Rural Development Policies and Sustainable Land Use in the ...

METHODS AND MODELS 35
Inclusion of endogenous explanatory
variables in equations (1)–(5) and (8) could
result in biased estimates. We use instrumental
variables (IV) estimation to address
the endogeneity problem in equations (1),
(5), and (8). Because the dependent variables
in equations (2)–(4) are limited dependent
variables [censored in equation (2)
and binary in equations (3) and (4)], it is not
technically appropriate to use IV estimation
for these equations. However, we tested linear
OLS versus IV versions of these models
using a Hausman (1978) exogeneity test, to
test whether endogeneity of the livelihood
strategies (LS ht
) and participation in programs
and organizations (P ht
) could be biasing
our results. For equations (3) and (4),
this amounts to assuming a linear probability
model rather than a nonlinear probit model
(only for the purposes of the exogeneity test).
For equation (2), we tested for exogeneity
using a truncated version of the regression
for family labor, dropping the observations
with zero family labor used on the plot. We
did this only for the family labor regression,
since there were few censored observations
for family labor input (only 35 out of 1635
observations), implying that the truncation
should have little effect on the validity of the
results (there were many censored observations
for the other types of labor input). We
also tested for exogeneity of these variables
(i.e., LS ht
and P ht
) in equations (5) and (8)
using a Hausman test. In no case did we
reject exogeneity of the livelihood strategies
and participation variables at the 10 percent
level. In all cases, the instrumental variables
used were found to be highly significant
predictors of the endogenous explanatory
variables (hence the instrumental variables
are “relevant”) and the validity of the exclusion
restrictions was accepted using
Hansen’s J test (Davidson and MacKinnon
2004) (the results of these tests are reported
in the discussion of the econometric results
in Chapter 5). These results give us confidence
that our results in estimating equations
(2)–(5) and (8) are not biased by endogeneity
of the livelihood strategies and
participation variables.
Based on these results, we treat livelihood
strategies and participation in programs and
organizations as exogenous variables in estimating
equation (1). We estimate equation
(1) several ways. First we estimate the full
model using ordinary least squares (OLS)
and IV estimation, including all of the variables
specified. In the full IV model, predicted
values of L hpt
, and predicted probabilities
of LM hpt
and IN hpt
from estimation
of equations (2)–(4) are used as instrumental
variables. 35 To identify additional
instrumental variables and improve the
performance of the models, we tested the
joint significance of subsets of the village-,
household-, and parcel-level variables using
Wald tests in both the full OLS and IV models,
and then estimated reduced OLS and IV
models that excluded variables that were
highly statistically insignificant (p-values
at least 0.20) in both of the full models. In
the reduced IV model, we tested the relevance
of the excluded instrumental variables
using joint significance tests for the firststage
regressions, and the validity of the
exclusion restrictions using Hansen’s J test
(see Davidson and MacKinnon 2004 for a
description of these tests). The excluded instrumental
variables were highly significant
predictors of all of the endogenous righthand
side variables in the annual crops
regression, and for most of the endogenous
variables in the perennial crops regression.
In both regressions, Hansen’s J test failed
to reject the exclusion restrictions. Thus we
have confidence that the reduced models are
valid. Hausman tests comparing the reduced
versions of the OLS and IV models were
conducted, and failed to reject the OLS
model in both the annuals and perennials regressions.
Thus, the OLS model is preferred
as the more efficient model in both cases,
35
The full IV model is identified by the nonlinearities in equations (2)–(4).