Some Specification Tests for the Linear Regression Model

Abstract

A great deal of recent work in econometrics has focused on the development of tests to detect violations of the assumptions of ordinary least squares regression. These tests are referred to collectively as specification tests. This article evaluates some important and computationally convenient specification tests for the normal regression model as applied to cross-sectional data. Because these tests achieve their optimal properties in large samples, their size and power in finite samples are of great interest and are evaluated with Monte Carlo simulations. Although the authors' experiments showed a tendency toward overrejection in some tests, their results suggest that specific variations of the RESET and information matrix tests behave quite well even in small samples. They conclude by proposing a strategy for the sequential application of specification tests.