Abstract
Rural
households in semi-arid areas often experience rainfall-related shocks that
result in low and uncertain income. Household’s survival depends on the ability
to anticipate and to cope with this uncertain income. Through time, households
have developed ex-ante risk management and ex-post risk coping strategies.
These include crop portfolio adjustments and off-farm activity diversification.
This paper investigates the role of rainfall variability and farmer risk
aversion behavior on household’s crop portfolio choice. To answer the research
questions Heckman’s selection model is used. The method was applied to a
four-year panel data of two districts in
The
study showed that farmer’s ex-ante strategic response to rainfall variability
is through diversification of crops to be grown. Choosing the crops most suited
to specific rainfall conditions was proven a strategy of farmers to cope with
unpredictable rainfall. In times of low rainfall, the dominant crops to be
chosen are teff and grass pea.
Ex-ante crop choice and
reliable water availability for farming can be viewed as complements. These complementarities
suggest that policies that focus on rainwater harvesting techniques and
promoting small-scale irrigation would promote fertilizer adoption.
Keywords:
rainfall variability, ex-ante risk management, ex-post risk coping strategies, crop
choice,
Introduction
It
is well known that households in semi-arid areas often experience
rainfall-related shocks that result in low and uncertain incomes (Dercon and
Hoddinott, 2003). A large body of literature explores the ex-ante and ex-post
responses to these shocks. One line of literature examines how households
respond to these shocks ex-post. Udry (1995) assesses the extent to which
saving allows households to smooth consumption, Fafchamps, et al. (1998) and Dercon (1998) focuses on the role of livestock
holdings as a means of smoothing consumption, and Kochar (1999) on the role of
off-farm labor supply as a response to income shocks. A second line of research
looks at the effectiveness of ex-ante income smoothing strategies in reducing
fluctuations in income. Dercon (1996), Larson and Plessmann (2002), and Morduch
(2002) find evidence that farmers choose to diversify into less profitable
crops or choose less productive technology.
In
the absence of credit and insurance markets for insuring risk ex-post against
adverse shocks, many farm families depend directly on diversity of their crops
for the food and fodder they use (Benin et
al., 2004). For example, diversification of crops grown in Tigray is often
considered as a precaution against rainfall variability. Moreover, risk
attitudes of farmers have also shown to influence crop choice and input
allocations (Ramaswami, 1992; Isik, 2002).
In
recent years using
To
answer the research questions Heckman’s selection model is used. Rainfall
variability and risk attitude of farmers are incorporated in the model. The
method is applied to a four-year panel data of two districts in Northern
Ethiopia Tigray.
The
rest of the paper is organized as follows: section 2 presents the theoretical
model. Section 3 presents the empirical model and estimation methods. Section 4
describes the data used. Estimation results are presents in section 5. Section 6
concludes.
2. Theoretical Model
A
household model was developed to investigate the relationship between crop
choice and rainfall variability and socio-economic characteristics. The model
draws upon the economic theory of farm households (Singh et al., 1986). The model explicitly accounts for the fact that farm
households in Tigray are both producers and consumers of their own agricultural
products. As a result, production decisions are influenced by consumption
needs, so that production and consumption decisions in the model are assumed to
be made jointly in response to rainfall uncertainty.
It
is assumed that agricultural households maximize the expected utility of profit
, where 
is profit and 
is the expectation
operator. Assume that farmer’s utility function is a von-Neumann Morgenstern
utility function, which is concave, continuous and differentiable function of
profits, thus 
and
. Outputs are assumed to be stochastic. This assumption seems
plausible, as rainfall risk is the major source of uncertainty in crop
production in northern 
(the output produced
on the farm of crop 
be a random variable
with subjective probability density function 
reflecting farmer’s output expectations. A farm household
allocates his total size of land 
to 
crops mainly: wheat 
, teff 
, barley 
, grass pea 
, and lentil
.
Farmer’s
utility maximization problem can be represented as follows:
(1)
where 
is the output price of crop ; 
, on-farm labor supply[1]; 
is a vector of
variable inputs (seed, fertilizer, and pesticide); 
is capita (value of
livestock and value of farm equipment) l; 
is amount of land
cultivated; 
is household characteristics, 
is district level characteristics (such as off-farm labor
market opportunities). Moreover, output is assumed to be a function of rainfall variability (
), and farmers risk attitude (
). 
is the variable input price of 
, 
. 
represents the expected total revenue from 
crops produced on the
farm and 
represents the total
variable cost of production and 
is the share of land
allocated to crop.
The optimal
risk responsive land allocation decision is derived by differentiating the
expected utility of profit with respect to the quantity of fixed input (i.e.,
land):
(2)
Where 
is the shadow price of land.
Condition (2)
states that the optimal share of land allocated to crop is equal to the shadow price of land. We assume the shadow
price of land is determined by household risk perception (rainfall
variability), household risk attitude, household characteristics, and market
characteristics.
