Partial identification with missing data: concepts and findings

The traditional way to cope with missing data problems has been to combine the available data with assumptions strong enough to point-identify the probability distribution describing a population. However, such assumptions often are not well motivated. An alternative approach is to first determine what may be inferred using the empirical evidence alone and then study the identifying power of credible assumptions. The generic result is that one may partially identify the probability distribution of interest: an identification region gives the set of distributions generated by combining the available data with all possible distributions of missing data. This expository article collects findings on partial identification with missing data. The focus is on identification of means, quantiles, and other parameters that respect stochastic dominance. It is shown how distributional assumptions using instrumental variables shrink the identification regions for these parameters. Findings are given on conditional prediction with missing data on outcomes or covariates.