earnings functions

U52071 Econometrics

Earnings Functions

Dr. Sara le Roux

Word Count: 1,999

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Introduction

In order to better understand labour market activity, the determinants of earnings and the

return of human capital must continue to be analysed. Using an Educational Attainment and

Earning Function (EAEF) data set, multiple variables will be examined in order to increase

the understanding of the determinants of hourly earnings in the United States. The variables

chosen have been selected through the review of academic literature. The final estimated

earnings function model will be analysed in order to understand the reason for the factors

influences on hourly earnings.

Literature Review

Jacob A. Mincer developed the framework for the human capital earnings function by

analysing the influence of years of schooling and work experience on earnings received by an

individual (Mincer, 1974). While inclusion of such variables support the explanation of the

variations in one’s earnings, further developments have been made in relation to the returns

of human capital investment as well as personal attributes.

Depending on one’s belief of innate ability, the inclusion of cognitive ability as well as

schooling may help enhance the understanding of the determinants of earnings. Psychologists

and economists have provided sufficient evidence of the effects of cognitive ability on one’s

possible earnings, suggesting that the inclusion of numerical and literary reasoning is

beneficial, supporting the explanation of earnings pattern (Hartog, et al., 2004).

For instance, the influence of gender on earnings has been researched repeatedly drawing on

the gender wage gap in the United States that persists through the 21st century. While

conclusions of such studies vary, the consistent theme suggests that discrimination is not a

main cause for the gender wage gap in recent years. Hours worked and occupations taken by

men and women continue to differ and thus help explain the earnings variations between the

two groups (Mandel and Semyonov, 2014).

As occupations plays a key role in the hourly earnings individuals may receive, developments

have also been made with regards to earnings in different sectors, particularly the variation in

the public and private sectors. Multiple researchers furthered this investigation in order to not

only determine the possibility of a significant sector pay gap, but to also explain the

reasoning for such earning variations (Ramoni-Perazzi and Bellante, 2002). The results

suggested that those in the public sector received higher earnings than those in the private

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sector. However, such findings have been criticised for omission of other factors which

overvalued findings (Allegretto and Keefe, 2010).

Variations in earnings of individuals that are married, compared to those that are single or

divorced, have been analysed and included in many studies related to earnings as well.

Polachek included these personal attributes in a piece of his research suggesting that the

returns of one’s marital status also vary dependent on their gender (Polachek, 2007).

Results

With consideration of the research aforementioned, the estimated earnings function model

was produced.

log (EARNINGS)= .7785 + .1176(S) + .0008 (EXP)2 -.1290(CATGOV)

-.0989(CATSE)+.0075(ASVABC)-.3212(FEMMARR)-.3516(FEMSIN)-.2635(FEMDIV)

-.1954(MALESING)-.1479(MALEDIV)

Total 179.764726 537 .334757405 Root MSE = .4433 Adj R-squared = 0.4130 Residual 103.565506 527 .196518986 R-squared = 0.4239 Model 76.1992208 10 7.61992208 Prob > F = 0.0000 F( 10, 527) = 38.77 Source SS df MS Number of obs = 538

_cons .7784659 .1498624 5.19 0.000 .4840648 1.072867 MALEDIV -.147902 .0694032 -2.13 0.034 -.284243 -.011561 MALESING -.195402 .0751161 -2.60 0.010 -.3429657 -.0478382 FEMDIV -.2634519 .0659753 -3.99 0.000 -.3930588 -.133845 FEMSING -.3516476 .0885173 -3.97 0.000 -.5255376 -.1777576 FEMMARR -.3212121 .0503865 -6.37 0.000 -.4201951 -.2222291 ASVABC .0075019 .002521 2.98 0.003 .0025495 .0124543 CATSE -.0988936 .1305476 -0.76 0.449 -.3553511 .157564 CATGOV -.1290022 .0458563 -2.81 0.005 -.2190857 -.0389187 EXPSQR .0007915 .0001668 4.74 0.000 .0004638 .0011193 S .1175536 .0102783 11.44 0.000 .0973622 .137745 LGEARN Coef. Std. Err. t P>|t| [95% Conf. Interval]

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Multiple Linear Assumptions

The OLS technique yields the most efficient linear estimators of the parameters as:

1. The relationship between log (EARNINGS) and the independent factors is linear.

2. The data collected for the EAEF data set is assumed to be drawn randomly.

3. The regression does not incur any cases of perfect collinearity; tested by the variance

inflation factor (Appendix 4).

4. The regression does not incur omitted variable bias as tested by the Ramsey Reset test

(Appendix 4). Therefore a zero conditional mean is assumed.

