Hausman (1978) developed a widely-used model specification test that has passed the test of time. In this paper, we show that the asymptotic variance of the difference of the two estimators can be a singular matrix. Three illustrative examples are used, namely an exogeneity test for the linear...

Standard tests are generally not applicable in panel data models with selection. The paper shows how the Hausman specification test and the Sargan–Hansen test for overidentifying restrictions can be generalized to panel data models with unobserved heterogeneity and sample selection.

This paper develops a modified version of the Sargan [Sargan, J.D., 1958. The estimation of economic relationships using instrumental variables. Econometrica 26 (3), 393–415] restrictions, and shows that it is numerically equivalent to the test statistic of Hahn and Hausman [Hahn, J., Hausman,...

Separability is an important feature of structural equations, as it implies the absence of unobservable heterogeneity of effects and has significant implications for identification and efficiency of estimation. This paper provides a nonparametric test for separability in structural equations....

This paper provides a nonparametric test of the specification of a transformation model. Specifically, we test whether an observable outcome Y is monotonic in the sum of a function of observable covariates X plus an unobservable error U. Transformation models of this form are commonly assumed in...

Testing for stochastic dominance among distributions is an important issue in the study of asset management, income inequality, and market efficiency. This paper conducts Monte Carlo simulations to examine the sizes and powers of several commonly used stochastic dominance tests when the...

We introduce tests for finite-sample linear regressions with heteroskedastic errors. The tests are exact, i.e., they have guaranteed type I error probabilities when bounds are known on the range of the dependent variable, without any assumptions about the noise structure. We provide upper bounds...