Partial identification with missing data: Concepts and findings

Charles F. Manski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)151-165
Number of pages15
JournalInternational Journal of Approximate Reasoning
Issue number2-3
StatePublished - Jun 2005


  • Bounds
  • Identification
  • Instrumental variables
  • Missing data
  • Prediction

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Artificial Intelligence
  • Applied Mathematics


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