly
higher from market prices for subsistence farmers of traditional 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. 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.7
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 maize, which constitutes 31% of all
plots and 65% of maize plots in the whole sample. 85% of the plots used in this subsample
are cultivated with traditional maize (Table 1 on the next page). 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 90% of the plots
in this region are cultivated with traditional varieties. On the other hand, Northwest Region
7For more details on the ENHRUM data see: http://precesam.colmex.mx
SHADOW PRICES OF TRADITIONAL MAIZE
10
includes states with higher GDP per capita, large scale farming and industrial production
(Chiquiar, 2005), where only 14% of plots are cultivated with traditional maize.
Table 1. Percentage of plots under different maize types by region
Maize type
Region
Improved Traditional Total
South-Southeast
10
90
100
Central
9
91
100
Western Cent.
22
78
100
Northwest
86
14
100
Northeast
20
80
100
Total
15
85
100
Table 2 demonstrates the differences between regions using other variables. We can
see that households in the South-Southeast and Central Regions are in the lower wealth
quintiles, own less land and are more likely to belong to an indigenous community. In the
Table 2. Means of some household characteristics by region
Region
South-Southeast
Central
Western Cent.
Northwest
Northeast
Total
Wealth
Owned
Indi- Sold
quintile land(ha.) genous maize
1.65
6.57
0.75
0.27
2.08
1.71
0.28
0.17
3.44
7.07
0.02
0.36
4.85
11.88
0.00
0.69
2.97
23.57
0.03
0.13
2.31
7.06
0.39
0.26
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. This suggests that market
prices for traditional maize are more likely to underestimate the value of this crop to the
farmer and illustrates the importance of understanding shadow prices of traditional maize
in Mexico. I use the subsample of traditional maize farmers in the next section to estimate
shadow prices of maize, test whether they are different from market prices and investigate
the determinants of this difference.
4.2. Estimating the production function and shadow prices of traditional maize.
Descriptive statistics of data used for estimations are given in Table 3. Estimating the
production function only for traditional maize can cause selection bias if there are some
SHADOW PRICES OF TRADITIONAL MAIZE
Table 3. Summary statistics
Variable
Definition
Mean Std. Dev.
Plot level variables (N=569)
lnoutput
log of maize output (kg.)
6.60
1.46
criolla
Dummy=1 if plot is cultivated with tra0.85
0.36
ditional maize variety (TV)
lnland
log of land cultivated (ha.)
0.1
1.05
lnseed
log of seed used in kg.
2.77
1.1
lninpcost
log of total costs of fertilizers and pesti4.03
4.43
cides ($MX)
log of total hours of labor used
3.43
0.8
lntotlab
lntotmaqhrs log of total hours of machinery used
0.29
3.7
drought
Dummy=1 if faced drought
0.3
0.46
soilq
Scale of soil quality (1: Bad, 2: Regular,
2.31
0.59
3: Good)
slope
Scale of slope (1: Plain, 2: Sloped, 3: Very
1.52
0.58
steep)
irrigD
Dummy=1 if plot is irrigated
0.15
0.36
walktime
Time it takes from the parcel to the com37.15
33.1
munity center (mins.)
Household level variables (N=380)
wqtile
Quintiles of the wealth index*
2.31
1.38
age
Household head’s age
50.77
14.95
educ
Household head’s education (years)
3.62
3.22
gender
Dummy=1 if household head is male
0.91
0.28
hhsize
Number of household members
4.97
2.43
indiglang
Dummy=1 if can speak indigenous lan0.39
0.49
guage very well
totown
Total area of land owned (ha.)
7.06
26.75
totanimals
Total number of animals at the beginning 17.52
24.54
of the year
totremit
Total remittances household received 3149.79
11615.88
($MX)
maizareash
Proportion of total area with maize
0.88
0.22
maizincshare Proportion of total farm income from
0.2
0.39
maize
maizsold
Proportion of maize production sold
0.14
0.3
totbuyD
Dummy=1 if bought maize during the
0.42
0.49
year
totsellD
Dummy=1 if sold maize during the year
0.26
0.44
Average # of households with off-farm in0.45
0.23
othersoffD
come in the same village
0.39
0.3
otherscredit Average # of households that had credit
in the same village
percTVloc
Proportion of plots cultivated with TV in
0.84
0.25
the village
alltrad
Dummy=1 if hh. cultivated only tradi0.84
0.37
tional maize varieties
allimp
Dummy=1 if hh. cultivated only im0.14
0.35
proved maize varieties
both
Dummy=1 if hh. cultivated both varieties
0.02
0.14
* Wealth index is generated using Principal Component Analysis based on the characteristics
of households’ primary residence, access to utilities, and ownership of TV and refrigerator.
11
SHADOW PRICES OF TRADITIONAL MAIZE
12
unobservable variables that affect both farmers’ crop choice and productivity (Vella, 1998).
