Impact Evaluation Methods: Difference in difference & Matching Africa Program for Education Impact Evaluation Impact Evaluation Methods: Difference in difference & Matching David Evans Impact Evaluation Cluster, AFTRL Slides by Paul J. Gertler & Sebastian Martinez AFRICA IMPACT EVALUATION INITIATIVE, AFTRL

Measuring Impact Randomized Experiments Quasi-experiments Randomized Promotion – Instrumental Variables Regression Discontinuity Double differences (Diff in diff) Matching

Impact = (Yt1-Yt0) - (Yc1-Yc0) Case 5: Diff in diff Compare change in outcomes between treatments and non-treatment Impact is the difference in the change in outcomes Impact = (Yt1-Yt0) - (Yc1-Yc0)

Outcome Treatment Group Control Group Time Treatment Average Treatment Effect Treatment Group Control Group Time Treatment

Outcome Treatment Group Control Group Time Treatment Measured effect without pre-measurement Treatment Group Control Group

EstimatedAverage Treatment Effect Outcome Average Treatment Effect EstimatedAverage Treatment Effect Treatment Group Control Group Time Treatment

Diff in diff What is the key difference between these two cases? Fundamental assumption that trends (slopes) are the same in treatments and controls (sometimes true, sometimes not) Need a minimum of three points in time to verify this and estimate treatment (two pre-intervention)

Third observation Second observation First observation Outcome Average Treatment Effect Treatment Group Third observation Control Group Second observation First observation Time Treatment

Examples Two neighboring school districts School enrollment or test scores are improving at same rate before the program (even if at different levels) One receives program, one does not Neighboring _______

Case 5: Diff in Diff Case 5 - Diff in Diff Not Enrolled Enrolled t-stat Mean change CPC 8.26 35.92 10.31 Linear Regression Multivariate Linear Regression Estimated Impact on CPC 27.66** 25.53** (2.68) (2.77) ** Significant at 1% level Case 5 - Diff in Diff

Impact Evaluation Example – Summary of Results Case 1 - Before and After Case 2 - Enrolled/Not Enrolled Case 3 - Randomization Case 4 - Regression Discontinuity Case 5 - Diff in Diff Multivariate Linear Multivariate Linear Estimated Impact on CPC 34.28** -4.15 29.79** 30.58** 25.53** (2.11) (4.05) (3.00) (5.93) (2.77) ** Significant at 1% level

Example Old-age pensions and schooling in South Africa Eligible if household member over 60 Not eligible if under 60 Used household with member age 55-60 Pensions for women and girls’ education

Measuring Impact Randomized Experiments Quasi-experiments Randomized Promotion – Instrumental Variables Regression Discontinuity Double differences (Diff in diff) Matching

Matching Pick the ideal comparison group that matches the treatment group from a larger survey. The matches are selected on the basis of similarities in observed characteristics. For example? This assumes no selection bias based on unobserved characteristics. Example: income Example: entrepreneurship Source: Martin Ravallion

Propensity-Score Matching (PSM) Controls: non-participants with same characteristics as participants In practice, it is very hard. The entire vector of X observed characteristics could be huge. Match on the basis of the propensity score P(Xi) = Pr (participationi=1|X) Instead of aiming to ensure that the matched control for each participant has exactly the same value of X, same result can be achieved by matching on the probability of participation. This assumes that participation is independent of outcomes given X (not true if important unobserved outcomes are affecting participation)

Steps in Score Matching Representative & highly comparable survey of non-participants and participants. Pool the two samples and estimate a logit (or probit) model of program participation: Gives the probability of participating for a person with X Restrict samples to assure common support (important source of bias in observational studies) For each participant find a sample of non-participants that have similar propensity scores Compare the outcome indicators. The difference is the estimate of the gain due to the program for that observation. Calculate the mean of these individual gains to obtain the average overall gain.

Density of scores for participants Region of common support High probability of participating given X 1 Propensity score

Steps in Score Matching Representative & highly comparable survey of non-participants and participants. Pool the two samples and estimate a logit (or probit) model of program participation: Gives the probability of participating for a person with X Restrict samples to assure common support (important source of bias in observational studies) For each participant find a sample of non-participants that have similar propensity scores Compare the outcome indicators. The difference is the estimate of the gain due to the program for that observation. Calculate the mean of these individual gains to obtain the average overall gain.

