Inference in the Threshold Model

This paper studies inference about the values of the parameters in the threshold model in a generalized method of moments (GMM) framework. First, we establish that the extensively studied least squares method leads to substantially oversized tests and confidence intervals when the coeffi cient change is not large. Second, by re-ordering the data to recast the threshold model as a structural break problem, we construct tests that control size under a large range of empirically relevant moderate coeffi cient changes and are approximately effi cient in a well-defined sense. Finally, we modify our approach to encompass inference problems in a variety of additional widely studied models. The accuracy of the asymptotic approximations is evaluated by Monte Carlo simulations. The empirical applicability is illustrated through two examples: (i) testing if public debt has a threshold effect on economic growth; and (ii) constructing a confidence interval for the tipping point in the segregation problem studied by Card, Mas, and Rothstein (2008).