Exponential empirical likelihood is not bartlett correctable

In a recent paper, DiCiccio, Hall and Romano established that Owen's empirical likelihood is Bartlett correctable This is an intriguing and perhaps surprising result and is the only nonparametric context in which Bartlett correctability is known to hold. An alternative, closely related nonparametric likelihood, referred to here as exponential empirical likelihood, may be constructed using Efron's method of nonparametric tilting. The purpose of this note is to show that exponential empirical likelihood is not Bartlett correctable.