2
17
Economists generally agree that an individual’s earnings are positively related to the knowledge and skills obtained through education and experience. Numerous studies show that, on average, people with more years of education do earn higher wages. Although some economists believe that education increases a worker’s productivity and thus differences in wages to a large degree “reflect the ‘skill premium’ commanded by relatively higher-educated, better-trained workers” (Henderson 1), others argue that differences in workers individual characteristics such as talents, personal skills and motivations are the driving forces behind the wage inequality. Supporters of the screening (signaling) theory argue that education allows employers “to screen individuals by innate ability” (Hoff and Stiglitz 405). This claim is based on two arguments: 1) innate abilities of an individual are known to him/her but unobserved by the potential employers and; 2) education is less costly for individuals with higher abilities (in terms of time and efforts required for studying) and, consequently, people with high abilities tend to obtain more education to “signal” to the employers their innate talents. The correlation between unobserved capabilities and education and difficulties in measuring innate abilities of workers makes distinguishing between the two effects difficult and, as some econometricians believe, lead to an overstatement of returns on education– creates a so called “ability bias”.
The estimation of returns on education has important policy implications. If education raises person’s earnings regardless of his/her abilities, then policies that improve the quality of education and provide financial assistance for those willing and able to study should be implemented. If, however, different abilities are the underlying reasons for earnings differentials, as the screening theory claims, then such policies would not be as beneficial.
The goal of my paper is to estimate the effect that education has and on wages and to determine how it changes when controlled for ability.
For my regression analysis I used the data for 935 men surveyed in 1980. The data set contains information on monthly earnings, education, experience, some demographic characteristics, job location and average weekly hours.
After omitting observations with missing values, I had 663 valid observations for male workers, ages 28-38. Among them, about 7.5% completed less than 12 years of schooling (do not have a High School Diploma) with average monthly wages of $760.20, about 40.70% are High School graduates with average monthly wages of $889.04, about 21.27% have associate degrees or some certificates and earn average monthly wages of $1027.49, 18.25% are college graduates with average monthly salaries of $1104.13 about 12.22% have postgraduate degrees or certificates and earn average monthly wages of $1220.15. About 90% of men are married, 8.14% are black and about 28% live in rural areas. The average wage in the sample is $ 988.48 per month.
Since there are no data available for workers’ occupations and wages vary significantly among different professions, I used a variable natural logarithm of monthly wages (lwage in the data set) as the dependent variable and chose a log-linear functional form for my model. The log-linear functional form allows to interpret effects that variables have on wages in percentage terms and to capture some curvature in the relationships between wages and explanatory variables.
The key explanatory variables in my base model are years of schooling and years of experience (educ and exper). The average years of schooling are approximately 13.68 years. The average years of experience in the sample are 11.40 years. There are, however, other factors (besides education and experience) that affect wages. I believe that skills related to a current occupation will have a positive effect on earnings, so the variable tenure (measured in years) is also included in the model. Some workers might suffer from racial discrimination in the labor market. To control for such possibility, I include a racial dummy variable, black. In part due to increased motivation to seek higher paid jobs and relief from the household responsibilities, married workers often have higher wages. Thus a dummy variable married is included in the model. Because of lower population density, cost of living and prevalence of low-skilled jobs, workers in rural and southern areas of the country tend to earn less. To account for this effect, I include the dummy variables urban and south. In addition, a family background affects individual’s professional and academic aspirations as well as personal characteristics, which might be valued by employers. Therefore I include variables birth order (brthord ), number of siblings (sibs) and parental education (Peduc). The firstborn children often baby sit younger siblings and tend to develop a sense of responsibility and independence in decision making. Children in large families, learn to carry on specific responsibilities as well as work as team members. These personal characteristics might be valued in the labor market. Since I am not interested whether a father’s or a mother’s education has a greater effect on earnings, but believe that the presence of a parent with a higher level of education is likely to encourage a child to obtain more education, I derive the variable parental education by choosing the maximum years of schooling of the two parents (=MAX(Q2:R2)).
