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1 Causal Inference Counterfactuals False Counterfactuals Before & After (Pre & Post) Enrolled & Not Enrolled (Apples & Oranges)

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1. Counterfactuals. False Counterfactuals. Before & After (Pre & Post). Enrolled & Not Enrolled (Apples & Oranges). Causal Inference. Estimate the causal effect (impact) of intervention (P) on outcome (Y). (P) = Program or Treatment (Y) = Indicator, Measure of Success. - PowerPoint PPT Presentation

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Page 1: Causal Inference

1Causal Inference

Counterfactuals

False CounterfactualsBefore & After (Pre &

Post)Enrolled & Not Enrolled (Apples &

Oranges)

Page 2: Causal Inference

Our Objective

Estimate the causal effect (impact) of intervention (P) on outcome (Y).

(P) = Program or Treatment (Y) = Indicator, Measure of Success

Example: What is the effect of a Cash Transfer Program (P) on Household Consumption (Y)?

“

Page 3: Causal Inference

Causal InferenceWhat is the impact of (P) on

(Y)?

α= (Y | P=1)-(Y | P=0)

Can we all go home?

Page 4: Causal Inference

Problem of Missing Data

For a program beneficiary:

α= (Y | P=1)-(Y | P=0)

we observe(Y | P=1): Household Consumption (Y) with a cash transfer program (P=1)

but we do not observe(Y | P=0): Household Consumption (Y) without a cash transfer program (P=0)

Page 5: Causal Inference

SolutionEstimate what would have happened to Y in the absence of P.

We call this the

Counterfactual.

The key to a

good impact

evaluation is a

valid counterfactu

al!

Page 6: Causal Inference

Estimating impact of P on Y

OBSERVE (Y | P=1)Outcome with treatment

ESTIMATE (Y | P=0) The Counterfactual

o Intention to Treat (ITT) –Those offered treatment

o Treatment on the Treated (TOT) – Those receiving treatment

o Use comparison or control group

α= (Y | P=1)-(Y | P=0)

IMPACT = - counterfactual

Outcome with

treatment

Page 7: Causal Inference

Example: What is the Impact of…

giving Fulanito

(P)

(Y)?

additional pocket money

on Fulanito’s consumption of candies

Page 8: Causal Inference

The Perfect CloneFulanito Fulanito’s

Clone

IMPACT=6-4=2 Candies

6 candies 4 candies

Page 9: Causal Inference

In reality, use statisticsTreatment Comparison

Average Y=6 candies Average Y=4 Candies

IMPACT=6-4=2 Candies

Page 10: Causal Inference

Finding good comparison groups

We want to find clones for the Fulanitos in our programs.

The treatment and comparison groups should

o have identical characteristicso except for benefiting from the

intervention.In practice, use program eligibility & assignment rules to construct valid

counterfactuals

With a good

comparison group, the

only reason for

different outcomes

between treatments

and controls is the

intervention (P)

Page 11: Causal Inference

Case Study: ProgresaNational anti-poverty program in Mexicoo Started 1997

o 5 million beneficiaries by 2004

o Eligibility – based on poverty index

Cash Transferso Conditional on school and health care

attendance.

Page 12: Causal Inference

Case Study: ProgresaRigorous impact evaluation with rich datao 506 communities, 24,000 households

o Baseline 1997, follow-up 2008

Many outcomes of interestHere: Consumption per capita

What is the effect of Progresa (P) on Consumption Per Capita (Y)?If impact is a reduction of $20 or more, then scale up nationally

Page 13: Causal Inference

Eligibility and Enrollment

Ineligibles(Non-Poor)

Eligibles(Poor)

Enrolled

Not Enrolled

Page 14: Causal Inference

1Causal Inference

Counterfactuals

False CounterfactualsBefore & After (Pre &

Post)Enrolled & Not Enrolled (Apples &

Oranges)

Page 15: Causal Inference

Counterfeit Counterfactual #1

Y

TimeT=0

Baseline

T=1

Endline

A-B = 4

A-C = 2

IMPACT?

B

A

C (counterfactual)

Before & After

Page 16: Causal Inference

Case 1: Before & AfterWhat is the effect of Progresa (P) on consumption (Y)?

Y

Time

T=1997

T=1998

α = $35

IMPACT=A-B= $35

B

A

233

268(1) Observe only beneficiaries (P=1)

(2) Two observations in time: Consumption at T=0and consumption at T=1.

Page 17: Causal Inference

Case 1: Before & After

Note: If the effect is statistically significant at the 1% significance level, we label the estimated impact with 2 stars (**).

Consumption (Y)

Outcome with Treatment (After) 268.7

Counterfactual (Before) 233.4

Impact(Y | P=1) - (Y | P=0)

35.3***

Estimated Impact on Consumption (Y)

Linear Regression35.27*

*

Multivariate Linear Regression

34.28**

Page 18: Causal Inference

Case 1: What’s the problem? Y

Time

T=0 T=1

α = $35

B

A

233

268

Economic Boom:o Real

Impact=A-Co A-B is an

overestimate

C ?

D ?

Impact?

Impact?

Economic Recession:o Real

Impact=A-Do A-B is an

underestimate

Before & After

doesn’t control

for other time-

varying factors!

Page 19: Causal Inference

1Causal Inference

Counterfactuals

False CounterfactualsBefore & After (Pre &

Post)Enrolled & Not Enrolled (Apples &

Oranges)

Page 20: Causal Inference

False Counterfactual #2

If we have post-treatment data ono Enrolled: treatment groupo Not-enrolled: “control” group

(counterfactual)Those ineligible to participate.Those that choose NOT to participate.

Selection Biaso Reason for not enrolling may be

correlated with outcome (Y)Control for observables.But not un-observables!

o Estimated impact is confounded with other things.

Enrolled & Not Enrolled

Page 21: Causal Inference

Measure outcomes in post-treatment (T=1)Case 2: Enrolled & Not Enrolled

Enrolled

Y=268

Not Enrolled

Y=290

Ineligibles(Non-Poor)

Eligibles(Poor)

In what ways might E&NE be different, other than their enrollment in the program?

Page 22: Causal Inference

Case 2: Enrolled & Not Enrolled

Consumption (Y)

Outcome with Treatment (Enrolled) 268Counterfactual (Not Enrolled) 290Impact(Y | P=1) - (Y | P=0) -22**

Estimated Impact on Consumption (Y)

Linear Regression -22**Multivariate Linear Regression -4.15

Note: If the effect is statistically significant at the 1% significance level, we label the estimated impact with 2 stars (**).

Page 23: Causal Inference

Progresa Policy Recommendation?

Will you recommend scaling up Progresa?

B&A: Are there other time-varying factors that also influence consumption?

E&BNE:o Are reasons for enrolling correlated with

consumption?o Selection Bias.

Impact on Consumption (Y)

Case 1: Before & After

Linear Regression35.27**

Multivariate Linear Regression

34.28**

Case 2: Enrolled & Not Enrolled

Linear Regression -22**Multivariate Linear Regression -4.15

Note: If the effect is statistically significant at the 1% significance level, we label the estimated impact with 2 stars (**).

Page 24: Causal Inference

B&ACompare: Same individuals Before and After they receive P.

Problem: Other things may have happened over time.

E&NECompare: Group of individuals Enrolled in a program with group that chooses not to enroll.Problem: Selection Bias. We don’t know why they are not enrolled.

Keep in Mind

Both counterfactuals may lead to biased estimates of the impact.

!


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