5. Through the use of the Bruesch Pagan test and the White test, the data has shown to

not violate homoscedasticity (Appendix 4).

6. Normality is assumed due to the normalisation of the errors through the use of log

(EARNINGS) and the large sample size 538.

Therefore, the OLS regression is the best linear, unbiased estimator with the standard

estimators following a standard normal distribution.

Log (EARNINGS): the natural log of hourly earnings

The dependent variable was generated as a logarithm in order to normalise errors associated

with earnings and to satisfy the Gauss Markov theorem (Appendix 1).

S: years of schooling (highest grade completed as of 2002)

The factor, years of schooling, was chosen in order to represent the framework developed by

Mincer. The results of the variable have been shown to be statistically significant as the null

hypothesis, that years of schooling is insignificant in relation to earnings, can be rejected at

the 0.00% significance level. Therefore, the results suggest that investing in one more year of

schooling, ceteris paribus, will lead to an increase in earnings of 11.7%. The original

regression produced included dummy variables of highest educational qualification achieved

in order to show that quality of schooling influences earnings (Eckstein and Nagypal, 2004).

However, such variables were proven to be statistically insignificant and therefore omitted

from the regression (Eckstein and Nagypal, 2004).

While the returns to schooling increase with the higher levels of education obtained, the

causal effect of such is widely debated. For instance, higher levels of schooling can be

associated with unobservable abilities such as one’s perseverance and motivation, suggesting

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those who obtain greater years of schooling have greater incentives to pursue a more

demanding yet rewarding occupation (Arkes, 1999). However, others believe the returns are

due to the high demand for better educated workers (Deschênes, 2002). With the growth of

the knowledge economy, such demand expansions may provide a plausible explanation for

the returns of schooling as higher educated workers provide valuable skills and enhance the

profits of the employer (OECD, 2007). With regards to both theories, it can be concluded

that the causal effect of higher levels of schooling can be associated with both the indirect

effects of greater levels of schooling in terms of signalling and determination as well as the

skills necessary to pursue the higher paid occupations with greater educational standards

(Ceci and Williams, 1997).

EXP2: Total years of out- of – school work experience (2002)

The choice to include experience squared was drawn from the original Mincer equation

which suggested that annual earnings doubled after the first few years of experience which

has continued to hold true today (Mincer, 1974) (Lemieux, 2003). Originally, both EXP and

EXP2 were included however both were shown to obtain insignificant t-statistics and p-values.

Therefore, experience squared was chosen in order to better explain the increasing rate of

returns of experience. Holding all other factors constant, the final regression suggests that 10

years of work experience lead to a .7945% increase in hourly earnings. Such returns are a

result of training and increased abilities associated with the particular job (Braga, 2013).

Therefore, with greater work experience, the individual becomes more productive thus

leading to a higher wage premium. While this supports the explanation of the returns of

experience, the signalling effect also plays a crucial role. Employers use signalling to

determine the ability of workers and associate an individual’s employment history with the

probability of the individual’s skill level (Braga, 2013).

While work experience is important, years of unemployment also have an influential role in

determining earnings due to the possibility of scarring effects; thus the years out of work

should also be included in further regression analysis (Braga, 2013).

ASVABC: Arithmetic reasoning (doubled), word knowledge, paragraph comprehension

ASVABC was included in order to determine the returns of one’s overall cognitive ability on

their hourly earnings. Cawley, et al. (2001), suggests that the returns of one’s ‘ability’ have

increased in recent years and Hartog, et al. (2004), emphasizes the importance of balanced

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abilities. ASVABC is proven to be statistically significant suggesting, ceteris paribus, a ten

point increase in an individual’s overall score will lead to a 7.5% increase in the individuals

hourly earnings. ASVABC is highly positively correlated with years of schooling however

this does not create an issue in the regression analysis.

Cognitive ability affects the productivity, acquisition of skills and a variety of behaviours that

will have an impact on an individual’s earnings (Heckman, et al., 2006). However, the causal

effect on one’s earnings is not direct as one’s cognitive abilities influences their time rate of

preference as well as their investment in educational attainment (Hartog et al., 2004)

(Golsteyn, et al., 2013). Therefore, cognitive ability is used as a signal to employers of an

individual’s innate abilities yet further research of non-cognitive abilities must be examined

in relation to earnings as such factors also play a crucial role (Hartog et al., 2004).

