Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia...
Transcript of Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia...
![Page 1: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/1.jpg)
Lecture 2: Causal Inference Using Observational Data
Sheetal SekhriUniversity of Virginia
BREAD IGC Summer School, India 2012
July 21, 2012
![Page 2: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/2.jpg)
Using Observational Data
• Many policies and programs are evaluated after theirimplementation
• Policy design can sometimes provide plausibly exogenousvariation
• Observational data that can be combined withinstitutional details for evaluation
• Applications may also lend themselves to naturalexperiments
• Observational data can also be used in such contexts
![Page 3: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/3.jpg)
Using Observational Data
• Many policies and programs are evaluated after theirimplementation
• Policy design can sometimes provide plausibly exogenousvariation
• Observational data that can be combined withinstitutional details for evaluation
• Applications may also lend themselves to naturalexperiments
• Observational data can also be used in such contexts
![Page 4: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/4.jpg)
Using Observational Data
• Many policies and programs are evaluated after theirimplementation
• Policy design can sometimes provide plausibly exogenousvariation
• Observational data that can be combined withinstitutional details for evaluation
• Applications may also lend themselves to naturalexperiments
• Observational data can also be used in such contexts
![Page 5: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/5.jpg)
Using Observational Data
• Many policies and programs are evaluated after theirimplementation
• Policy design can sometimes provide plausibly exogenousvariation
• Observational data that can be combined withinstitutional details for evaluation
• Applications may also lend themselves to naturalexperiments
• Observational data can also be used in such contexts
![Page 6: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/6.jpg)
Using Observational Data
• Many policies and programs are evaluated after theirimplementation
• Policy design can sometimes provide plausibly exogenousvariation
• Observational data that can be combined withinstitutional details for evaluation
• Applications may also lend themselves to naturalexperiments
• Observational data can also be used in such contexts
![Page 7: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/7.jpg)
Benefits of Using Observational Data
• Time horizon relative to field experiments
• Not as expensive
• Externally valid inference (depending on the data anddesign)
• Less fraught with behavioral concerns
![Page 8: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/8.jpg)
Benefits of Using Observational Data
• Time horizon relative to field experiments
• Not as expensive
• Externally valid inference (depending on the data anddesign)
• Less fraught with behavioral concerns
![Page 9: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/9.jpg)
Benefits of Using Observational Data
• Time horizon relative to field experiments
• Not as expensive
• Externally valid inference (depending on the data anddesign)
• Less fraught with behavioral concerns
![Page 10: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/10.jpg)
Benefits of Using Observational Data
• Time horizon relative to field experiments
• Not as expensive
• Externally valid inference (depending on the data anddesign)
• Less fraught with behavioral concerns
![Page 11: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/11.jpg)
Limitations of Using Observational Data
• Selection concerns
• Data quality
• Data limitations - not all desired data for an applicationmay exist
• Data restrictions
![Page 12: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/12.jpg)
Limitations of Using Observational Data
• Selection concerns
• Data quality
• Data limitations - not all desired data for an applicationmay exist
• Data restrictions
![Page 13: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/13.jpg)
Limitations of Using Observational Data
• Selection concerns
• Data quality
• Data limitations - not all desired data for an applicationmay exist
• Data restrictions
![Page 14: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/14.jpg)
Limitations of Using Observational Data
• Selection concerns
• Data quality
• Data limitations - not all desired data for an applicationmay exist
• Data restrictions
![Page 15: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/15.jpg)
Working with Observational Data- Methods
• Difference-in-Difference (DID)
• Regression Discontinuity Design (RDD)
![Page 16: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/16.jpg)
Working with Observational Data- Methods
• Difference-in-Difference (DID)
• Regression Discontinuity Design (RDD)
![Page 17: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/17.jpg)
Difference-in-Difference
• Most popular method used in empirical analysis
• Emulate an experiment with treatment and comparisongroups
