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Chapter 10 Regression with Panel Data. 2 Regression with Panel Data (SW Chapter 10)

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Presentation on theme: "Chapter 10 Regression with Panel Data. 2 Regression with Panel Data (SW Chapter 10)"— Presentation transcript:

1 Chapter 10 Regression with Panel Data

2 2 Regression with Panel Data (SW Chapter 10)

3 3 Notation for panel data

4 4 Panel data notation, ctd.

5 5 Why are panel data useful?

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

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

8 8 U.S. traffic death data for 1988

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

10 10 These omitted factors could cause omitted variable bias.

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

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

13 13

14 14

15 15 Example: Traffic deaths and beer taxes

16 16 FatalityRate v. BeerTax:

17 17 Fixed Effects Regression (SW Section 10.3)

18 18

19 19

20 20 The regression lines for each state in a picture

21 21

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

23 23 Fixed Effects Regression: Estimation

24 24 1. n-1 binary regressors OLS regression

25 25 2. Entity-demeaned OLS regression

26 26 Entity-demeaned OLS regression, ctd.

27 27 Entity-demeaned OLS regression, ctd.

28 28 Example: Traffic deaths and beer taxes in STATA

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

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

31 31

32 32

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

34 34 Time fixed effects only

35 35 Two formulations for time fixed effects

36 36 Time fixed effects: estimation methods

37 37

38 38 Combined entity and time fixed effects

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

40 40 A. Extension of LS Assumptions to Panel Data

41 41 Assumption #1: E(u it |X i1,…,X iT, i) = 0

42 42 Assumption #2: (X i1,…,X iT,Y i1,…,Y iT ), i =1,…,n, are i.i.d. draws from their joint distribution.

43 43 Assumption #5: corr(u it,u is |X it,X is, i) = 0 for t s

44 44 Assumption #5 in a picture:

45 45 What if Assumption #5 fails: so corr(u it,u is |X it,X is, i) 0?

46 46 B. Standard Errors

47 47 Sampling distribution of fixed effects estimator, ctd.

48 48 Sampling distribution of fixed effects estimator, ctd.

49 49 Case I: when u it, u is are uncorrelated

50 50 Case II: u it and u is are correlated – so Assumption 5 fails

51 51 Case II: Clustered Standard Errors

52 52 Comments on clustered standard errors:

53 53 Comments on clustered standard errors, ctd.

54 54 Comments on clustered standard errors, ctd.

55 55 Implementation in STATA

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

57 57 Try adding year effects:

58 58

59 59 Fixed Effects Regression Results Dependent variable: Fatality rate

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

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

62 62 Drunk driving laws and traffic deaths, ctd.

63 63

64 64

65 65

66 66

67 67

68 68

69 69 The drunk driving panel data set

70 70 Why might panel data help?

71 71

72 72

73 73 Empirical Analysis: Main Results

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

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

76 76


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