CATGOV: Work in the Public Sector, CATSE: Work through self-employment

While the research conducted suggests a significant variation in earnings of those working in

the public and private sectors, the self-employed sector was included in order to allow the

private sector to represent the base category and to avoid the dummy variable trap. Therefore,

while self-employed individual’s earnings are not statistically significant (p-value=.449), the

inclusion of the variable is necessary to accurately portray the variations between the

government sector and the private sector. Therefore, those in the public sector earn 12.9%

less than those in the private sector when all other factors are held constant.

However, this does not suggest that a significant earnings gap exists as the two sectors

employee characteristics vary. For instance, the public sector obtains a higher proportion of

the female and married work force than the private sector (Ramoni-Perazzi and Bellante, 2002).

Such characteristics will influence an individual’s earnings, suggesting the wage gap between

the public and private sector may not exist. In order to accurately examine earnings

differentials, the individuals compared must have similar characteristics and occupations

however, many researchers have found drawing such comparisons difficult (Bewerunge and

Rosen, 2015). Additionally, while the government sector is suggested to earn less than those

in the private sector, compensation packages should also be taken into consideration;

individuals in the public sector tend to have higher pension plans and benefit schemes

(Allegretto and Keefe, 2010).

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FEMMARR: Married Female, FEMSING: Single Female, FEMDIV: Female Divorced,

MALESING: Single Male, MALEDIV: Divorced Male

The use of an interaction variables is necessary in order to observe the gender gap and the

marital status gap between genders. Polachek (2007), Gorman (1999), and Cotter, et al.

(2004) all suggest the relationship between gender and marital status to have a significant

impact on one’s earnings. With all factors found to be statistically significant, the results

suggest that married females earn 32.12% less, single females earn 35.16% less, divorced

females earn 26.35% less, single males earn 19.54% less, and divorced males earn 14.79%

less than married males, ceteris paribus.

According to the results both males and females obtain marriage premiums however, this

may not be correlated to personal attribute discrimination. The causal effects on earnings vary

for the two genders as married men tend to pursue steadier employment compared to their

single counterparts while married women tend to have obtained high educational

qualifications (Gorman, 1999) (Lerman and Wilcox, 2014). Such results suggest that marriage

is an indicator of one’s ability with the wage gap between men and women decreasing as both

genders engage in the competition for power at a higher level than their single counterparts

(Gorman, 1999). With regards to divorce, in many cases the female work force participation

rate increases due to economic pressures while the opposite occurs for men whose

responsibility tends to decrease (Avellar and Smock, 2005).

Additionally, one’s earnings can also be influenced by the presence of dependents and

therefore such should be included in further studies as research contradicts the findings

provided (Lerman and Wilcox, 2014).

Conclusion and Future Alterations

Through the research conducted, it can be concluded that Mincer’s original factors do

contribute to the determinants of earnings however, many other variables also play a roll. The

other factors such as cognitive ability, occupational sector, gender and marital status do

influence individual earnings however, the causal effects of such may not be direct and in

many cases relate to experience and years of schooling. In order to increase the goodness of

fit of regression analysis for earnings, further data collection should ensue to incorporate

periods of unemployment, non-cognitive abilities, the presence of dependents and

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occupational benefits.

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References

Allegretto, S. and Keefe, J. (2010). The Truth about Public Employees in California: They

are Neither Overpaid nor Overcompensated. Policy Brief. [online] Berkely: Institute

for Research on Labor and Employment. Available at: http://www.irle.berkeley.edu/

cwed/wp/2010-03.pdf [Accessed 8 Apr. 2016].

Arkes, J. (1999). What Do Educational Credentials Signal and Why Do Employers Value

Credentials?. Economics of Education Review, 18(1), pp.133-141.

Avellar, S. and Smock, P. (2005). The economic consequences of the dissolution of

cohabiting unions. J Marriage and Family, 67(2), pp.315-327.

Bewerunge, P. and Rosen, H. (2013). Wages, Pensions, and Public-Private Sector

Compensation Differentials for Older Workers. PAR, 2(2).

Braga, Breno. Schooling, Experience, Career Interruptions, And Earnings. University of

Michigan, 2013. Web. 1 Apr. 2016.

Ceci, Stephen J, and Wendy M. Williams. "Schooling Intelligence And Earnings". American

Psychologyst 52.10 (2016): n. pag. Web. 4 Apr. 2016.

Cawley, J., Heckman, J. and Vytlacil, E. (2001). Three observations on wages and measured

cognitive ability. Labour Economics, 8(4), pp.419-442.

Cotter, D., Hermsen, J. and Vanneman, R. (2004). Gender Inequality at Work. [online] New

York City: Russell Sage Foundation. Available at: http://www.vanneman.umd.edu/

papers/ cotter_etal.pdf [Accessed 8 Apr. 2016].

Deschênes, O. (2002). An Econometric Analysis of the Returns to Education in the United

States. Dissertation Awards. [online] Princeton: W.E. Upjohn Institute for

Employment Research. Available at: http://research.upjohn.org/cgi/viewcontent.cgi?

article=1029&context=dissertation_awards [Accessed 9 Apr. 2016].

Eckstein, Z. and Nagypal, E. (2004). The Evolution of U.S. Earnings Inequaliy: 1961-2002.

Federal Reserve Bank of Minneapolis Quarterly Review,[online] 28(2), pp.10-29.

Available at: https://www.minneapolisfed,org/research/qr/qr2822.pdf [Accessed 18

Mar. 2016]

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Golsteyn, B., Gronqvist, H. and Lindahl, L. (2013). Time Preferences and Lifetime

Outcomes. Discussion Paper Series. Bonn: IZA.

Gorman, E. (1999). Bringing Home the Bacon: Marital Allocation of Income-Earning

Responsibility, Job Shifts, and Men's Wages. Journal of Marriage and the Family,

61(1), p.110.

Hartog, J., Van Praag, M. and Van Der Sluis, J. (2010). If You Are So Smart, Why Aren't

You an Entrepreneur? Returns to Cognitive and Social Ability: Entrepreneurs Versus

Employees. Journal of Economics & Management Strategy, 19(4), pp.947-989.

Heckman, J., Stixrud, J. and Urzua, S. (2006). The Effects of Cognitive and Noncognitive

Abilities on Labor Market Outcomes and Social Behavior. Journal of Labor

Economics, 24(3), pp.411-482.

Lemieux, Thomas. (2003). The "Mincer Equation" Thirty Years After Schooling, Experience,

And Earnings. Berkeley: Center of Labor Economics, University of California, 2003.

Web. 9 Apr. 2016. Working Paper.

Lerman, R. and Wilcox, W. (2014). For Richer, For Poorer: How Family Structures

Economic Success. [online] Institute for Family Studies. Available at:

http://www.aei.org/wp-content/uploads/2014/10/IFS-ForRicherForPoorer-

Final_Web.pdf [Accessed 8 Apr. 2016].

Mandel, H. and Semyonov, M. (2014). Gender Pay Gap and Employment Sector: Sources of

Earnings Disparities in the United States, 1970–2010. Demography, 51(5), pp.1597-

1618.

OECD, (2007). Lifelong Learning and Human Capital. Policy Brief. [online] OECD.

Available at: http://www.forschungsnetzwerk.at/downloadpub/OECD-Letter-LLL.pdf

[Accessed 10 Mar. 2016].

Ramoni-Perazzi, J. and Bellante, D. (2011). Wage Differentials Between The Public And The

Private Sector: How Comparable Are The Workers?. Journal of Business &

Economics Research (JBER), 4(5).

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. gen LGEARN= ln(EARNINGS)

Appendices

Appendix 1

0.2

.4.6

.8Density

1 2 3 4 5LGEARN

0.02

.04

.06

Density

0 50 100 150EARNINGS

12

12

34

5LGEARN

5 10 15 20S

12

34

5LGEARN

0 5 10 15 20 25EXP

Appendix 2

scatter LGEARN S

scatter LGEARN EXP

13

12

34

5LGEARN

36 38 40 42 44 46AGE

12

34

5LGEARN

10 20 30 40 50 60HOURS

scatter LGEARN AGE

scatter LGEARN HOURS

As shown by the graphs above, there are two consistent outliers where LGEARN>5 and LGEARN <1.

Therefore, in order to have accurate results, both outliers will be omitted. The outliers are found in DATA (edit).

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As ETHWHITE has the highest frequency, ETHWHITE will be the base category.

(1 observation deleted). drop in 280

(1 observation deleted). drop in 63

. gen EXP3= EXP-EXPSQR

. gen EXPSQR= EXP*EXP

Total 538 100.00 1 269 50.00 100.00 0 269 50.00 50.00 FEMALE Freq. Percent Cum.

. tab FEMALE

Total 538 100.00 1 269 50.00 100.00 0 269 50.00 50.00 MALE Freq. Percent Cum.

. tab MALE

Total 538 100.00 1 441 81.97 100.00 0 97 18.03 18.03 ETHWHITE Freq. Percent Cum.

. tab ETHWHITE

Total 538 100.00 1 63 11.71 100.00 0 475 88.29 88.29 ETHBLACK Freq. Percent Cum.

. tab ETHBLACK

Total 538 100.00 1 34 6.32 100.00 0 504 93.68 93.68 ETHHISP Freq. Percent Cum.