• Uses panel data and is a two way fixed effects model
![Page 18: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/18.jpg)
Difference-in-Difference
• Most popular method used in empirical analysis
• Emulate an experiment with treatment and comparisongroups
• Uses panel data and is a two way fixed effects model
![Page 19: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/19.jpg)
Difference-in-Difference
• Most popular method used in empirical analysis
• Emulate an experiment with treatment and comparisongroups
• Uses panel data and is a two way fixed effects model
![Page 20: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/20.jpg)
DID- Basic Idea
• With panel data on the treated group, can compare preand post intervention or policy change
• But any discerned effect can arise due to secular changes
• Panel data on comparison group can provide thecounterfactual
• What would happen to treated group over time inabsence of treatment
![Page 21: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/21.jpg)
DID- Basic Idea
• With panel data on the treated group, can compare preand post intervention or policy change
• But any discerned effect can arise due to secular changes
• Panel data on comparison group can provide thecounterfactual
• What would happen to treated group over time inabsence of treatment
![Page 22: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/22.jpg)
DID- Basic Idea
• With panel data on the treated group, can compare preand post intervention or policy change
• But any discerned effect can arise due to secular changes
• Panel data on comparison group can provide thecounterfactual
• What would happen to treated group over time inabsence of treatment
![Page 23: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/23.jpg)
DID- Basic Idea
• With panel data on the treated group, can compare preand post intervention or policy change
• But any discerned effect can arise due to secular changes
• Panel data on comparison group can provide thecounterfactual
• What would happen to treated group over time inabsence of treatment
![Page 24: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/24.jpg)
DID- Implementation
• Isolate the design using tabular or graphic representation
• Formalize using regression analysis
![Page 25: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/25.jpg)
DID- Implementation
• Isolate the design using tabular or graphic representation
• Formalize using regression analysis
![Page 26: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/26.jpg)
Tabular Representation
DID
Before After DifferenceTreatmentControlDifference
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Tabular Representation
DID
Before After DifferenceTreatment YT1 YT2
ControlDifference
![Page 28: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/28.jpg)
Tabular Representation
DID
Before After DifferenceTreatment YT1 YT2
Control YC1 YC2
Difference
![Page 29: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/29.jpg)
Tabular Representation
DID
Before After DifferenceTreatment YT1 YT2 ∆YT = YT2 − YT1
Control YC1 YC2
Difference
![Page 30: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/30.jpg)
Tabular Representation
DID
Before After DifferenceTreatment YT1 YT2 ∆YT = YT2 − YT1
Control YC1 YC2 ∆YC = YC2 − YC1
Difference
![Page 31: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/31.jpg)
Tabular Representation
DID
Before After DifferenceTreatment YT1 YT2 ∆YT = YT2 − YT1
Control YC1 YC2 ∆YC = YC2 − YC1
Difference ∆YT − ∆YC
![Page 32: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/32.jpg)
DID- Identifying Assumption
• Control group shows the time path of the treatmentgroup without the intervention
• Time trends in absence of treatment should be the same
• Levels can be different
• If different time trends, effect over or under stated
• Identifying assumption- No differential pre-trends
![Page 33: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/33.jpg)
DID- Identifying Assumption
• Control group shows the time path of the treatmentgroup without the intervention
• Time trends in absence of treatment should be the same
• Levels can be different
• If different time trends, effect over or under stated
• Identifying assumption- No differential pre-trends
![Page 34: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/34.jpg)
DID- Identifying Assumption
• Control group shows the time path of the treatmentgroup without the intervention
• Time trends in absence of treatment should be the same
• Levels can be different
• If different time trends, effect over or under stated
• Identifying assumption- No differential pre-trends
![Page 35: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/35.jpg)
DID- Identifying Assumption
• Control group shows the time path of the treatmentgroup without the intervention
• Time trends in absence of treatment should be the same
• Levels can be different
• If different time trends, effect over or under stated
• Identifying assumption- No differential pre-trends
![Page 36: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/36.jpg)
