where σε
2 is the variance of the error term in the selection equation (1), which can be assumed to
be equal to 1, since the coefficients are estimable up to scale factor (Maddala, 1983); σ1
2 and σ0
2 are
the variances of the error terms in the outcome functions; and σε1 is the covariance between u1 and
ε ; σε 0 is the covariance between u0 and ε . The covariance between u1 and u0 is not reported since
y1 and y0 are not observed simultaneously.
Following Lokshin and Sajaia (2004), the full maximum likelihood estimation analytical approach was
defined based on the trivariate normal distribution, with zero mean and covariance matrix Σ, as follows: