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Twoway Fixed Effects with Differential Timing

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Causal Inference
This chapter is in the book Causal Inference
Difference-in-Differences 461Identification of causal effects would need for the treatment itself tobeexogenoustosuchchangesinthecomposition.Final thoughts.There are a few other caveats I’d like to make beforemovingon.First,itisimportanttoremembertheconceptswelearnedin the early DAG chapter. In choosing covariates in a DD design, youmust resist the temptation to simply load the regression up with akitchen sink of regressors. You should resist if only because in sodoing,youmayinadvertentlyincludeacollider,andifacollideriscondi-tionedon,itintroducesstrangepatternsthatmaymisleadyouandyouraudience. There is unfortunately no way forward except, again, deepinstitutionalfamiliaritywithboththefactorsthatdeterminedtreatmentassignmentontheground,aswellaseconomictheoryitself.Second,another issue I skipped over entirely is the question of how the out-come is modeled. Very little thought if any is given to how exactlywe should model some outcome. Just to take one example, shouldwe use the log or the levels themselves? Should we use the quarticroot? Should we use rates? These, it turns, out are critically impor-tantbecauseformanyofthem,theparalleltrendsassumptionneededforidentificationwillnotbeachieved—eventhoughitwillbeachievedunder some other unknown transformation. It is for this reason thatyou can think of many DD designs as having a parametric elementbecause you must make strong commitments about the functionalformitself.Icannotprovideguidancetoyouonthis,exceptthatmaybeusingthepre-treatmentleadsasawayoffindingparallelismcouldbeausefulguide.TwowayFixedEffectswithDifferentialTimingIhaveabumperstickeronmycarthatsays“IloveFederalism(forthe natural experiments)” (Figure 69). I made these bumper stickersfor my students to be funny, and to illustrate that the United States isanever-endinglaboratory.Becauseofstatefederalism,eachUSstatehas been given considerable discretion to govern itself with policiesandreforms.Yet,becauseitisaunionofstates,USresearchershave
© Yale University Press, New Haven

Difference-in-Differences 461Identification of causal effects would need for the treatment itself tobeexogenoustosuchchangesinthecomposition.Final thoughts.There are a few other caveats I’d like to make beforemovingon.First,itisimportanttoremembertheconceptswelearnedin the early DAG chapter. In choosing covariates in a DD design, youmust resist the temptation to simply load the regression up with akitchen sink of regressors. You should resist if only because in sodoing,youmayinadvertentlyincludeacollider,andifacollideriscondi-tionedon,itintroducesstrangepatternsthatmaymisleadyouandyouraudience. There is unfortunately no way forward except, again, deepinstitutionalfamiliaritywithboththefactorsthatdeterminedtreatmentassignmentontheground,aswellaseconomictheoryitself.Second,another issue I skipped over entirely is the question of how the out-come is modeled. Very little thought if any is given to how exactlywe should model some outcome. Just to take one example, shouldwe use the log or the levels themselves? Should we use the quarticroot? Should we use rates? These, it turns, out are critically impor-tantbecauseformanyofthem,theparalleltrendsassumptionneededforidentificationwillnotbeachieved—eventhoughitwillbeachievedunder some other unknown transformation. It is for this reason thatyou can think of many DD designs as having a parametric elementbecause you must make strong commitments about the functionalformitself.Icannotprovideguidancetoyouonthis,exceptthatmaybeusingthepre-treatmentleadsasawayoffindingparallelismcouldbeausefulguide.TwowayFixedEffectswithDifferentialTimingIhaveabumperstickeronmycarthatsays“IloveFederalism(forthe natural experiments)” (Figure 69). I made these bumper stickersfor my students to be funny, and to illustrate that the United States isanever-endinglaboratory.Becauseofstatefederalism,eachUSstatehas been given considerable discretion to govern itself with policiesandreforms.Yet,becauseitisaunionofstates,USresearchershave
© Yale University Press, New Haven

