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7 Estimating average treatment effects

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Panel Methods for Finance
This chapter is in the book Panel Methods for Finance
7 EstimatingaveragetreatmenteffectsAsubstantialpartoftheempiricalliteratureattemptstoidentifycausaleffects,andthetopicofcausalinferencehasbeenreceivingincreasingamountsofattentioninre-centyears.Muchofthisliteratureisframedastheestimationoftreatmenteffects(oras“programmeevaluation”).Atreatmenteffectreferstothecausalimpactofacer-taintreatment(policy,event,decision)uponagivenoutcome.Becausetheeffectofatreatmentmaydifferacrossfirmsandselectionintotreatmentmaybenonrandom,the estimation of treatment effects is nontrivial. In the simplest case, the treatmenteffectissimplythecoefficientforatreatmentindicatorinalinearregressionmodel.Becauseweareinterestedinthecausaleffectoftreatment,weneedtoworryabouten-dogeneityofthetreatmentdummy.Thatis,weneedtoworryaboutthequestionhowunitsareselected,orselectthemselves,intotreatment.Whentheeffectofatreatmentdiffersacrossunits,additionalissuesemerge,includingthequestionwhich(average)treatmenteffectwewishtoestimate.In this chapter, we provide a brief review of the literature on the estimation ofaveragetreatmenteffects,withparticularattentiontoitsuseinfinance.Theadvan-tageofhavingpaneldataisthatmultipleobservationsonthesameunitsareavail-able,whichideallyincludeobservationsbeforeandaftertreatmenthasoccurred.Thisway, a comparison before and after can be combined with a comparison with firmsthatarenottreated(thecontrolgroup).Suchdifference-in-differencesapproachesareverypopularinempiricalwork.Section7.1discussesthepotentialoutcomesframe-work, which underlies much of the recent literature. It provides a convenient wayto illustrate the identification challenge (the fact that counterfactual outcomes arenot observed), and helps introducing several solutions. Section 7.2 considers possi-blesolutionsifitcanbeassumedthattreatmentisindependentofthepotentialout-comes,conditionaluponasetofcovariates.Thisincludesinverseprobabilityweight-ing(IPW),regression-adjustmentandmatching.Section7.3introducesregressiondis-continuitydesign(RDD).Wethenmovetomorechallengingcaseswheretreatmentispotentiallyendogenous,conditionaluponasetofcovariates.Section7.4relatestheal-ternativeoutcomesframeworktothemoretraditionalswitchingregressionmodel.InSection7.5,wecomebacktotheroleofinstrumentalvariablesestimationinthepres-enceofheterogeneoustreatmenteffects,anddiscusstheconceptofalocalaveragetreatmenteffect(LATE).Allapproachesareimplicitlyorexplicitlybasedonacomparisonofoutcomesforunitsthattreatedwiththoseofoneormore(potentiallyhypothetical)unitsthatarenot treated. The panel nature of the data is reflected in the calculation of the cor-responding standard errors, or in the use of lagged variables as conditioning vari-ablesorinstruments.InSection7.6,weconcludethischapterwithadiscussionofthedifference-in-differencesapproach,whichcomparesoutcomesbeforeandaftertreat-ment,andbetweengroupsofunitsthatreceivetreatmentanddoesthatdonot.Thiscan be combined with some of the earlier approaches, such as matching. However,https://doi.org/10.1515/9783110660739-007
© 2021 Walter de Gruyter GmbH, Berlin/Boston

