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Differences-in-Differences Differences-in-Differences

Differences-in-Differences - PowerPoint Presentation

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Differences-in-Differences - PPT Presentation

November 10 2009 Erick Gong Thanks to Null amp Miguel Agenda Class Scheduling DiffinDiff Math amp Graphs Case Study STATA Help Class Scheduling Nov 10 DiffinDiff Nov 17 Power Calculations amp Guest Speaker ID: 675785

diff post differences pre post diff pre differences amp treatment effect program data time difference group malaria people class control treat regression

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Slide1

Differences-in-Differences

November

10, 2009

Erick Gong

Thanks

to Null

&

Miguel Slide2

Agenda

Class Scheduling

Diff-in-Diff (Math & Graphs)

Case Study

STATA HelpSlide3

Class Scheduling

Nov 10: Diff-in-Diff

Nov 17: Power Calculations & Guest Speaker

Nov 24: Class poll: Who will be here?

Dec 1: Review & Presentations

Class Poll: Who will be presenting their research proposals? Slide4

The Big Picture

What is this class really about, anyway?Slide5

The Big Picture

What is this class really about, anyway?

CausalitySlide6

The Big Picture

What is this class really about, anyway?

Causality

What is our biggest problem?Slide7

The Big Picture

What is this class really about, anyway?

Causality

What is our biggest problem?

Omitted variable biasSlide8

Omitted Variable Bias

The actual cause is unobserved

e.g. higher wages for educated actually caused by motivation, not schooling

Happens when people get to choose their own level of the “treatment” (broadly construed)

Selection bias

Non-random program placement

Because of someone else’s choice, “control” isn’t a good

counterfactual

for treatedSlide9

Math Review

(blackboard)Slide10

Math Review

for those of you looking at these slides later, here’s what we just wrote down:

(1) Yi = a +

bTi

+ cXi + ei

(2) E(Yi | Ti=1) – E(Yi | Ti=0)

=

[

a + b + cE(Xi | Ti=1) + E(ei | Ti=1)

]

[

a + 0 + cE(Xi | Ti=0) + E(ei | Ti=0)

]

= b + c

[

E(Xi | Ti=1) – E(Xi | Ti=0)

]

True effect

“Omitted variable/selection bias” termSlide11

What if we had data from before the program?

What if we estimated this equation using data from before the program?

(1) Yi = a + bTi + cXi + ei

Specifically, what would our estimate of b be?

Slide12

What if we had data from before the program?

What if we estimated this equation using data from before the program?

(1) Yi = a +

bTi

+

cXi

+

ei

(2)

E(Y

i0

| T

i1

=1

) –

E(Y

i0

| T

i1

=0

)

=

[

a +

0

+

cE

(X

i0

|

T

i1

=1

) +

E(e

i0

| T

i1

=1

)

]

[

a + 0 +

cE

(X

i0

| T

i1

=0

) +

E(e

i0

| T

i1

=0

)

]

= c

[

E(Xi | Ti=1) – E(Xi | Ti=0)

]

“Omitted variable/selection bias” term

ALL THAT’S LEFT IS THE PROBLEMATIC TERM – HOW COULD THIS BE HELPFUL TO US?Slide13

Differences-in-Differences

(just what it sounds like)

Use two periods of data

add second subscript to denote time

= {E(Y

i1

| T

i1

=1) – E(Y

i1

| T

i1

=0)}

(difference

btwn

T&C, post)

– {E(Y

i0

| T

i1

=1) – E(Y

i0

| T

i1

=0)}

– (difference

btwn

T&C, pre)

=

b + c

[

E(X

i1

| T

i1

=1) – E(X

i1

| T

i1

=0)

]

c

[

E(X

i0

| T

i1

=1) – E(X

i0

| T

i1

=0)

]Slide14

Differences-in-Differences

(just what it sounds like)

Use two periods of data

add second subscript to denote time

= {E(Y

i1

| T

i1

=1) – E(Y

i1

| T

i1

=0)}

(difference

btwn

T&C, post)

– {E(Y

i0

| T

i1

=1) – E(Y

i0

| T

i1

=0)}

– (difference

btwn T&C, pre) = b + c [E(Xi1 | Ti1=1) – E(Xi1 | Ti1=0)] – c [E(Xi0 | Ti1=1) – E(Xi0 | Ti1=0)] = b YAY!Assume differences between X don’t change over time.Slide15

Differences-in-Differences, Graphically

Pre

Post

Treatment

ControlSlide16

Differences-in-Differences, Graphically

Pre

Post

Effect of program using only pre- & post- data from T group (ignoring general time trend).Slide17

Differences-in-Differences, Graphically

Pre

Post

Effect of program using only T & C comparison from post-intervention (ignoring pre-existing differences between T & C groups).Slide18

Differences-in-Differences, Graphically

Pre

PostSlide19

Differences-in-Differences,

Graphically

Pre

Post

Effect of program difference-in-difference (taking into account pre-existing differences between T & C and general time trend).Slide20

Identifying Assumption

Whatever happened to the control group over time is what would have happened to the treatment group in the absence of the program.

