Misspecification testing in systems of equations

Abstract

This dissertation is a set of related papers on the application of the "principle of statistical adequacy" to single and multi-equation econometric models.

The first chapter lays out the intended scope of the dissertation and defines the principle of statistical adequacy.

The second chapter reviews the formulation of tests of statistical adequacy for multivariate models, and describes the implementation of these tests. The first approach that is discussed is to select particular functions of the variables involved that should be orthogonal under the null hypothesis of no misspecification, and the sample analog of these functions is used as a basis for constructing misspecification tests. As an extension of this idea, it is argued that viewing the model in explicit probabilistic terms provides a basis for developing a set of orthogonality conditions that can be tested in terms of all the probabilistic assumptions underlying the model. The formulation of misspecification tests via auxiliary regressions using general polynomial functions and the implementation of these tests via a menu-driven econometric modeling computer program is described.

The third chapter reports the results of an empirical application of the principle of Statistical adequacy to the modeling of inflation/unemployment trade-offs for the U.S. Using a Statistically adequate “reduced-form" as the basis, a number of competing theoretical models are considered. The use of graphical techniques and formal misspecification tests in determining the adequacy of the statistical model are emphasized. It is found that none of the competing theoretical explanations of aggregate labor market behavior are acceptable in terms of the over-identifying restrictions imposed or their own statistical adequacy.

The final chapter is an example of how one might proceed when a specification failures the criteria of statistical adequacy. For U.S. interest rates, it is shown that linear-homoskedastic autoregessions do not adequately account for the leptokurtosis and non-linear temporal dependence in the data. Using the evidence provided by preliminary data analysis as a guide, the Student’s t autoregressive model with dynamic heteroskedasticity is estimated for the log differences in three interest rate series. The estimation and misspecification testing results suggest that the STAR model adequately accounts for the probabilistic features of the data: bell-shape symmetry; leptokurtosis; first and second-order temporal dependence. In contrast, a number of other heteroskedastic specifications are estimated, and found to be statistically inadequate.