PSM vs an experiment Pure experiment does not require the untestable assumption of independence conditional on observables PSM requires large samples and good data

Lessons on Matching Methods Typically used for IE when neither randomization, RD or other quasi-experimental options are not possible (i.e. no baseline) Be cautious of ex-post matching: Matching on variables that change due to participation (i.e., endogenous) What are some variables that won’t change? Matching helps control for OBSERVABLE differences

More Lessons on Matching Methods Matching at baseline can be very useful: Estimation: Combine with other techniques (i.e. diff in diff) Know the assignment rule (match on this rule) Sampling: Selecting non-randomized control sample Need good quality data Common support can be a problem

Case 7: Matching Age Head -0.03 0.00 Educ Head -0.05 0.01 Age Spouse Case 7 - PROPENSITY SCORE: Pr(treatment=1) Variable Coef. Std. Err. Age Head -0.03 0.00 Educ Head -0.05 0.01 Age Spouse -0.02 Educ Spouse -0.06 Ethnicity 0.42 0.04 Female Head -0.23 0.07 Constant 1.6 0.10 P-score Quintiles Xi T C t-score Age Head 68.04 67.45 -1.2 53.61 53.38 -0.51 44.16 44.68 1.34 37.67 38.2 1.72 32.48 32.14 -1.18 Educ Head 1.54 1.97 3.13 2.39 2.69 1.67 3.25 3.26 -0.04 3.53 3.43 -0.98 2.98 3.12 1.96 Age Spouse 55.95 55.05 -1.43 46.5 46.41 0.66 39.54 40.01 1.86 34.2 34.8 1.84 29.6 29.19 -1.44 Educ Spouse 1.89 2.19 2.47 2.61 2.64 0.31 3.17 3.19 0.23 3.34 -0.78 2.37 2.72 1.99 Ethnicity 0.16 0.11 -2.81 0.24 0.27 -1.73 0.3 0.32 1.04 0.14 0.13 -0.11 0.7 -2.3 Female Head 0.19 0.21 0.92 0.42 -1.4 0.092 0.088 -0.35 0.35 -0.34 0.008 0.83 Quintile 4 Quintile 5 Quintile 1 Quintile 2 Quintile 3

Case 7: Matching 1.16 7.06+ Estimated Impact on CPC (3.59) (3.65) Linear Regression Multivariate Linear Regression Estimated Impact on CPC 1.16 7.06+ (3.59) (3.65) ** Significant at 1% level, + Significant at 10% level Case 7 - Matching

Impact Evaluation Example – Summary of Results Case 1 - Before and After Case 2 - Enrolled/Not Enrolled Case 3 - Randomization Case 4 - Regression Discontinuity Case 5 - Diff in Diff Case 6 - IV (TOT) Case 7 - Matching Multivariate Linear Multivariate Linear 2SLS Estimated Impact on CPC 34.28** -4.15 29.79** 30.58** 25.53** 30.44** 7.06+ (2.11) (4.05) (3.00) (5.93) (2.77) (3.07) (3.65) ** Significant at 1% level

Measuring Impact Experimental design/randomization Quasi-experiments Regression Discontinuity Double differences (Diff in diff) Other options Instrumental Variables Matching Combinations of the above

Remember….. Objective of impact evaluation is to estimate the CAUSAL effect of a program on outcomes of interest In designing the program we must understand the data generation process behavioral process that generates the data how benefits are assigned Fit the best evaluation design to the operational context

Design When to use Advantages Disadvantages Randomization Whenever possible When an intervention will not be universally implemented Gold standard Most powerful Not always feasible Not always ethical Random Promotion When an intervention is universally implemented Learn and intervention Only looks at sub-group of sample Regression Discontinuity If an intervention is assigned based on rank Assignment based on rank is common Only look at sub-group of sample Double differences If two groups are growing at similar rates Eliminates fixed differences not related to treatment Can be biased if trends change Matching One other methods are not possible Overcomes observed differences between treatment and comparison Assumes no unobserved differences (often implausible)