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There are 6 linear regression models, 5 with income (in 1,000 dollars) as the dependent variable and one with logged income as the dependent variable. The analysis is based on a nationally representative sample of men and women aged 35 to 59 who are currently employed in Korea in 2012. (Variables: PEARNK =yearly income in $1,000 US dollars, DPEARN =yearly income in US dollars, LDPEARN=logged yearly income in US dollars Gender: FEM =fem (1=female, 0=male) Age: AGE20=respondent’s age minus 20 (NOTE: RAGE20=0 at age 20) Education: CEDUYR=years of schooling centered at the sample mean (CEDUYR=EDUYR- mean(EDUYR)) CEDUYRSQ=CEDUYR squared Employment status: EMPLOYEE (1=paid employee, 0=non-paid-employee), (The omitted category includes self-employed and family worker.) Working hours: WRKHRS=total working hours in the past year WRKHRSSQ=WRKHRS*WRKHRS Marital status: MS23= previously married (widowed or divorced/separated) (1=previously married, 0=else) MS4= (1=never married, 0=else) (omitted category is currently married) Interaction terms between fem and other independent variables: FEM_variables = FEM * variables PART I. DYEARN as the dependent variable: Models 1 through 5. 1. Using Models 1 & 2, decompose the total effect of “female (FEM)” on income (PEARNK) into the direct and indirect effects. Interpret the results. 2. Using Models 2 & 3, decompose the total effect of “female (FEM)” on income (DPEARN) into the direct and indirect effects. Interpret the results. 3. Refer to Model 5. Find the value of R2 . Interpret the value. 4. In Models 5, examine the coefficient for the interaction term between “female (FEM)” and “marital status (MS23 and MS4)”, i.e., bFMS23, bFMS4, and test whether each of the interaction effects is statistically significant. Interpret the results, using both the main effects and interaction effect. 5. In Model 5, first test two hypotheses, H0: βCEDUYRSQ = 0 & H0: βFCEDUYRSQ = 0. Then, discuss the exact relationship between “years of schooling” and “income,” separately for men and women. 6. Refer to Model 5: Calculate the predicted incomes for the following two groups FOR EACH GENDER—(1) paid employee (EMPLOYEE=1) with 12 years of schooling (2) non-paidemployee (EMPLOYEE=0) with 12 years of schooling. Assume: age 40 (RAGE20=20), currently married (MS23=MS4=0), 2000 hours of working (WRKHRS=2000) PART II. LPYEARN as the dependent variable: Model 6. 7. Refer to Model 6. What is the effect of age (AGE20) on logged income? Then, what is the effect of age (AGE20) on income (non-logged)? Estimate the effects separately for men and women. log: /Volumes/MYPASSPORT/Class_Spring2016/RunStata/out605_Midterm.log . . use koweps2012sn.dta, clear . . keep if wst4==0 //---only Working persons . keep if age20>15 //--------30 or older . keep if age20<40 //--------59 or younger . *--------------------------------DV's . gen pearnk=pearn/100 //one unit is about $1000 . gen dpearn=pearn*10 //one unit is about $1 . gen ldpearn=log(dpearn+1) . *--------------------------------IV's . gen ms23=(ms2==1|ms3==1) . gen wrkhrssq=wrkhrs*wrkhrs . egen meduyr=mean(eduyr) . gen ceduyr=eduyr-meduyr . gen ceduyrsq=ceduyr*ceduyr . gen employee=wst1 . gen fage20=fem*age20 . gen fceduyr=fem*ceduyr . gen femployee=fem*employee . gen fwrkhrs=fem*wrkhrs . gen fms23=fem*ms23 . gen fms4=fem*ms4 . gen fceduyrsq=fem*ceduyrsq . . sum pearnk dpearn ldpearn fem age20 ceduyr ceduyrsq /// > employee wrkhrs ms23 ms4 /// > fage20 fceduyr fceduyrsq fms23 fms4 Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- pearnk | 3,605 29.65831 24.58631 0 235.25 dpearn | 3,605 29658.31 24586.31 0 235250 ldpearn | 3,605 9.566093 2.301179 0 12.36841 fem | 3,605 .4085992 .4916431 0 1 age20 | 3,605 24.87712 5.355782 16 34 -------------+--------------------------------------------------------- ceduyr | 3,605 -4.26e-08 2.84889 -12.6932 5.306796 ceduyrsq | 3,605 8.11392 14.65103 .4805317 