Indirect Inference with Endogenously Missing Exogenous Variables

We consider consistent estimation of parameters in a structural model by Indirect Inference (II) when the exogenous variables can be missing at random (MAR) endogenously. We demonstrate that II procedures which simply discard sample units with missing observations can yield inconsistent estimates of the true structural parameters. By inverse probability weighting (IPW) the “complete case” observations, i.e., sample units with no missing variables for the observed and simulated samples, we propose a new method of II to consistently estimate the structural parameters of interest. Asymptotic properties of the new estimator are discussed. An illustration is provided based on a multinomial probit model. A small scale Monte-Carlo study in this model demonstrates the severe bias incurred by existing II estimators, and its subsequent correction by our new II estimator.
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