How to Make Causal Inferences with Time-Series Cross-Sectional Data

How to Make Causal Inferences with Time-Series Cross-Sectional Data

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Matthew Blackwell

April 13, 2013
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  1. How to Make Causal Inferences with Time-Series Cross-Sectional Data Matthew

    Blackwell University of Rochester Adam Glynn Harvard University
  2. How to Make Causal Inferences with Time-Series Cross-Sectional Data

  3. How to Make Causal Inferences with Time-Series Cross-Sectional Data Very

    Carefully.
  4. How to Make Causal Inferences with Time-Series Cross-Sectional Data Using

    weights.
  5. ۺ܎˞଀ ۢ܎˞଀ ۹܎˞଀ ۢ܎ ۹܎ ۺ܎

  6. What is the effect of A on Y? ۺ܎˞଀ ۢ܎˞଀

    ۹܎˞଀ ۢ܎ ۹܎ ۺ܎
  7. What is the effect of A on Y? contemporaneous ۺ܎˞଀

    ۢ܎˞଀ ۹܎˞଀ ۢ܎ ۹܎ ۺ܎
  8. What is the effect of A on Y? treatment history

    ۺ܎˞଀ ۢ܎˞଀ ۹܎˞଀ ۢ܎ ۹܎ ۺ܎
  9. Shouldn't we have more notation?

  10. ۢ ܎  ۢ଀  Ɛ  ۢ܎ Treatment history

    Shouldn't we have more notation?
  11. ۢ ܎  ۢ଀  Ɛ  ۢ܎ Treatment history

    Shouldn't we have more notation? Specific instance of a treatment history ۼ ܎  ۼ଀  Ɛ  ۼ܎
  12. ۢ ܎  ۢ଀  Ɛ  ۢ܎ Treatment history

    ۺ܎ ۼ ܎ Potential outcomes Shouldn't we have more notation? Specific instance of a treatment history ۼ ܎  ۼ଀  Ɛ  ۼ܎
  13. The effect of history

  14. The effect of history ণ ۼ ܎  ۼƓ ܎

     ۦ=ۺ܎ ۼ ܎ ˞ ۺ܎ ۼƓ ܎ ? Average Treatment History Effect
  15. The effect of history ণ ۼ ܎  ۼƓ ܎

     ۦ=ۺ܎ ۼ ܎ ˞ ۺ܎ ۼƓ ܎ ? Average Treatment History Effect ATHE
  16. The effect of history ণ ۼ ܎  ۼƓ ܎

     ۦ=ۺ܎ ۼ ܎ ˞ ۺ܎ ۼƓ ܎ ? Average Treatment History Effect 1 1 1 1 1 1 1 ATHE
  17. The effect of history ণ ۼ ܎  ۼƓ ܎

     ۦ=ۺ܎ ۼ ܎ ˞ ۺ܎ ۼƓ ܎ ? Average Treatment History Effect 1 1 1 1 1 1 1 0 0 0 0 0 0 0 vs ATHE
  18. The effect of history

  19. The effect of history Blip Effect ণ۽ ۼ ܎˞଀ 

    ۦ=ۺ܎ ۼ ܎˞଀   ˞ ۺ܎ ۼ ܎˞଀   ?
  20. The effect of history 1 0 0 0 0 0

    0 0 vs 0 0 0 0 0 0 Blip Effect ণ۽ ۼ ܎˞଀  ۦ=ۺ܎ ۼ ܎˞଀   ˞ ۺ܎ ۼ ܎˞଀   ?
  21. The effect of history 1 0 0 0 0 0

    0 0 vs 0 0 0 0 0 0 Blip Effect ণ۽ ۼ ܎˞଀  ۦ=ۺ܎ ۼ ܎˞଀   ˞ ۺ܎ ۼ ܎˞଀   ?
  22. The effect of history 1 0 0 0 0 vs

    0 0 0 1 1 1 Blip Effect ণ۽ ۼ ܎˞଀  ۦ=ۺ܎ ۼ ܎˞଀   ˞ ۺ܎ ۼ ܎˞଀   ? 1 1 1
  23. The effect of history 1 0 vs 1 1 1