The last two variables are IQ and KWW. While the IQ score is widely used as a measure of general intelligence, the KWW score , Knowledge of the World of Work, (less known) is used as a measure of an individual’s knowledge of various occupations and related duties (Regan, Oxaca and Burghardt 42). Although it is questionable whether IQ and KWW scores reflect abilities that are rewarded in the labor market, the descriptive statistics show that sampled workers with IQ scores above 100 (average),on average, earn higher wages and attain more education than workers with average and below average IQ scores ($1081.27 and 14.63 years vs. $866.91 and 12.42 years). In order to detect a possible bias, I do not include these two variables in my first regression, but add them later as proxy variables for ability. Definitions and descriptive statistics of the variables are presented in Table 1. Variables do not exhibit multicollinearity (coefficients of correlation can be found in Table 2)
I do not include the variables hours (average weekly hours) and age (worker’s age) in my regression analysis. . Although it might be argued that some individuals work longer hours and thus earn more, this relationship between hours worked and wages depend on his/her pay basis. While hourly-paid workers may increase their wages by working more hours, salaried workers often may work more or less hours with very little or no effect on their earnings. Unfortunately, there is no information on workers pay bases or/and occupations (from which I could probably assume whether a worker paid hourly or per week). Thus to avoid a misrepresentation, I do not include the variable hours in my model. Though a worker’s age might increase the likelihood of an unlawful layoff (for older workers), it is unlikely to have a direct effect on his/her wages. Age might be used as a proxy for experience. In this regression analysis, however, such a proxy is unnecessary, because the variable years of experience is available in the data set. Therefore, the variable age will not provide any additional information.
My base regression model for estimating the rate of return on education takes the following form:
Ln(Wage)i=β0+β1Educi+β2Experi+β3Tenurei+β4Marriedi+β5Blacki+β6Southi+β7Urbani+β8Sibsi+β9Brthordi+β10Peduci+εi (1)
Table 3 shows the results of estimating this equation. All the variables, except birth order and the number of siblings, are significant at the 5 percent level. Although it is tempting to conclude that these variables have no effect on earnings, I refrain from such conclusion until all the variables are included in the regression. All estimated coefficients take the expected signs.
Holding other variables constant, an estimated rate of return to each additional year of education is 6.12%.
The results of the regression show that the model explains 24.89% of variance in log of monthly wages in the sample (Adjusted R2=0.24892).
My next step is to add the first proxy for ability, IQ, to the model:
Ln(Wage)i=β0+β1Educi+β2Experi+β3Tenurei+β4Marriedi+β5Blacki+β6Southi+β7Urbani+β8Sibsi+β9Brthordi+β10Peduci+ β11IQi+εi (2)
The results of this regression are presented in Table 4. The estimate for IQ is positive and is statistically significant (p-value 0.00316197). At this stage, ability appears to affect wages. The increased value of the adjusted R2 (25.77%) and the decreased value of the sum of squared residuals (82.10) indicate that the addition of the variable IQ improved the fit of the model. Although most coefficients did not change significantly, the rate of return to education dropped from 6.12% to 5.05%, confirming that the return to education is influenced by the worker’s IQ. Another, and rather surprising result, is a large increase in the coefficient for race. The estimate for the dummy variable black increased from -15.64% to -11.74%.
Moreover, the variable IQ affected statistical significance of other variables. The variables south and parental education became insignificant at the 5% level (the t-statistics are -1.69 and 1.94 respectively).
To see which of the variables representing ability has a greater impact on returns on education, I replace the variable IQ with KWW:
Ln(Wage)i=β0+β1Educi+β2Experi+β3Tenurei+β4Marriedi+β5Blacki+β6Southi+β7Urbani+β8Sibsi+β9Brthordi+β10Peduci+ β12KWWi+εi (3)
The results of this regression are reported in Table 5. The impact of the variable KWW on the regression as a whole seems to be almost identical to the impact of the variable IQ. The values of the adjusted R2 and the sum of squared residuals hardly changed (25.54% and 82.37 respectively). The variable KWW seems to have a somewhat smaller impact on the rate of return on education—the coefficient is slightly higher with KWW (5.63%) in the regression than with IQ (5.05%). But the difference is minute. Nevertheless, unlike the variable IQ, the variable KWW affected returns on experience and tenure. The coefficients slightly changed, perhaps, due to the nature of the test: workers with more years of experience in the labor market would be expected to score higher on the test.
