Impact Evaluation Methods: Causal Inference

1. Sebastian Martinez Impact Evaluation Cluster, AFTRL Impact Evaluation Methods: Causal Inference Slides by Paul J. Gertler & Sebastian Martinez

2. Motivation • “Traditional” M&E: • Is the program being implemented as designed? • Could the operations be more efficient? • Are the benefits getting to those intended? • Monitoring trends • Are indicators moving in the right direction? •  NO inherent Causality • Impact Evaluation: • What was the effect of the program on outcomes? • Because of the program, are people better off? • What would happen if we changed the program? •  Causality

3. Policy Intervention Monitoring Impact Evaluation Increase Access and Quality in Early Child Education • Construction • Feeding • Quality -New classrooms -SES of students • # of Meals • Use of curriculum -Increased attendance • health/growth • Cognitive Development Improve learning in Science and Math in high school • Upgrade science laboratories • Training of instructors - # equipped labs • # trained instructors • Lab attendance & use • Learning • Labor market • University enrollment Improve quality of instruction in higher education • Teacher training • Online courses • # of training sessions • # of internet terminals • Learning • Attendance/drop out • Labor market

4. Motivation • Objective in evaluation is to estimate the CAUSAL effect of intervention X on outcome Y • What is the effect of a cash transfer on household consumption? • For causal inference we must understand the data generation process • For impact evaluation, this means understanding the behavioral process that generates the data • how benefits are assigned

5. Causation versus Correlation • Recall: correlation is NOT causation • Necessary but not sufficient condition • Correlation: X and Y are related • Change in X is related to a change in Y • And…. • A change in Y is related to a change in X • Causation – if we change X how much does Y change • A change in X is related to a change in Y • Not necessarily the other way around

6. Causation versus Correlation • Three criteria for causation: • Independent variable precedes the dependent variable. • Independent variable is related to the dependent variable. • There are no third variables that could explain why the independent variable is related to the dependent variable • External validity • Generalizability: causal inference to generalize outside the sample population or setting

7. Motivation • The word cause is not in the vocabulary of standard probability theory. • Probability theory: two events are mutually correlated, or dependent  if we find one, we can expect to encounter the other. • Example age and income • For impact evaluation, we supplement the language of probability with a vocabulary for causality.

8. Statistical Analysis & Impact Evaluation • Statistical analysis: Typically involves inferring the causal relationship between X and Y from observational data • Many challenges & complex statistics • Impact Evaluation: • Retrospectively: • same challenges as statistical analysis • Prospectively: • we generate the data ourselves through the program’s design  evaluation design • makes things much easier!

9. How to assess impact • What is the effect of a cash transfer on household consumption? • Formally, program impact is: α = (Y | P=1) - (Y | P=0) • Compare same individual with & without programs at same point in time • So what’s the Problem?

10. Solving the evaluation problem • Problem: we never observe the same individual with and without program at same point in time • Need to estimate what would have happened to the beneficiary if he or she had not received benefits • Counterfactual: what would have happened without the program • Difference between treated observation and counterfactual is the estimated impact

11. Estimate effect ofXonY • Compare same individual with & without treatment at same point in time (counterfactual): • Program impact is outcome with program minus outcome without program sick 10 days sick 2 days Impact = 2 - 10 = - 8 days sick!

12. Finding a good counterfactual • The treated observation and the counterfactual: • have identical factors/characteristics, except for benefiting from the intervention • No other explanations for differences in outcomes between the treated observation and counterfactual • The only reason for the difference in outcomes is due to the intervention

13. Measuring Impact Tool belt of Impact Evaluation Design Options: • Randomized Experiments • Quasi-experiments • Regression Discontinuity • Difference in difference – panel data • Other (using Instrumental Variables, matching, etc) • In all cases, these will involve knowing the rule for assigning treatment

14. Choosing your design • For impact evaluation, we will identify the “best” possible design given the operational context • Best possible design is the one that has the fewest risks for contamination • Omitted Variables (biased estimates) • Selection (results not generalizable)

15. Case Study • Effect of cash transfers on consumption • Estimate impact of cash transfer on consumption per capita • Make sure: • Cash transfer comes before change in consumption • Cash transfer is correlated with consumption • Cash transfer is the only thing changing consumption • Example based on Oportunidades

16. Oportunidades • National anti-poverty program in Mexico (1997) • Cash transfers and in-kind benefits conditional on school attendance and health care visits. • Transfer given preferably to mother of beneficiary children. • Large program with large transfers: • 5 million beneficiary households in 2004 • Large transfers, capped at: • $95 USD for HH with children through junior high • $159 USD for HH with children in high school

