Efficient Conditionally Similar-on-the-Boundary Tests

• Departmental Seminar

Date and Location

Wednesday, January 23, 2013, 10:30 AM - 12:00 PM

Abstract

This paper presents a new class of tests for hypothesis testing problems with a notable feature: a boundary-sufficient statistic. Examples include testing in Linear Instrumental Variables Regression, testing in a class of weakly identified Generalized Method of Moments models, and testing for dynamic effects in a Structural Vector Autoregression identified using external instruments. The new tests minimize a weighted sum of the average rates of Type I and TypeII error (average risk), while controlling the conditional rejection probability on the boundary of the null hypothesis; in this sense they are efficient conditionally similar on the boundary (ECS). ECS tests are admissible within the class of procedures that control the rate of Type I error by conditioning on the boundary-sufficient statistic. Moreover,they verify an important finite-sample optimality property: admissibility within the class of all tests, provided the boundary-sufficient statistic is boundedly complete. The theory developed in this paper yields novel—analytically optimal—testsfor the examples mentioned above. This paper also shows that the Anderson and Rubin (1949) test for Linear Instrumental Variables Regression and Stock and Wright's (2000) S-tests for the Generalized Method of Moments framework are ECS in a wide variety of "just-identified" models.