This paper by J. A. Hausman discusses specification tests in econometrics, focusing on the importance of testing for the orthogonality assumption ($E(\epsilon | X) = 0$) and the sphericality assumption ($V(\epsilon | X) = \sigma^2 I$). The author proposes a general form of specification test that aims to provide powerful tests for the orthogonality assumption. The key idea is to use an alternative estimator that is unbiased under both the null and alternative hypotheses, and to compare it with the efficient estimator. The difference between these two estimators, denoted as $\hat{q}$, is used to construct a test statistic. The paper also addresses the issue of pretesting and minimum mean square error estimation, and provides two empirical examples to illustrate the application of the proposed tests. The first example tests the time series-cross section specification, while the second example tests the simultaneous equation specification.This paper by J. A. Hausman discusses specification tests in econometrics, focusing on the importance of testing for the orthogonality assumption ($E(\epsilon | X) = 0$) and the sphericality assumption ($V(\epsilon | X) = \sigma^2 I$). The author proposes a general form of specification test that aims to provide powerful tests for the orthogonality assumption. The key idea is to use an alternative estimator that is unbiased under both the null and alternative hypotheses, and to compare it with the efficient estimator. The difference between these two estimators, denoted as $\hat{q}$, is used to construct a test statistic. The paper also addresses the issue of pretesting and minimum mean square error estimation, and provides two empirical examples to illustrate the application of the proposed tests. The first example tests the time series-cross section specification, while the second example tests the simultaneous equation specification.