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Essays on Optimal Tests for Parameter Instability
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There are a large number of tests for parameter instability designed for specific types of unstable parameter processes and error distributions. However, it is difficult to identify those types in practice based on a priori knowledge. My dissertation studies methods and conditions under which asymptotically efficient tests are obtained without the knowledge of the unstable parameter process and the error distribution. I first derive an asymptotically optimal test in a general parametric model and examine conditions under which the knowledge of the unstable parameter process is inappropriate. The test is then extended to a model with unknown error distribution. It is shown to be possible not to lose any asymptotic power by not knowing the true error distribution.
Efficient Tests for Parameter Instability When the Error Distribution is Unknown (job market paper)
This chapter examines asymptotically efficient tests for parameter instability in general semiparametric models in which the error distribution is unknown but treated as an infinite dimensional nuisance parameter. I first derive the asymptotic power envelope with unknown density and suggest conditions under which a semiparametric model would have the same asymptotic power envelope with known error distribution. The conditions are weak enough to cover a wide range of error distributions by relaxing the twice differentiability and allowing for skewness. An efficient test statistic is then suggested, which is adaptive in the sense that allowing unknown error distribution gives no loss of asymptotic power. This implies that the knowledge of the error distribution is asymptotically irrelevant under mild conditions. Monte Carlo experiments show that the adaptive test has improved small sample powers over the existing tests under various error distributions. The test is used to examine the parameter stability in several predictive models for post-Volcker U.S. inflation.
Optimal Tests for Parameter Instability in General Time Series Models
It
is difficult to select the appropriate test for parameter instability in
empirical work because there are a large number of tests designed for
different possible unstable processes. Elliott and Müller (2006) resolve this problem by providing conditions under
which a large class of breaking processes lead to asymptotically equivalent
optimal tests. Their finding, however, is restricted to linear conditional mean
equations with normal error distributions. I improve upon their work in two
ways. First, I show that the asymptotic equivalency of the efficient tests for
parameter instabilities holds even in a broader set of parametric models which
includes nonlinear ones with non-Gaussian error distribution. It implies that
the knowledge of the unstable parameter process is asymptotically irrelevant
for testing purposes. Second, I suggest a test statistic that is asymptotically
optimal for a broad set of unstable parameter processes which allows for both
structural breaks and time varying parameters. Monte Carlo studies show that
the suggested test has better small sample powers against various breaking
processes, compared to the existing optimal tests.
Testing Parameter Stability in Quantile Models for the U.S. Macroeconomy (in progress)
This chapter examines the parameter instabilities in various U.S. macroeconomic models. Conditional quantile models, rather than the traditional conditional mean ones, are considered for the test in that the quantile model generally provides a more nuanced view of economic relationships and the risk structure. Lee's (2007) efficient test is used for monthly data from the postwar U.S. economy. In terms of the models for inflation, the test suggests that the quantile relationships are unstable. The instabilities are not reduced even in the great moderation.
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