## Transcribed Text

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

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.

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....