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398_39_solutions-instructor-manual_14-introduction-panel-data-models_im_ch14.pdf

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Department
Economics
Course
Economics 2122A/B
Professor
Terry Biggs
Semester
Winter

Description
Dougherty: Introduction to Econometrics 4e Instructor’s Manual 14 INTRODUCTION TO PANEL DATA MODELS 14.1 Introduction 14.2 Fixed effects regressions 14.3 Random effects regressions 14.1 Download the OECD2000 data set from the website. See Appendix B for details. The data set contains 32 variables: ID This is the country identification, with 1=Australia, 2=Austria, 3=Belgium, 4=Canada, 5=Denmark, 6=Finland, 7=France, 8=Germany, 9=Greece, 10=Iceland, 11=Ireland, 12=Italy, 13=Japan, 14=Korea, 15=Luxembourg, 16=Mexico, 17=Netherlands, 18=New Zealand, 19=Norway, 20=Portugal, 21=Spain, 22=Sweden, 23=Switzerland, 24=Turkey, 25=United Kingdom, 26=United States. Four countries that have recently joined the OECD, the Czech Republic, Hungary, Poland, and Slovakia, are excluded because their data do not go back far enough. ID01–26 These are individual country dummy variables. For example, ID09 is the dummy variable for Greece. E Average annual percentage rate of growth of employment for country i during time period t. G Average annual percentage rate of growth of GDP for country i during time period t. TIME There are three time periods, denoted 1, 2, and 3. They refer to average annual data for 1971–80, 1981–90, and 1991–2000. TIME2 Dummy variable defined to be equal to 1 when TIME=2, 0 otherwise. TIME3 Dummy variable defined to be equal to 1 when TIME=3, 0 otherwise. Perform a pooled OLS regression of E on G. Regress E on G, TIME2, and TIME3. Perform appropriate statistical tests and give an interpretation of the regression results. Answer: . reg E G TIME2 TIME3 Source | SS df MS Number of obs = 78 -------------+------------------------------ F( 3, 74) = 6.74 Model | 12.4981266 3 4.16604221 Prob > F = 0.0004 Residual | 45.7284673 74 .61795226 R-squared = 0.2146 -------------+------------------------------ Adj R-squared = 0.1828 Total | 58.2265939 77 .756189531 Root MSE = .7861 ------------------------------------------------------------------------------ E | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- G | .270974 .0606487 4.47 0.000 .1501289 .3918191 TIME2 | .3165385 .2233278 1.42 0.161 -.1284519 .7615289 TIME3 | .3118686 .2234753 1.40 0.167 -.1334157 .7571529 _cons | -.1472293 .2729668 -0.54 0.591 -.6911275 .3966689 ------------------------------------------------------------------------------ The regression suggests that the employment growth rate increases by 0.27 of a percentage point for every percentage point increase in the GDP growth rate. The intercept is small and insignificant. The interdecennial time shifts likewise are not significant. © C. Dougherty 2011. All rights reserved. INTRODUCTION TO PANEL DATA MODELS 2 14.2 Using the OECD2000 data set perform a (within-groups) fixed effects regression of E on G, TIME2, and TIME3. Perform appropriate statistical tests, give an interpretation of the regression coefficients, and comment on R . Answer: . xtreg E G TIME2 TIME3, fe Fixed-effects (within) regression Number of obs = 78 Group variable (i) : ID Number of groups = 26 R-sq: within = 0.1410 Obs per group: min = 3 between = 0.3168 avg = 3.0 overall = 0.2146 max = 3 F(3,49) = 2.68 corr(u_i, Xb) = -0.0445 Prob > F = 0.0570 ------------------------------------------------------------------------------ E | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- G | .2851358 .1023042 2.79 0.008 .0795477 .4907239 TIME2 | .3278352 .2283511 1.44 0.157 -.1310535 .786724 TIME3 | .3233233 .2287614 1.41 0.164 -.1363899 .7830365 _cons | -.1998293 .4088132 -0.49 0.627 -1.02137 .6217115 -------------+---------------------------------------------------------------- sigma_u | .47312507 sigma_e | .76895916 rho | .27461027 (fraction of variance due to u_i) ------------------------------------------------------------------------------ F test that all u_i=0: F(25, 49) = 1.13 Prob > F = 0.3454 The coefficients and their interpretation are very similar to those for the pooled OLS regression. 