## Transcribed Text

This exercise will empirically explore howwork experience affects hourly wage rates.
We use the dataset which contains data on hourly wage rates (variable: wage), posteducationyears of experience (variable: exper) andother variables for 1000individuals.
a. We generate the variable: lwage, which is defined as the logarithm of variable
wage. Figure 1 shows the summary statistics (including mean, variance, skewness,
kurtosis) for variables: wage, lwage and exper. Check whether these variables are
normally distributed. You may use the 95% significance level for your hypotheses
tests. (Advice: Clearly show null/alternative hypotheses, test statistics, rejection
region, conclusion for each variable)
b. Weestimatelinear,loglinearandlog-logmodel specifications toexaminetheeffect
of experience on wage. These regression results are shown in Figure 2.
i. Write down the fitted modes for each specification.
ii. Obtain the 99% C.I. for the slope parameter in the linear specification.
iii. Testthe null hypothesis that the intercept in the log-linear model is 0 against
its right tail alternative. (Advice: Clearly write down the null/alternative
hypotheses, test statistics, rejection region and conclusion. You may set the
Type I error at α = 0.05.)
c. UsingresultsfromFigure2,whatisthepredictedhourlywageforanindividualwith
10yearsof experience for eachmodel specification? Howdoyour results compare?
2
d. Using results from Figure 2, what is the elasticity of experience to wage for each
specification?
e. UsingresultsfromFigure2,comparetheR2 ofthelinearmodelwiththegeneralized
R2
from the log-linear models? What can you conclude? (Advice: You need to
calculate the generalized R2 using information from Figure 2).
f. Figure 3shows the summary statistics ofthe residuals fromthe linearmodel(residlinear) and the residuals from the log-linear model (residuallogl). Check whether
the residuals from the linear and log-linear model are normally distributed. You
may use the 95% significance level for your hypotheses tests. (Advice: Clearly
show null/alternative hypotheses, test statistics, rejection region, conclusion for
each variable)
g. Overall, which model specification would you choose? Justify your answer with
findings from previous sections.
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Figure 1: Summary statistics of wage, lwage and exper
. sum wage, detail
earnings per hour
Percentiles Smallest
1% 3.895 2.03
5% 7.2 2.5
10% 8.275 2.83 Obs 1,000
25% 12 2.88 Sum of Wgt. 1,000
50% 16.5 Mean 20.20122
75% 25.4
Largest
72.13
Std. Dev. 12.1038
90% 36.96 72.13 Variance 146.5021
95% 45.175 72.13 Skewness 1.478395
99% 62.58 72.13 Kurtosis 5.475637
. sum lwage, detail
lwage
1%
Percentiles
1.359627
Smallest
.7080358
5% 1.974081 .9162908
10% 2.113237 1.040277 Obs 1,000
25% 2.484907 1.05779 Sum of Wgt. 1,000
50% 2.80336 Mean 2.84477
75% 3.234744
Largest
4.27847
Std. Dev. .5710783
90% 3.609836 4.27847 Variance .3261304
95% 3.810542 4.27847 Skewness -.0561999
99% 4.136147 4.27847 Kurtosis 3.08314
. sum exper, detail
post education years experience
1%
Percentiles
5
Smallest
3
5% 7 3
10% 9 4 Obs 1,000
25% 15 4 Sum of Wgt. 1,000
50% 27 Mean 26.501
75% 36.5
Largest
58
Std. Dev. 12.99041
90% 43 59 Variance 168.7507
95% 47.5 63 Skewness .1219864
99% 55.5 64 Kurtosis 2.150823
.
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Figure 2: Ordinary Least Squares regression Outputs
. reg wage exper
Source SS df MS
Model 563.899211 1 563.899211
Residual 145791.662 998 146.08383
Total 146355.561 999 146.502063
. reg lwage exper
Source SS df MS
Model .892358779 1 .892358779
Residual 324.911879 998 .325563005
Total 325.804237 999 .326130368
. reg lwage lexper
Source SS df MS
Model 3.86415199 1 3.86415199
Residual 321.940085 998 .322585256
Total 325.804237 999 .326130368
.
Number of obs = 1,000
F(1, 998) = 3.86
Prob > F = 0.0497
R-squared = 0.0039
Adj R-squared = 0.0029
Root MSE = 12.087
Number of obs = 1,000
F(1, 998) = 2.74
Prob > F = 0.0981
R-squared = 0.0027
Adj R-squared = 0.0017
Root MSE = .57058
Number of obs = 1,000
F(1, 998) = 11.98
Prob > F = 0.0006
R-squared = 0.0119
Adj R-squared = 0.0109
Root MSE = .56797
wage Coef. Std. Err. t P>|t| [95% Conf. Interval]
exper .0578356 .0294371 1.96 0.050 .0000698 .1156014
_cons 18.66852 .8687121 21.49 0.000 16.96381 20.37323
lwage Coef. Std. Err. t P>|t| [95% Conf. Interval]
exper .0023007 .0013897 1.66 0.098 -.0004263 .0050277
_cons 2.783798 .0410102 67.88 0.000 2.703322 2.864274
lwage Coef. Std. Err. t P>|t| [95% Conf. Interval]
lexper .100985 .0291778 3.46 0.001 .0437282 .1582418
_cons 2.529811 .092757 27.27 0.000 2.34779 2.711832
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Figure 3: Summary statistics of OLS residuals from linear model (residlinear) and loglinear model (residuallogl)
. sum residlinear, detail
residlinear
1%
Percentiles
-16.23426
Smallest
-18.84381
5% -13.08766 -18.28813
10% -11.78101 -17.90359 Obs 1,000
25% -8.401573 -17.52359 Sum of Wgt. 1,000
50% -3.538217
Largest
Mean
Std. Dev.
-1.84e-07
12.08046
75% 5.26518 51.20589
90% 16.52141 51.3794 Variance 145.9376
95% 24.71182 52.24693 Skewness 1.465559
99% 41.47007 52.94096 Kurtosis 5.456175
.
. sum residuallogl, detail
residuallogl
1%
Percentiles
-1.470989
Smallest
-2.103371
5% -.8650622 -1.936529
10% -.7182188 -1.84448 Obs 1,000
25% -.3761723 -1.795029 Sum of Wgt. 1,000
50% -.0392261
Largest
Mean
Std. Dev.
-3.46e-09
.5702956
75% .3922077 1.411846
90% .757394 1.415255 Variance .3252371
95% .9512334 1.446357 Skewness -.0662608
99% 1.263653 1.473965 Kurtosis 3.087397

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