DID- Identifying Assumption
• Control group shows the time path of the treatmentgroup without the intervention
• Time trends in absence of treatment should be the same
• Levels can be different
• If different time trends, effect over or under stated
• Identifying assumption- No differential pre-trends
![Page 37: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/37.jpg)
Difference in Difference
Time
Outcome
Pre-treatment
Control group Treatment group
![Page 38: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/38.jpg)
Difference in Difference
Time
Outcome
Post-treatmentPre-treatment
Control group Treatment group
![Page 39: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/39.jpg)
Difference in Difference
Time
Outcome
Post-treatmentPre-treatment
Control group Treatment group
![Page 40: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/40.jpg)
Difference in Difference
Time
Outcome
Post-treatmentPre-treatment
Control group Treatment group
Treatment effect comparing Treatment & control group in post period
![Page 41: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/41.jpg)
Difference in Difference
Time
Outcome
Post-treatmentPre-treatment
Control group Treatment group
![Page 42: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/42.jpg)
Difference in Difference
Time
Outcome
Post-treatmentPre-treatment
Control group Treatment group
Treatment effect comparing just the Treatmentgroup in pre & post period
![Page 43: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/43.jpg)
Difference in Difference
Time
Outcome
Post-treatmentPre-treatment
Control group Treatment group
![Page 44: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/44.jpg)
Difference in Difference
Time
Outcome
Post-treatmentPre-treatment
Control group Treatment group
Difference-in-Difference: Treatment effect by comparing the Treatmentgroup in pre & post period after eliminating pre-existing difference b/w Treatment and Control group
![Page 45: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/45.jpg)
Difference in Difference: Parallel Trend Assumption
Time
Outcome
Post-treatmentPre-treatment
Control group Treatment group
Difference-in-Difference
![Page 46: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/46.jpg)
Difference in Difference: Parallel Trend Assumption
Time
Outcome
Post-treatmentPre-treatment
Control group Treatment group
![Page 47: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/47.jpg)
Difference in Difference: Parallel Trend Assumption
Time
Outcome
Post-treatmentPre-treatment
Control group Treatment group
![Page 48: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/48.jpg)
Difference in Difference: Parallel Trend Assumption Violated
Time
Outcome
Post-treatmentPre-treatment
Control group Treatment group
![Page 49: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/49.jpg)
DID- Regression Analysis
• Suppose our policy change effects villages such that a setof villages are treated
• We have data over time for all villages
• The panel has only 2 time periods
• Post is an indicator that switches to 1 after theintervention
• T is an indicator that takes value 1 for the villages to betreated
![Page 50: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/50.jpg)
DID- Regression Analysis
• Suppose our policy change effects villages such that a setof villages are treated
• We have data over time for all villages
• The panel has only 2 time periods
• Post is an indicator that switches to 1 after theintervention
• T is an indicator that takes value 1 for the villages to betreated
![Page 51: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/51.jpg)
DID- Regression Analysis
• Suppose our policy change effects villages such that a setof villages are treated
• We have data over time for all villages
• The panel has only 2 time periods
• Post is an indicator that switches to 1 after theintervention
• T is an indicator that takes value 1 for the villages to betreated
![Page 52: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/52.jpg)
DID- Regression Analysis
• Suppose our policy change effects villages such that a setof villages are treated
• We have data over time for all villages
• The panel has only 2 time periods
• Post is an indicator that switches to 1 after theintervention
• T is an indicator that takes value 1 for the villages to betreated
![Page 53: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/53.jpg)
DID- Regression Analysis
• Suppose our policy change effects villages such that a setof villages are treated
• We have data over time for all villages
• The panel has only 2 time periods
• Post is an indicator that switches to 1 after theintervention
• T is an indicator that takes value 1 for the villages to betreated
![Page 54: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/54.jpg)
DID- Regression Analysis
• Outcome variable Y varies by villages and time
• Yit = α0 + α1 Post + α2 T + α3 Post ∗ T + εit
• The panel has only 2 time periods
• Post is an indicator that switches to 1 after theintervention
• T is an indicator that takes value 1 for the villages to betreated