At last, I ran the regression with both proxies for ability:
Ln(Wage)i=β0+β1Educi+β2Experi+β3Tenurei+β4Marriedi+β5Blacki+β6Southi+β7Urbani+β8Sibsi+β9Brthordi+β10Peduci+ β11IQi+ β12KWWi+εi (4)
The results of this regression can be found in Table 6. The fit of the regression improved—the adjusted R2 increased to 26.15% and the sum of squared residuals decreased to 81.56. Both proxies for ability are statistically significant at the 5% level. Although the return on years of schooling decreased even more and is now 4.53%, indicating that the previously estimated returns to education were positively biased, the effect of education on earnings is significant. Before proceeding further, I conduct the global F-test to check the overall adequacy of the model for predicting wages.
H0: β1=β2=β3=β4=β5=β6=β7=β8=β9=β10=β11=β12=0
HA: At least one of the coefficients is not equal to 0.
r=12 d.f=650 α=0.05
Test Statistics:
F=20.54
Rejection region:
F> 1.7671
Since the calculated F value is greater than the critical F-value, I reject the null hypothesis at the 5% level of significance. The test indicates that the model is adequate for explaining variability of wages.
Now that the usefulness of the model has been verified, I perform the t-test to determine whether education has a positive effect on wages:
H0: β1=0
HA: β1>0
d.f=650 α=0.05 t0.05= 1.647202
Test statistics:
t=
0.045330337-0
=5.183323294
0.00874542
Rejection Region: t≥1.647202
Since the calculated t value falls in the rejection region, I reject the null hypothesis at the 5 percent level of significance. The test confirms that education has a positive statistically significant effect on wages.
According to the results of this regression, the estimated increase in wages with additional year of experience is 1.43%. And an additional year with current employer raises worker’s earnings by approximately 0.8%. The regression results also confirm existence of a “marriage premium”–married workers earn approximately 19.76% more. Male workers in urban areas earn 19.26% more than male workers in rural areas with the same characteristics, i.e., education, experience, tenure, marital status, race and family characteristics.
To determine whether worker’s ability affects his/her wages, I perform an F-test for joint significance of variables IQ and KWW:
H0: β11=β12=0
HA: At least one of the coefficients is not equal to 0.
R=2 d.f=650 α=0.01
Test Statistics:
F=
(83.207236-81.558914)/2
=6.57
81.558914/650
Rejection region:
F> 4.638
Since the calculated F value is greater than the critical F-value, I reject the null hypothesis at the 1% level of significance. The test indicates that the variables IQ and KWW improve the usefulness of the model in predicting wages. The test seems to support the argument of the screening theory that workers’ abilities affect their earnings: workers with IQ scores 110 (high average), for instance, on average earn 3.07% more than workers with average IQ scores.
The presence of the variables IQ and KWW affected not only returns on education, experience and tenure but other variables as well. The estimated difference in wages due to racial discrimination is now10.41% (5.24% below estimated in the initial regression). In addition, parental education appears to have statistically insignificant effect on wages when controlled for ability.
In order to decide whether a worker’s family background has any impact on his/her earnings, I use the F-test. The results of estimating restricted model are shown in Table 7.
Ln(Wage)i=β0+β1Educi+β2Experi+β3Tenurei+β4Marriedi+β5Blacki+β6Southi+β7Urbanii+ β11IQi+ β12KWWi+εi (5)
H0: β9=β10= β11 =0
HA: At least one of the coefficients is not equal to 0.
r=3 d.f=650 α=0.05
Test Statistics:
F=
(82.365031-81.558914)/3
=2.1415
81.558914/650
Rejection region:
F> 2.619
Since the computed value of F does not fall in the rejection region, I fail to reject the null hypothesis at 5% level of significance. The test result is somewhat unexpected and contradicts my hypothesis that family background of an individual affects his/her wages—family characteristics seem to have no or very little effect on wages. Though the sum of squared residuals slightly increased and the value of adjusted R2 decreased to 25.77%, exclusion of variables parental education, birth order and number of siblings had practically no effect on estimates for the remaining parameters. Thus these variables, perhaps, should be dropped from the model.
