A simple approximation for the bivariate normal cumulative distribution function (BNCDF) based on the error function is derived. The worst error of our method is found to four decimal places under various configurations considered in this paper's Table 1. This finding is much better than that in...

It is found in Lee (2000) and Rabe-Hesketh et al. (2005) that the typical numerical-integral procedure suggested by Butler and Moffitt (1982) for the random effects probit model becomes biased when the correlation coefficient within each unit is relatively large. This could possibly explain why...

This paper derives an analytic approximation formula for the likelihood function of the true random effects stochastic frontier model of Greene (2005) with a time span T = 2. Gaussian quadrature procedure and simulation-based method is not re- quired for the closed-form approach. Combining the...