14.3 Perform the corresponding LSDV regression, using OLS to regress E on G, TIME2, TIME3, and the country dummy variables (a) dropping the intercept, and (b) dropping one of the dummy variables. Perform appropriate statistical tests and give an interpretation of the coefficients in each case. Explain why either the intercept or one of the dummy variables must be dropped. Answer: (a) Dropping the intercept: . reg E G TIME2 TIME3 D*, nocon Source | SS df MS Number of obs = 78 -------------+------------------------------ F( 29, 49) = 5.59 Model | 95.7883873 29 3.30304784 Prob > F = 0.0000 Residual | 28.9736111 49 .591298185 R-squared = 0.7678 -------------+------------------------------ Adj R-squared = 0.6303 Total | 124.761998 78 1.5995128 Root MSE = .76896 ------------------------------------------------------------------------------ E | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- G | .2851358 .1023042 2.79 0.008 .0795477 .4907239 TIME2 | .3278352 .2283511 1.44 0.157 -.1310535 .786724 TIME3 | .3233233 .2287614 1.41 0.164 -.1363899 .7830365 DAUS | .5272063 .6016461 0.88 0.385 -.6818468 1.736259 DAUT | -.6606943 .5709007 -1.16 0.253 -1.807962 .4865736 DBEL | -.7027302 .5575206 -1.26 0.213 -1.82311 .4176495 DCAN | .8596027 .6034043 1.42 0.161 -.3529836 2.072189 DDEN | -.3040316 .5252448 -0.58 0.565 -1.35955 .7514873 DFIN | -.7224872 .5827997 -1.24 0.221 -1.893667 .4486926 DFRA | -.5394103 .5561799 -0.97 0.337 -1.657096 .578275 28.11.2010 INTRODUCTION TO PANEL DATA MODELS 3 DGER | -.5800678 .5388773 -1.08 0.287 -1.662982 .5028466 DGRE | -.2079644 .557905 -0.37 0.711 -1.329116 .9131876 DICE | .4533005 .6468998 0.70 0.487 -.8466932 1.753294 DIRE | -.1878446 .7473691 -0.25 0.803 -1.689739 1.31405 DITA | -.70514 .5546562 -1.27 0.210 -1.819763 .4094833 DJAP | -.3722712 .606942 -0.61 0.542 -1.591967 .8474244 DKOR | -.8475396 .9325661 -0.91 0.368 -2.721601 1.026522 DLUX | -.3759881 .6767538 -0.56 0.581 -1.735976 .9839997 DMEX | .0142914 .6517056 0.02 0.983 -1.29536 1.323943 DNET | .0992652 .5667011 0.18 0.862 -1.039563 1.238094 DNZ | .3784728 .5360674 0.71 0.484 -.6987951 1.455741 DNOR | -.1302623 .6190878 -0.21 0.834 -1.374366 1.113841 DPOR | -.2768885 .6238941 -0.44 0.659 -1.530651 .9768736 DSPA | -.66578 .5872128 -1.13 0.262 -1.845828 .5142682 DSWE | -.5230541 .527388 -0.99 0.326 -1.58288 .5367717 DSWI | .0937435 .5005294 0.19 0.852 -.9121079 1.099595 DTUR | -.0550511 .6747581 -0.08 0.935 -1.411028 1.300926 DUK | -.4576309 .5440726 -0.84 0.404 -1.550986 .6357239 DUSA | .693391 .6009887 1.15 0.254 -.5143409 1.901123 ------------------------------------------------------------------------------ The coefficients of the dummy variables indicate that countries such as Australia, Canada, New Zealand, and the USA have been more successful in creating employment, controlling for the growth rate of GDP, than European countries such as France, Germany, Italy, and the UK. However none of the fixed effects is significant individually. Their joint explanatory power is tested in item (4). (b) Retaining the intercept, dropping DAUS. . drop DAUS . reg E G TIME2 TIME3 D* Source | SS df MS Number of obs = 78 -------------+------------------------------ F( 28, 49) = 1.77 Model | 29.2529828 28 1.04474939 Prob > F = 0.0399 Residual | 28.9736111 49 .591298185 R-squared = 0.5024 -------------+------------------------------ Adj R-squared = 0.2181 Total | 58.2265939 77 .756189531 Root MSE = .76896 ------------------------------------------------------------------------------ E | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- G | .2851358 .1023042 2.79 0.008 .0795477 .4907239 TIME2 | .3278352 .2283511 1.44 0.157 -.1310535 .786724 TIME3 | .3233233 .2287614 1.41 0.164 -.1363899 .7830365 DAUT | -1.187901 .6298235 -1.89 0.065 -2.453578 .0777771 DBEL | -1.229936 .6320795 -1.95 0.057 -2.500148 .0402747 DCAN | .3323963 .6278584 0.53 0.599 -.9293324 1.594125 DDEN | -.8312379 .6421394 -1.29 0.202 -2.121665 .4591896 DFIN | -1.249694 .6285693 -1.99 0.052 -2.512851 .0134637 DFRA | -1.066617 .6323595 -1.69 0.098 -2.337391 .2041573 DGER | -1.107274 .6369755 -1.74 0.088 -2.387324 .172776 DGRE | -.7351707 .6320011 -1.16 0.250 -2.005224 .5348829 DICE | -.0739058 .6314364 -0.12 0.907 -1.342825 1.195013 DIRE | -.7150509 .6594065 -1.08 0.284 -2.040178 .610076 DITA | -1.232346 .6326904 -1.95 0.057 -2.503785 .0390926 DJAP | -.8994775 .6279059 -1.43 0.158 -2.161302 .3623465 DKOR | -1.374746 .7575444 -1.81 0.076 -2.897088 .1475965 DLUX | -.9031944 .6372069 -1.42 0.163 -2.18371 .3773208 DMEX | -.5129149 .6321984 -0.81 0.421 -1.783365 .7575353 DNET | -.4279412 .63043 -0.68 0.500 -1.694838 .8389554 DNZ | -.1487335 .6379183 -0.23 0.817 -1.430678 1.133211 DNOR | -.6574687 .6284157 -1.05 