To correct for possible selection bias, I use the two step Heckman procedure to estimate
the production function for traditional maize. In the first step we need to have at least one
variable that affects selection into traditional maize farming but not productivity. I use two
variables to identify the selection equation: the maximum years of education of household
head’s parents; and the percentage of total plots that are cultivated with traditional maize in
the same village.8 These variables are likely to affect farmers’ choice of crops (i.e., whether
he will choose to cultivate traditional maize or not) but not the production after this choice
has been made. Farmers from educated families may be more likely to try modern maize
varieties, but parent’s education should not effect farmers production function once the crop
choice is made. Also, if the farmer lives in a village where a high percentage of plots are
cultivated with traditional maize, he will be more likely to cultivate traditional maize. But
this variable should not affect farmers’ production function after controlling for the village
level correlation.9
The estimation results for the production function and the selection equation are given
in Table 4 on the next page, where I use a Cobb-Douglas production function in the second
step after correcting for zero inputs (i.e. adding 0.01 to zero inputs so that the logarithm
is defined).10 A widely cited problem with Cobb-Douglas production function estimates is
the appearance negative marginal products (Barrett et al., 2005), but all of the estimated
marginal products for all factors of production estimated here are positive. The regression
standard errors are clustered at the village level to correct for potential error correlation due
to unobserved village characteristics that are common to all households. 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
of all households in the sample.
8This variable excludes the plots of the farmer to prevent endogeneity.
9I have tested the validity of exclusion restrictions by regressing the predicted residuals from the second
step equation on the two variables. Regression results indicate that the residuals in the production function equation are not correlated with either of the variables except through their impact on selection into
traditional variety farming (i.e., very low R-squared and insignificant coefficients).
10I have also estimated a production function with the more flexible Translog specification. The qualitative
results are the same and the quantitative results do not change significantly. Moreover, the Bayesian Schwarz
Information Criterion suggests a better fit for the Cobb Douglas form. I report the more tractable CobbDouglas results and use these estimates in obtaining the shadow prices.
SHADOW PRICES OF TRADITIONAL MAIZE
13
Table 4. Two-step Heckman estimation results for the production function
of traditional maize
Variable
Coefficient
(p-value)
Production function for TV: Dep.var=lnoutput
lnland
0.16
(0.11)
lnseed
0.27∗∗∗
(0.00)
lninpcost
0.07∗∗∗
(0.00)
lntotlab
0.33∗∗∗
(0.00)
lntotmaqhrs
0.02
(0.27)
drought
-0.19
(0.18)
soilq
0.18
(0.12)
slope
-0.08
(0.61)
irrigD
0.62∗∗∗
(0.00)
age
-0.01
(0.29)
educ
0.00
(0.85)
South-Southeast
-1.21∗∗
(0.03)
Central
-1.04∗
(0.06)
Western Cent.
-0.80
(0.10)
Northwest
2.84∗∗∗
(0.00)
Intercept
5.49∗∗∗
(0.00)
Selection Equation: Dep.var=1 if cultivated TV
pareduc
0.11∗∗
(0.05)
percTVloc
1.48∗∗∗
(0.00)
totpar
-0.13∗
(0.09)
superficie
0.02
(0.65)
hhsize
0.08∗
(0.06)
soilq
0.24
(0.18)
slope
0.22
(0.21)
irrigD
-0.67∗∗
(0.04)
age
0.02∗∗∗
(0.00)
educ
-0.01
(0.84)
South-Southeast
0.80∗∗
(0.02)
Central
0.61
(0.12)
Western Cent.
0.47
(0.22)
Northwest
-1.17∗∗
(0.02)
Intercept
-2.67∗∗∗
(0.00)
N
569
Significance levels :
∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
Using the estimated marginal product of labor and wages in the formula for shadow
prices (i.e. ρ̂a =
w
),
Mˆ
PL
I calculate the shadow prices of traditional maize for each farmer.11
11This 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 a production function
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
SHADOW PRICES OF TRADITIONAL MAIZE
14
Table 5 shows the summary statistics of the estimated shadow prices and market prices of
traditional maize in local markets. We can see that the average shadow price is higher than
the average market price, and the shadow price for subsistence farmers is higher than that
of farmers who sell some maize in the market.
Table 5. Summary statistics for estimated shadow prices and observed
market prices
Variable
Mean St.Dev. No.Obs.
Shadow price for full sample
20.21
31.07
481
Shadow price for sellers
10.26
14.63
130
Shadow price for non-sellers
23.89
34.57
351
Observed market price/kg.
1.97
0.62
481
Following Jacoby (1993), I test the null hypothesis of a separable model (i.e. shadow
prices and market prices are the same) by first running the following regression:
ρ̂a = α + βpa + u
(27)
and testing the null hypothesis of:
H0 : α = 0,
β = 1.
(28)
There may be selection bias in Equation 27 if there are unobservables that increase the
likelihood of selling maize for some farmers that are correlated with shadow prices. The
possible selection bias could be controlled with panel data methods, however, given the lack
of panel data, I use t-tests to see whether the distribution of some key variables, which are
likely to cause selection bias, are different across subsistence and commercial farmers. I test
the following variables: the time it takes to go to the market; tractor ownership; age and
education. I fail to reject the null hypothesis that the distributions of these variables are
the same for the two groups of farmers and conclude that selection bias is not significant
for this sample.
