Estimation of a latent linear model based on the rank statistics of the dependent variable.

In this paper we study a new type of latent model in which only the rank statistics of the depen- dent variable is observed. This problem appears naturally in the microeconometric literature, in particular in the case of the parametric estimation of a production function when the output is poorly observed. A full information approach seems difficult. So we consider another model which describes part of the information of the first one. This second model is Probit model with serial correlations. The inferential problems (test and estimation) have been studied in the literature but not from this viewpoint. We show by simulations that the proposed estimators behave nicely even in relatively small samples. We also perform the estimation of a production function on a real data set.