  Parameters defined via general estimating equations (GEE) can be estimated by
maximizing the empirical likelihood (EL). Newey and Smith [Econometrica 72
(2004) 219--255] have recently shown that this EL estimator exhibits desirable
higher-order asymptotic properties, namely, that its $O(n^{-1})$ bias is small
and that bias-corrected EL is higher-order efficient. Although EL possesses
these properties when the model is correctly specified, this paper shows that,
in the presence of model misspecification, EL may cease to be root n convergent
when the functions defining the moment conditions are unbounded (even when
their expectations are bounded). In contrast, the related exponential tilting
(ET) estimator avoids this problem. This paper shows that the ET and EL
estimators can be naturally combined to yield an estimator called exponentially
tilted empirical likelihood (ETEL) exhibiting the same $O(n^{-1})$ bias and the
same $O(n^{-2})$ variance as EL, while maintaining root n convergence under
model misspecification.
