The Relationship among the Specification Tests of Hausman, Ramsey, and Chow

This article describes a relationship between the tests for specification error in regression models introduced by Ramsey (1969) and Hausman (1978). It also shows that the Chow (1960) test for structural shift can be viewed as a special case of specification error tests. This article shows the common structure of these tests. The common basis is the comparison of alternative estimators of regression coefficients. Under the null hypothesis, one estimator is efficient and consistent and the other is consistent. The probability limits of the two estimators are different under the alternative hypothesis.