This paper considers a nonparametric conditional moment test of stability of an econometric model against the alternative of instability. The alternative hypothesis allows for more than one structural change, although in this case it has to be fairly smooth. This complements existing results for stability in a parametric setting. Also, it is shown that the test is always consistent, unlike the available “parametric” tests, which normally rely on the assumption of a correct specification of the model, at least under the null hypothesis of no structural instability. Moreover, we show that the test has local power comparable to the parametric ones; that is, its asymptotic efficiency is greater than zero. A Monte Carlo experiment about the performance of our test is described
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