Econometrica: Nov 2007, Volume 75, Issue 6

Testing for Regime Switching

https://doi.org/10.1111/j.1468-0262.2007.00809.x
p. 1671-1720

Jin Seo Cho, Halbert White

We analyze use of a quasi‐likelihood ratio statistic for a mixture model to test the null hypothesis of one regime versus the alternative of two regimes in a Markov regime‐switching context. This test exploits mixture properties implied by the regime‐switching process, but ignores certain implied serial correlation properties. When formulated in the natural way, the setting is nonstandard, involving nuisance parameters on the boundary of the parameter space, nuisance parameters identified only under the alternative, or approximations using derivatives higher than second order. We exploit recent advances by Andrews (2001) and contribute to the literature by extending the scope of mixture models, obtaining asymptotic null distributions different from those in the literature. We further provide critical values for popular models or bounds for tail probabilities that are useful in constructing conservative critical values for regime‐switching tests. We compare the size and power of our statistics to other useful tests for regime switching via Monte Carlo methods and find relatively good performance. We apply our methods to reexamine the classic cartel study of Porter (1983) and reaffirm Porter's findings.

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Supplemental Material

Testing for Regime Switching, Supplementary material

This file contains the program code that generates the approximated tail lower bound distribution of the QLR tet statistic given in the papger, for the four different cases considered in Table 1 and obtained by Theorem 7.

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Testing for Regime Switching, Supplementary material

The program code that generates the approximated tail lower bound distribution of the QLR tet statistic given in the papger.

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Testing for Regime Switching, Supplementary material

This file contains an explanation for the two software supplementary files.

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