Agriculture Reference
In-Depth Information
unpooled sample, it is left out of the logit estimates in tables 5.9. As table 5.9 illustrates, the
estimated coefficients for individual inputs add further support to the model. In all cases the
coefficients have the predicted sign, and in the majority of the cases they are statistically
significant. Although the magnitude and significance of the coefficient estimates vary from
input to input, this evidence shows that the relationships found in table 5.8 are robust and
generally hold across many different crop inputs.
Estimation of Cropshare Rules
As the two sets of first-order conditions (equations 5.5, 5.6, 5.7, and 5.8) imply, once the
decision about input cost sharing has been made, the optimal cropshare rule can be chosen.
The optimal input share
(q
∗
=
q
∗
=
s)
1or
and the potential for soil exploitation will both
s
∗
. Prediction 5.3 states that when inputs are not shared,
output share will rise as the number of other
influence the optimal cropshare,
inputs increases, because the distortions will
be spread across more margins. Predictions 5.2 and 5.6 imply that as the potential for soil
exploitation increases, the more likely the contract will be an input-output contract and thus
the lower will be the output share to the farmer. For each contract
k
i
the model is
ln
(s
i
/(
1
−
s
i
))
=
Zη
+
Q
i
θ
+
i
,
(5.11)
where
Z
is a row vector of explanatory variables,
η
is a column vector of unknown
coefficients,
Q
i
is the number of inputs paid fully by the farmer,
θ
is the corresponding
coefficient, and
i
is an error term. The natural logarithm of the output share ratio, ln
(s/(
1
−
s))
, is used instead of the output share because
s
is a limited-dependent variable, where
0
1. Table 5.10 shows the results of ordinary least squares (OLS) estimation of
equation 5.11 using three different specifications.
16
Prediction 5.3 is tested using the variable INPUTS, which measures the number of inputs
for which the farmer pays all costs
<s<
and is expected to be correlated positively to the
farmer's share of the crop. In all specifications we find the estimated coefficient to be positive
and statistically significant.
We test prediction 5.2 using several variables to measure the potential for soil exploitation.
In the first two specifications, the variables IRRIGATED and ROW CROP measure the
potential for the farmer to exploit the soil. As discussed in chapter 4, IRRIGATED indicates
land that is less subject to soil exploitation and ROW CROP indicates the opposite. Thus,
the estimated coefficients are expected to be negative for ROW CROP and positive for
IRRIGATED. In both specifications the estimated coefficients have the expected sign and are
statistically significant. In the last equation, dummy variables for specific crops—CORN,
OATS, SOYBEANS, and WHEAT—are included instead of ROW CROP. Because CORN
and SOYBEANS are row crops, we expect their coefficients to be negative. OATS and
(Q)