. tab ETHHISP

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As CATPRI has the highest frequency, CATPRI will be the bas category

Total 538 100.00 1 381 70.82 100.00 0 157 29.18 29.18 CATPRI Freq. Percent Cum.

. tab CATPRI

Total 538 100.00 1 12 2.23 100.00 0 526 97.77 97.77 CATSE Freq. Percent Cum.

. tab CATSE

Total 538 100.00 1 144 26.77 100.00 0 394 73.23 73.23 CATGOV Freq. Percent Cum.

. tab CATGOV

Total 538 100.00 1 38 7.06 100.00 0 500 92.94 92.94 EDUCMAST Freq. Percent Cum.

. tab EDUCMAST

Total 538 100.00 1 2 0.37 100.00 0 536 99.63 99.63 EDUCPHD Freq. Percent Cum.

. tab EDUCPHD

Total 538 100.00 1 6 1.12 100.00 0 532 98.88 98.88 EDUCPROF Freq. Percent Cum.

. tab EDUCPROF

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As EDUCHSD has the highest frequency, EDUCHSD will be the base category.

POV78 has a smaller sample size than the other factors. This is a case that involves 27 missing data. After viewing these cases in Data>Data Editor> Data (edit), it was found that those who chose not to answer were not from one area of society, therefore it was still random and therefore there is no issue with using POV78 in the analysis.

Total 538 100.00 1 53 9.85 100.00 0 485 90.15 90.15 EDUCDO Freq. Percent Cum.

. tab EDUCDO

Total 538 100.00 1 260 48.33 100.00 0 278 51.67 51.67 EDUCHSD Freq. Percent Cum.

. tab EDUCHSD

Total 538 100.00 1 48 8.92 100.00 0 490 91.08 91.08 EDUCAA Freq. Percent Cum.

. tab EDUCAA

Total 538 100.00 1 115 21.38 100.00 0 423 78.62 78.62 EDUCBA Freq. Percent Cum.

. tab EDUCBA

Total 511 100.00 1 60 11.74 100.00 0 451 88.26 88.26 POV78 Freq. Percent Cum.

. tab POV78

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As REGS has the highest frequency, REGS will be the base category.

Total 538 100.00 1 196 36.43 100.00 0 342 63.57 63.57 REGS Freq. Percent Cum.

. tab REGS

Total 538 100.00 1 88 16.36 100.00 0 450 83.64 83.64 REGW Freq. Percent Cum.

. tab REGW

Total 538 100.00 1 167 31.04 100.00 0 371 68.96 68.96 REGNC Freq. Percent Cum.

. tab REGNC

Total 538 100.00 1 87 16.17 100.00 0 451 83.83 83.83 REGNE Freq. Percent Cum.

. tab REGNE

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Appendix 3

reg LGEARN S EXP EXPSQR HOURS FEMALE ETHBLACK ETHHISP EDUCPROF EDUCPHD EDUCMAST EDUCBA EDUCAA EDUCDO SINGLE DIVORCED CATGOV CATSE ASVABC WEIGHT02 WEIGHT85 POV78 REGNE REGNC REGW


_cons 1.063731 .3599352 2.96 0.003 .3565096 1.770952 REGW .0848559 .0631034 1.34 0.179 -.0391333 .2088451 REGNC -.0257336 .0516917 -0.50 0.619 -.1273005 .0758333 REGNE .0849833 .0620442 1.37 0.171 -.0369247 .2068912 POV78 .0744471 .0691743 1.08 0.282 -.0614705 .2103647 WEIGHT85 .0011613 .0011124 1.04 0.297 -.0010245 .0033471 WEIGHT02 -.0017327 .0008241 -2.10 0.036 -.003352 -.0001134 ASVABC .006937 .0030015 2.31 0.021 .0010395 .0128345 CATSE -.0457673 .1470793 -0.31 0.756 -.3347572 .2432226 CATGOV -.1074076 .0486381 -2.21 0.028 -.2029745 -.0118406 DIVORCED -.0345675 .0493907 -0.70 0.484 -.1316132 .0624781 SINGLE -.1182797 .061138 -1.93 0.054 -.238407 .0018477 EDUCDO -.0787207 .0832991 -0.95 0.345 -.2423915 .08495 EDUCAA -.0086768 .0804777 -0.11 0.914 -.166804 .1494504 EDUCBA .1694305 .0912289 1.86 0.064 -.0098212 .3486823 EDUCMAST .0933016 .1343766 0.69 0.488 -.1707292 .3573324 EDUCPHD .5242722 .3352128 1.56 0.118 -.1343731 1.182918 EDUCPROF .4589953 .2452932 1.87 0.062 -.0229709 .9409614 ETHHISP -.047859 .0882445 -0.54 0.588 -.2212469 .125529 ETHBLACK -.0513109 .0741067 -0.69 0.489 -.19692 .0942982 FEMALE -.2155014 .0502238 -4.29 0.000 -.314184 -.1168188 HOURS .0049252 .0024814 1.98 0.048 .0000497 .0098007 EXPSQR .0007949 .0008755 0.91 0.364 -.0009253 .0025152 EXP -.0010129 .026698 -0.04 0.970 -.0534705 .0514448 S .086391 .0200515 4.31 0.000 .0469926 .1257893 LGEARN Coef. Std. Err. t P>|t| [95% Conf. Interval]

