We investigate the problem of testing structural changes in nonparametric instrumental regressions via the Fourier transform of data. Our approach does not rely on the availability of instruments, and it avoids smoothed nonparametric estimation of the unknown structural function. Thus, it is free of both the “curse of dimensionality” and the “ill-posed inverse” problems. Compared to the existing methods that use instruments, our test is asymptotically more powerful. 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.

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