    Blip Effect ণ۽ ۼ ܎˞଀  ۦ=ۺ܎ ۼ ܎˞଀   ˞ ۺ܎ ۼ ܎˞଀   ? 1 1 1 1 1 1 1 1 1
  24. The effect of history

  25. The effect of history Contemporaneous Effect of Treatment ণ܎ 

    ۦ=ণ۽ ۼ ܎˞଀ ?
  26. The effect of history Contemporaneous Effect of Treatment ণ܎ 

    ۦ=ণ۽ ۼ ܎˞଀ ? CET
  27. The effect of history 1 0 vs Contemporaneous Effect of

    Treatment ণ܎  ۦ=ণ۽ ۼ ܎˞଀ ? CET
  28. The effect of history 1 0 vs Contemporaneous Effect of

    Treatment ণ܎  ۦ=ণ۽ ۼ ܎˞଀ ? CET Marginalize over the past
  29. TSCS data under sequential ignorability Treatment is unrelated to the

    potential outcomes ...conditional on the covariate history. ۺ܎ ۼ ܎ е е ۢ܎ ^۹ ܎  ۺ ܎˞଀  ۢ ܃܎˞଀  ۼ ܎˞଀
  30. How conditioning leads you astray

  31. How conditioning leads you astray ...for some questions.

  32. How conditioning leads you astray ...for some questions. ۺ܎ 

    ঑૿ ঑଀ ۢ܎ ঑ଁ ۹܎ ঑ଂ ۺ܎˞଀ ঑ଃ ۢ܎˞଀
  33. ۺ܎˞଀ ۢ܎˞଀ ۢ܎ ۹܎ ۺ܎ How conditioning leads you astray

    ...for some questions. ۺ܎  ঑૿ ঑଀ ۢ܎ ঑ଁ ۹܎ ঑ଂ ۺ܎˞଀ ঑ଃ ۢ܎˞଀
  34. ۺ܎˞଀ ۢ܎˞଀ ۢ܎ ۹܎ ۺ܎ How conditioning leads you astray

    ...for some questions. We “fix” these ۺ܎  ঑૿ ঑଀ ۢ܎ ঑ଁ ۹܎ ঑ଂ ۺ܎˞଀ ঑ଃ ۢ܎˞଀
  35. ۺ܎˞଀ ۢ܎˞଀ ۢ܎ ۹܎ ۺ܎ How conditioning leads you astray

    ...for some questions. We “fix” these ۺ܎  ঑૿ ঑଀ ۢ܎ ঑ଁ ۹܎ ঑ଂ ۺ܎˞଀ ঑ଃ ۢ܎˞଀
  36. ۺ܎˞଀ ۢ܎˞଀ ۢ܎ ۹܎ ۺ܎ How conditioning leads you astray

    We “fix” these ...for some questions. ۺ܎  ঑૿ ঑଀ ۢ܎ ঑ଁ ۹܎ ঑ଂ ۺ܎˞଀ ঑ଃ ۢ܎˞଀
  37. ۺ܎˞଀ ۢ܎˞଀ ۢ܎ ۹܎ ۺ܎ How conditioning leads you astray

    ...for some questions. ۺ܎  ঑૿ ঑଀ ۢ܎ ঑ଁ ۹܎ ঑ଂ ۺ܎˞଀ ঑ଃ ۢ܎˞଀
  38. ۺ܎˞଀ ۢ܎˞଀ ۢ܎ ۹܎ ۺ܎ How conditioning leads you astray

    এ૾ ...for some questions. ۺ܎  ঑૿ ঑଀ ۢ܎ ঑ଁ ۹܎ ঑ଂ ۺ܎˞଀ ঑ଃ ۢ܎˞଀
  39. ۺ܎˞଀ ۢ܎˞଀ ۢ܎ ۹܎ ۺ܎ How conditioning leads you astray

    এ૾ ? ? ? ? ? ? ...for some questions. ۺ܎  ঑૿ ঑଀ ۢ܎ ঑ଁ ۹܎ ঑ଂ ۺ܎˞଀ ঑ଃ ۢ܎˞଀
  40. ۺ܎˞଀ ۢ܎˞଀ ۢ܎ ۹܎ ۺ܎ How conditioning leads you astray