Prob > F = 0.1721 F( 3, 486) = 1.67

( 3) REGW = 0 ( 2) REGNE = 0 ( 1) REGNC = 0

. test REGNC REGNE REGW

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reg LGEARN S EXP EXPSQR HOURS FEMALE ETHBLACK ETHHISP EDUCPROF EDUCPHD EDUCMAST EDUCBA EDUCAA EDUCDO SINGLE DIVORCED CATGOV CATSE ASVABC WEIGHT02 WEIGHT85 POV78


_cons 1.024884 .3563237 2.88 0.004 .3247696 1.724999 POV78 .0638884 .0690799 0.92 0.356 -.0718417 .1996184 WEIGHT85 .001105 .0011116 0.99 0.321 -.0010791 .0032891 WEIGHT02 -.0017381 .0008252 -2.11 0.036 -.0033595 -.0001166 ASVABC .0067314 .0030035 2.24 0.025 .0008301 .0126326 CATSE -.0263661 .1469422 -0.18 0.858 -.3150821 .26235 CATGOV -.1121518 .0484675 -2.31 0.021 -.207382 -.0169216 DIVORCED -.0371574 .0494406 -0.75 0.453 -.1342996 .0599848 SINGLE -.1137423 .0610589 -1.86 0.063 -.2337125 .0062278 EDUCDO -.0709275 .0832229 -0.85 0.394 -.2344461 .0925911 EDUCAA -.0135949 .0794473 -0.17 0.864 -.1696951 .1425053 EDUCBA .1600461 .0897189 1.78 0.075 -.016236 .3363281 EDUCMAST .0639536 .1323555 0.48 0.629 -.1961021 .3240092 EDUCPHD .5624287 .3348663 1.68 0.094 -.0955257 1.220383 EDUCPROF .4206625 .2425134 1.73 0.083 -.0558345 .8971595 ETHHISP -.0177439 .0862284 -0.21 0.837 -.1871678 .15168 ETHBLACK -.0656652 .0715144 -0.92 0.359 -.2061786 .0748482 FEMALE -.2273139 .0500262 -4.54 0.000 -.3256068 -.129021 HOURS .0044175 .0024756 1.78 0.075 -.0004467 .0092817 EXPSQR .0006359 .0008703 0.73 0.465 -.001074 .0023459 EXP .0040281 .0265812 0.15 0.880 -.0481993 .0562555 S .0918058 .0197851 4.64 0.000 .0529314 .1306802 LGEARN Coef. Std. Err. t P>|t| [95% Conf. Interval]

Prob > F = 0.1654 F( 3, 489) = 1.70

( 3) HOURS = 0 ( 2) POV78 = 0 ( 1) WEIGHT85 = 0

. test WEIGHT85 POV78 HOURS

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reg LGEARN S EXP EXPSQR FEMALE ETHBLACK ETHHISP EDUCPROF EDUCPHD EDUCMAST EDUCBA EDUCAA EDUCDO SINGLE DIVORCED CATGOV CATSE ASVABC WEIGHT02


