# 1 Basic Econometrics (Econ 205) Should read Chapter 10 Panel data GH 5 due next Tue, and GH 6 due next Thur RAP should be progressing … Read Acemoglu,

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1 Basic Econometrics (Econ 205) Should read Chapter 10 Panel data GH 5 due next Tue, and GH 6 due next Thur RAP should be progressing … Read Acemoglu, Johson, Robinson, and Yared (AER, 2008) for Tue March 20 th.

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 A panel data set looks like this …

8 U.S. traffic death data for 1982:

9 U.S. traffic death data for 1988

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

11 Panel Data with 2 Time Periods

12

13

14 FatalityRate v. BeerTax: Ziliak & McCloskey (2004)?

15 Fixed Effects Regression

16

17

18 The regression lines for each state

19

20 Two ways to write the fixed effects model

21 Estimation of Fixed Effects Models

22 1. n-1 binary regressors OLS regression

23 2. Entity-demeaned OLS regression

24 Entity-demeaned OLS regression, ctd.

25 Entity-demeaned OLS regression, ctd.

26 Example: Traffic deaths and beer taxes in STATA

Example: A better way in STATA 27. iis state. tis year. xtreg vfrall beertax, fe robust ; Fixed-effects (within) regression Number of obs = 336 Group variable: state Number of groups = 48 R-sq: within = 0.0407 Obs per group: min = 7 between = 0.1101 avg = 7.0 overall = 0.0934 max = 7 F(1,47) = 5.05 corr(u_i, Xb) = -0.6885 Prob > F = 0.0294 (Std. Err. adjusted for 48 clusters in state) ------------------------------------------------------------------------------ | Robust vfrall | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- beertax | -.6558736.2918556 -2.25 0.029 -1.243011 -.0687358 _cons | 2.377075.1497966 15.87 0.000 2.075723 2.678427 -------------+---------------------------------------------------------------- sigma_u |.7147146 sigma_e |.18985942 rho |.93408484 (fraction of variance due to u_i) ------------------------------------------------------------------------------ We should use xtreg in this case because those robust standard errors employ a small-sample correction designed for T fixed, n, while areg designed for n fixed, T (Cameron & Trivedi 2009, p. 253)

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

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

30

31

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33. bysort state: egen meantax = mean(beertax). gen devmean_beertax = beertax - meantax. list state year beertax meantax devmean_beertax +------------------------------------------------+ | state year beertax meantax devmean~x | |------------------------------------------------| 1. | AL 1982 1.539379 1.623793 -.0844132 | 2. | AL 1983 1.788991 1.623793.1651981 | 3. | AL 1984 1.714286 1.623793.090493 | 4. | AL 1985 1.652542 1.623793.0287497 | 5. | AL 1986 1.609907 1.623793 -.0138856 | |------------------------------------------------| 6. | AL 1987 1.56 1.623793 -.0637927 | 7. | AL 1988 1.501444 1.623793 -.122349 | 8. | AZ 1982.2147971.3110403 -.0962432 | 9. | AZ 1983.206422.3110403 -.1046183 | 10. | AZ 1984.2967033.3110403 -.014337 | |------------------------------------------------| 11. | AZ 1985.3813559.3110403.0703156 | 12. | AZ 1986.371517.3110403.0604767 | 13. | AZ 1987.36.3110403.0489597 | 14. | AZ 1988.346487.3110403.0354467 |

34

35. xtline beertax, overlay. xtline beertax if state==37 | state==45 | state==13 | state==41 | state==53 | state==56, overlay

36 Panel data with Time Fixed Effects

37 Time fixed effects only

38 Two formulations

39 Estimtation of Time fixed effects

40. tab year, gen(yr) Year | Freq. Percent Cum. ------------+----------------------------------- 1982 | 48 14.29 14.29 1983 | 48 14.29 28.57 1984 | 48 14.29 42.86 1985 | 48 14.29 57.14 1986 | 48 14.29 71.43 1987 | 48 14.29 85.71 1988 | 48 14.29 100.00 ------------+----------------------------------- Total | 336 100.00. sum y* Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- year | 336 1985 2.002983 1982 1988 yngdrv | 336.1859299.0248736.073137.281625 yr1 | 336.1428571.350449 0 1 yr2 | 336.1428571.350449 0 1 yr3 | 336.1428571.350449 0 1 -------------+-------------------------------------------------------- yr4 | 336.1428571.350449 0 1 yr5 | 336.1428571.350449 0 1 yr6 | 336.1428571.350449 0 1 yr7 | 336.1428571.350449 0 1

41. xtreg vfr beertax yr2 yr3 yr4 yr5 yr6 yr7, fe robust Fixed-effects (within) regression Number of obs = 336 Group variable: state Number of groups = 48 R-sq: within = 0.0803 Obs per group: min = 7 between = 0.1101 avg = 7.0 overall = 0.0876 max = 7 F(7,47) = 4.36 corr(u_i, Xb) = -0.6781 Prob > F = 0.0009 (Std. Err. adjusted for 48 clusters in state) ------------------------------------------------------------------------------ | Robust vfr | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- beertax | -.6399799.3570783 -1.79 0.080 -1.358329.0783691 yr2 | -.0799029.0350861 -2.28 0.027 -.1504869 -.0093188 yr3 | -.0724206.0438809 -1.65 0.106 -.1606975.0158564 yr4 | -.1239763.0460559 -2.69 0.010 -.2166288 -.0313238 yr5 | -.0378645.0570604 -0.66 0.510 -.1526552.0769262 yr6 | -.0509021.0636084 -0.80 0.428 -.1788656.0770615 yr7 | -.0518038.0644023 -0.80 0.425 -.1813645.0777568 _cons | 2.42847.2016885 12.04 0.000 2.022725 2.834215 -------------+---------------------------------------------------------------- sigma_u |.70945965 sigma_e |.18788295 rho |.93446372 (fraction of variance due to u_i) ------------------------------------------------------------------------------

42 Combining entity & time fixed effects

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