Forchini, Giovanni
(1998)
Exact distribution theory for some econometric problems.
*University of Southampton, Doctoral Thesis*.

## Abstract

This thesis consists of three papers which deal with three different econometric problems but have a common approach: exact distribution theory.

In the first paper, "Conditional Inference in Possibly Unidentified Structural Equations", we tackle the problem of inference in structural equations which can be unidentified. It is well known that both the small sample and the asymptotic properties of the usual estimators for the parameters break down when a structural equation is unidentified, but no practical procedure has been developed to take account of this possibility. We suggest that, in possibly unidentified models, inference should be made conditional on an identification test statistic, and show that the identification test statistic should be considered as an index of precision for inference.

The second paper "The Geometry of Similar Tests for Structural Change", characterises similar tests for structural change in the linear model under the hypothesis of normality of errors. We show that uniformly most powerful similar tests do not exist when it is not known where the structural breaks occur. We argue that the geometry of the testing problem generates an "intrinsic difficulty", which makes testing for structural change pointless if no information about the change points is available. Since this affects the power of all testing procedures, we emphasise the importance of reporting a measure of the intrinsic difficulty.

The third paper "Miscellaneous Results for the Gaussian AR(1) Model" shows that the density of the maximum likelihood estimator for the parameter of an AR(1) model with zero start-up value is well defined and analytic almost everywhere.

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