An analysis of the small sample behaviour of some econometric test statistics

Podivinsky, Jan Michael (1988) An analysis of the small sample behaviour of some econometric test statistics. University of Southampton, Doctoral Thesis.

Abstract

Asymptotic econometric test procedures are well known to be potentially inaccurate when applied to dynamic models estimated from finite samples of data. This thesis considers alternative techniques to examine the small sample behaviour of econometric statistics. These are then applied to three classes of tests in dynamic models. Edgeworth approximations are used to provide adjusted critical values for two asymptotically equivalent tests of non-tested hypotheses, and the empirical sizes of these tests are assessed by Monte Carlo simulation. This can often correct for much of the discrepancy between the tests' nominal and empirical sizes, particularly for the Wald CPE test. A simulation study of Wald and likelihood ratio tests of common factor restrictions indicates that both tests can have poor small sample properties. The Wald test and its power function are found to be non-monotonic for alternative hypotheses sufficiently far from the null hypothesis. In the third application, direct and indirect tests of weak exogeneity are examined. In particular Lagrange multiplier tests are found to have adequate performance in finite samples. Finally, it is argued that the assessment of the adequacy or otherwise of asymptotic tests in dynamic models must become more routine and more efficient.

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