COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1731 Semiparametric Efficiency Bound for Models of Sequential Moment
Restrictions Chunrong Ai and Xiaohong Chen October 2009 This paper computes the semiparametric efficiency bound for finite dimensional
parameters identified by models of sequential moment restrictions containing unknown
functions. Our results extend those of Chamberlain (1992b) and Ai and Chen (2003) for
semiparametric conditional moment restriction models with identical information sets to
the case of nested information sets, and those of Chamberlain (1992a) and Brown and Newey
(1998) for models of sequential moment restrictions without unknown functions to cases
with unknown functions of possibly endogenous variables. Our bound results are applicable
to semiparametric panel data models and semiparametric two stage plug-in problems. As an
example, we compute the efficiency bound for a weighted average derivative of a
nonparametric instrumental variables (IV) regression, and find that the simple plug-in
estimator is not efficient. Finally, we present an optimally weighted, orthogonalized,
sieve minimum distance estimator that achieves the semiparametric efficiency bound. |
