ASYMPTOTIC BIAS FOR QUASI-MAXIMUM-LIKELIHOOD ESTIMATORS IN CONDITIONAL HETEROSKEDASTICITY MODELS

Virtually all applications of time-varying conditional variance models use a quasi-maximum-likelihood estimator (QMLE). Consistency of a QML E requires an identification condition that the quasi-log-likelihood h ave a unique maximum at the true conditional mean and relative scale p arameters. We show that the identification condition holds for a non-G aussian QMLE if the conditional mean is identically zero or if a symme try condition is satisfied. Without symmetry, an additional parameter, for the location of the innovation density, must be added for identif ication. We calculate the efficiency loss from adding such a parameter under symmetry, when the parameter is not needed. We also show that t here is no efficiency loss for the conditional variance parameters of a GARCH process.