MMC techniques for limited dependent variables models: Implementation by the branch-and-bound algorithm

We propose a finite sample approach to some of the most common limited dependent variables models. The method rests on the maximized Monte Carlo (MMC) test technique proposed by Dufour 1998. Monte Carlo tests with nuisance parameters: a general approach to finite-sample inference and nonstandard asymptotics. Journal of Econometrics, this issue]. We provide a general way for implementing tests and confidence regions. We show that the decision rule associated with a MMC test may be written as a Mixed Integer Programming problem. The branch-and-bound algorithm yields a global maximum in finite time. An appropriate choice of the statistic yields a consistent test, while fulfilling the level constraint for any sample size. The technique is illustrated with numerical data for the logit model.