Pre

Post

Effect of program difference-in-difference (taking into account pre-existing differences between T & C and general time trend).Slide21

Graphing Exercise

Form Groups of 3-4

4 Programs

Pre-Post Treatment Effect

Take the difference of post-treatment outcome vs. pre-treatment outcome

Post-intervention (Treatment vs. Control) Comparison

Circle what you think is pre-post effect and post-intervention treat vs. control effect

Ask group volunteersSlide22

Uses of Diff-in-Diff

Simple two-period, two-group comparison

very useful in combination with other methodsSlide23

Uses of Diff-in-Diff

Simple two-period, two-group comparison

very useful in combination with other methods

Randomization

Regression Discontinuity

Matching (propensity score)Slide24

Uses of Diff-in-Diff

Simple two-period, two-group comparison

very useful in combination with other methods

Randomization

Regression Discontinuity

Matching (propensity score)

Can also do much more complicated “cohort” analysis, comparing many groups over many time periodsSlide25

The (Simple) Regression

Y

i,t

= a + bTreat

i,t

+ cPost

i,t

+ d(Treat

i,t

Post

i,t

)+ e

i,t

Treat

i,t

is a binary indicator (“turns on” from 0 to 1) for being in the treatment group

Post

i,t

is a binary indicator for the period after treatment

and

Treat

i,t

Post

i,t

is the interaction (product)

Interpretation of

a, b, c, d is “holding all else constant”Slide26

Putting Graph & Regression Together

Pre

Post

Y

i,t

= a + bTreat

i,t

+ cPost

i,t

+ d(Treat

i,t

Post

i,t

)+ e

i,t

d

is the causal effect of treatment

a

a + c

a + b

a + b + c + dSlide27

Putting Graph & Regression Together

Pre

Post

Y

i,t

= a +

bTreat

i,t

+

cPost

i,t

+ d(

Treat

i,t

Post

i,t

)+

e

i,t

a

a + c

a + b

a + b + c + d

Single Diff 2= (

a+b+c+d

)-(

a+c

) = (

b+d

)

Single Diff 1= (

a+b

)-(a)=bSlide28

Putting Graph & Regression Together

Pre

Post

Y

i,t

= a +

bTreat

i,t

+

cPost

i,t

+ d(

Treat

i,t

Post

i,t

)+

e

i,t

Diff-in-Diff=(Single Diff 2-Single Diff 1)=(

b+d

)-b=d

a

a + c

a + b

a + b + c + d

Single Diff 2 = (

a+b+c+d

)-(

a+c

) = (

b+d

)

Single Diff 1= (

a+b

)-(a)=bSlide29

Cohort Analysis

When you’ve got richer data, it’s not as easy to draw the picture or write the equations

cross-section (lots of individuals at one point in time)

time-series (one individual over lots of time)

repeated cross-section (lots of individuals over several times)

panel (lots of individuals, multiple times for each)

Basically, control for each time period and each “group” (fixed effects) – the coefficient on the treatment dummy is the effect you’re trying to estimateSlide30

DiD Data Requirements

Either repeated cross-section or panel

Treatment can’t happen for everyone at the same time

If you believe the identifying assumption, then you can analyze policies ex post

Let’s us tackle really big questions that we’re unlikely to be able to randomizeSlide31

Malaria Eradication in the Americas (Bleakley 2007)

Question: What is the effect of malaria on economic development

?

Data: Malaria Eradication in United States South (1920’s) Brazil, Colombia, Mexico (1950’s)

Diff-in-Diff: Use birth cohorts (old people vs. young people) & (regions with lots of malaria vs. little malaria)

Idea: Young Cohort X Region w/malaria

Result: This group higher income & literacySlide32

What’s the intuition

Areas with high pre-treatment malaria will most benefit from malaria eradication

Young people living in these areas will benefit most (older people might have partial immunity)

Comparison Group: young people living in low pre-treatment malaria areas (malaria eradication will have little effect here)Slide33

Robustness Checks

If possible, use data on multiple pre-program periods to show that difference between treated & control is stable

Not necessary for trends to be parallel, just to know function for each

If possible, use data on multiple post-program periods to show that unusual difference between treated & control occurs only concurrent with program

Alternatively, use data on multiple indicators to show that response to program is only manifest for those we expect it to be (e.g. the diff-in-diff estimate of the impact of ITN distribution on diarrhea should be zero)Slide34

Intermission

Come back if intro to PS4

STATA tipsSlide35

Effect of 2ndary School Construction in Tanzania

Villages

“Treatment Villages” got 2ndary schools

“Control Villages” didn’t

Who benefits from 2ndary schools?

Young People benefit

Older people out of school shouldn’t benefit

Effect: (Young People X Treatment Villages)