Conclusion
An individual’s wage is determined by numerous factors. Among them, the most fundamental are knowledge, skills, ability and luck. Some of these factors are easier to measure than other. Education is traditionally viewed as the main source of knowledge and skills which are valued in the labor market. The estimation of returns on education, however, is not an easy task. Although through my regression analysis I found evidence of an upward ability bias, the marginal return on education is still quite high and statistically significant. After controlling for ability, the estimated return on an additional year of education for male workers with the same abilities, experience and other characteristics is 4.53%.
One of the main issues of concern for policymakers is the economic well-being of the population, which is measured with poverty rates and average wages. As my regression analysis shows, education increases workers’ wages regardless of their abilities. Thus, policies directed on improvement of education and providing financial assistance in obtaining more education to those in need will benefit society as a whole. For an individual, on the other hand, education still remains the first step on the way to success in the labor market.
Table 1: Descriptive Statistics
Variables
Description
Mean
Median
Standard Deviation
Minimum
Maximum
wage
Monthly earnings in dollars
988.48
937
406.5115119
115
3078
lwage
Natural log of monthly earnings
6.81
6.842683
0.412206453
4.744932
8.032035
educ
Years of education
13.68
13
2.231405597
9
18
exper
Years of experience
11.40
11
4.258397196
1
22
tenure
Years with current employer
7.22
7
5.055690459
0
22
married
Takes 1 if married
0.90
1
0.299621776
0
1
black
Takes 1 if black
0.08
0
0.273728342
0
1
south
Takes 1 if live in south
0.32
0
0.467890576
0
1
urban
Takes 1 if live in SMSA
0.72
1
0.449603727
0
1
sibs
Number of siblings
2.85
2
2.240895542
0
14
brthord
Birth order
2.18
2
1.48761173
1
10
Peduc
Maximum years of education completed by one of the parents
11.56
12
2.727012032
2
18
IQ
IQ score
102.48
104
14.68611745
54
145
KWW
Knowledge of the World Work score
36.19
37
7.529187963
13
56
Table 2: Correlations
Educ
exper
tenure
married
black
south
urban
sibs
brthord
Peduc
IQ
KWW
educ
1
exper
-0.4508
1
tenure
-0.0301
0.2901
1
married
-0.0567
0.0985
0.0701
1
black
-0.1156
0.0215
-0.0543
-0.0483
1
south
-0.0573
-0.0340
-0.0884
0.0033
0.1836
1
urban
0.1002
-0.0380
-0.0310
-0.0394
0.0755
-0.1146
1
sibs
-0.1972
0.0131
-0.0493
0.0019
0.2692
0.0474
-0.0444
1
brthord
-0.1762
0.0437
-0.0168
-0.0144
0.1276
0.1322
-0.0246
0.5783
1
Peduc
0.4217
-0.2170
0.0088
-0.0384
-0.1952
-0.1334
0.0898
-0.2228
-0.2575
1
IQ
0.5435
-0.2316
0.0185
-0.0124
-0.3108
-0.1627
0.0555
-0.2473
-0.2033
0.3504
1
KWW
0.4063
0.0216
0.1700
0.0575
-0.2371
-0.0792
0.1103
-0.2493
-0.1516
0.2808
0.4103
1
Table 3:Results of the regression #1
Regression Statistics
Multiple R
0.510166137
R Square
0.260269487
Adjusted R Square
0.248923927
Standard Error
0.35723726
Observations
663
ANOVA
df
SS
MS
F
Significance F
Regression
10
29.27593798
2.927593798
22.94020625
4.79527E-37
Residual
652
83.20723603
0.12761846
Total
662
112.483174
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