    এ૾ ? ? ? ? ? ? ...for some questions. CET: (1,0) vs (0,0) ATHE: (0,1) vs (0,0) ATHE: (1,1) vs (0,0)  এ૾ ̪ এଁ ̪ এ૾ এଁ ۺ܎  ঑૿ ঑଀ ۢ܎ ঑ଁ ۹܎ ঑ଂ ۺ܎˞଀ ঑ଃ ۢ܎˞଀
  41. How weighting can help

  42. ۺ܎˞଀ ۢ܎˞଀ ۢ܎ ۹܎ ۺ܎ How weighting can help

  43. ۺ܎˞଀ ۢ܎˞଀ ۢ܎ ۹܎ ۺ܎ How weighting can help ۸܃܎

     ܎ ಿ ܍଀  2T=ۢ܃܍ ^ۢ܎˞଀  ۹܎  ۺ܎˞଀ ? 
  44. ۺ܎˞଀ ۢ܎˞଀ ۢ܎ ۹܎ ۺ܎ How weighting can help ۸܃܎

     ܎ ಿ ܍଀  2T=ۢ܃܍ ^ۢ܎˞଀  ۹܎  ۺ܎˞଀ ?  We weight to create balance
  45. ۺ܎˞଀ ۢ܎˞଀ ۢ܎ ۹܎ ۺ܎ How weighting can help We

    weight to create balance ۸܃܎  ܎ ಿ ܍଀  2T=ۢ܃܍ ^ۢ܎˞଀  ۹܎  ۺ܎˞଀ ? 
  46. ۺ܎˞଀ ۢ܎˞଀ ۢ܎ ۹܎ ۺ܎ How weighting can help ۸܃܎

     ܎ ಿ ܍଀  2T=ۢ܃܍ ^ۢ܎˞଀  ۹܎  ۺ܎˞଀ ?  Unconfounded No posttreatment bias
  47. How weighting can help

  48. How weighting can help ۦ=ۺ܎ ۼ܎  ۼ܎˞଀ ? 

    ۦ۸ =ۺ܎ ^ۢ܎  ۼ܎  ۢ܎˞଀  ۼ܎˞଀ ?  ঑૿ ঑଀ ۼ܎ ঑ଁ ۼ܎˞଀
  49. How weighting can help ۦ=ۺ܎ ۼ܎  ۼ܎˞଀ ? 

    ۦ۸ =ۺ܎ ^ۢ܎  ۼ܎  ۢ܎˞଀  ۼ܎˞଀ ?  ঑૿ ঑଀ ۼ܎ ঑ଁ ۼ܎˞଀ WLS
  50. How weighting can help ۦ=ۺ܎ ۼ܎  ۼ܎˞଀ ? 

    ۦ۸ =ۺ܎ ^ۢ܎  ۼ܎  ۢ܎˞଀  ۼ܎˞଀ ?  ঑૿ ঑଀ ۼ܎ ঑ଁ ۼ܎˞଀ WLS CET: (1,0) vs (0,0) ATHE: (0,1) vs (0,0) ATHE: (1,1) vs (0,0)  এ૾  ঑ଁ  ঑଀ ঑ଁ
  51. The Long Arm of the Democratic Peace?

  52. The Long Arm of the Democratic Peace? Democracy in year

    t War in year t
  53. The Long Arm of the Democratic Peace? Democracy in year

    t War in year t Democratic Peace Literature
  54. The Long Arm of the Democratic Peace? Democracy in year

    t War in year t Democratic Peace Literature History of Democracy
  55. The Long Arm of the Democratic Peace? Democracy in year

    t War in year t Democratic Peace Literature History of Democracy Can we estimate this?
  56. %FQFOEFOU WBSJBCMF %JTQVUF #,5 .JTTQFDJĕFE *158 .PEFM $VNVMBUJWF .PEFM .4.