![Page 55: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/55.jpg)
DID- Regression Analysis
• Outcome variable Y varies by villages and time
• Yit = α0 + α1 Post + α2 T + α3 Post ∗ T + εit
• The panel has only 2 time periods
• Post is an indicator that switches to 1 after theintervention
• T is an indicator that takes value 1 for the villages to betreated
![Page 56: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/56.jpg)
DID- Regression Analysis
• Outcome variable Y varies by villages and time
• Yit = α0 + α1 Post + α2 T + α3 Post ∗ T + εit
• The panel has only 2 time periods
• Post is an indicator that switches to 1 after theintervention
• T is an indicator that takes value 1 for the villages to betreated
![Page 57: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/57.jpg)
DID- Regression Analysis
• Outcome variable Y varies by villages and time
• Yit = α0 + α1 Post + α2 T + α3 Post ∗ T + εit
• The panel has only 2 time periods
• Post is an indicator that switches to 1 after theintervention
• T is an indicator that takes value 1 for the villages to betreated
![Page 58: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/58.jpg)
DID- Regression Analysis
• Outcome variable Y varies by villages and time
• Yit = α0 + α1 Post + α2 T + α3 Post ∗ T + εit
• The panel has only 2 time periods
• Post is an indicator that switches to 1 after theintervention
• T is an indicator that takes value 1 for the villages to betreated
![Page 59: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/59.jpg)
Tabular Representation
DID
Before After DifferenceTreatment α0 + α2
ControlDifference
![Page 60: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/60.jpg)
Tabular Representation
DID
Before After DifferenceTreatment α0 + α2 α0 + α1 + α2 + α3
ControlDifference
![Page 61: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/61.jpg)
Tabular Representation
DID
Before After DifferenceTreatment α0 + α2 α0 + α1 + α2 + α3 α1 + α3
ControlDifference
![Page 62: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/62.jpg)
Tabular Representation
DID
Before After DifferenceTreatment α0 + α2 α0 + α1 + α2 + α3 α1 + α3
Control α0
Difference
![Page 63: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/63.jpg)
Tabular Representation
DID
Before After DifferenceTreatment α0 + α2 α0 + α1 + α2 + α3 α1 + α3
Control α0 α0 + α1
Difference
![Page 64: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/64.jpg)
Tabular Representation
DID
Before After DifferenceTreatment α0 + α2 α0 + α1 + α2 + α3 α1 + α3
Control α0 α0 + α1 α1
Difference
![Page 65: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/65.jpg)
Tabular Representation
DID
Before After DifferenceTreatment α0 + α2 α0 + α1 + α2 + α3 α1 + α3
Control α0 α0 + α1 α1
Difference α3
![Page 66: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/66.jpg)
DID- Robustness and Extension
• With many years data before the intervention, possible tocheck for pre-trends to make estimation more credible
• Common support required - check for significant overlapin distributions of T and C
• Placebo test- No effect should be discerned if treatmentis randomly considered to occur in any year prior toactual date
• Balance across treatment and control- selection model toshow determinants of treatment not time varying
![Page 67: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/67.jpg)
DID- Robustness and Extension
• With many years data before the intervention, possible tocheck for pre-trends to make estimation more credible
• Common support required - check for significant overlapin distributions of T and C
• Placebo test- No effect should be discerned if treatmentis randomly considered to occur in any year prior toactual date
• Balance across treatment and control- selection model toshow determinants of treatment not time varying
![Page 68: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/68.jpg)
DID- Robustness and Extension
• With many years data before the intervention, possible tocheck for pre-trends to make estimation more credible
• Common support required - check for significant overlapin distributions of T and C
• Placebo test- No effect should be discerned if treatmentis randomly considered to occur in any year prior toactual date
• Balance across treatment and control- selection model toshow determinants of treatment not time varying
![Page 69: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/69.jpg)
DID- Robustness and Extension
• With many years data before the intervention, possible tocheck for pre-trends to make estimation more credible
• Common support required - check for significant overlapin distributions of T and C
• Placebo test- No effect should be discerned if treatmentis randomly considered to occur in any year prior toactual date
• Balance across treatment and control- selection model toshow determinants of treatment not time varying
![Page 70: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/70.jpg)
DID- Extension
• Yit = β0 + Tt + Vi + β2 Tt ∗ Vi + εit
• Tt full set of year fixed effects
• Vi full set of village fixed effects
• Allows for covariance between Tt and Tt ∗ Vi and Vi andTt ∗ Vi
