Date of Award
1984
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Abstract
In this thesis the analytic techniques of Edgeworth and Nagar's expansion and approximate slope are used to examine small sample properties of estimators and test statistics in some econometric models. The chapters are largely self-contained.;Chapter one provides some definitions, hypothesis test construction methods, and a decription of techniques to be used and models to be studied.;In chapter two, Edgeworth expansions are used to examine the properties of LR, W and LM test for linear restrictions on regression parameters in the standard one-equation model with Student's t errors. Edgeworth size-correction factors are found to be more effective than degrees-of-freedom-based corrections.;Chapter three examines three aspects of the regression model with first order autoregressive errors. First, it is shown that the Lm test statistic for the existence of this kind of autocorrelation is numerically insensitive to whether the error terms have normal or Student's t distributions. Second, Nagar's expansion techniques are used to compare the efficiency of various estimators of the regression coefficients (icluding iterative). The results largely support the results of previous Monte Carlo studies. Finally, an Edgeworth expansion is used to provide a size correction factor for the Wald test for a zero coefficient restriction.;Chapter four deals with the test for existence of contemporaneous correlation between errors of different regression equations. This is a relevant pre-test for specification of SURE models. A variety of tests are presented, including one based on the Union-Intersection (UI) test construction principle. Relationships between the tests in some special cases are discussed, including a comparison of their approximate slopes. The UI test is exact, easy to use, but may have lower power.;Chapter five deals with the Cox and J tests for choosing between two non-tested single equation models. An Edgeworth expansion for the J test under both models is obtained, as well as a size correction factor. The approximate slopes of Cox and J tests are used to explore situations where the small sample properties of the two tests may differ substantially.
Recommended Citation
Magee, Lonnie John, "Analytic Studies In Econometric Inference With Small Samples" (1984). Digitized Theses. 1352.
https://ir.lib.uwo.ca/digitizedtheses/1352