1. Panel Data

2. Assembling the Data insheet using marriage-data.csv, c d u "background-data", clear d u "experience-data", clear u "wage-data", clear d reshape long lwage, i(nr) j(year) sort nr year merge 1:1 nr year using "marriage-data" drop _merge merge 1:1 nr year using "experience-data" drop _merge merge n:1 nr using "background-data" drop _merge d sum save "data-exercise-11-nls", replace

3. (2) Is the data balanced? xtset nr year panel variable: nr (strongly balanced) time variable: year, 1980 to 1987 delta: 1 unit What does being balanced mean?

4. (3) First Step. reg lwage married Source | SS df MS Number of obs = 4360 -------------+------------------------------ F( 1, 4358) = 191.75 Model | 52.1141809 1 52.1141809 Prob > F = 0.0000 Residual | 1184.41546 4358.271779592 R-squared = 0.0421 -------------+------------------------------ Adj R-squared = 0.0419 Total | 1236.52964 4359.283672779 Root MSE =.52132 ------------------------------------------------------------------------------ lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- married |.2203038.0159094 13.85 0.000.1891134.2514942 _cons | 1.552436.010541 147.28 0.000 1.53177 1.573101 ------------------------------------------------------------------------------

5. (4) Controls. reg lwage married exper union educ black hisp Source | SS df MS Number of obs = 4360 -------------+------------------------------ F( 6, 4353) = 163.11 Model | 226.971557 6 37.8285928 Prob > F = 0.0000 Residual | 1009.55809 4353.231922372 R-squared = 0.1836 -------------+------------------------------ Adj R-squared = 0.1824 Total | 1236.52964 4359.283672779 Root MSE =.48158 ------------------------------------------------------------------------------ lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- married |.1127231.0156735 7.19 0.000.0819951.1434511 exper |.0501619.0028974 17.31 0.000.0444815.0558423 union |.1836459.0171274 10.72 0.000.1500675.2172243 educ |.1036792.0045625 22.72 0.000.0947343.1126242 black | -.1424234.023598 -6.04 0.000 -.1886875 -.0961593 hisp |.0127569.0208347 0.61 0.540 -.0280897.0536036 _cons |.0225412.0630948 0.36 0.721 -.1011567.1462391 ------------------------------------------------------------------------------

6. (5) Panel Data. xtreg lwage married exper union educ black hisp, fe note: educ omitted because of collinearity note: black omitted because of collinearity note: hisp omitted because of collinearity Fixed-effects (within) regression Number of obs = 4360 Group variable: nr Number of groups = 545 R-sq: within = 0.1672 Obs per group: min = 8 between = 0.0001 avg = 8.0 overall = 0.0513 max = 8 F(3,3812) = 255.03 corr(u_i, Xb) = -0.1575 Prob > F = 0.0000 ------------------------------------------------------------------------------ lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- married |.0610384.0182929 3.34 0.001.0251736.0969032 exper |.0598672.0025835 23.17 0.000.054802.0649325 union |.083791.019414 4.32 0.000.045728.1218539 educ | 0 (omitted) black | 0 (omitted) hisp | 0 (omitted) _cons | 1.211888.0169244 71.61 0.000 1.178706 1.24507 -------------+---------------------------------------------------------------- sigma_u |.40514496 sigma_e |.35352815 rho |.56772216 (fraction of variance due to u_i) ------------------------------------------------------------------------------ F test that all u_i=0: F(544, 3812) = 10.08 Prob > F = 0.0000 Why have ‘black’, ‘educ’ and ‘hisp’ been dropped from the regression? What variation are we working off when we include fixed effects?

7. Collinearity IDYearID1_FEID2_FEID3_FEIncomeMarriedBlackNational GDP 1995_FE 11995100100005001 11996100100006000 11997100125107000 21995010200115001 21996010175016000 21997010175017000 31995001150105001 31996001300106000 31997001200107000 etc 

8. (6) Clustering xtreg lwage married exper union, fe cluster(nr) Fixed-effects (within) regression Number of obs = 4360 Group variable: nr Number of groups = 545 R-sq: within = 0.1672 Obs per group: min = 8 between = 0.0001 avg = 8.0 overall = 0.0513 max = 8 F(3,544) = 136.41 corr(u_i, Xb) = -0.1575 Prob > F = 0.0000 (Std. Err. adjusted for 545 clusters in nr) ------------------------------------------------------------------------------ | Robust lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- married |.0610384.0212076 2.88 0.004.0193796.1026972 exper |.0598672.0033717 17.76 0.000.0532441.0664904 union |.083791.0231101 3.63 0.000.0383951.1291868 _cons | 1.211888.0216293 56.03 0.000 1.169401 1.254375 -------------+---------------------------------------------------------------- sigma_u |.40514496 sigma_e |.35352815 rho |.56772216 (fraction of variance due to u_i) ------------------------------------------------------------------------------

