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Basic Econometrics (Econ 205)

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

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Basic Econometrics (Econ 205)

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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 20th .

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

  13. Fixed Effects Regression

  14. The regression lines for each state

  15. Two ways to write the fixed effects model

  16. Estimation of Fixed Effects Models

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

  18. 2. “Entity-demeaned” OLS regression

  19. Entity-demeaned OLS regression, ctd.

  20. Entity-demeaned OLS regression, ctd.

  21. Example: Traffic deaths and beer taxes in STATA

  22. Example: A better way in STATA . 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)

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

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

  25. . xtsum state year vfrbeertax Variable | Mean Std. Dev. Min Max | Observations -----------------+--------------------------------------------+---------------- state overall | 30.1875 15.30985 1 56 | N = 336 between | 15.44883 1 56 | n = 48 within | 0 30.1875 30.1875 | T = 7 | | year overall | 1985 2.002983 1982 1988 | N = 336 between | 0 1985 1985 | n = 48 within | 2.002983 1982 1988 | T = 7 | | vfr overall | 2.040444 .5701938 .82121 4.21784 | N = 336 between | .5461407 1.110077 3.653197 | n = 48 within | .1794253 1.45556 2.962664 | T = 7 | | beertax overall | .513256 .4778442 .0433109 2.720764 | N = 336 between | .4789513 .0481679 2.440507 | n = 48 within | .0552203 .1415352 .7935126 | T = 7

  26. . 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 | . sumbeertaxdevmean_beertax Variable | Obs MeanStd. Dev. Min Max -------------+-------------------------------------------------------- beertax | 336 .513256 .4778442 .0433109 2.720764 devmean_be~x | 336 2.96e-09 .0552203 -.3717208 .2802565

  27. . xtsum state year vfrbeertax Variable | Mean Std. Dev. Min Max | Observations -----------------+--------------------------------------------+---------------- state overall | 30.1875 15.30985 1 56 | N = 336 between | 15.44883 1 56 | n = 48 within | 0 30.1875 30.1875 | T = 7 | | year overall | 1985 2.002983 1982 1988 | N = 336 between | 0 1985 1985 | n = 48 within | 2.002983 1982 1988 | T = 7 | | vfr overall | 2.040444 .5701938 .82121 4.21784 | N = 336 between | .5461407 1.110077 3.653197 | n = 48 within | .1794253 1.45556 2.962664 | T = 7 | | beertax overall | .513256 .4778442 .0433109 2.720764 | N = 336 between | .4789513 .0481679 2.440507 | n = 48 within | .0552203 .1415352 .7935126 | T = 7 . collapsebeertax, by(state) . sum Variable | Obs MeanStd. Dev. Min Max -------------+-------------------------------------------------------- state | 48 30.1875 15.44883 1 56 beertax | 48 .513256 .4789513 .0481679 2.440507

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

  29. Panel data with Time Fixed Effects

  30. Time fixed effects only

  31. Two formulations

  32. Estimtation of Time fixed effects

  33. . 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

  34. . 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) ------------------------------------------------------------------------------

  35. Combining entity & time fixed effects

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