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

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

Case 5: Diff in diff ► Compare change in outcomes between treatments and non-treatment  Impact is the difference in the change in outcomes ► Impact = (Y t 1 -Y t 0 ) - (Y c 1 -Y c 0 )

Time Treatment Outcome Treatment Group Control Group Average Treatment Effect

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

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

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)

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

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 Not EnrolledEnrolledt-stat Mean change CPC Case 5 - Diff in Diff Linear RegressionMultivariate 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 Regression Multivariate Linear Regression Multivariate Linear Regression Multivariate Linear Regression Multivariate Linear Regression Estimated Impact on CPC 34.28** **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  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(X i ) = Pr (participation i =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 1. Representative & highly comparable survey of non-participants and participants. 2. Pool the two samples and estimate a logit (or probit) model of program participation: Gives the probability of participating for a person with X 3. 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 0 1 Propensity score Region of common support Density of scores for participants High probability of participating given X

Steps in Score Matching 1. Representative & highly comparable survey of non- participants and participants. 2. Pool the two samples and estimate a logit (or probit) model of program participation: Gives the probability of participating for a person with X 3. Restrict samples to assure common support (important source of bias in observational studies) 4. For each participant find a sample of non- participants that have similar propensity scores 5. Compare the outcome indicators. The difference is the estimate of the gain due to the program for that observation. 6. 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 Case 7 - PROPENSITY SCORE: Pr(treatment=1) VariableCoef.Std. Err. Age Head Educ Head Age Spouse Educ Spouse Ethnicity Female Head Constant

Case 7: Matching Linear RegressionMultivariate Linear Regression Estimated Impact on CPC (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 Regression Multivariate Linear Regression Multivariate Linear Regression Multivariate Linear Regression Multivariate Linear Regression2SLS Multivariate Linear Regression Estimated Impact on CPC 34.28** **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

DesignWhen to useAdvantagesDisadvantages 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)