Observational Data Using Stata Chuck Huber StataCorp chuberstatacom ERMs Outline Description of the dataset Unobserved confounding and endogeneity Nonrandom treatment assignment Missing not at random MNAR and selection bias ID: 1009944
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1. Causal Inference for ComplexObservational Data Using StataChuck HuberStataCorpchuber@stata.com
2. ERMs OutlineDescription of the datasetUnobserved confounding and endogeneityNonrandom treatment assignmentMissing not at random (MNAR) and selection biasTreatment effects
3. The Research QuestionFictional State University (FSU) has developed a new study-skills program with the goal of improving the grade point averages of their students.
4. The Data
5. The Data
6. The Data
7. The Data
8. The Data
9. The Data
10. The Data
11. The DataStudents who participated in the program had lower GPAs?!?!?
12. The Data
13. The DataStudents who participated in the program had higher GPAs when we account for high school GPA.
14. The Data
15. The Data
16. The DataWhat was the effect of the study program on students GPAs?
17. OutlineDescription of the datasetUnobserved confounding and endogeneityNonrandom treatment assignmentMissing not at random (MNAR) and selection biasTreatment effects
18. Observed and Unobserved Factors
19. Endogeneity“An explanatory variable in a multiple regression model that is correlated with the error term…” (Wooldridge*, pg 838).*Jeffrey M. Wooldridge (2009) Introductory Econometrics: A Modern Approach, 4th ed.
20. Omitted Variable Bias
21. Confounding“…X and Y are confounded when there is a third variable Z that influences both X and Y…” (Pearl*, pg 193).*Judea Pearl (2009) Causality: Models, Reasoning, and Inference, 2nd ed.
22. Unobserved Confounding
23. Observed and Unobserved Factors High school GPASAT ScoresParents IncomeSexetc…AbilityMotivationSleepSupportetc…
24. Unobserved Confounding )
25. Unobserved Confounding and Endogeneity) )* )* hsgpa = (factors NOT related to Ability) + (Ability + error)
26. Unobserved Confounding and EndogeneityhsgpagpaAbilityε) income
27. Unobserved Confounding and EndogeneityhsgpagpaAbilityincomehs_compε2ε1)* )*
28. Unobserved Confounding and Endogeneityhsgpagpaincomehs_compε2ε1
29. Unobserved Confounding and Endogeneityhsgpagpaincomehs_compε2ε1AbilityAbility)* )*
30. Unobserved Confounding and Endogeneityhsgpagpaincomehs_compε2ε1Ability)* )*
31. Unobserved Confounding and Endogeneityhsgpagpaincomehs_compε2ε1
32. Unobserved Confounding and Endogeneity
33. Unobserved Confounding and Endogeneity
34. Unobserved Confounding and Endogeneityeregress gpa income, /// endogenous(hsgpa = hs_comp income) Primary modelAuxillary model
35. Unobserved Confounding and Endogeneity
36. Unobserved Confounding and Endogeneity
37. Unobserved Confounding and Endogeneity
38. OutlineDescription of the datasetUnobserved confounding and endogeneityNonrandom treatment assignmentMissing not at random (MNAR) and selection biasTreatment effects
39. Random Treatment Assignment
40. Nonrandom Treatment Assignment
41. Nonrandom Treatment Assignment A student’s decision to enroll in the study program is based on observed and unobserved factors.
42. Unobserved Confounding )
43. Endogenous Treatment) )* )* P(program=1) = (factors NOT related to Ability) + (Ability + error)
44. Endogenous Treatmenthsgpagpaincomehs_compε2ε1 P(program=1)scholarshipε3
45. Endogenous Treatmenteregress gpa income, /// endogenous(hsgpa = hs_comp income) /// entreat(program = income scholarship, nointeract)Primary modelAuxillary model
46. Endogenous Treatment
47. Endogenous Treatment
48. Endogenous Treatment
49. OutlineDescription of the datasetUnobserved confounding and endogeneityNonrandom treatment assignmentMissing not at random (MNAR) and selection biasTreatment effects
50. No Missingness
51. Missing Completely at Random (MCAR)
52. Missing at Random (MAR)
53. Missing Not at Random (MNAR)
54. MNAR and Selection Bias
55. Endogenous Sample Selection A student’s decision to drop out of school is based on observed and unobserved factors.
56. Endogenous Sample Selection)*
57. Endogenous Sample Selectionhsgpagpaincomehs_compε2ε1 P(program=1)scholarshipε3 P(graduate=1)roommateε4
58. Endogenous Sample Selectioneregress gpa income, /// endogenous(hsgpa = hs_comp income) /// entreat(program = income scholarship, nointeract) /// select(graduate = income roommate)Primary modelAuxillary model
59. Endogenous Sample Selection
60. Endogenous Sample Selection
61. Endogenous Sample Selectiongpa = -0.6 + 0.3*treatment + 0.9*hsgpa + 0.8*incomeTrue Model (simulated)
62. OutlineDescription of the datasetUnobserved confounding and endogeneityNonrandom treatment assignmentMissing not at random (MNAR) and selection biasTreatment effects
63. ERM Postestimationestat teffectsmarginsmarginsplotpredict
64. estat teffects
65. estat teffects, atet
66. margins
67. marginsplot. marginsplot
68. More ERMseregress – continuous outcomeseintreg – interval outcomeseprobit – binary outcomeseoprobit – ordinal outcomes
69. ERMs For Panel Dataxteregress – continuous outcomesxteintreg – interval outcomesxteprobit – binary outcomesxteoprobit – ordinal outcomes
70. More About ERMsERMs can include:polynomials of endogenous covariatesinteractions of endogenous covariatesinteractions of endogenous with exogenous covariates
71. Cautionary NoteNothing about ERMs magically extracts causal relationships. As with any regression analysis of observational data, the causal interpretation must be based on a reasonable underlying scientific rationale.
72. chuber@stata.comThanks for coming!Questions?You can download the slides, datasets, and do-files here:https://tinyurl.com/2019CausalInference