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Title: Robust Bayesian inference for moment condition models Authors:  Zhichao Liu - Monash University (Australia)
Catherine Forbes - Monash University (Australia) [presenting]
Heather Anderson - Monash University (Australia)
Abstract: A new robust Bayesian exponentially tilted empirical likelihood (RBETEL) inferential methodology is proposed which is suitable for moment condition models when data may be contaminated by outliers. It is built upon the Bayesian exponentially tilted empirical likelihood (BETEL) method, justified by the fact that an empirical likelihood (EL) can be interpreted as the nonparametric limit of a Bayesian procedure when the implied probabilities are obtained from maximizing entropy subject to some given moment constraints. The BETEL method is found to be linked to a general framework which updates prior belief via a loss function. After demonstrating that the BETEL loss function is related to the EL ratio, a loss function for the new RBETEL method arises naturally as the EL ratio evaluated on some sub-samples. The resulting posterior distribution for the parameters is shown to be a coherent representation of the subjective uncertainty in the minimizer of the expected loss. A controlled simulation experiment is conducted to investigate the performance of the RBETEL method. We find that the proposed methodology produces reliable posterior inference for the fundamental relationships that are embedded in the majority of the data, even when outliers are present in the dataset. The method is also illustrated in an empirical study relating inflation and economic openness.