Comparing specification tests and classical tests
Jerry A. Hausman, William E. Taylor · DSpace@MIT (Massachusetts Institute of Technology) · 1980
A parametric restriction is often interesting because it makes pos^iible simplifications or Improvements in estimators for the parameters of primary interest.In such cases, a specification test examines the effect of imposing the restrictions on the estimator, whereas classical tests exar.ine the restrictions themselves in light of the data.In some circumstances, this leads to discrepancies in large sample behavior between (i) specification tests and (ii) likelihood ratio, Wald, and Lagrange multiplier tests.We examine this distinction in three cases of recent interest: exclusion restrictions in a simple linear model, parametric restrictions in a general non-linear implicit model, and exogeneity restrictions in a simultaneous equations model.