Using
the first order condition one can derive the optimal land allocation demand
function for crop. Crop’s land demand function can be expressed as:
(3)
The reduced
form optimal share of land allocated to crop is a function of all variable input prices, expected output
prices, on-farm labor supply, total cultivated land size, capital, and farmers
risk perception (rainfall variability) and farmer’s risk attitude. The share of
land allocated to each crop is also a function of household and village level
characteristics.
The optimal
demand function for the land allocated to crop can be expressed as
follows:
(4)
The
allocation is done subject to the constraint that the total land area is fixed
in the short run. Equation (4) is the risk responsive input demand function and
is the theoretical framework for specification of the share of land allocated
to each crop under rainfall risk.
Economic
theory states that a risk neutral farmer will allocate its land such that
expected marginal returns are equalized across crops. When expected return of
the land allocated to one crop is greater more land is allocated to that crop
and less will be allocated to the rest of the crops. However, if farmers are
risk-averse and the expected utility of choosing one crop to be grown is
greater then more land is allocated to this crop. Here it might be the case
that farmers may be willing to accept lower returns by choosing less risky
crops.
3. Empirical Model and Estimation
In
this section the empirical model of crop choice and the land share model are
presented. Here it is tested whether sample selection bias exists. It is
hypothesized that if the expected marginal utility of one crop is greater than
of another crop more land is allocated to this crop. As both the farmer’s crop
choice and land allocation decision are influenced by the expected utility of
the farmer, there is a possibility that the error terms of the crop choice
model and the land share model are correlated. Therefore the land share model
should account for the factors that determine the farmer’s crop choice and sample
selection bias should be tested for.
Crop Choice Model
The
crop choice model is binary and models the probability of choosing a crop to be
planted. Equation (3) is used to derive the crop choice model.
(5)
Where 
is an unobserved
latent variable. What is observed is a dichotomous variable 
, which takes the value of 
if crop is chosen to be planted on the specified plot and zero
otherwise. 
is a vector of independent variables that are hypothesized to
influence choice of crops to be planted, 
is a vector of parameters 
is the distribution function, 
is a normally
distributed error with zero mean and variance 
.
In
this section the probability of choosing a crop to be planted is estimated by a
probit model. From the estimated model the Inverse Mills Ratio (IMR) was
derived that was included in the land allocation model to test whether there is
a selection bias or not (Maddala, 1983: 158; Green, 2003: 757-761).
The
explanatory variables included in the crop choice model are prices of outputs,
prices of variable inputs (seed, fertilizer, and insecticides), capital (value
of livestock and value of agricultural equipments), family labor input,
household characteristics (head age, dummy for head education), off-farm
income, rainfall variables (Gurgand index,), index of farmers risk preference,
and district characteristics (proxy for distance to the capital city). A
district dummy variable equal to 1 if the district is Enderta, zero otherwise.
Land Allocation Model
The
dependent variable in the land share allocation model is the share of land
allocated to each crop. Then the observed allocation can be denoted as:
(6)
Where 
is a latent variable that is observed for values greater than
0 
) and is censored for values less than or equal to 0. 
is a vector of exogenous variables that are hypothesized to
influence the land allocation decision, 
is a vector of unknown
parameters and 
is a normally distributed error with zero mean and variance 
.
It is assumed
that and follow a bivariate normal distribution with correlation
. The model that applies to the observation of equation (6)
is:
(7)
Where 
and
(8)
Equation (8)
is the IMR (for details see Green 2003: 782-783). The term 
and 
are
the normal and the cumulative distribution function respectively, 
and 
are the standard deviation of and respectively. Rewriting
the land allocation model (equation 6) yields:
(9)
Where 
is a normally distributed error term 
).
If
and are uncorrelated, then
equation (9) can be estimated using ordinary least squares. However, if and are significantly correlated, then there is a problem of
sample selection bias and the estimates of the land allocation model (equation
9) must be corrected. Hence, the least squares method of regressing 
on is an inconsistent estimator of if the second term on the right-hand side of equation (9) is
non-zero. Under the joint normality assumption of
a selection model is used to estimate the land allocation
model to each crop (equation 9) (Heckman, 1979; Amemiya, 1985; and Wooldridge,
2002).[2]
Heckman’s (1979) idea is to first estimate equation (5) by probit maximum
likelihood and then obtain an estimate of and
. In the second step, the IMR () is included as a separate explanatory variable in the land
allocation model (equation 9).
The
choice of explanatory variables to be included in each of the two models is
problematic. It is possible that
, that is the same set of explanatory variables can be
included in the land allocation model (equation 9) and crop choice model
(equation 5). In this case the identification of comes from the nonlinearity of the IMR. Because the IMR is a
nonlinear function of the variables included in the first-stage probit model,
then the second equation (equation 9) is identified even if (Wooldridge, 2002: 564). In this study we used a district
dummy as an identification restriction. It is hypothesized that access to
markets (proxy by a district dummy) may affect the decision of crops to be
grown but not the proportion of land allocated to the crop.