_cons 1.151234 .3258879 3.53 0.000 .5110122 1.791455 WEIGHT02 -.0008966 .0005338 -1.68 0.094 -.0019452 .0001521 ASVABC .0058937 .0028304 2.08 0.038 .0003333 .0114541 CATSE -.0808688 .1326565 -0.61 0.542 -.3414784 .1797409 CATGOV -.1306717 .0464789 -2.81 0.005 -.2219817 -.0393617 DIVORCED -.039446 .048195 -0.82 0.413 -.1341272 .0552351 SINGLE -.1102905 .0587745 -1.88 0.061 -.2257557 .0051747 EDUCDO -.0502894 .0798614 -0.63 0.529 -.2071808 .106602 EDUCAA -.0230543 .0766031 -0.30 0.764 -.1735445 .1274359 EDUCBA .1395625 .0839804 1.66 0.097 -.0254207 .3045458 EDUCMAST .0482204 .1256945 0.38 0.701 -.1987121 .2951529 EDUCPHD .5438575 .3300802 1.65 0.100 -.1046 1.192315 EDUCPROF .4024053 .2211385 1.82 0.069 -.0320313 .8368418 ETHHISP -.0042951 .0832683 -0.05 0.959 -.1678794 .1592891 ETHBLACK -.0637572 .0688514 -0.93 0.355 -.1990188 .0715044 FEMALE -.2704827 .0445963 -6.07 0.000 -.3580941 -.1828713 EXPSQR .0003735 .0008409 0.44 0.657 -.0012785 .0020254 EXP .0134988 .0256681 0.53 0.599 -.0369273 .0639248 S .0970566 .0184817 5.25 0.000 .0607485 .1333647 LGEARN Coef. Std. Err. t P>|t| [95% Conf. Interval]

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reg LGEARN S EXPSQR FEMALE ETHBLACK ETHHISP EDUCPROF EDUCPHD EDUCMAST EDUCBA EDUCAA EDUCDO SINGLE DIVORCED CATGOV CATSE ASVABC WEIGHT02


_cons 1.241467 .2768696 4.48 0.000 .6975461 1.785387 WEIGHT02 -.0008829 .0005328 -1.66 0.098 -.0019296 .0001638 ASVABC .0057792 .00282 2.05 0.041 .0002392 .0113192 CATSE -.0908151 .13121 -0.69 0.489 -.3485818 .1669517 CATGOV -.1297609 .0464144 -2.80 0.005 -.2209436 -.0385782 DIVORCED -.0394665 .0481614 -0.82 0.413 -.1340814 .0551483 SINGLE -.1090723 .058688 -1.86 0.064 -.224367 .0062224 EDUCDO -.0494686 .0797906 -0.62 0.536 -.2062202 .1072829 EDUCAA -.0209302 .0764433 -0.27 0.784 -.1711058 .1292454 EDUCBA .1438787 .0835202 1.72 0.086 -.0201998 .3079572 EDUCMAST .048628 .1256046 0.39 0.699 -.1981268 .2953829 EDUCPHD .5469865 .3297969 1.66 0.098 -.1009116 1.194885 EDUCPROF .407615 .2207627 1.85 0.065 -.0260814 .8413115 ETHHISP -.0067396 .0830806 -0.08 0.935 -.1699544 .1564752 ETHBLACK -.065861 .0686872 -0.96 0.338 -.2007996 .0690776 FEMALE -.2706316 .0445643 -6.07 0.000 -.3581799 -.1830833 EXPSQR .0008066 .0001692 4.77 0.000 .0004742 .001139 S .0977067 .0184274 5.30 0.000 .0615053 .133908 LGEARN Coef. Std. Err. t P>|t| [95% Conf. Interval]

Prob > F = 0.1653 F( 6, 520) = 1.53

( 6) EDUCDO = 0 ( 5) EDUCAA = 0 ( 4) EDUCBA = 0 ( 3) EDUCMAST = 0 ( 2) EDUCPHD = 0 ( 1) EDUCPROF = 0

. test EDUCPROF EDUCPHD EDUCMAST EDUCBA EDUCAA EDUCDO

Prob > F = 0.6284 F( 2, 520) = 0.46

( 2) ETHHISP = 0 ( 1) ETHBLACK = 0

. test ETHBLACK ETHHISP

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reg LGEARN S EXPSQR FEMALE SINGLE DIVORCED CATGOV CATSE ASVABC WEIGHT02

reg LGEARN S EXPSQR FEMALE SINGLE DIVORCED CATGOV CATSE ASVABC


_cons .9270868 .1797296 5.16 0.000 .5740139 1.28016 WEIGHT02 -.0009792 .0005251 -1.87 0.063 -.0020107 .0000522 ASVABC .0074234 .0025094 2.96 0.003 .0024937 .012353 CATSE -.0968084 .1307174 -0.74 0.459 -.3535984 .1599816 CATGOV -.1442568 .0457267 -3.15 0.002 -.2340855 -.0544282 DIVORCED -.0434619 .0480051 -0.91 0.366 -.1377664 .0508425 SINGLE -.1133074 .0573432 -1.98 0.049 -.2259561 -.0006587 FEMALE -.281553 .0439069 -6.41 0.000 -.3678067 -.1952994 EXPSQR .0008209 .0001674 4.90 0.000 .000492 .0011498 S .1181213 .0102724 11.50 0.000 .0979415 .1383012 LGEARN Coef. Std. Err. t P>|t| [95% Conf. Interval]