• Systematic differences between villages allowed
• Allow for intervention to occur in years with differentoutcome variable
![Page 71: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/71.jpg)
DID- Extension
• Yit = β0 + Tt + Vi + β2 Tt ∗ Vi + εit
• Tt full set of year fixed effects
• Vi full set of village fixed effects
• Allows for covariance between Tt and Tt ∗ Vi and Vi andTt ∗ Vi
• Systematic differences between villages allowed
• Allow for intervention to occur in years with differentoutcome variable
![Page 72: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/72.jpg)
DID- Extension
• Yit = β0 + Tt + Vi + β2 Tt ∗ Vi + εit
• Tt full set of year fixed effects
• Vi full set of village fixed effects
• Allows for covariance between Tt and Tt ∗ Vi and Vi andTt ∗ Vi
• Systematic differences between villages allowed
• Allow for intervention to occur in years with differentoutcome variable
![Page 73: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/73.jpg)
DID- Extension
• Yit = β0 + Tt + Vi + β2 Tt ∗ Vi + εit
• Tt full set of year fixed effects
• Vi full set of village fixed effects
• Allows for covariance between Tt and Tt ∗ Vi and Vi andTt ∗ Vi
• Systematic differences between villages allowed
• Allow for intervention to occur in years with differentoutcome variable
![Page 74: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/74.jpg)
DID- Extension
• Yit = β0 + Tt + Vi + β2 Tt ∗ Vi + εit
• Tt full set of year fixed effects
• Vi full set of village fixed effects
• Allows for covariance between Tt and Tt ∗ Vi and Vi andTt ∗ Vi
• Systematic differences between villages allowed
• Allow for intervention to occur in years with differentoutcome variable
![Page 75: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/75.jpg)
DID- Extension
• Yit = β0 + Tt + Vi + β2 Tt ∗ Vi + εit
• Tt full set of year fixed effects
• Vi full set of village fixed effects
• Allows for covariance between Tt and Tt ∗ Vi and Vi andTt ∗ Vi
• Systematic differences between villages allowed
• Allow for intervention to occur in years with differentoutcome variable
![Page 76: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/76.jpg)
Regression Discontinuity Design- RDD
• Resource allocation based on a cutoff- scores, date ofbirth, rationing cutoffs
• Can use an RD design in such settings
• Powerful way of addressing selection
• Observable characteristics in T and C can be different
• Common support not needed
![Page 77: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/77.jpg)
Regression Discontinuity Design- RDD
• Resource allocation based on a cutoff- scores, date ofbirth, rationing cutoffs
• Can use an RD design in such settings
• Powerful way of addressing selection
• Observable characteristics in T and C can be different
• Common support not needed
![Page 78: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/78.jpg)
Regression Discontinuity Design- RDD
• Resource allocation based on a cutoff- scores, date ofbirth, rationing cutoffs
• Can use an RD design in such settings
• Powerful way of addressing selection
• Observable characteristics in T and C can be different
• Common support not needed
![Page 79: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/79.jpg)
Regression Discontinuity Design- RDD
• Resource allocation based on a cutoff- scores, date ofbirth, rationing cutoffs
• Can use an RD design in such settings
• Powerful way of addressing selection
• Observable characteristics in T and C can be different
• Common support not needed
![Page 80: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/80.jpg)
Regression Discontinuity Design- RDD
• Resource allocation based on a cutoff- scores, date ofbirth, rationing cutoffs
• Can use an RD design in such settings
• Powerful way of addressing selection
• Observable characteristics in T and C can be different
• Common support not needed
![Page 81: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/81.jpg)
RDD- Basic Idea
• The control and treated observations are very similararound the cutoff
• Scoring barely above the cutoff matter of chance
• Unobservable characteristics like ability very similar butone group gets treatment and other does not
• Selection process completely known and can be modeled
• Regression function between assignment and outcomevariable determined
![Page 82: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/82.jpg)
RDD- Basic Idea
• The control and treated observations are very similararound the cutoff
• Scoring barely above the cutoff matter of chance
• Unobservable characteristics like ability very similar butone group gets treatment and other does not
• Selection process completely known and can be modeled
• Regression function between assignment and outcomevariable determined
![Page 83: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/83.jpg)
RDD- Basic Idea
• The control and treated observations are very similararound the cutoff
• Scoring barely above the cutoff matter of chance
• Unobservable characteristics like ability very similar butone group gets treatment and other does not