161.1174 employee | 3,605 .436061 .4959637 0 1 wrkhrs | 3,605 2238.027 758.116 64 3600 ms23 | 3,605 .1042996 .3056912 0 1 -------------+--------------------------------------------------------- ms4 | 3,605 .0834951 .2766676 0 1 fage20 | 3,605 10.37892 12.94831 0 34 fceduyr | 3,605 -.2335893 1.90084 -12.6932 5.306796 fceduyrsq | 3,605 3.666756 11.65088 0 161.1174 fms23 | 3,605 .0640777 .2449252 0 1 -------------+--------------------------------------------------------- fms4 | 3,605 .0180305 .1330802 0 1 . . reg pearnk fem age20 //MODEL 1 Source | SS df MS Number of obs = 3,605 -------------+---------------------------------- F(2, 3602) = 419.62 Model | 411675.627 2 205837.813 Prob > F = 0.0000 Residual | 1766894.74 3,602 490.531578 R-squared = 0.1890 -------------+---------------------------------- Adj R-squared = 0.1885 Total | 2178570.37 3,604 604.486784 Root MSE = 22.148 ------------------------------------------------------------------------------ pearnk | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- fem | -21.60018 .7528926 -28.69 0.000 -23.07631 -20.12404 age20 | -.1155319 .0691131 -1.67 0.095 -.2510365 .0199728 _cons | 41.35822 1.760897 23.49 0.000 37.90577 44.81068 ------------------------------------------------------------------------------ . reg pearnk fem age20 ceduyr //MODEL 2 Source | SS df MS Number of obs = 3,605 -------------+---------------------------------- F(3, 3601) = 460.23 Model | 603793.621 3 201264.54 Prob > F = 0.0000 Residual | 1574776.75 3,601 437.316509 R-squared = 0.2772 -------------+---------------------------------- Adj R-squared = 0.2765 Total | 2178570.37 3,604 604.486784 Root MSE = 20.912 ------------------------------------------------------------------------------ pearnk | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- fem | -19.37458 .7187686 -26.96 0.000 -20.78381 -17.96534 age20 | .4114189 .0699321 5.88 0.000 .2743084 .5485294 ceduyr | 2.785459 .1328956 20.96 0.000 2.524901 3.046017 _cons | 27.33983 1.792122 15.26 0.000 23.82615 30.8535 ------------------------------------------------------------------------------ . reg pearnk fem age20 ceduyr employee //MODEL 3 Source | SS df MS Number of obs = 3,605 -------------+---------------------------------- F(4, 3600) = 460.11 Model | 736983.491 4 184245.873 Prob > F = 0.0000 Residual | 1441586.88 3,600 400.4408 R-squared = 0.3383 -------------+---------------------------------- Adj R-squared = 0.3376 Total | 2178570.37 3,604 604.486784 Root MSE = 20.011 ------------------------------------------------------------------------------ pearnk | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- fem | -16.78873 .7022594 -23.91 0.000 -18.16559 -15.41186 age20 | .5132731 .0671514 7.64 0.000 .3816145 .6449317 ceduyr | 2.137509 .1320389 16.19 0.000 1.87863 2.396387 employee | 13.3611 .7326148 18.24 0.000 11.92472 14.79748 _cons | 17.92316 1.790944 10.01 0.000 14.41179 21.43453 ------------------------------------------------------------------------------ . reg pearnk fem age20 ceduyr employee wrkhrs ms23 ms4 //MODEL 4 Source | SS df MS Number of obs = 3,605 -------------+---------------------------------- F(7, 3597) = 307.88 Model | 816249.631 7 116607.09 Prob > F = 0.0000 Residual | 1362320.74 3,597 378.738043 R-squared = 0.3747 -------------+---------------------------------- Adj R-squared = 0.3735 Total | 2178570.37 3,604 604.486784 Root MSE = 19.461 ------------------------------------------------------------------------------ pearnk | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- fem | -15.77108 .7024905 -22.45 0.000 -17.1484 -14.39376 age20 | .420267 .0663506 6.33 0.000 .2901785 .5503556 ceduyr | 2.161441 .129452 16.70 0.000 1.907634 2.415247 employee | 11.97536 .7206225 16.62 0.000 10.56249 13.38823 wrkhrs | .0052384 .0004409 11.88 0.000 .0043739 .0061029 ms23 | -2.813534 1.09021 -2.58 0.010 -4.951025 -.6760419 ms4 | -8.671379 1.206848 -7.19 0.000 -11.03755 -6.305204 _cons | 9.719225 2.058062 4.72 0.000 5.68414 13.75431 ------------------------------------------------------------------------------ . reg pearnk fem age20 ceduyr ceduyrsq employee wrkhrs ms23 ms4 /// > fceduyr fceduyrsq fms23 fms4 //MODEL 5 Source | SS df MS Number of obs = 3,605 -------------+---------------------------------- F(12, 3592) = 191.93 Model | 851151.394 12 70929.2828 Prob > F = 0.0000 Residual | 1327418.98 3,592 369.548713 R-squared = -------------+---------------------------------- Adj R-squared = Total | 2178570.37 3,604 604.486784 Root MSE = 19.224 ------------------------------------------------------------------------------ pearnk | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- fem | -19.25532 .8450062 -22.79 0.000 -20.91206 -17.59858 age20 | .3596694 .066113 5.44 0.000 .2300466 .4892923 ceduyr | 2.304896 .1672366 13.78 0.000 1.977007 2.632784 ceduyrsq | .0431023 .0331682 1.30 0.194 -.021928 .1081327 employee | 11.12392 .7196587 15.46 0.000 9.712935 12.5349 wrkhrs | .0051947 .000439 11.83 0.000 .0043339 .0060554 ms23 | -10.15148 1.69034 -6.01 0.000 -13.4656 -6.83736 ms4 | -13.0009 1.369313 -9.49 0.000 -15.68561 -10.31619 fceduyr | -.1219426 .2583821 -0.47 0.637 -.6285329 .3846478 fceduyrsq | .1075309 .0476398 2.26 0.024 .014127 .2009347 fms23 | 12.52857 2.188304 5.73 0.000 8.23813 16.81901 fms4 | 17.094 2.865261 5.97 0.000 11.4763 22.7117 _cons | 12.36277 2.065847 5.98 0.000 8.31242 16.41312 ------------------------------------------------------------------------------ . . reg ldpearn fem age20 ceduyr employee wrkhrs ms23 ms4 /// > fage20 fceduyr fms23 fms4 //MODEL 6 Source | SS df MS Number of obs = 3,605 -------------+---------------------------------- F(11, 3593) = 107.38 Model | 4721.84067 11 429.258243 Prob > F = 0.0000 Residual | 14362.8668 3,593 3.99745805 R-squared = 0.2474 -------------+---------------------------------- Adj R-squared = 0.2451 Total | 19084.7074 3,604 5.29542382 Root MSE = 1.9994 ------------------------------------------------------------------------------ ldpearn | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- fem | -.86624 .3623263 -2.39 0.017 -1.576626 -.1558543 age20 | .0111835 .008684 1.29 0.198 -.0058425 .0282095 ceduyr | .0379773 .0174181 2.18 0.029 .0038269 .0721276 employee | 1.004671 .0743701 13.51 0.000 .8588591 1.150483 wrkhrs | .0001888 .0000456 4.14 0.000 .0000994 .0002782 ms23 | -.2815952 .1758028 -1.60 0.109 -.6262785 .0630882 ms4 | -.6050776 .143731 -4.21 0.000 -.8868801 -.3232751 fage20 | -.027737 .014105 -1.97 0.049 -.0553917 -.0000824 fceduyr | .1610903 .0265632 6.06 0.000 .1090098 .2131708 fms23 | 1.716996 .2276266 7.54 0.000 1.270706 2.163286 fms4 | 1.389801 .2978055 4.67 0.000 .8059167 1.973686 _cons | 9.05147 .2575198 35.15 0.000 8.54657 9.55637 ------------------------------------------------------------------------------ . . log close

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PART I. DYEARN as the dependent variable: Models 1 through 5.

1. Using Models 1 & 2, decompose the total effect of “female (FEM)” on income (PEARNK) into the direct and indirect effects. Interpret the results.

Model 1:
The coefficient of fem in model 1 is -21.60018, it means that female yearly income in $1,000 US dollars is 21.60018 less compare to male assuming other things are constant. This is direct effect of fem variable.
The coefficient of fem in model 1 is -21.60018, it means that female yearly income in $1,000 US dollars is 21.60018 less compare to male and if there is a one unit increase in age then female yearly income in US dollars will be -.1155319 unit less. This is the indirect effect of fem variable.

Model 2:
The coefficient of fem in model 2 is -19.37458, it means that female yearly income in US doll yearly income in $1,000 US dollars ars is 19.37458 less compare to male assuming other things are constant. This is direct effect of fem variable....

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