1 An Introduction to the Econometrics of Program Evaluation
1.1 Introduction
1.2 Statistical Setup, Notation, and Assumptions
1.2.1 Identification Under Random Assignment
1.2.2 A Bayesian Interpretation of ATE Under Randomization
1.2.3 Consequences of Nonrandom Assignment and Selection Bias
1.3 Selection on Observables and Selection on Unobservables
1.3.1 Selection on Observables (or Overt Bias) and Conditional Independence Assumption
1.3.2 Selection on Unobservables (or Hidden Bias)
1.3.3 The Overlap Assumption
1.4 Characterizing Selection Bias
1.4.1 Decomposing Selection Bias
1.5 The Rationale for Choosing the Variables to Control for
1.6 Partial Identification of ATEs: The Bounding Approach
1.7 A Guiding Taxonomy of the Econometric Methods for Program Evaluation
1.8 Policy Framework and the Statistical Design for Counterfactual Evaluation
1.9 Available Econometric Software
1.10 A Brief Outline of the Book
References
2 Methods Based on Selection on Observables
2.1 Introduction
2.2 Regression-Adjustment
2.2.1 Regression-Adjustment as Unifying Approach Under Observable Selection
2.2.2 Linear Parametric Regression-Adjustment:
The Control-Function Regression
2.2.3 Nonlinear Parametric Regression-Adjustment
2.2.4 Nonparametric and Semi-parametric Regression-Adjustment
2.3 Matching
2.3.1 Covariates and Propensity-Score Matching
2.3.2 Identification of ATEs Under Matching
2.3.3 Large Sample Properties of Matching Estimator(s)
2.3.4 Common Support
2.3.5 Exact Matching and the "Dimensionality Problem"
2.3.6 The Properties of the Propensity-Score
2.3.7 Quasi-exact Matching Using the Propensity-Score
2.3.8 Methods for Propensity-Score Matching
2.3.9 Inference for Matching Methods
2.3.10 Assessing the Reliability of CMI by Sensitivity
Analysis
2.3.11 Assessing Overlap
2.3.12 Coarsened-Exact Matching
2.4 Reweighting
2.4.1 Reweighting and Weighted Least Squares
2.4.2 Reweighting on the Propensity-Score Inverse-Probability
2.4.3 Sample Estimation and Standard Errors for ATEs
2.5 Doubly-Robust Estimation
2.6 Implementation and Application of Regression-Adjustment
2.7 Implementation and Application of Matching
2.7.1 Covariates Matching
2.7.2 Propensity-Score Matching
2.7.3 An Example of Coarsened-Exact Matching Using cem
2.8 Implementation and Application of Reweighting
2.8.1 The Stata Routine treatrew
2.8.2 The Relation Between treatrew and Stata 13 teffects ipw
2.8.3 An Application of the Doubly-Robust Estimator
References
3 Methods Based on Selection on Unobservables
3.1 Introduction
3.2 Instrumental-Variables
3.2.1 IV Solution to Hidden Bias
3.2.2 IV Estimation of ATEs
3.2.3 IV with Observable and Unobservable Heterogeneities
3.2.4 Problems with IV Estimation
3.3 Selection-Model
3.3.1 Characterizing OLS Bias within a Selection-Model
3.3.2 A Technical Exposition of the Selection-Model
3.3.3 Selection-Model with a Binary Outcome
3.4 Difference-in-Differences
3.4.1 DID with Repeated Cross Sections
3.4.2 DID with Panel Data
3.4.3 DID with Matching
3.5 Implementation and Application of IV and Selection-Model
3.5.1 The Stata Command ivtreatreg
3.5.2 A Monte Carlo Experiment
3.5.3 An Application to Determine the Effect of Education on Fertility
3.5.4 Applying the Selection-Model Using etregress
3.6 Implementation and Application of DID
3.6.1 DID with Repeated Cross Sections
3.6.2 DID Application with Panel Data
References
4 Local Average Treatment Effect and Regression-Discontinuity-Design
4.1 Introduction
4.2 Local Average Treatment Effect
4.2.1 Randomization Under Imperfect Compliance
4.2.2 Wald Estimator and LATE
4.2.3 LATE Estimation
4.2.4 Estimating Average Response for Compliers
4.2.5 Characterizing Compliers
4.2.6 LATE with Multiple Instruments and Multiple Treatment
4.3 Regression-Discontinuity-Design
4.3.1 Sharp RDD
4.3.2 Fuzzy RDD
4.3.3 The Choice of the Bandwidth and Polynomial Order
4.3.4 Accounting for Additional Covariates
4.3.5 Testing RDD Reliability
4.3.6 A Protocol for Practical Implementation of RDD
4.4 Application and Implementation
4.4.1 An Application of LATE
4.4.2 An Application of RDD by Simulation
4.4.3 An Application of RDD to Real Data
References
5 Difference-in-Differences with Many Pre- and Post-Treatment Times
5.1 Introduction
5.2 The TVDIFF Model
5.2.1 Testing the "Common Trend" Assumption
5.2.2 An Application of the TVDIFF Model
5.3 The TFDIFF Model
5.3.1 Generalization to More Than Three Times
5.3.2 Testing the Parallel-Trend Assumption
5.3.3 An Application of the TFDIFF Model
5.4 Parallel-Trend Test in the Presence of Effect Anticipation
5.5 Conclusion
References
6 Synthetic Control Method
6.1 Introduction
6.2 The SCM Model
6.3 SCM Inference
6.4 Application
6.5 Conclusions
References