• Selection process completely known and can be modeled
• Regression function between assignment and outcomevariable determined
![Page 84: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/84.jpg)
RDD- Basic Idea
• The control and treated observations are very similararound the cutoff
• Scoring barely above the cutoff matter of chance
• Unobservable characteristics like ability very similar butone group gets treatment and other does not
• Selection process completely known and can be modeled
• Regression function between assignment and outcomevariable determined
![Page 85: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/85.jpg)
RDD- Basic Idea
• The control and treated observations are very similararound the cutoff
• Scoring barely above the cutoff matter of chance
• Unobservable characteristics like ability very similar butone group gets treatment and other does not
• Selection process completely known and can be modeled
• Regression function between assignment and outcomevariable determined
![Page 86: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/86.jpg)
20
40
60
80
Tes
t S
core
10 20 30 40 50 60 70 80 90 100Assignment Variable
Regression Discontinuity: No Effect
Control Group Treatment Group
![Page 87: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/87.jpg)
20
40
60
80
Tes
t S
core
10 20 30 40 50 60 70 80 90 100Assignment Variable
Regression Discontinuity: Significant Effect
Control Group Treatment Group
![Page 88: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/88.jpg)
20
40
60
80
Tes
t S
core
10 20 30 40 50 60 70 80 90 100Assignment Variable
Regression Discontinuity: Significant Effect
Control Group Treatment Group
![Page 89: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/89.jpg)
20
40
60
80
Tes
t S
core
10 20 30 40 50 60 70 80 90 100Assignment Variable
Regression Discontinuity: Significant Effect
Control Group Treatment Group
![Page 90: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/90.jpg)
20
40
60
80
Tes
t S
core
10 20 30 40 50 60 70 80 90 100Assignment Variable
Regression Discontinuity: Significant Effect
Control Group Treatment Group
![Page 91: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/91.jpg)
20
40
60
80
Tes
t S
core
10 20 30 40 50 60 70 80 90 100Assignment Variable
Regression Discontinuity: Significant Effect
Control Group Treatment Group
Counterfactual
Regression
![Page 92: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/92.jpg)
20
40
60
80
Tes
t S
core
10 20 30 40 50 60 70 80 90 100Assignment Variable
Regression Discontinuity: Significant Effect
Control Group Treatment Group
Counterfactual
Regression
Treatment Effect
![Page 93: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/93.jpg)
RDD- Implementation
• Probability of treatment should be discontinuous at thecutoff- T sample on one side
• Those offered T should take it up and control groupsshould not be able to get treated
• Sharp versus fuzzy design require different approaches
• The pr of T changes from 0 to 1 at the cutoff in sharpdesign
• If the pr does not change very sharply or the over ridesare high, use assignment as IV for treatment
![Page 94: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/94.jpg)
RDD- Implementation
• Probability of treatment should be discontinuous at thecutoff- T sample on one side
• Those offered T should take it up and control groupsshould not be able to get treated
• Sharp versus fuzzy design require different approaches
• The pr of T changes from 0 to 1 at the cutoff in sharpdesign
• If the pr does not change very sharply or the over ridesare high, use assignment as IV for treatment
![Page 95: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/95.jpg)
RDD- Implementation
• Probability of treatment should be discontinuous at thecutoff- T sample on one side
• Those offered T should take it up and control groupsshould not be able to get treated
• Sharp versus fuzzy design require different approaches
• The pr of T changes from 0 to 1 at the cutoff in sharpdesign
• If the pr does not change very sharply or the over ridesare high, use assignment as IV for treatment
![Page 96: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/96.jpg)
RDD- Implementation
• Probability of treatment should be discontinuous at thecutoff- T sample on one side
• Those offered T should take it up and control groupsshould not be able to get treated
• Sharp versus fuzzy design require different approaches
• The pr of T changes from 0 to 1 at the cutoff in sharpdesign
• If the pr does not change very sharply or the over ridesare high, use assignment as IV for treatment
![Page 97: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/97.jpg)
RDD- Implementation
• Probability of treatment should be discontinuous at thecutoff- T sample on one side
• Those offered T should take it up and control groupsshould not be able to get treated
• Sharp versus fuzzy design require different approaches
• The pr of T changes from 0 to 1 at the cutoff in sharpdesign
• If the pr does not change very sharply or the over ridesare high, use assignment as IV for treatment
![Page 98: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/98.jpg)
