Using Implied Probabilities to Improve Estimation with Unconditional Moment Restrictions

In this paper, we investigate the information content of implied probabilities (Back and Brown, 1993) to improve estimation in unconditional moment conditions models. We propose and evaluate two 3-step euclidian empirical likelihood estimators and their bias-correction versions for weakly dependent data. The first one is the time series extension of the 3S-EEL proposed by Antoine, Bonnal and Renault (2007).The second one is new and uses in contrast only an estimator of the weighting matrix at an efficient 2-step GMM estimator, while leaving unrestricted the Jacobian matrix. Both estimators use implied probabilities to achieve higher-order improvements relative to the traditional GMM estimator. A Monte-Carlo study reveals that the finite and large sample properties of the (bias-corrected) 3-step estimators compare very favorably to the existing approaches: the 2-step GMM and the continuous updating estimator. As an application, we re-assess the empirical evidence regarding the New Keynesian Phillips curve in the US.