7 EstimatingaveragetreatmenteffectsAsubstantialpartoftheempiricalliteratureattemptstoidentifycausaleffects,andthetopicofcausalinferencehasbeenreceivingincreasingamountsofattentioninre-centyears.Muchofthisliteratureisframedastheestimationoftreatmenteffects(oras“programmeevaluation”).Atreatmenteffectreferstothecausalimpactofacer-taintreatment(policy,event,decision)uponagivenoutcome.Becausetheeffectofatreatmentmaydifferacrossfirmsandselectionintotreatmentmaybenonrandom,the estimation of treatment effects is nontrivial. In the simplest case, the treatmenteffectissimplythecoefficientforatreatmentindicatorinalinearregressionmodel.Becauseweareinterestedinthecausaleffectoftreatment,weneedtoworryabouten-dogeneityofthetreatmentdummy.Thatis,weneedtoworryaboutthequestionhowunitsareselected,orselectthemselves,intotreatment.Whentheeffectofatreatmentdiffersacrossunits,additionalissuesemerge,includingthequestionwhich(average)treatmenteffectwewishtoestimate.In this chapter, we provide a brief review of the literature on the estimation ofaveragetreatmenteffects,withparticularattentiontoitsuseinfinance.Theadvan-tageofhavingpaneldataisthatmultipleobservationsonthesameunitsareavail-able,whichideallyincludeobservationsbeforeandaftertreatmenthasoccurred.Thisway, a comparison before and after can be combined with a comparison with firmsthatarenottreated(thecontrolgroup).Suchdifference-in-differencesapproachesareverypopularinempiricalwork.Section7.1discussesthepotentialoutcomesframe-work, which underlies much of the recent literature. It provides a convenient wayto illustrate the identification challenge (the fact that counterfactual outcomes arenot observed), and helps introducing several solutions. Section 7.2 considers possi-blesolutionsifitcanbeassumedthattreatmentisindependentofthepotentialout-comes,conditionaluponasetofcovariates.Thisincludesinverseprobabilityweight-ing(IPW),regression-adjustmentandmatching.Section7.3introducesregressiondis-continuitydesign(RDD).Wethenmovetomorechallengingcaseswheretreatmentispotentiallyendogenous,conditionaluponasetofcovariates.Section7.4relatestheal-ternativeoutcomesframeworktothemoretraditionalswitchingregressionmodel.InSection7.5,wecomebacktotheroleofinstrumentalvariablesestimationinthepres-enceofheterogeneoustreatmenteffects,anddiscusstheconceptofalocalaveragetreatmenteffect(LATE).Allapproachesareimplicitlyorexplicitlybasedonacomparisonofoutcomesforunitsthattreatedwiththoseofoneormore(potentiallyhypothetical)unitsthatarenot treated. The panel nature of the data is reflected in the calculation of the cor-responding standard errors, or in the use of lagged variables as conditioning vari-ablesorinstruments.InSection7.6,weconcludethischapterwithadiscussionofthedifference-in-differencesapproach,whichcomparesoutcomesbeforeandaftertreat-ment,andbetweengroupsofunitsthatreceivetreatmentanddoesthatdonot.Thiscan be combined with some of the earlier approaches, such as matching. However,https://doi.org/10.1515/9783110660739-007
© 2021 Walter de Gruyter GmbH, Berlin/Boston

Chapters in this book

  1. Frontmatter I
  2. Preface VII
  3. Acknowledgments IX
  4. Contents XI
  5. Acronyms XV
  6. 1 Introduction 1
  7. 2 Linear static models 9
  8. 3 Dealing with heterogeneity and endogeneity: fixed effects, IV and GMM 68
  9. 4 Outliers, missing values and other data issues 107
  10. 5 Linear dynamic models 126
  11. 6 Models with limited dependent variables 145
  12. 7 Estimating average treatment effects 208
  13. Bibliography 255
  14. Index 275
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https://doi.org/10.1515/9783110660739-007

Chapters in this book

  1. Frontmatter I
  2. Preface VII
  3. Acknowledgments IX
  4. Contents XI
  5. Acronyms XV
  6. 1 Introduction 1
  7. 2 Linear static models 9
  8. 3 Dealing with heterogeneity and endogeneity: fixed effects, IV and GMM 68
  9. 4 Outliers, missing values and other data issues 107
  10. 5 Linear dynamic models 126
  11. 6 Models with limited dependent variables 145
  12. 7 Estimating average treatment effects 208
  13. Bibliography 255
  14. Index 275
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