17. Oportunidades Evaluation • Phasing in of intervention • 50,000 eligible rural communities • Random sample of of 506 eligible communities in 7 states - evaluation sample • Random assignment of benefits by community: • 320 treatment communities (14,446 households) • First transfers distributed April 1998 • 186 control communities (9,630 households) • First transfers November 1999

18. Oportunidades Example

19. Common Counterfeit Counterfactuals 1. Before and After: 2. Enrolled / Not Enrolled: 2005 2007 Sick 2 days Sick 15 days Impact = 15 - 2 = 13 more days sick? Sick 2 days Sick 1 day Impact = 2 - 1 = + 1 day sick?

20. “Counterfeit” CounterfactualNumber 1 • Before and after: • Assume we have data on • Treatment households before the cash transfer • Treatment households after the cash transfer • Estimate “impact” of cash transfer on household consumption: • Compare consumption per capita before the intervention to consumption per capita after the intervention • Difference in consumption per capita between the two periods is “treatment”

21. Case 1: Before and After • Compare Y before and after intervention αi = (CPCit | T=1) - (CPCi,t-1| T=0) • Estimate of counterfactual (CPCi,t| T=0) = (CPCi,t-1| T=0) • “Impact” = A-B CPC Before After A B t-1 t Time

22. Case 1 - Before and After Control - Before Treatment - After t-stat Mean 233.48 268.75 16.3 Case 1 - Before and After Linear Regression Multivariate Linear Regression 35.27** 34.28** Estimated Impact on CPC (2.16) (2.11) ** Significant at 1% level Case 1: Before and After

23. Case 1: Before and After • Compare Y before and after intervention αi = (CPCit | T=1) - (CPCi,t-1| T=0) • Estimate of counterfactual (CPCi,t| T=0) = (CPCi,t-1| T=0) • “Impact” = A-B • Does not control for time varying factors • Recession: Impact = A-C • Boom: Impact = A-D CPC Before After A D? B C? t-1 t Time

24. “Counterfeit” CounterfactualNumber 2 • Enrolled/Not Enrolled • Voluntary Inscription to the program • Assume we have a cross-section of post-intervention data on: • Households that did not enroll • Households that enrolled • Estimate “impact” of cash transfer on household consumption: • Compare consumption per capita of those who did not enroll to consumption per capita of those who enrolled • Difference in consumption per capita between the two groups is “treatment”

25. Case 2 - Enrolled/Not Enrolled Not Enrolled Enrolled t-stat Mean CPC 290.16 268.7541 5.6 Case 2 - Enrolled/Not Enrolled Linear Regression Multivariate Linear Regression -22.7** -4.15 Estimated Impact on CPC (3.78) (4.05) ** Significant at 1% level Case 2: Enrolled/Not Enrolled

26. Those who did not enroll…. • Impact estimate: αi = (Yit | P=1) - (Yj,t| P=0) , • Counterfactual: (Yj,t| P=0) ≠ (Yi,t| P=0) • Examples: • Those who choose not to enroll in program • Those who were not offered the program • Conditional Cash Transfer • Job Training program • Cannot control for all reasons why some choose to sign up & other didn’t • Reasons could be correlated with outcomes • We can control for observables….. • But are still left with the unobservables

27. Case 1 - Before and After Case 2 - Enrolled/Not Enrolled Linear Multivariate Linear Linear Multivariate Linear Regression Regression Regression Regression Estimated Impact 35.27** 34.28** -22.7** -4.15 on CPC (2.16) (2.11) (3.78) (4.05) ** Significant at 1% level Impact Evaluation Example:Two counterfeit counterfactuals • What is going on?? • Which of these do we believe? • Problem with Before-After: • Can not control for other time-varying factors • Problem with Enrolled-Not Enrolled: • Do no know why the treated are treated and the others not

28. Solution to the Counterfeit Counterfactual Sick 2 days Sick 10 days Observe Y with treatment ESTIMATE Y without treatment Impact = 2 - 10 = - 8 days sick! On AVERAGE, is a good counterfactual for

29. Possible Solutions… • We need to understand the data generation process • How beneficiaries are selected and how benefits are assigned • Guarantee comparability of treatment and control groups, so ONLY difference is the intervention

30. Measuring Impact • Experimental design/randomization • Quasi-experiments • Regression Discontinuity • Double differences (diff in diff) • Other options