0.301 -1.920317 .60538 DPOR | -.8040948 .6287595 -1.28 0.207 -2.067634 .4594447 28.11.2010 INTRODUCTION TO PANEL DATA MODELS 4 DSPA | -1.192986 .6282681 -1.90 0.063 -2.455538 .0695656 DSWE | -1.05026 .6412241 -1.64 0.108 -2.338849 .2383276 DSWI | -.4334628 .656352 -0.66 0.512 -1.752451 .8855258 DTUR | -.5822574 .6367468 -0.91 0.365 -1.861848 .6973332 DUK | -.9848372 .6353825 -1.55 0.128 -2.261686 .2920117 DUSA | .1661847 .6278534 0.26 0.792 -1.095534 1.427903 _cons | .5272063 .6016461 0.88 0.385 -.6818468 1.736259 ------------------------------------------------------------------------------ One might compare the two dummy variable regressions. There are only two substantive differences. One is the interpretation of the tests of the coefficients of the dummy variables. The 2 other is R . In the second regression this is computed conventionally. In the first, it is a pseudo- R because the regression lacks an intercept and thus in general it is not possible to decompose the variance of the dependent variable into the variance of the fitted values and the variance of the residuals. In actual fact, since the regressions are substantively identical, R ought to be the same, and indeed would be it were measured as the variance of the fitted values divided by the variance of the actual values, or 1 minus the variance of the residuals divided by the variance of the actual values. In Stata the pseudo-R is computed as 1 minus the variance of the residuals divided by the mean square of the dependent variable. Since the mean square of a variable is 2 2 larger than its variance, the pseudo-R is lower than the true R in this case. 14.4 Perform a test for fixed effects in the OECD2000 regression by evaluating the explanatory power of the country dummy variables as a group. Answer: To test the joint explanatory power of the dummy variables, one compares RSS from either regression in Exercise 14.3, 28.97, with that in Exercise 14.1, 45.73: (45.73 28.97)/25 F(25,49)  1.13 28.97/49 The critical value of F(25,50) at the 5 percent level is 1.73, so the fixed effects do not jointly have significant explanatory power. This accounts for the fact that in this case the OLS and fixed effects regressions produced similar results. 14.5 Download the NLSY2000 data set from the website. See Appendix B for details. This contains the variables found in the EAEF data sets for the years 1980–94, 1996, 1998, and 2000 (there were no surveys in 1995, 1997, or 1999). Assuming that a random effects model is appropriate, investigate the apparent impact of unobserved heterogeneity on estimates of the coefficient of schooling by fitting the same earnings function, first using pooled OLS, then using random effects. Answer: The point estimates are quite similar. The main difference is that the ethnicity coefficients are smaller with random effects. . reg LGEARN S EXP ASVABC MALE ETHBLACK ETHHISP Source | SS df MS Number of obs = 42815 -------------+------------------------------ F( 6, 42808) = 4093.62 Model | 3939.82979 6 656.638299 Prob > F = 0.0000 Residual | 6866.62551 42808 .160405193 R-squared = 0.3646 -------------+------------------------------ Adj R-squared = 0.3645 Total | 10806.4553 42814 .252404711 Root MSE = .40051 ------------------------------------------------------------------------------ LGEARN | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- 28.11.2010 INTRODUCTION TO PANEL DATA MODELS 5 S | .0560438 .0010582 52.96 0.000 .0539697 .0581179 EXP | .033278 .0003934 84.58 0.000 .0325068 .0340491 ASVABC | .0111145 .00029 38.33 0.000 .0105461 .0116828 MALE | .1963033 .0039257 50.00 0.000 .1886089 .2039978 ETHBLACK | -.0438291 .0067187 -6.52 0.000 -.0569978 -.0306604 ETHHISP | .055776 .0081145 6.87 0.000 .0398714 .0716805 _cons | 5.312909 .0136431 389.42 0.000 5.286169 5.33965 ------------------------------------------------------------------------------ . xtreg LGEARN S EXP ASVABC MALE ETHBLACK ETHHISP, re Random-effects GLS regression Number of obs = 42815 Group variable (i): ID Number of groups = 5107 R-sq: within = 0.2576 Obs per group: min = 1 between = 0.4460 avg = 8.4 overall = 0.3644 max = 18 Random effects u_i ~ Gaussian Wald chi2(6) = 17155.30 corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ LGEARN | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- S | .0571317 .001909 29.93 0.000 .0533902 .0608732 EXP | .0326118 .0003084 105.74 0.000 .0320073 .03321
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