Efficient Tests under a Weak Convergence Assumption
43 Pages Posted: 15 Mar 2008 Last revised: 21 Jan 2009
Date Written: December 2008
The paper studies the asymptotic efficiency and robustness of hypothesis tests when models of interest are defined in terms of a weak convergence property. The null and local alternatives induce different limiting distributions for a random element, and a test is considered robust if it controls asymptotic size for all data generating processes for which the random element has the null limiting distribution. Under weak regularity conditions, asymptotically robust and efficient tests are then simply given by efficient tests of the limiting problem - that is, with the limiting random element assumed observed - evaluated at sample analogues. These tests typically coincide with suitably robustified versions of optimal tests in canonical parametric versions of the model. This paper thus establishes an alternative and broader sense of asymptotic efficiency for many previously derived tests in econometrics, such as tests for unit roots, parameter stability tests and tests about regression coefficients under weak instruments.
Keywords: robustness, unit root test, semiparametric efficiency
JEL Classification: C12, C14
Suggested Citation: Suggested Citation