5.305937968
0.143916722
36.868113
1.2407E-161
5.023341919
5.588534017
educ
0.061161295
0.007640862
8.004501913
5.5094E-15
0.046157636
0.076164955
exper
0.01632547
0.003870203
4.218245784
2.81075E-05
0.008725906
0.023925033
tenure
0.008790444
0.002906445
3.024466057
0.002588633
0.003083325
0.014497563
married
0.204897947
0.046738891
4.383885495
1.35876E-05
0.113121079
0.296674815
black
-0.156467081
0.054655272
-2.862799413
0.004333985
-0.26378862
-0.049145543
south
-0.061210506
0.030981192
-1.975731136
0.048606446
-0.122045427
-0.000375584
urban
0.19929221
0.031555264
6.315656536
4.97902E-10
0.137330036
0.261254384
sibs
0.00585853
0.007937403
0.738091561
0.460724382
-0.009727419
0.021444479
brthord
-0.018111359
0.011720817
-1.545230061
0.122775836
-0.041126451
0.004903733
Peduc
0.0129322
0.005837182
2.215486819
0.027071388
0.001470262
0.024394139
Table 4: Results of the regression#2
Regression Statistics
Multiple R
0.519721068
R Square
0.270109989
Adjusted R Square
0.257776978
Standard Error
0.355125614
Observations
663
ANOVA
df
SS
MS
F
Significance F
Regression
11
30.38282887
2.762075352
21.9013824
3.56955E-38
Residual
651
82.10034513
0.126114201
Total
662
112.483174
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
5.097930215
0.159366123
31.98879478
1.1636E-135
4.78499687
5.410863559
educ
0.050451094
0.008412132
5.997420456
3.32466E-09
0.033932925
0.066969264
exper
0.016399211
0.003847407
4.262406123
2.32151E-05
0.008844394
0.023954029
tenure
0.008673671
0.002889534
3.001754685
0.002787056
0.002999746
0.014347596
married
0.203702378
0.046464368
4.384055738
1.35804E-05
0.112464355
0.294940401
black
-0.117446161
0.055905904
-2.100782779
0.036044009
-0.227223704
-0.007668617
south
-0.052395498
0.030941458
-1.693375191
0.090862462
-0.113152538
0.008361543
urban
0.198682525
0.031369414
6.333638315
4.46579E-10
0.137085144
0.260279906
sibs
0.007296729
0.007905404
0.923005192
0.35634646
-0.008226423
0.02281988
brthord
-0.017156326
0.011655993
-1.471888773
0.141534159
-0.040044182
0.005731531
Peduc
0.011354992
0.005827049
1.948669286
0.051764164
-8.7076E-05
0.022797059
IQ
0.003533193
0.001192606
2.962582209
0.003161971
0.001191377
0.005875008
Table 5:Results of the regression#3
Regression Statistics
Multiple R
0.517445512
R Square
0.267749858
Adjusted R Square
0.255376968
Standard Error
0.355699307
Observations
663
ANOVA
df
SS
MS
F
Significance F
Regression
11
30.11735391
2.737941265
21.64004148
9.81808E-38
Residual
651
82.36582009
0.126521997
Total
662
112.483174
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
5.264671914
0.14418783
36.51259539
1.0958E-159
4.981542859
5.54780097
educ
0.053164506
0.008215655
6.471121685
1.91383E-10
0.03703214
0.069296871
exper
0.014316784
0.003931474
3.641581213
0.000292505
0.00659689
0.022036677
tenure
0.007870067
0.002915857
2.699058502
0.007134062
0.002144454
0.013595681
married
0.197249146
0.046632095
4.229901052
2.67325E-05
0.105681773
0.28881652
black
-0.133834257
0.055123124
-2.427914968
0.015455911
-0.242074724
-0.025593791
south
-0.062306665
0.030850742
-2.019616374
0.043832421
-0.122885574
-0.001727755
urban
0.191686486
0.031557534
6.074190925
2.11939E-09
0.129719712
0.253653261
sibs
0.008039811
