Estimation of the probit model with autocorrelated errors via the MCECM algorithm

Estimation of the probit model with autocorrelated errors often involves the calculation of a multiple integral which is usually intractable. A stochastic version of the EM algorithm is proposed to solve the problem. The approach implements the E-step by retrieving the latent values via a Monte Carlo method (MCE-step) and replaces the M-step by a sequence of conditional maximizations (CM-step). The practicality of this MCECM algorithm is illustrated by estimating the reaction function of the monetary policy in Taiwan by a probit model with first-order serial correlation.