Working Paper

Abstract

This paper develops new statistical inference methods for the parameters in threshold regression models. In particular, the authors develop a test for homogeneity of the threshold parameter and a test for linear restrictions on the regression coefficients. The tests are built upon a transformed partial-sum process after re-ordering the observations based on the rank of the threshold variable, which recasts the crosssectional threshold problem into the time-series structural break analogue. The asymptotic distributions of the test statistics are derived using this novel approach, and the finite sample properties are studied in Monte Carlo simulations. The authors apply the new tests to the tipping point problem studied by Card, Mas, and Rothstein (2008), and statistically justify that the location of the tipping point varies acrosstracts.