  Parameters defined via General Estimating Equations (GEE) can be estimated by
maximizing the Empirical Likelihood (EL). Newey and Smith (2004) 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.
