Testing for linearity in the context of Markov switching models is complicated because standard regularity conditions for likelihood based inference are violated. This is due to the fact that, under the null hypothesis of linearity, some parameters are not identified and scores are identically zero. Thus the asymptotic distribution of the test statistic of interest does not possess the standard χ 2 -distribution. In this paper we propose a bootstrap resampling scheme to approximate the distribution of the test statistic of interest under the null of linearity. The procedure is relatively easy to program and the computation requirements are reasonable. We investigate the performance of the bootstrap-based test using Monte Carlo simulations. We find that the test works well and outperforms the Hansen test and the Carrasco et al. test. The use of the various methods is also illustrated by means of empirical examples.

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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 nonlinearities 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.JEL classification: C12; C13; C15; C32; E24.

The aim of this paper is to identify the different sources of persistence of output fluctuations. We propose an unobserved components model that allows us to decompose GDP series into a trend component and a cyclical component. We let the drift of the trend component switch between different regimes according to a first-order Markov process. To calculate an appropriate p-value for a test of linearity we propose a bootstrap procedure, which allows for general forms of heteroscedasticity. The performance of the bootstrap is checked by means of a Monte Carlo simulation. Our study concerns the USA. We find that cyclical shocks appear to play an important role on the observed persistence of output.