Testing Separate Regression Models Subject to Specification Error

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Abstract
Within the framework of linear regression, errors arising from artificial inclusion or exclusion of variables are considered with augmentations or restrictions on a given maintained hypothesis. This permits exploitation of relations between tests based on Wald and Lagrange Multiplier Principles. It is demonstrated that the standard F test, though based on biased estimators, is nevertheless valid. The traditional analysis of misspecification is applied to the linear specialization of tests for separate families of hypotheses. An empirical example is provided examining the effect of labour legislation on the growth of Canadian trade union membership, using annual data for 1925-72.
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