Non‐stationary regression with logistic transition

Abstract

Summary This paper studies the non-stationary regression model with logistic transition in level or in slope. In the model, the level or slope is specified as a functional coefficient specified parametrically as the logistic function of an integrated state variable driven by a general linear process. For such a model, we derive the limit distributions of the non-linear least squares (NLS) estimators and their t-statistics. As for many other types of non-stationary non-linear regressions, the NLS estimators and the usual t-tests are generally inefficient and invalid in our model. We propose a new procedure, which yields efficient estimators and valid tests. Our simulation shows that they perform noticeably better than the standard NLS estimators and tests. Finally, our model and methodology are used to investigate the long-run relationship between per capita real income and consumption using US data.