0.007948365
1.01150493
0.312150619
-0.007567701
0.023647322
brthord
-0.018872788
0.011674092
-1.616638666
0.106440745
-0.041796183
0.004050607
Peduc
0.011455328
0.005840199
1.961461823
0.050250964
-1.25616E-05
0.022923218
KWW
0.005625086
0.002181257
2.578827824
0.010132009
0.001341942
0.00990823
Table 6: Results of the regression#4
Regression Statistics
Multiple R
0.524331415
R Square
0.274923432
Adjusted R Square
0.261537403
Standard Error
0.354224861
Observations
663
ANOVA
df
SS
MS
F
Significance F
Regression
12
30.92426029
2.57702169
20.53808741
2.18154E-38
Residual
650
81.55891372
0.125475252
Total
662
112.483174
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
5.091557447
0.158991503
32.02408533
8.8686E-136
4.779358266
5.403756627
educ
0.045330337
0.00874542
5.183323294
2.91344E-07
0.02815764
0.062503033
exper
0.014750082
0.003918904
3.763827872
0.000182473
0.007054835
0.022445328
tenure
0.007937809
0.002903893
2.733506245
0.006436931
0.002235662
0.013639955
married
0.197616539
0.046439021
4.255398466
2.39389E-05
0.106427865
0.288805213
black
-0.104096466
0.056133197
-1.854454616
0.06412684
-0.214320836
0.006127903
south
-0.054447415
0.030878781
-1.763263119
0.078325918
-0.115081663
0.006186832
urban
0.192554928
0.031428587
6.126744617
1.55416E-09
0.130841069
0.254268788
sibs
0.008888236
0.007922485
1.121899962
0.262319243
-0.006668529
0.024445001
brthord
-0.017903168
0.011631986
-1.53913249
0.124258598
-0.04074399
0.004937654
Peduc
0.010356658
0.005832105
1.775801035
0.076233483
-0.00109539
0.021808707
IQ
0.003069347
0.001210357
2.535902398
0.011448859
0.000692664
0.00544603
KWW
0.004591081
0.002210153
2.077268743
0.038168875
0.000251177
0.008930986
Table 7: Results of the regression#5
Regression Statistics
Multiple R
0.517452292
R Square
0.267756875
Adjusted R Square
0.257664703
Standard Error
0.355152472
Observations
663
ANOVA
df
SS
MS
F
Significance F
Regression
9
30.11814313
3.346460348
26.53114536
3.65762E-39
Residual
653
82.36503088
0.126133279
Total
662
112.483174
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
5.121754614
0.14682191
34.88413005
2.5557E-151
4.833454581
5.410054647
educ
0.04918157
0.008539515
5.759293
1.30099E-08
0.032413347
0.065949792
exper
0.014162514
0.003914038
3.618388941
0.000319357
0.006476893
0.021848134
tenure
0.007918069
0.002910755
2.720280295
0.006696273
0.0022025
0.013633638
married
0.19780494
0.046512412
4.252734475
2.42027E-05
0.106472999
0.289136881
black
-0.104401155
0.054735828
-1.907364123
0.0569119
-0.211880626
0.003078315
south
-0.065509978
0.030604427
-2.140539248
0.032680947
-0.125604942
-0.005415014
urban
0.193411776
0.031438729
6.152022738
1.33386E-09
0.131678574
0.255144978
KWW
0.004809015
0.002195837
2.190059909
0.028872862
0.000497261
0.00912077
IQ
0.003312779
0.001205005
2.749183135
0.006139632
0.000946627
0.005678931
Bibliography
1. Henderson, Nell. “Greenspan Says Worker’s Lack of Skills Lowers Wages.” Washington Post 22 July 2004
2. Hoff, Karla and Joseph E. Stiglitz. 2000. “Modern Economic Theory and Development”,
3. Regan, Tracy L., Ronald L. Oxaca and Galen Burghardt. 2003. “A Human Capital Model of the Effects of Abilities and Family Background on Optimal Schooling Levels”, p.42