TY  - JOUR
AU  - Burnside,Craig
AU  - Eichenbaum,Martin
TI  - Small Sample Properties of Generalized Method of Moments Based Wald     Tests
JF  - National Bureau of Economic Research Technical Working Paper Series
VL  - No. 155
PY  - 1994
Y2  - May 1994
UR  - http://www.nber.org/papers/t0155
L1  - http://www.nber.org/papers/t0155.pdf
N1  - Author contact info:
Craig Burnside
Department of Economics
Duke University
213 Social Sciences Building
Durham, NC 27708-0097
Tel: 919/660-1808
Fax: 919/684-8974
E-Mail: craig.burnside@duke.edu

Martin S. Eichenbaum
Department of Economics
Northwestern University
2003 Sheridan Road
Evanston, IL  60208
Tel: 847/491-8232
Fax: 847/491-7001
E-Mail: eich@northwestern.edu
AB  - This paper assesses the small sample properties of Generalized Method of Moments (GMM) based Wald statistics.  The analysis is conducted assuming that the data generating process corresponds to (i) a simple vector white noise process and (ii) an equilibrium business cycle model.  Our key findings are that the small sample size of the Wald tests exceeds their asymptotic size, and that their size increases uniformly with the dimensionality of joint hypotheses.  For tests involving even moderate numbers of moment restrictions, the small sample size of the tests greatly exceeds their asymptotic size.  Relying on asymptotic distribution theory leads one to reject joint hypothesis tests far too often.  We argue that the source of the problem is the difficulty of estimating the spectral density matrix of the GMM residuals, which is needed to conduct inference in a GMM environment.  Imposing restrictions implied by the underlying economic model being investigated or the null hypothesis being tested on this spectral density matrix can lead to substantial improvements in the small sample properties of the Wald tests.
ER  -