where Yi is a binary variable equal to 1 if household i adopts the new technology; XiT is a set
of observed farm household variables influencing the choice of technology; and εi T is the
random variable of the estimated equation.
MiJ , are binary endogenous variables equal to 1 if the ith household participates in the Jth
migration alternative, i.e. to temporary, permanent or international migration40 (and zero if
there is no migrant members); XiM is a vector of household characteristics influencing the
decision to migrate (different effects may result across the three typologies of migration) and
ZJiM are exogenous variables to be used in the “first stage” of the system as instruments for
the endogenous migration variables; εJiM is the random variable of each migration equation.
Endogenous migration variables are correlated with the disturbance of the adoption equation,
violating the assumption of ordinary least squares (Wu-Hausman F test rejects the null
hypothesis that migration typologies are exogenous variables at 0.01 significance level)41;
further, the simultaneous decision problem entails that the error terms among equations are
(cross-) correlated as well. We use 3sls estimation in order to take account of both
simultaneity and endogeneity biases.
Three-stage estimator uses an instrumental variables procedure to produce consistent
estimates and generalised least squares to account for correlation structure in the disturbances
across equations. Heckman and MaCurdy (1985) show that in case of simultaneous linear
probability models, instrumental variable procedure produces consistent estimates.
This approach is the most tractable for our aim at estimating causal or potential effect of
migration on the propensity to adopt risky technologies, rather than latent index coefficients
(see Angrist, 2001)42. This is so because the two-stage and single-stage estimates are directly
comparable. For robustness purpose, though, Table A.2 in appendix presents structural results
of a probit adoption model estimated using instrumental-variable-probit (or Amemiya
40 This is done in the same way as for the multinomial logit above, making categories mutually exclusive (i.e.
household cannot belong to more than one category).
41 For comparison purposes, the adoption equation has been estimated using simple OLS but results are not
encouraging for migration typologies. However, the estimation procedure ignores the problem of endogeneity of
migration decisions and the possible cross-equation correlation. As a raw check of endogeneity, we also included
three interacted variables between typologies of migration and the size of land owned by household. Signs of
interaction variables for permanent and international migration turn to be significant, suggesting that these types
of migrations coupled with land ownership may have a potential effect on the propensity to adopt a superior
agricultural technology.
42 Limited dependent variable models with dummy endogenous regressors were first estimated using
distributional assumptions and maximum likelihood (Heckman, 1978, Amemiya, 1978, Newey, 1985). Angrist
(2001) argues that if the aim is to estimate causal or potential effect on the outcome of interest - rather than
structural parameters of latent variables model - linear models are no less appropriate for binary dependent
variables than non-linear models.
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