_cons .7401779 .1495433 4.95 0.000 .4464063 1.03395 ASVABC .0073392 .0025149 2.92 0.004 .0023988 .0122796 CATSE -.1008548 .1310052 -0.77 0.442 -.358209 .1564994 CATGOV -.1402013 .0457818 -3.06 0.002 -.2301378 -.0502647 DIVORCED -.0384281 .0480413 -0.80 0.424 -.1328032 .0559471 SINGLE -.1217837 .0572965 -2.13 0.034 -.2343403 -.0092271 FEMALE -.2488299 .0403429 -6.17 0.000 -.3280818 -.169578 EXPSQR .0007907 .000167 4.73 0.000 .0004625 .0011188 S .1185608 .0102938 11.52 0.000 .0983391 .1387825 LGEARN Coef. Std. Err. t P>|t| [95% Conf. Interval]

23

As MALEMARR and FEMMARR have the same and highest frequency, MARRMALE is chosen as the base category as research conducted suggests that males receive a marriage premium (Lerman and Wilcox, 2014).

Total 538 100.00 1 56 10.41 100.00 0 482 89.59 89.59 MALEDIV Freq. Percent Cum.

. tab MALEDIV

Total 538 100.00 1 45 8.36 100.00 0 493 91.64 91.64 MALESING Freq. Percent Cum.

. tab MALESING

Total 538 100.00 1 168 31.23 100.00 0 370 68.77 68.77 MALMARR Freq. Percent Cum.

. tab MALMARR

Total 538 100.00 1 70 13.01 100.00 0 468 86.99 86.99 FEMDIV Freq. Percent Cum.

. tab FEMDIV

Total 538 100.00 1 31 5.76 100.00 0 507 94.24 94.24 FEMSING Freq. Percent Cum.

. tab FEMSING

Total 538 100.00 1 168 31.23 100.00 0 370 68.77 68.77 FEMMARR Freq. Percent Cum.

. tab FEMMARR

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reg LGEARN S EXPSQR CATGOV CATSE ASVABC FEMMARR FEMSING FEMDIV MALESING MALEDIV


_cons .7784659 .1498624 5.19 0.000 .4840648 1.072867 MALEDIV -.147902 .0694032 -2.13 0.034 -.284243 -.011561 MALESING -.195402 .0751161 -2.60 0.010 -.3429657 -.0478382 FEMDIV -.2634519 .0659753 -3.99 0.000 -.3930588 -.133845 FEMSING -.3516476 .0885173 -3.97 0.000 -.5255376 -.1777576 FEMMARR -.3212121 .0503865 -6.37 0.000 -.4201951 -.2222291 ASVABC .0075019 .002521 2.98 0.003 .0025495 .0124543 CATSE -.0988936 .1305476 -0.76 0.449 -.3553511 .157564 CATGOV -.1290022 .0458563 -2.81 0.005 -.2190857 -.0389187 EXPSQR .0007915 .0001668 4.74 0.000 .0004638 .0011193 S .1175536 .0102783 11.44 0.000 .0973622 .137745 LGEARN Coef. Std. Err. t P>|t| [95% Conf. Interval]

25

Appendix 4 Testing for MLR Assumptiona

Prob > F = 0.2547 F(3, 524) = 1.36 Ho: model has no omitted variablesRamsey RESET test using powers of the fitted values of LGEARN

. ovtest

Mean VIF 1.32 CATSE 1.02 0.982838 CATGOV 1.13 0.886198 FEMSING 1.16 0.858541 MALESING 1.18 0.844620 MALEDIV 1.23 0.813190 EXPSQR 1.24 0.804954 FEMDIV 1.35 0.741447 FEMMARR 1.49 0.669958 ASVABC 1.60 0.625203 S 1.79 0.557450 Variable VIF 1/VIF

. vif

26

Prob > chi2 = 0.0941 chi2(1) = 2.80

Variables: fitted values of LGEARN Ho: Constant varianceBreusch-Pagan / Cook-Weisberg test for heteroskedasticity

. hettest

Total 62.17 56 0.2659 Kurtosis 7.52 1 0.0061 Skewness 18.17 10 0.0521 Heteroskedasticity 36.48 45 0.8134 Source chi2 df p

Cameron & Trivedi's decomposition of IM-test

Prob > chi2 = 0.8134 chi2(45) = 36.48

against Ha: unrestricted heteroskedasticityWhite's test for Ho: homoskedasticity

. estat imtest, white

earnings functions

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