Publication Type

Journal Article

Version

acceptedVersion

Publication Date

11-2018

Abstract

Two test statistics are proposed to determine model specification after a model is estimated by an MCMC method. The first test is the MCMC version of IOSA test and its asymptotic null distribution is normal. The second test is motivated from the power enhancement technique of Fan et al. (2015). It combines a component (J1) that tests a null point hypothesis in an expanded model and a power enhancement component (J0) obtained from the first test. It is shown that J0 converges to zero when the null model is correctly specified and diverges when the null model is misspecified. Also shown is that J1 is asymptotically χ2 -distributed, suggesting that the second test is asymptotically pivotal, when the null model is correctly specified. The main feature of the first test is that no alternative model is needed. The second test has several properties. First, its size distortion is small and hence bootstrap methods can be avoided. Second, it is easy to compute from MCMC output and hence is applicable to a wide range of models, including latent variable models for which frequentist methods are difficult to use. Third, when the test statistic rejects the null model and J1 takes a large value, the test suggests the source of misspecification. The finite sample performance is investigated using simulated data. The method is illustrated in a linear regression model, a linear state-space model, and a stochastic volatility model using real data.

Keywords

Specification test, Point hypothesis test, Latent variable models, Markov chain Monte Carlo, Power enhancement technique, Information matrix

Discipline

Econometrics

Research Areas

Econometrics

Publication

Journal of Econometrics

Volume

207

Issue

1

First Page

237

Last Page

260

ISSN

0304-4076

Identifier

10.1016/j.jeconom.2018.08.001

Publisher

Elsevier: 24 months

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.1016/j.jeconom.2018.08.001

Included in

Econometrics Commons

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