Local maximum likelihood techniques with categorical data

In this paper we provide asymptotic theory of local maximum likelihood techniques for estimating a regression model where some regressors are discrete. Our methodology and theory are particularly useful for models that give us a likelihood of the unknown functions we can use to identify and estimate the underlying model. This is the case when the conditional density of the variable of interest, given the explanatory variables, is known up to a set of unknown functions. Examples of such models include probit and logit models, truncated regression models, stochastic frontier models, etc. In developing the theory we use the Racine and Li (2004) kernels for discrete regressors. The asymptotic properties of the resulting estimator are derived and the method is illustrated in various simulated scenarios. The results indicate a great flexibility of the approach and good performances in various complex scenarios, even with moderate sample sizes