1. Regression with Panel Data
Chapter 10
Regression with Panel Data

2. Regression with Panel Data (SW Chapter 10)

3. Notation for panel data

4. Panel data notation, ctd.

5. Why are panel data useful?

6. Example of a panel data set: Traffic deaths and alcohol taxes

7. U.S. traffic death data for 1982:

8. U.S. traffic death data for 1988

9. Why might there be higher more traffic deaths in states that have higher alcohol taxes?

10. These omitted factors could cause omitted variable bias.

11. Example #2: cultural attitudes towards drinking and driving:

12. Panel Data with Two Time Periods (SW Section 10.2)

15. Example: Traffic deaths and beer taxes

16. FatalityRate v. BeerTax:

17. Fixed Effects Regression (SW Section 10.3)

20. The regression lines for each state in a picture

22. Summary: Two ways to write the fixed effects model “n-1 binary regressor” form

23. Fixed Effects Regression: Estimation

24. 1. “n-1 binary regressors” OLS regression

25. 2. “Entity-demeaned” OLS regression

26. Entity-demeaned OLS regression, ctd.

27. Entity-demeaned OLS regression, ctd.

28. Example: Traffic deaths and beer taxes in STATA

29. Example, ctd. For n = 48, T = 7:

30. By the way… how much do beer taxes vary?

33. Regression with Time Fixed Effects (SW Section 10.4)

34. Time fixed effects only

35. Two formulations for time fixed effects

36. Time fixed effects: estimation methods

38. Combined entity and time fixed effects

39. The Fixed Effects Regression Assumptions and Standard Errors for Fixed Effects Regression (SW Section 10.5 and App. 10.2)

40. A. Extension of LS Assumptions to Panel Data

41. Assumption #1: E(uit|Xi1,…,XiT,i) = 0

42. Assumption #2: (Xi1,…,XiT,Yi1,…,YiT), i =1,…,n, are i. i. d
Assumption #2: (Xi1,…,XiT,Yi1,…,YiT), i =1,…,n, are i.i.d. draws from their joint distribution.

43. Assumption #5: corr(uit,uis|Xit,Xis,i) = 0 for t  s

44. Assumption #5 in a picture:

45. What if Assumption #5 fails: so corr(uit,uis|Xit,Xis,i) 0?

46. B. Standard Errors

47. Sampling distribution of fixed effects estimator, ctd.

48. Sampling distribution of fixed effects estimator, ctd.

49. Case I: when uit, uis are uncorrelated

50. Case II: uit and uis are correlated – so Assumption 5 fails

51. Case II: Clustered Standard Errors

52. Comments on clustered standard errors:

53. Comments on clustered standard errors, ctd.

54. Comments on clustered standard errors, ctd.

55. Implementation in STATA

56. Case II: treat uit and uis as possibly correlated

57. Try adding year effects:

59. Fixed Effects Regression Results Dependent variable: Fatality rate

60. Summary: SEs for Panel Data in a picture:

61. Application: Drunk Driving Laws and Traffic Deaths (SW Section 10.6)

62. Drunk driving laws and traffic deaths, ctd.

69. The drunk driving panel data set

70. Why might panel data help?

73. Empirical Analysis: Main Results

74. Digression: extensions of the “n-1 binary regressor” idea

75. Summary: Regression with Panel Data (SW Section 10.7)