Randomized Evaluations: Applications Kenny Ajayi September 22, 2008 Global Poverty and Impact Evaluation

Review  Causation and Correlation (5 factors)  X → Y  Y → X  X → Y and Y → X  Z → X and Z → Y  X ‽ Y

Review  Causation and Correlation (5 factors)  X → Ycausality  Y → Xreverse causality  X → Y and Y → Xsimultaneity  Z → X and Z → Yomitted variables / confounding  X ‽ Y spurious correlation  Reduced-form relationship between X and Y

Review  Exogenous

Review  Exogenous  Endogenous

Review  Exogenous  Endogenous  External Validity

Review  Exogenous  Endogenous  External Validity  Natural Experiment

Practical Applications  Noncompliance  Cost Benefit Analysis  Theory and Mechanisms

Kling, Liebman and Katz (2007)  Do neighborhoods affect their residents?

Do neighborhoods affect their residents?  Positively

Do neighborhoods affect their residents?  Positively  Social connections, role models, security, community resources

Do neighborhoods affect their residents?  Positively  Social connections, role models, security, community resources  Negatively

Do neighborhoods affect their residents?  Positively  Social connections, role models, security, community resources  Negatively  Discrimination, competition with advantaged peers

Do neighborhoods affect their residents?  Positively  Social connections, role models, security, community resources  Negatively  Discrimination, competition with advantaged peers  Not at all

Do neighborhoods affect their residents?  Positively  Social connections, role models, security, community resources  Negatively  Discrimination, competition with advantaged peers  Not at all  Only family influences, genetic factors, individual human capital investments or broader non-neighborhood environment matter

Do neighborhoods affect their residents?  What is Y?

Do neighborhoods affect their residents?  What is Y?  Adults  Self sufficiency  Physical & mental health  Youth  Education (reading/math test scores)  Physical & mental health  Risky behavior

Kling, Liebman and Katz (2007)  Do neighborhoods affect their residents?  X → Ycausality  Y → Xreverse causality  X → Y and Y → Xsimultaneity  Z → X and Z → Yomitted variables / confounding  X ‽ Y spurious correlation

Neighborhood Effects  Natural Experiment

Neighborhood Effects  Natural Experiment  Hurricane Katrina  Can we randomly assign people to live in different neighborhoods?

Neighborhood Effects  Natural Experiment  Hurricane Katrina  Can we randomly assign people to live in different neighborhoods?  Sort of…

Moving to Opportunity  Solicit volunteers to participate  Randomly assign each volunteer an option  Control  Section 8  Section 8 with restriction (low poverty neighborhood)  Volunteers decide whether to move  Compliers: use voucher  Non-compliers: don’t move

Moving to Opportunity Public housing residents VolunteerSection 8Move Don’t move Control Restricted Section 8 Don’t move Move Don’t volunteer

Non-random Participation  Why is this OK?  Volunteers presumably care about their neighborhood environment, so should be the target when thinking about uptake for the use of housing vouchers BUT  Results might not generalize to other populations with different characteristics

Treatment and Compliance  With perfect compliance:  Pr(X=1│Z=1)=1  Pr(X=1│Z=0)=0  With imperfect compliance:  1>Pr(X=1│Z=1)>Pr(X=1│Z=0)>0 Where X - actual treatment Z - assigned treatment

Some Econometrics  Intention-to-treat (ITT) Effects  Differences between treatment and control group means

Some Econometrics  Intention-to-treat (ITT) Effects  Differences between treatment and control group means ITT = E(Y|Z = 1) – E(Y|Z = 0) Y - outcome Z - assigned treatment

Some Econometrics  Intention-to-treat (ITT) Effects  Writing this relationship in mathematical notation Y = Zπ 1 + Wβ 1 + ε 1 Individual wellbeing (Y) depends on whether or not the individual is assigned to treatment (Z), baseline characteristics (W), and whether or not the individual got lucky (ε) π 1 - effect of being assigned to treatment group = (effect of actually moving) x (compliance rate)

Some Econometrics  Effect of Treatment on the Treated (TOT)  Differences between treatment and control group means Differences in compliance for treatment and control groups

Some Econometrics  Effect of Treatment on the Treated (TOT)  Differences between treatment and control group means Differences in compliance for treatment and control groups  TOT = “Wald Estimator” = E(Y|Z = 1) – E(Y|Z = 0) E(X|Z = 1) – E(X|Z = 0) Y - outcome Z - assigned treatment X - actual treatment (i.e. compliance)

Some More Econometrics  Estimate TOT using instrumental variables  Use offer of a MTO voucher as an instrument for MTO voucher use

Some More Econometrics  Estimate TOT using instrumental variables  Use offer of a MTO voucher as an instrument for MTO voucher use. In mathematical notation: (1)X = Z ρ d + W β d + ε d 1. Predict whether people use voucher (X), given their assigned treatment (Z) and observable characteristics (W)

