Preface Introduction The Reflection Problem The Law of Decreasing Credibility Identification and Statistical Inference Prediction and Decisions Coping with Ambiguity Organization of the Book The Developing Literature on Partial Identification PART I: PREDICTION WITH INCOMPLETE DATA 1. Conditional Prediction 1.1. Predicting Criminality 1.2. Probabilistic Prediction Conditional Distributions Best Predictors Specifying a Loss Function 1.3. Estimation of Best Predictors from Random Samples Covariates with Positive Probability Covariates with Zero Probability but on the Support Covariates off the Support 1.

4. Extrapolation Invariance Assumptions and Shape Restrictions Testing and Using Theories 1.5. Predicting High School Graduation Complement 1A. Best Predictors Under Square and Absolute Loss Square Loss Absolute Loss Complement 1B. Nonparametric Regression Analysis Consistency of the Local-Average Estimate Choosing an Estimate Complement 1C. Word Problems 2. Missing Outcomes 2.

1. Anatomy of the Problem Identification of Event Probabilities Identification of Quantiles 2.2. Bounding the Probability of Exiting Homelessness Is the Cup Part Empty or Part Full? 2.3. Means of Functions of the Outcome Bounded Random Variables Unbounded Random Variables 2.4. Parameters that Respect Stochastic Dominance 2.

5. Distributional Assumptions Missingness at Random Refutable and Non-refutable Assumptions Refutability and Credibility 2.6. Wage Regressions and the Reservation Wage Model of Labor Supply Homogeneous Reservation Wages Other Cases of Missingness by Choice 2.7. Statistical Inference Sample Analogs of Identification Regions Confidence Sets Testing Refutable Assumptions Complement 2A. Interval Measurement of Outcomes Measurement Devices with Bounded Range Complement 2B. Jointly Missing Outcomes and Covariates Conditioning on a Subset of the Outcomes Illustration: Bounding the Probability of Employment and the Unemployment Rate Complement 2C.

Convergence of Sets to Sets 3. Instrumental Variables 3.1. Distributional Assumptions and Credible Inference Assumptions Using Instrumental Variables 3.2. Missingness at Random Conditioning is not Controlling 3.3. Statistical Independence Binary Outcomes Identifying Power Combining Multiple Surveys 3.

4. Equality of Means Means Missing at Random Mean Independence 3.5. Inequality of Means Means Missing Monotonically Monotone Regressions Complement 3A. Imputations and Nonresponse Weights Imputations Nonresponse Weights Complement 3B. Conditioning on the Propensity Score Complement 3C. Word Problems 4. Parametric Prediction 4.

1. The Normal-Linear Model of Market and Reservation Wages 4.2. Selection Models A Semiparametric Model 4.3. Parametric Models for Best Predictors Identification of the Parameters and the Best Predictor Linear-Index Models Statistical Inference Complement 4A. Minimum-Distance Estimation of Partially Identified Models 5. Decomposition of Mixtures 5.

1. The Inferential Problem and Some Manifestations The Problem in Abstraction Ecological Inference C.