       %FNPDSBDZ #MJQ ˞૿ଅ଄଀ˣˣˣ ૿଀ଅ૿ $VNVMBUJWF %FNPDSBDZ ˞૿૿଀૿ ˞૿૿ଃ଄ˣˣˣ ૿૿଀ଁ ૿૿଀ଂ (SPXUI ˞ଂଇଂଆˣˣˣ ˞ଃଂଅ૿ˣˣˣ 0CTFSWBUJPOT ଁ૿ ଃଃଇ ଁ૿ ଃଃଇ ଁ૿ ଃଃଇ /PUF ˣQ ˣˣQ ˣˣˣQ Revisiting Beck, Katz, and Tucker (1998)
  57. %FQFOEFOU WBSJBCMF %JTQVUF #,5 .JTTQFDJĕFE *158 .PEFM $VNVMBUJWF .PEFM .4.

       %FNPDSBDZ #MJQ ˞૿ଅ଄଀ˣˣˣ ૿଀ଅ૿ $VNVMBUJWF %FNPDSBDZ ˞૿૿଀૿ ˞૿૿ଃ଄ˣˣˣ ૿૿଀ଁ ૿૿଀ଂ (SPXUI ˞ଂଇଂଆˣˣˣ ˞ଃଂଅ૿ˣˣˣ 0CTFSWBUJPOT ଁ૿ ଃଃଇ ଁ૿ ଃଃଇ ଁ૿ ଃଃଇ /PUF ˣQ ˣˣQ ˣˣˣQ Revisiting Beck, Katz, and Tucker (1998)
  58. Democracy in year t War in year t Economic Growth

    in year t History of Democracy Misspecification of an ATHE Time-Varying Confounder
  59. %FQFOEFOU WBSJBCMF %JTQVUF #,5 .JTTQFDJĕFE *158 .PEFM $VNVMBUJWF .PEFM .4.

       %FNPDSBDZ #MJQ ˞૿ଅ଄଀ˣˣˣ ૿଀ଅ૿ $VNVMBUJWF %FNPDSBDZ ˞૿૿଀૿ ˞૿૿ଃ଄ˣˣˣ ૿૿଀ଁ ૿૿଀ଂ (SPXUI ˞ଂଇଂଆˣˣˣ ˞ଃଂଅ૿ˣˣˣ 0CTFSWBUJPOT ଁ૿ ଃଃଇ ଁ૿ ଃଃଇ ଁ૿ ଃଃଇ /PUF ˣQ ˣˣQ ˣˣˣQ Revisiting Beck, Katz, and Tucker (1998)
  60. TSCS data under unmeasured confounding

  61. TSCS data under unmeasured confounding ۺ܃܎ ۼ ܎ е е

    ۢ܃܎ ^۹ ܃܎  ۢ ܃܎˞଀  ۼ ܎˞଀  ۶
  62. TSCS data under unmeasured confounding Treatment is unrelated to the

    potential outcomes ۺ܃܎ ۼ ܎ е е ۢ܃܎ ^۹ ܃܎  ۢ ܃܎˞଀  ۼ ܎˞଀  ۶
  63. TSCS data under unmeasured confounding Treatment is unrelated to the

    potential outcomes ...conditional on the covariate history ۺ܃܎ ۼ ܎ е е ۢ܃܎ ^۹ ܃܎  ۢ ܃܎˞଀  ۼ ܎˞଀  ۶
  64. TSCS data under unmeasured confounding Treatment is unrelated to the

    potential outcomes ...conditional on the covariate history ۺ܃܎ ۼ ܎ е е ۢ܃܎ ^۹ ܃܎  ۢ ܃܎˞଀  ۼ ܎˞଀  ۶ ...and a time-fixed unmeasured confounder.
  65. How unit-specific weighting can help

  66. How unit-specific weighting can help ۺ܎˞଀ ۢ܎˞଀ ۢ܎ ۹܎ ۺ܎

    ۶
  67. How unit-specific weighting can help ۺ܎˞଀ ۢ܎˞଀ ۢ܎ ۹܎ ۺ܎

    ۶ ۸܃܎  ܎ ಿ ܍଀  2T=ۢ܃܍ ^ۢ܎˞଀  ۹܎  ۺ܎˞଀  ۶?
  68. How unit-specific weighting can help ۺ܎˞଀ ۢ܎˞଀ ۢ܎ ۹܎ ۺ܎

