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We propose a simple method of testing for parameter constancy in regression models with stationary data that allow for coefficients that vary smoothly over time. The method is shown to have good statistical properties. A sieve bootstrapping procedure is suggested to improve the finite sample size of the test for a large number of time polynomials in autoregressive models. We revisited Hansen's study (Journal of Economic Perspectives, Vol. 15 (2001), pp. 117–128) of structural breaks in a first-order autoregressive model of labor productivity in the US manufacturing/durables sector and found evidence of time-varying autoregressive parameter.