Some More Econometrics  Estimate TOT using instrumental variables  Use offer of a MTO voucher as an instrument for MTO voucher use. In mathematical notation: (1)X = Z ρ d + W β d + ε d (2)Y = Xγ 2 + W β 2 + ε 2 1. Predict whether people use voucher (X), given their assigned treatment (Z) and observable characteristics (W) 2. Estimate how much individual wellbeing (Y) depends on predicted compliance (X) and observable characteristics (W)

Some Econometrics  Effect of Treatment on the Treated (TOT)  Writing the reduced-form relationship in mathematical notation Y = Xγ 2 + Wβ 2 + ε 2 Individual wellbeing (Y) depends on whether or not the individual complies with treatment (X), baseline characteristics (W), and whether or not the individual got lucky (ε) Note:γ 2 - effect of actually moving (i.e. compliance) = effect of being assigned to treatment group compliance rate

Moving to Opportunity Public housing residents VolunteerSection 8Move Don’t move Control Restricted Section 8 Don’t move Move Don’t volunteer

Moving to Opportunity Public housing residents VolunteerSection 8Move Don’t move Control Restricted Section 8 Don’t move Move Don’t volunteer INTENTION TO TREAT

Moving to Opportunity Public housing residents VolunteerSection 8Move Don’t move Control Restricted Section 8 Don’t move Move Don’t volunteer EFFECT OF TREATMENT ON THE TREATED

Results  Positive effects  Teenage girls  Adult mental health  Negative effects  Teenage boys  No effects  Adult economic self-sufficiency & physical health  Younger children  Increasing effects for lower poverty rates

Limitations  Can’t fully separate relocation effect from neighborhood effect  Can’t observe spillovers into receiving neighborhoods

Some Thoughts  We can still estimate impacts in cases where we don’t have full compliance  Policies sometimes target people who are different from the general population (i.e. those more likely to take up a program) BUT  We have to be careful about generalizing these results for other populations ( external validity )

Practical Applications  Noncompliance  Cost Benefit Analysis  Theory and Mechanisms

Duflo, Kremer & Robinson (2008)  Why don’t Kenyan farmers use fertilizer?

Duflo, Kremer & Robinson (2008)  Why don’t Kenyan farmers use fertilizer?  Low returns  High cost  Preference for traditional farming methods  Lack of information

Is Fertilizer Use Profitable?  What is Y (outcome)?  Crop yield  Rate of return over the season  What is X (observed)?  Fertilizer  Hybrid seed

Is Fertilizer Use Profitable?  What is Z (unobserved)?

Is Fertilizer Use Profitable?  What is Z (unobserved)?  Farmer experience/ability  Farmer resources  Weather  Soil quality  Market conditions

Correlation or Causation? Fertilizer Use (X) and Crop Yield (Y)

Correlation or Causation? Fertilizer Use (X) and Crop Yield (Y)  X → Ycausality  Y → Xreverse causality  X → Y and Y → Xsimultaneity  Z → X and Z → Yomitted variables / confounding  X ‽ Y spurious correlation

Fertilizer Experiment  How could we test the effect of fertilizer use on crop yield using randomization?

Fertilizer Experiment  Randomly select participating farmers  Measure 3 adjacent equal-sized plots on each farm  Randomly assign farming package for each plot  Top dressing fertilizer (T 1 )  Fertilizer and hybrid seed (T 2 )  Traditional seed (C)  Weigh each plot’s yield at harvest

Fertilizer Experiment  Calculate rate of return over the season: value of treatment -comparison -value of plot output plot outputinput RR = value of input

Results

Some Thoughts  More comprehensive package increased yield BUT  Lower cost package had highest rate of return  Lab results don’t always apply in the field  Think about the COSTS and BENEFITS

Practical Applications  Noncompliance  Cost Benefit Analysis  Theory and Mechanisms

Karlan and Zinman (2007)  What is the optimal loan contract?

Objectives  Profitability  Gross Revenue  Repayment  Targeted Access  Poor households  Female microentrepreneurs  Sustainability

Theory of Change Loan Profits contract  Mechanisms  How do we expect a change to affect the outcome?  What assumptions are we making?  Can we test if they are true?

Loan Offer Experiment  What is Y?  Take-up  Loan size  Default  What is X?  Interest rate  Maturity  How sensitive are borrowers to interest rates and maturities?

Loan Offer Experiment

Results  Downward sloping demand curves  Loan size more responsive to loan maturity than to interest rate

Some Limitations  Again, results apply only to people who had previously borrowed from the lender.  Elasticities apply to direct mail solicitations and might not hold for other loan offer methods

Final Thoughts  Randomized evaluation can have many applications beyond merely looking at reduced-form relationships between X and Y