    ۶ ۸܃܎  ܎ ಿ ܍଀  2T=ۢ܃܍ ^ۢ܎˞଀  ۹܎  ۺ܎˞଀  ۶? Weighting balances the treatment groups.
  69. ۺ܎˞଀ ۢ܎˞଀ ۢ܎ ۹܎ ۺ܎ How unit-specific weighting can help

    ۶ ۸܃܎  ܎ ಿ ܍଀  2T=ۢ܃܍ ^ۢ܎˞଀  ۹܎  ۺ܎˞଀  ۶?
  70. A weighting approach to fixed effects

  71. A weighting approach to fixed effects 1 Estimate unit-specific probability

    of treatment over time and construct weights.
  72. A weighting approach to fixed effects 1 Estimate unit-specific probability

    of treatment over time and construct weights. 2 Estimate a pooled outcome model with unit-specific weights
  73. k-order sequential ignorability

  74. k-order sequential ignorability ۺ܃܎ ۼ ܎ е е ۢ܃܎ ^۹

    ܃܎̂܎˞܅  ۢ ܃܎˞଀̂܎˞܅  ۼ ܎˞଀̂܎˞܅  ۶
  75. k-order sequential ignorability Only the last k periods matter. ۺ܃܎

    ۼ ܎ е е ۢ܃܎ ^۹ ܃܎̂܎˞܅  ۢ ܃܎˞଀̂܎˞܅  ۼ ܎˞଀̂܎˞܅  ۶
  76. Blip effect: (1,0) vs (0,0) Time periods Blip effect 10

    25 50 75 100 125 0.2 0.3 0.4 0.5 0.6 0.7
  77. Blip effect: (1,0) vs (0,0) Time periods Blip effect 10

    25 50 75 100 125 0.2 0.3 0.4 0.5 0.6 0.7
  78. Pooled Blip effect: (1,0) vs (0,0) Time periods Blip effect

    10 25 50 75 100 125 0.2 0.3 0.4 0.5 0.6 0.7 • • • • • •
  79. Pooled Outcome fixed effects Blip effect: (1,0) vs (0,0) Time

    periods Blip effect 10 25 50 75 100 125 0.2 0.3 0.4 0.5 0.6 0.7 • • • • • •
  80. Pooled Outcome fixed effects Blip effect: (1,0) vs (0,0) IPTW

    true weights Time periods Blip effect 10 25 50 75 100 125 0.2 0.3 0.4 0.5 0.6 0.7 • • • • • •
  81. Pooled IPTW fixed effects Outcome fixed effects IPTW true weights

    Blip effect: (1,0) vs (0,0) Time periods Blip effect 10 25 50 75 100 125 0.2 0.3 0.4 0.5 0.6 0.7 • • • • • •
  82. Treatment History Effect: (1,1) vs (0,0) Time periods ATHE 10

    25 50 75 100 125 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
  83. Treatment History Effect: (1,1) vs (0,0) Time periods ATHE 10

    25 50 75 100 125 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Time periods ATHE 10 25 50 75 100 125 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
  84. Pooled Treatment History Effect: (1,1) vs (0,0) Time periods ATHE

    10 25 50 75 100 125 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 • • • • • •
  85. Pooled Outcome fixed effects Treatment History Effect: (1,1) vs (0,0)

    Time periods ATHE 10 25 50 75 100 125 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 • • • • • •
  86. Pooled Outcome fixed effects IPTW true weights Treatment History Effect:

    (1,1) vs (0,0) Time periods ATHE 10 25 50 75 100 125 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 • • • • • •
  87. Pooled IPTW fixed effects Outcome fixed effects IPTW true weights

    Treatment History Effect: (1,1) vs (0,0) Time periods ATHE 10 25 50 75 100 125 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 • • • • • •
  88. How to make causal inferences with TSCS data

  89. How to make causal inferences with TSCS data Very carefully

  90. How to make causal inferences with TSCS data Very carefully

    Even under strong assumptions, conditional estimators cannot recover ATHEs.
  91. How to make causal inferences with TSCS data Very carefully

    Using weights Even under strong assumptions, conditional estimators cannot recover ATHEs.
  92. How to make causal inferences with TSCS data Very carefully

    Using weights Even under strong assumptions, conditional estimators cannot recover ATHEs. A fixed effects weighting approach can recover ATHEs and CETs even with unmeasured confounding.