The null hypothesis in Equation 28 is rejected for both subsistence farmers and the
commercial farmers by the F-test. However, individual t-tests (i.e. testing α = 0 and
β = 1 separately) fail to reject both hypotheses only for farmers who sold some maize in
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
15
the market. It is clear that subsistence farmers have significantly higher shadow prices than
commercial farmers. We can conclude that the estimated shadow prices of traditional maize
for subsistence farmers in the sample are significantly different from market prices. This
result confirms that market prices do not fully capture the value of traditional maize for
subsistence farmers in rural Mexico (Berthaud and Gepts, 2004; Dyer-Leal et al., 2002).
Understanding the determinants of the wedge between these two sets of prices of traditional maize can provide important policy implications for conservation of the genetic
diversity they maintain. 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. I analyze the determinants of this wedge 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, plot characteristics
and indicators of market participation. We can now regress the wedge between shadow
and market prices on these variables to understand the key factors that are correlated with
it. 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). The regression results are given in Table 6 on the
following page, 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. Because the dependent variable is derived from a variable that is estimated
with error, there is an additional source of variance in the standard errors of this estimation.
The test statistics will not be valid unless the standard errors are corrected (Dumont et al.,
2005). One way to correct for this bias is bootstrapping, and I report the bootstrapped
regression results here (Cameron and Trivedi, 2005).
Household wealth, household head’s age and education are among the variables shown
to be positively correlated with cultivation of modern varieties at the expense of traditional
varieties in the empirical literature (Feder and Umali, 1993; Bellon and Taylor, 1993). However these variables are not significant in the current sample. Male farmers value traditional
maize higher than females, indicating that among the non-market values, production characteristics, the value of being a good farmer and preserving the family seeds may be more
SHADOW PRICES OF TRADITIONAL MAIZE
16
Table 6. Decomposition of the difference between estimated shadow prices
and market prices (Bootstrapped, 1000 replications)
Variable
Coefficient
(p-value)
Dep.var: (ρ̂a − pa )
wqtile
-2.15
(0.35)
gender
11.20∗
(0.06)
age
0.08
(0.66)
educ
-2.29
(0.32)
educ2
0.22
(0.29)
indiglang
7.28∗
(0.09)
hhsize
0.33
(0.81)
totown
-0.05
(0.81)
totanimals
0.26
(0.24)
maizareash
11.48
(0.14)
totremit
0.00
(0.88)
othersoffD
2.95
(0.73)
otherscredit
-12.21
(0.28)
soilq
-8.87∗
(0.09)
irrigD
-17.06∗∗∗
(0.00)
walktime
0.10∗
(0.05)
South-Southeast
20.35∗
(0.08)
Central
8.52
(0.48)
Western Cent.
26.40∗∗
(0.04)
Northwest
43.50∗
(0.05)
constant
0.91
(0.98)
N
351
Significance levels :
∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
important than the consumption characteristics (e.g. culinary superiority) women tend to
care about.
Another variable in the literature often found to affect farmer’s likelihood of conserving landraces is belonging to an indigenous group (Turrent and Serratos-Hernandez, 2004;
Perales et al., 2005). The coefficient on the indigenous language dummy is significant and
positive, which confirms this finding. The non-market values of traditional maize captured
in shadow prices are higher for indigenous farmers, which underlines their role as stewards
of genetic diversity.
The variables that represent market performance in the farmer’s village include; total remittances received, the percentage of farmers who have off farm income, and the percentage
of farmers who have some kind of credit in the same village. None of these variables significantly affect the difference between shadow and market prices. This finding indicates that
SHADOW PRICES OF TRADITIONAL MAIZE
17
farmer valuation of traditional maize varieties does not decrease with improved access to
off-farm labor, credit and migration markets, which restores hopes for de-facto conservation
of maize landraces.
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). The results confirm this with a positive and significant coefficient on the time it takes farmers to walk from their plots to the community
center. The more isolated the farmers’ plots, the higher the shadow price. Irrigation and
high soil quality are negatively correlated with shadow prices. A more effective way of conserving the genetic diversity in such areas may be off-farm conservation rather than on-farm
conservation.
Programs for on-farm conservation of genetic diversity of maize in Mexico will be more
cost effective if targeted at isolated communities with indigenous populations where defacto conservation is more likely. More resources may be needed in regions where 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.
5. Summary and Conclusions
In this paper, I developed a theoretical model to derive estimable shadow prices for
non-marketed crops in an agricultural household setting. This model allows us to econometrically analyze the determinants of the difference between shadow prices and market
prices, which reflects farmers’ incentives for growing subsistence crops. 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 estimated householdspecific 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, ethnicity, isolation,
access to irrigation, and soil quality. These determinants can be used as guides to efficiently
SHADOW PRICES OF TRADITIONAL MAIZE
18
allocate public and private funds for the conservation of traditional maize varieties in Mexico
and other crops elsewhere.
SHADOW PRICES OF TRADITIONAL MAIZE
19
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PRECESAM Folletin Informativo No 3.