Abstract :
We derive the semiparametric efficiency bound in dynamic models of conditional
quantiles under a sole strong mixing assumption. We also provide an expression
of Stein’s (1956) least favorable parametric submodel. Our approach is as follows:
First, we construct a fully parametric submodel of the semiparametric model defined
by the conditional quantile restriction that contains the data generating process. We
then compare the asymptotic covariance matrix of the MLE obtained in this submodel
with those of the M-estimators for the conditional quantile parameter that are
consistent and asymptotically normal. Finally, we show that the minimum asymptotic
covariance matrix of this class of M-estimators equals the asymptotic covariance
matrix of the parametric submodel MLE. Thus, (i) this parametric submodel is
a least favorable one, and (ii) the expression of the semiparametric efficiency bound
for the conditional quantile parameter follows.
