A model-free consistent test for structural change in regression possibly with endogeneity

Abstract Structural instability leads to misleading inference and imprecise prediction of time series models that assume stationarity. We propose a model-free consistent test for structural change in regression by testing the instability of the Fourier transform of data. This novel approach avoids smoothed nonparametric estimation of the unknown regression function and so is free of the “curse of dimensionality” problem. Unlike the existing literature, we allow for endogenous and discrete regressors. By using a proper choice of weighting functions for the transform parameters in the Fourier transform, we avoid numerical integration so that our test statistic is easy to compute. Our test statistic has a convenient asymptotic N ( 0 , 1 ) distribution under the null hypothesis of no structural change and is consistent against a large class of smooth structural changes as well as abrupt structural breaks with unknown break dates. A Monte Carlo study and an empirical application show that our test performs reasonably well in finite samples.