Regression Discontinuity: Sharp Design
0.2
.4.6
.81
Tre
atm
ent
10 20 30 40 50 60 70 80 90 100Assignment Variable
![Page 99: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/99.jpg)
Regression Discontinuity: Fuzzy Design
0.2
.4.6
.81
Tre
atm
ent
10 20 30 40 50 60 70 80 90 100Assignment Variable
![Page 100: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/100.jpg)
RDD- Implementation
• Parametric , semi-parametric or non parametric methodscan be used for estimation
• Mis-specified functional form can be a problem
• Discontinuity in regression functions at the cutoff is thetreatment effect
• Functional forms can generate spurious effects or biasedeffects
• Non linear functional forms estimated as linear regressionfunctions is an example
![Page 101: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/101.jpg)
RDD- Implementation
• Parametric , semi-parametric or non parametric methodscan be used for estimation
• Mis-specified functional form can be a problem
• Discontinuity in regression functions at the cutoff is thetreatment effect
• Functional forms can generate spurious effects or biasedeffects
• Non linear functional forms estimated as linear regressionfunctions is an example
![Page 102: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/102.jpg)
RDD- Implementation
• Parametric , semi-parametric or non parametric methodscan be used for estimation
• Mis-specified functional form can be a problem
• Discontinuity in regression functions at the cutoff is thetreatment effect
• Functional forms can generate spurious effects or biasedeffects
• Non linear functional forms estimated as linear regressionfunctions is an example
![Page 103: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/103.jpg)
RDD- Implementation
• Parametric , semi-parametric or non parametric methodscan be used for estimation
• Mis-specified functional form can be a problem
• Discontinuity in regression functions at the cutoff is thetreatment effect
• Functional forms can generate spurious effects or biasedeffects
• Non linear functional forms estimated as linear regressionfunctions is an example
![Page 104: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/104.jpg)
RDD- Implementation
• Parametric , semi-parametric or non parametric methodscan be used for estimation
• Mis-specified functional form can be a problem
• Discontinuity in regression functions at the cutoff is thetreatment effect
• Functional forms can generate spurious effects or biasedeffects
• Non linear functional forms estimated as linear regressionfunctions is an example
![Page 105: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/105.jpg)
20
40
60
80
Tes
t S
core
10 20 30 40 50 60 70 80 90 100Assignment Variable
Threats to RD: Nonlinear Functional Form
Treatment Group Control Group
![Page 106: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/106.jpg)
20
40
60
80
Tes
t S
core
10 20 30 40 50 60 70 80 90 100Assignment Variable
Threats to RD: Nonlinear Functional Form
Treatment Group Control Group
![Page 107: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/107.jpg)
20
40
60
80
Tes
t S
core
10 20 30 40 50 60 70 80 90 100Assignment Variable
Threats to RD: Nonlinear Functional Form
Treatment Group Control Group
![Page 108: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/108.jpg)
20
40
60
80
Tes
t S
core
10 20 30 40 50 60 70 80 90 100Assignment Variable
Threats to RD: Nonlinear Functional Form
Treatment Group Control Group
Treatment Effect
![Page 109: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/109.jpg)
20
40
60
80
Tes
t S
core
10 20 30 40 50 60 70 80 90 100Assignment Variable
Threats to RD: Nonlinear Functional Form
Treatment Group Control Group
Treatment Effect
![Page 110: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/110.jpg)
RDD- Functional Form
• Visual inspection of the data - normalize the AV bysubtracting the cutoff from the observation score
• Over fitting the model allowing for interaction terms aswell
• Will reduce power and need a lot of data around he cutoff
• Sensitivity analysis to different functional forms
![Page 111: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/111.jpg)
RDD- Functional Form
• Visual inspection of the data - normalize the AV bysubtracting the cutoff from the observation score
• Over fitting the model allowing for interaction terms aswell
• Will reduce power and need a lot of data around he cutoff
• Sensitivity analysis to different functional forms
![Page 112: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/112.jpg)
RDD- Functional Form
• Visual inspection of the data - normalize the AV bysubtracting the cutoff from the observation score
• Over fitting the model allowing for interaction terms aswell
• Will reduce power and need a lot of data around he cutoff
• Sensitivity analysis to different functional forms
![Page 113: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/113.jpg)
RDD- Functional Form
• Visual inspection of the data - normalize the AV bysubtracting the cutoff from the observation score
• Over fitting the model allowing for interaction terms aswell
