An Efficient Decomposition of the Expectation of the Maximum with Normally Distributed Errors

In structural dynamic discrete choice models, one way to allow correlation across errors associated with different choices is to use the multivariate normal distribution. Unfortunately, the expectation of the maximum with normally distributed errors is relatively difficult to evaluate. In this paper, however, I show that this expectation can be decomposed as a linear combination of multivariate normal CDFs. With simulated data, I show that an estimation algorithm based on this decomposition can estimate a model both more quickly and more accurately than an algorithm based on Monte Carlo integration