Maximum Likelihood Estimator for Multivariate Binary Response Models

Abstract

The paper considers a multivariate binary response model that allows for a range of response distribution functions and pairwise response dependencies. The maximum likelihood estimator (MLE) for the model is derived and its asymptotic distribution and convergence properties are established. First, the analytically tractable closed form of necessary binary response probabilities is obtained. Second, the asymptotic information matrix is derived. Third, it is shown that identification is possible under fairly modest model assumptions. Fourth, the MLE for this model is consistent, asymptotically normal, and achieves the Cramer-Rao lower bound; the estimator for this model has a semi-quadratic rate of convergence, which is standard for maximum likelihood estimators.

Keywords: multivariate probit, multivariate logit, identification, information matrix, analytically tractable maximum likelihood

JEL Classification: C13, C35, C18