9. (7) Are dummies equivalent to FE?. reg lwage married exper union i.nr, cluster(nr) Linear regression Number of obs = 4360 F( 2, 544) =. Prob > F =. R-squared = 0.6147 Root MSE =.35353 (Std. Err. adjusted for 545 clusters in nr) ------------------------------------------------------------------------------ | Robust lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- married |.0610384.0226704 2.69 0.007.0165062.1055706 exper |.0598672.0036043 16.61 0.000.0527872.0669472 union |.083791.0247041 3.39 0.001.0352639.132318

10. (7) Time FE? Why not include Experience?. xtreg lwage married union i.year, fe cluster(nr) Fixed-effects (within) regression Number of obs = 4360 Group variable: nr Number of groups = 545 R-sq: within = 0.1689 Obs per group: min = 8 between = 0.0789 avg = 8.0 overall = 0.1026 max = 8 F(9,544) = 42.75 corr(u_i, Xb) = 0.0455 Prob > F = 0.0000 (Std. Err. adjusted for 545 clusters in nr) ------------------------------------------------------------------------------ | Robust lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- married |.0583372.0228114 2.56 0.011.013528.1031464 union |.0833697.0246533 3.38 0.001.0349423.1317971 | year | 1981 |.1135489.0263198 4.31 0.000.061848.1652498 1982 |.1676693.0259521 6.46 0.000.1166907.218648 1983 |.2109386.0266852 7.90 0.000.1585199.2633572 1984 |.2784071.0295839 9.41 0.000.2202945.3365197 1985 |.327462.0289156 11.32 0.000.270662.384262 1986 |.3868075.0302537 12.79 0.000.327379.4462359 1987 |.447037.0292727 15.27 0.000.3895357.5045382 | _cons | 1.361709.0217851 62.51 0.000 1.318915 1.404502 -------------+---------------------------------------------------------------- sigma_u |.38216008 sigma_e |.35343397 rho |.53899212 (fraction of variance due to u_i) ------------------------------------------------------------------------------

11. (8) Driven By Divorce?. xtreg lwage married union i.year if everdivorce == 0, fe cluster(nr) Fixed-effects (within) regression Number of obs = 3792 Group variable: nr Number of groups = 474 R-sq: within = 0.1708 Obs per group: min = 8 between = 0.0834 avg = 8.0 overall = 0.1039 max = 8 F(9,473) = 44.98 corr(u_i, Xb) = 0.0456 Prob > F = 0.0000 (Std. Err. adjusted for 474 clusters in nr) ------------------------------------------------------------------------------ | Robust lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- married |.0631041.0273805 2.30 0.022.0093017.1169066 union |.07263.0250568 2.90 0.004.0233935.1218665 | year | 1981 |.1211224.0271089 4.47 0.000.0678536.1743912 1982 |.1672227.0269524 6.20 0.000.1142615.2201839 1983 |.219521.0275964 7.95 0.000.1652942.2737478 1984 |.2828337.0312869 9.04 0.000.2213551.3443122 1985 |.3269934.0306809 10.66 0.000.2667057.3872812 1986 |.3897902.0324352 12.02 0.000.3260552.4535251 1987 |.4581408.0317265 14.44 0.000.3957985.5204831 | _cons | 1.359177.0218908 62.09 0.000 1.316162 1.402192 -------------+---------------------------------------------------------------- sigma_u |.38405618 sigma_e |.35830293 rho |.5346494 (fraction of variance due to u_i) ------------------------------------------------------------------------------

12. (8) Driven by Divorce 2?. xtreg lwage married union i.year if everdivorce == 1, fe cluster(nr) Fixed-effects (within) regression Number of obs = 568 Group variable: nr Number of groups = 71 R-sq: within = 0.1663 Obs per group: min = 8 between = 0.1058 avg = 8.0 overall = 0.1110 max = 8 F(9,70) = 6.21 corr(u_i, Xb) = 0.0697 Prob > F = 0.0000 (Std. Err. adjusted for 71 clusters in nr) ------------------------------------------------------------------------------ | Robust lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- married |.0305923.0349467 0.88 0.384 -.0391067.1002913 union |.1277057.0596013 2.14 0.036.0088347.2465766 | year | 1981 |.064469.0568619 1.13 0.261 -.0489385.1778764 1982 |.16627.0565055 2.94 0.004.0535734.2789667 1983 |.1538386.0637881 2.41 0.019.0266171.28106 1984 |.2469232.0565838 4.36 0.000.1340703.3597761 1985 |.3212491.0619483 5.19 0.000.197697.4448011 1986 |.3546588.0628833 5.64 0.000.2292421.4800755 1987 |.3573659.0668428 5.35 0.000.2240521.4906797 | _cons | 1.38598.0568407 24.38 0.000 1.272615 1.499346 -------------+---------------------------------------------------------------- sigma_u |.36780709 sigma_e |.31952552 rho |.56989994 (fraction of variance due to u_i) ------------------------------------------------------------------------------.