as an indicator of a simultaneous decision to reject sharecropping. As a result, owner-farming and fixed-
rent farming are pooled as a common alternative to sharecropping.
The Land Extent Equations
We also carry out least squares regressions for the extent of land leased by each type of tenant to
determine whether this adjustment process occurs within each group. If the evidence of adjustment is
weak within groups, we can conclude that the adjustment process is carried out primarily in the first stage
where contracts are assigned to the tenants, and not by the size of the farm allocated to each tenant. This
result would confirm the claim of the theoretical model that type of contract, and not the individual farm
size, is the key choice variable in the leasing model. Since tenants of either type are a subset of our
sample, selectivity correction terms are included to obtain consistent estimates. We follow a two-step
method analogous to that of Heckman [1976] where the predicted probability of the subset is estimated in
the first stage, and a selectivity correction term based on this predicted probability is included in the second
stage linear regression to obtain consistent estimates of the parameters. The only difference from
Heckman’s original method is the use of multinomial and bivariate probit equations for selection. The
leasing equation for observations with Y=j is,
Hj = β ' x + θj λj + η j
[44]
The selectivity terms, λj, are constructed from the predicted probability of choice j computed from the
choice equations. If the multinomial logit model is used as the selection equation, the selectivity term, λj, is
calculated using the predicted probability for Y=j (equation [41]).
φ ( H,)
[45]
Âj =^(Hj), where Hj =φ-1( Pj )
23