Nonstationary Logistic Regression

Abstract

In this paper, we consider the logistic regression model with an integrated regressor driven by a general linear process. In particular, we derive the limit distributions of the nonlinear least squares (NLS) estimators and their t-ratios of the parameters in the model. It is shown that the NLS estimators are generally not efficient. Moreover, the t-ratios for the level parameters have limit distributions that are nonnormal and dependent upon nuisance parameters, due to the asymptotic correlation between the innovations of the regressor and the regression errors. We propose an efficient NLS procedure to deal with the inefficiency of the estimators and inferential difficulty. The new NLS procedure yields estimators that are efficient and have asymptotically normal t-ratios. The finite sample properties of the usual and efficient NLS estimators and their t-statistics are investigated through Monte Carlo simulations.