Chapters in this book

  1. Frontmatter i
  2. Contents vii
  3. Acknowledgments ix
  4. Introduction
  5. Introductory Note 1
  6. What Is Causal Inference? 3
  7. Do Not Confuse Correlation with Causality 6
  8. OptimizationMakes Everything Endogenous 8
  9. Example: Identifying Price Elasticity of Demand 10
  10. Conclusion 14
  11. Probability and Regression Review 16
  12. Directed Acyclic Graphs
  13. Introduction 96
  14. Introduction to DAG Notation 97
  15. Potential Outcomes Causal Model
  16. Introduction 119
  17. Physical Randomization 123
  18. Randomization Inference 148
  19. Conclusion 174
  20. Matching and Subclassification
  21. Subclassification 175
  22. Exact Matching 191
  23. Approximate Matching 198
  24. Regression Discontinuity
  25. Huge Popularity of Regression Discontinuity 241
  26. Estimation Using an RDD 252
  27. Challenges to Identification 282
  28. Replicating a Popular Design: The Close Election 289
  29. Regression Kink Design 312
  30. Conclusion 313
  31. Instrumental Variables
  32. History of Instrumental Variables: Father and Son 315
  33. Intuition of Instrumental Variables 319
  34. Homogeneous Treatment Effects 323
  35. Parental Methamphetamine Abuse and Foster Care 329
  36. The Problem of Weak Instruments 337
  37. Heterogeneous Treatment Effects 346
  38. Applications 352
  39. Popular IV Designs 359
  40. Conclusion 384
  41. Panel Data
  42. DAG Example 386
  43. Estimation 388
  44. Data Exercise: Survey of Adult Service Providers 396
  45. Conclusion 405
  46. Difference-in-Differences
  47. John Snow’s Cholera Hypothesis 406
  48. Estimation 411
  49. Inference 423
  50. Providing Evidence for Parallel Trends Through Event Studies and Parallel Leads 425
  51. The Importance of Placebos in DD 433
  52. Twoway Fixed Effects with Differential Timing 461
  53. Conclusion 509
  54. Synthetic Control
  55. Introducing the Comparative Case Study 511
  56. Prison Construction and Black Male Incarceration 525
  57. Conclusion 540
  58. Bibliography 541
  59. Permissions 555
  60. Index 561
Readers are also interested in:
https://doi.org/10.12987/9780300255881-042

Chapters in this book

  1. Frontmatter i
  2. Contents vii
  3. Acknowledgments ix
  4. Introduction
  5. Introductory Note 1
  6. What Is Causal Inference? 3
  7. Do Not Confuse Correlation with Causality 6
  8. OptimizationMakes Everything Endogenous 8
  9. Example: Identifying Price Elasticity of Demand 10
  10. Conclusion 14
  11. Probability and Regression Review 16
  12. Directed Acyclic Graphs
  13. Introduction 96
  14. Introduction to DAG Notation 97
  15. Potential Outcomes Causal Model
  16. Introduction 119
  17. Physical Randomization 123
  18. Randomization Inference 148
  19. Conclusion 174
  20. Matching and Subclassification
  21. Subclassification 175
  22. Exact Matching 191
  23. Approximate Matching 198
  24. Regression Discontinuity
  25. Huge Popularity of Regression Discontinuity 241
  26. Estimation Using an RDD 252
  27. Challenges to Identification 282
  28. Replicating a Popular Design: The Close Election 289
  29. Regression Kink Design 312
  30. Conclusion 313
  31. Instrumental Variables
  32. History of Instrumental Variables: Father and Son 315
  33. Intuition of Instrumental Variables 319
  34. Homogeneous Treatment Effects 323
  35. Parental Methamphetamine Abuse and Foster Care 329
  36. The Problem of Weak Instruments 337
  37. Heterogeneous Treatment Effects 346
  38. Applications 352
  39. Popular IV Designs 359
  40. Conclusion 384
  41. Panel Data
  42. DAG Example 386
  43. Estimation 388
  44. Data Exercise: Survey of Adult Service Providers 396
  45. Conclusion 405
  46. Difference-in-Differences
  47. John Snow’s Cholera Hypothesis 406
  48. Estimation 411
  49. Inference 423
  50. Providing Evidence for Parallel Trends Through Event Studies and Parallel Leads 425
  51. The Importance of Placebos in DD 433
  52. Twoway Fixed Effects with Differential Timing 461
  53. Conclusion 509
  54. Synthetic Control
  55. Introducing the Comparative Case Study 511
  56. Prison Construction and Black Male Incarceration 525
  57. Conclusion 540
  58. Bibliography 541
  59. Permissions 555
  60. Index 561
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