Abstract :
Andrews ~1999, Econometrica 67, 1341–1383! derived the first-order asymptotic
theory for a very general class of estimators when a parameter is on a boundary+
We derive the second-order asymptotic theory in this setting in some special cases+
We focus on the behavior of the quasi maximum likelihood estimator ~QMLE! in
stationary and nonstationary generalized autoregressive conditionally heteroskedastic
~GARCH! models when constraints are imposed in the maximization procedure+
We show how in this case both a first- and a second-order bias appear in
the estimator and how the bias can be quite large+ We provide two types of bias
correction mechanisms for the researcher to choose in practice: either to bias correct
only for a first-order bias or for a first- and second-order bias+ We show that
when some constraints are imposed, it is advisable to bias correct not only for the
first-order bias but also for the second-order bias+
