A new test for hysteresis based on a nonlinear unobserved components model is proposed. Observed unemployment rates are decomposed into a natural rate component and a cyclical component. Threshold type nonlinearites are introduced by allowing past cyclical unemployment to have a different impact on the natural rate depending on the regime of the economy. The impact of lagged cyclical shocks on the current natural component is the measure of hysteresis. To derive an appropriate p-value for a test for hysteresis two alternative bootstrap algorithms are proposed: the first is valid under homoskedastic errors and the second allows for heteroskedasticity of unknown form. A Monte Carlo simulation study shows the good performance of both bootstrap algorithms. The bootstrap testing procedure is applied to data from Italy, France and the United States. We find evidence of hysteresis for all countries under study.
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