Skills, Partnerships and Tenancy in Sri Lankan Rice Farms

The coefficients estimates, βj, can then be interpreted as the marginal effect of x_i on the relative
log odds ratio between the choice j and choice 0.

Bivariate Probit Model of Contract Choice

The bivariate probit model jointly estimates probit equations for the leasing and contract choices
with correlated error terms. The specification of this standard model is

L = β x + ε ₁,      L = 1 if L* > 0, 0 otherwise

S * = β2 x + ε 2,      S = 1 if S * > 0, 0 otherwise

ε 1, ε2 ~ N(0,0, σ₁, σ2, p)

where L^* and S^* are the underlying choice variables for the extent of land leased-in and the extent of land
sharecropped, L and S are the observed choices and x is a vector of explanatory variables that includes F,
X, H and Z. The functional form is used to identify the model with the same set of explanatory variables
in both equations because it is difficult to find identifying variables for either equation.

Since we do not observe the contract choice for the farmers who choose to self-cultivate, the
standard model must be modified to incorporate the fact that the contract choice (S) exists only if the
leasing choice (L) is positive. This gives rise to a bivariate probit model with three types of probabilities:

P^rob( L =^1, S =⁰⁾ = ^φ2(- ^β2x 2^{, β χ} 1^,-p )

P^rob( L = ^1, S = ¹) = ^φ2( ^β2^χ 2^{, β}1'^χ 1^, p )

Prob(L = 0)        = (1) - Φ(β1'x 1), (2) 1-Φ(β1x 1)

The first specification, proposed by Wynand and van Praag (1981), treats S as a truncated
variable at L=0. The second variant, due to Meng and Schmidt (1985), defines S as a zero-censored
variable when L=0. The obvious difference is that the latter method treats the choice to reject leasing-in

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