Moment inequalities in the context of simulated and predicted variables
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Citation (published version)Hiroaki Kaido, Jiaxuan Li, Marc Rysman. 2018. "Moment Inequalities in the Context of Simulated and Predicted Variables." CeMMAP working paper No. CWP26/18
This paper explores the effects of simulated moments on the performance of inference methods based on moment inequalities. Commonly used confidence sets for parameters are level sets of criterion functions whose boundary points may depend on sample moments in an irregular manner. Due to this feature, simulation errors can affect the performance of inference in non-standard ways. In particular, a (first-order) bias due to the simulation errors may remain in the estimated boundary of the confidence set. We demonstrate, through Monte Carlo experiments, that simulation errors can significantly reduce the coverage probabilities of confidence sets in small samples. The size distortion is particularly severe when the number of inequality restrictions is large. These results highlight the danger of ignoring the sampling variations due to the simulation errors in moment inequality models. Similar issues arise when using predicted variables in moment inequalities models. We propose a method for properly correcting for these variations based on regularizing the intersection of moments in parameter space, and we show that our proposed method performs well theoretically and in practice.
No CWP26/18, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies