R E G R E S S I O N D I S C O N T I N U I T Y I PMAP 8521: Program - - PowerPoint PPT Presentation

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R E G R E S S I O N D I S C O N T I N U I T Y I PMAP 8521: Program - - PowerPoint PPT Presentation

Apr 11, 2023 712 likes •1.16k views

R E G R E S S I O N D I S C O N T I N U I T Y I PMAP 8521: Program Evaluation for Public Service November 4, 2019 Fill out your reading report on iCollege! P L A N F O R T O D A Y Jumps and cutoffs Measuring the size of the discontinuity

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R E G R E S S I O N D I S C O N T I N U I T Y I

PMAP 8521: Program Evaluation for Public Service November 4, 2019

Fill out your reading report

  • n iCollege!
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P L A N F O R T O D A Y Jumps and cutoffs RDD with R Measuring the size of the discontinuity Main RDD concerns

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J U M P S & C U TO F F S

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Think of five social programs that use eligibility cutoffs to determine who can access the program

Federal/state/local governments; school districts; nonprofits; etc.

How is eligibility measured? What’s the cutoff?

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K E Y T E R M S Running/forcing variable

Index or measure that determines eligibility

Cutoff/cutpoint/threshold

Number that formally assigns access to program

Outcome

The thing you want to see the causal effect on

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M A I N I N T U I T I O N People right before and right after the cutoff are essentially the same This mimics the idea of treatment and control groups

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Control group Treatment group Cutoff Causal effect

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M E A S U R I N G T H E S I Z E O F T H E D I S C O N T I N U I T Y

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The size of the discontinuity depends

  • n how you draw the trend lines on

each side of the cutoff

There’s no one right way to draw lines! Parametric Nonparametric Bandwidths Kernels

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P A R A M E T R I C L I N E S Formulas with parameters

y = mx + b

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y = β0 + β1x1 + β2x2

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y = β0 + β1x1

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P A R A M E T R I C L I N E S Formulas with parameters

y = mx + b

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y = β0 + β1x1 + β2x2

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Not just for straight lines! Make curvy with exponents

y = β0 + β1x1 + β2x2

1

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y = β0 + β1x1

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y = β0 + β1x1 + β2x2

1

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y = β0 + β1x1 + β2x2

1 + β3x3 1

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M E A S U R I N G T H E G A P

y = β0 + β1Running variable (centered) + β2Indicator for treatment

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ID

  • utcome

running_var running_var_ centered treatment 1 90.0 64

  • 6

FALSE 2 85.7 70 TRUE 3 85.8 73 3 TRUE 4 85.7 60

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FALSE 5 84.4 71 1 TRUE

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N O N P A R A M E T R I C L I N E S Lines without parameters

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Loess

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Loess Y = mx + b

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Loess Y = mx + b Y = mx + nx2 + b

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All you really care about is the area right around the cutoff

Observations far away from cutoff don’t really matter

B A N D W I D T H S Bandwidth = window around cutoff where you focus your analysis

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Loess Y = mx + b Y = mx + b

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You care the most about observations right by the cutoff, so give them extra weight K E R N E L S Kernel = method for assigning importance to values by distance to cutoff

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M A I N R D D C O N C E R N S

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G R E E D Y M E T H O D You need lots of data, since you’re throwing lots of it away

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Bandwidth = $20,000

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Bandwidth = $10,000

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L A T E V S . A T E You’re only measuring the ATE for people in the bandwidth Local Average Treatment Effect (LATE)

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N O N C O M P L I A N C E People on the margin of the discontinuity might end up in/out of the program

The ACA, Medicaid, and 138% of the poverty line

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Sharp discontinuity

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Fuzzy discontinuity

Address with instrumental variables (next week!)

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R D D W I T H R

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1: Is assignment to treatment rule-based?

If not, stop!

2: Is design fuzzy or sharp?

Either is fine; sharp is easier.

3: Is there a discontinuity in running variable at cutpoint?

Hopefully not.

4: Is there a discontinuity in outcome variable at cutpoint in running variable?

Hopefully.

5: How big is the gap?

Measure parametrically and nonparametrically.