Abstract

We study the beha viour of the informa tionma trix (IM) test when ma ximum likelihoodestima torsa re repla ced with robust estima tors. The la tter ma yunma sk outliersa nd hence improve the power of the test. We investiga te in deta il the loca la symptotic power of the IM test in the norma l model, for va rious estima torsa nd undera ra nge of lo ca#a lterna#jS es. These loca# a#FjAzS9PP es include conta#O#P4jS9 neighbourhoods, Student's t (with degrees of freedoma#domSP hing infinity) , skewness,a nda tilted norma l. Simula tion studies for fixed a# terna# ives confirm tha t in ma# y ca#P# the use of robust estima# ors substa ntia lly increa ses the power of the IM test. JEL cla# sifica##A0 : C12, C15 Key-words: informa tion ma trix test, robustness Corresponding author. Address: K.U.Leuven, Department of Economics, Naamsestraat 69, 3000 Leuven, BelgP m. Tel. +32 16 326652. Fax +32 16 326796. Email: dirk.hoorelbeke@econ.kuleuven.ac.be Introducti White (1982) introduced the informa tion ma trix (IM) test a# a# omnibus test for misspecifica#j#0 ofa pa ra metric model. The test exploits the wellknown property tha t, a# the model, the sum of the Hessi a# of the loglikelihood a# d the outer product of the score h a# zero expecta#OqS . So if, a# pa ra meter estima#Sj , the sa mplea ver a#S of the sum of the Hessi a# a# d the outer product of the score di#ers significa ntly from zero, this is evidence a#OAO st the model. The IM test is typica#P# implemented using ma ximum likelihood (ML) estima tes of thepa ra meters. In this pa per we explore the potentia# of repla##F g the ML estima#Sj with robust estima#SO s. Specifica#O tention is given to the e#ect on power, conjecturing tha tunma sking outliers will lea# to a# incr ea# ed power of the IM test. In mostca# es consider...

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