• Will reduce power and need a lot of data around he cutoff
• Sensitivity analysis to different functional forms
![Page 114: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/114.jpg)
RDD- Functional Form
• Non parametric approaches - local linear regressions
• Sensitivity to bandwidth and kernel choice
• In semi parametric approaches, smooth functionestimated with splines and covariates can be controlled
![Page 115: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/115.jpg)
RDD- Functional Form
• Non parametric approaches - local linear regressions
• Sensitivity to bandwidth and kernel choice
• In semi parametric approaches, smooth functionestimated with splines and covariates can be controlled
![Page 116: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/116.jpg)
RDD- Functional Form
• Non parametric approaches - local linear regressions
• Sensitivity to bandwidth and kernel choice
• In semi parametric approaches, smooth functionestimated with splines and covariates can be controlled
![Page 117: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/117.jpg)
RDD- Threats to the Validity
• The cutoffs should be unknown to the population
• Cutoffs should not be manipulated
• Testing for manipulation, can perform Mcrary’s test
• Other potential outcomes should be continuous to avoidalternative confounding interpretations
• Test for continuity of several available control variables
![Page 118: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/118.jpg)
RDD- Threats to the Validity
• The cutoffs should be unknown to the population
• Cutoffs should not be manipulated
• Testing for manipulation, can perform Mcrary’s test
• Other potential outcomes should be continuous to avoidalternative confounding interpretations
• Test for continuity of several available control variables
![Page 119: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/119.jpg)
RDD- Threats to the Validity
• The cutoffs should be unknown to the population
• Cutoffs should not be manipulated
• Testing for manipulation, can perform Mcrary’s test
• Other potential outcomes should be continuous to avoidalternative confounding interpretations
• Test for continuity of several available control variables
![Page 120: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/120.jpg)
RDD- Threats to the Validity
• The cutoffs should be unknown to the population
• Cutoffs should not be manipulated
• Testing for manipulation, can perform Mcrary’s test
• Other potential outcomes should be continuous to avoidalternative confounding interpretations
• Test for continuity of several available control variables
![Page 121: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/121.jpg)
RDD- Threats to the Validity
• The cutoffs should be unknown to the population
• Cutoffs should not be manipulated
• Testing for manipulation, can perform Mcrary’s test
• Other potential outcomes should be continuous to avoidalternative confounding interpretations
• Test for continuity of several available control variables
![Page 122: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/122.jpg)
Threats to RD: Manipulation of the
Assignment Variable
![Page 123: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/123.jpg)
Threats to RD: Manipulation of the
Assignment Variable
McCrary Test (2008) • Statistical test for testing discontinuity of the assignment variable at
the cutoff point
![Page 124: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/124.jpg)
Threats to RD: Manipulation of the
Assignment Variable
McCrary Test (2008) • Statistical test for testing discontinuity of the assignment variable at
the cutoff point
• Assignment variable satisfying “McCrary” Test
0
.1.2
.3.4
.5
46 48 50 52 54
![Page 125: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/125.jpg)
Threats to RD: Manipulation of the
Assignment Variable
McCrary Test (2008) • Statistical test for testing discontinuity of the assignment variable at
the cutoff point
• Assignment variable violating “McCrary” Test
0
.1.2
.3.4
.5
46 48 50 52 54
![Page 126: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/126.jpg)
RDD- LATE Estimator
• The limitation of RDD - effect isolated at cutoff
• Cutoff may not be policy relevant or results may not beexternally valid
• RD frontier can arise if cutoff varies by years or sites
• Can pool different cutoff to get a more general estimatefor the range over which cutoff varies
• More generalizable but masks heterogeneity
![Page 127: Sheetal Sekhri University of Virginia BREAD IGC Summer ... · Sheetal Sekhri University of Virginia BREAD IGC Summer School, India 2012 July 21, 2012. Using Observational Data Many](https://reader034.fdocuments.in/reader034/viewer/2022050217/5f638ca55c4654666725f5ac/html5/thumbnails/127.jpg)
RDD- LATE Estimator
• The limitation of RDD - effect isolated at cutoff
• Cutoff may not be policy relevant or results may not beexternally valid
• RD frontier can arise if cutoff varies by years or sites
• Can pool different cutoff to get a more general estimatefor the range over which cutoff varies
• More generalizable but masks heterogeneity