TY - JOUR
AU - Andrews,Donald W.K.
AU - Moreira,Marcelo
AU - Stock,James H.
TI - Optimal Invariant Similar Tests for Instrumental Variables Regression
JF - National Bureau of Economic Research Technical Working Paper Series
VL - No. 299
PY - 2004
Y2 - August 2004
DO - 10.3386/t0299
UR - http://www.nber.org/papers/t0299
L1 - http://www.nber.org/papers/t0299.pdf
N1 - Author contact info:
Donald Andrews
E-Mail: donald.andrews@yale.edu
Marcelo Moreira
Department of Economics
Getulio Vargas Foundation - 11th floor
Praia de Botafogo 190
Rio de Janeiro - RJ 22250-040
E-Mail: mjmoreira@fgv.br
James H. Stock
Department of Economics
Harvard University
Littauer Center M26
Cambridge, MA 02138
Tel: 617/496-0502
Fax: 617/495-7730
E-Mail: James_Stock@harvard.edu
AB - This paper considers tests of the parameter on endogenous variables in an instrumental variables regression model. The focus is on determining tests that have certain optimal power properties. We start by considering a model with normally distributed errors and known error covariance matrix. We consider tests that are similar and satisfy a natural rotational invariance condition. We determine tests that maximize weighted average power (WAP) for arbitrary weight functions among invariant similar tests. Such tests include point optimal (PO) invariant similar tests. The results yield the power envelope for invariant similar tests. This allows one to assess and compare the power properties of existing tests, such as the Anderson-Rubin, Lagrange multiplier (LM), and conditional likelihood ratio (CLR) tests, and new optimal WAP and PO invariant similar tests. We find that the CLR test is quite close to being uniformly most powerful invariant among a class of two-sided tests. A new unconditional test, P*, also is found to have this property. For one-sided alternatives, no test achieves the invariant power envelope, but a new test. the one-sided CLR test. is found to be fairly close. The finite sample results of the paper are extended to the case of unknown error covariance matrix and possibly non-normal errors via weak instrument asymptotics. Strong instrument asymptotic results also are provided because we seek tests that perform well under both weak and
ER -