Lecture2full

# Lecture2full - 1 File C\WINWORD\ECONMET\Lecture2 full...

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Unformatted text preview: 1 File: C:\WINWORD\ECONMET\Lecture2 full version.DOC UNIVERSITY OF STRATHCLYDE APPLIED ECONOMETRICS LECTURE NOTES MODEL MIS-SPECIFICATION AND MIS-SPECIFICATION TESTING Aims The estimates derived from linear regression techniques, and inferences based on those estimates, are only valid under certain conditions - conditions that amount to the regression model being "well-specified". In this set of notes, we investigate how one might test whether an econometric model is well-specified. We have four main objectives. (1) To examine what is meant by the misspecification of an econometric model. (2) To identify the consequences of estimating a misspecified econometric model. (3) To present a testing framework that can be used to detect the presence of model misspecification. (4) To discuss appropriate responses a researcher could make when confronted by evidence of model misspecification. (1) Introduction Assume that a researcher wishes to do an empirical analysis of a relationship suggested by some economic or finance theory. He or she may be interested in estimating (unknown) parameter values, or may be interested in testing some hypothesis implied by a particular theory. An appropriate procedure might consist of the following steps: Step 1: Specify a statistical model that is consistent with the relevant prior theory, in the sense that it embodies the theoretical relationship that the researcher believes exists between a set of variables. Notice that this first step requires that at least two choices be made: (i) The choice of the set of variables to include in the model. (ii) The choice of functional form of the relationship (is it linear in the variables, linear in the logarithms of the variables, etc.?) Step 2: Select an estimator which is known in advance to possess certain desired properties provided the regression model in question satisfies a particular set of conditions. In many circumstances, the estimator selected will be the OLS estimator. The OLS estimator is known to be BLUE (best, linear, unbiased estimator) under the validity of a particular set of assumptions. Even under less restrictive assumptions, the OLS estimator may still be the most appropriate one to use. However, there may be circumstances where we shall wish to use some other estimator. We shall denote the regression model as statistically well-specified for a given estimator if each one of the set of assumptions which makes that estimator optimal is satisfied. The regression model will be called statistically misspecified for that particular estimator (or just misspecified) if one or more of the assumptions is not satisfied. Step 3: Estimate the regression model using the chosen estimator....
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Lecture2full - 1 File C\WINWORD\ECONMET\Lecture2 full...

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