Colleen P Cahill Writing Sample Econometrics II Select Pages

Running head: CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 1

A Study of How the Return to Education and the Gender Gap Have Changed from the Year 2000

for Each of the Periods 2001-2010

Colleen Cahill

University of South Florida

Econometrics II / ECO 6425

November 14, 2011

Dr. Beom S. Lee

CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 2

Abstract

This paper takes a simplistic view of the issues of the wage gap and the return to education. It

does not attempt to explain why the persistence of the wage gap remains or why more education

and experience is viewed as positively correlated with higher income. The first goal of the paper

is to utilize a basic wage equation to see if a change in the wage gap occurs, what that change is,

and if it is statistically significant for the period 2000 to each of the years 2001 through 2010.

The second goal is to utilize that same basic wage equation to see if the return to education

contributes to higher income in a statistically significant way for these same periods. The process

is then repeated with a wage equation with more controls added to it per the literature to see if

the results vary at all from the original regressions.


A Study of How the Return to Education and the Gender Gap Have Changed from the

Year 2000 for Each of the Periods 2001-2010

In 1963, the Equal Pay Act, which aimed at abolishing wage disparity based on gender,

was passed, amending the Fair Labor Standards Act. Although this wage disparity, often referred

to as the gender gap, has declined over the past half century in the United States from just over

60 percent in 1960 (National Committee on Pay Equity, 2011), it still exists and women’s

earnings as a percentage of men’s have recently been reported to be 77 percent as of 2010

(DeNavas-Walt, Proctor, & Smith, 2011). This persistent disparity has been the subject of much

research, especially since women have surpassed their male peers in educational expectations

and degree attainment since the 1990s (Peter, Horn, & Carroll, 2005). That the wage gap still

exists is a somewhat puzzling dilemma since there is a general expectation that more education

and experience equals higher income.

This paper takes a simplistic view of the issues of the wage gap and the return to

education. In no way does it attempt to explain why the persistence of the wage gap remains or

why more education and experience is viewed as positively correlated with higher income.

Some of the reasons for these observations will be discussed in a review of the literature; but this

paper takes these observations as given and instead has several straight forward goals. The first

goal is to utilize a basic wage equation to see if a change in the wage gap occurs, what that

change is, and if it is statistically significant. The second goal is to utilize that same basic wage

equation to see if the return to education contributes to higher income in a statistically significant

way. The process is repeated with a wage equation with more controls added to it per the

literature. The period of study is each year of the most recent decade, 2001 through 2010, as

compared to the year 2000. I have chosen this period primarily because it occurs after women


surpassed men in educational attainment in the 1990’s. I have also chosen to compare a ten year

period in order to ascertain differences between individual periods, especially those containing

recessionary years. In addition, the ranking of U.S. education compared to other OECD

countries has fallen during this time (Liepmann, 2011). It is of interest to see if the return to

education has any corresponding decline as well.

In order to conduct the study, data from the Current Population Survey (CPS), available

from the U.S. Census Bureau (U.S. Census Bureau, 2000-2010), is utilized. The basic wage

equation used is modified from one found in Wooldridge (2009, p. 447). Admittedly, the wage

equation is quite simplistic, as will be seen from a review of the literature. But for the goals of

this paper, a simplistic model seems appropriate.

Literature Survey and Discussion of the Data

There are a proliferation of studies involving the gender wage gap and the return to

education in the literature. The studies I surveyed which focus on the wage gap, are primarily

concerned with the issue of what factors contribute to the disparity. There are several broad

categories that these factors fall into. One category involves personal choices made by women in

regard to participation in the labor force (Korenman & Neumark, 1992; Welch, 2000). Another

focuses on male-female differences in skills, and yet a further centers on differences in the

treatment of equally qualified men and women (Blau & Kahn, 1994). The studies I surveyed on

the return to education are clearly intertwined with those studies involving wage disparity.

Although several of the papers address the return to education of the population in general, a

number specifically address a male-female disparity of this return. This is also the case in a few

of the papers which are primarily concerned with the wage gap, as the disparity in the return to

education is seen as a contributing factor. In addition, several of the studies present potential


problems with using the basic wage equation, including endogeneity of variables and bias. All of

these issues are briefly addressed below.

Lower participation rates and career disruptions of women as compared to men are seen

to be contributing factors to the wage disparity (Bowlus, 1997; Wood, Corcoran, & Courant,

1993). In general, having children is found to lower income for women, especially when a

woman has more than two children (Fleisher & Rhodes, 1979; Korenman & Neumark, 1992).

This is because the associated “human capital depreciation” and decline of experience and tenure

relative to men has a negative impact on women’s wages (Mincer & Ofek, 1982). Exasperating

this negative impact of career disruptions, may be an observed increase in the return to

experience. Since women, on average, are reported to have less experience relative to men, as

the return to experience increases, it may contribute to a widening of the pay gap (Blau & Kahn,

1997).

Several factors which fall into what may be termed “sexist family decision rules” (Frank,

1978) also contribute to lower wages for females. A married woman’s housework time has been

found to be, on average, three times that of a married man’s (Hersh & Stratton, 1997). This

lowers a woman’s working time relative to a man’s and in turn has a negative impact on her

wages. Another factor is that of wives who follow their husbands to a particular geographic

location (Frank, 1978). A negative impact on the wife’s income is often observed because the

geographic location is chosen as a match for the husband’s skills and job needs, not the wife’s.

The wife often settles for an imperfect match, and thus a lower wage. A somewhat ironic finding

about the return to education between husbands and wives is that it has been found that a

woman’s education may be positively correlated with her husband’s income (Lefgren &


below a comparable man’s wage in 2010. Recall, the difference in 2000 was estimated to be

34%, so a narrowing of approximately 5 percentage points is estimated to have occurred.

Estimation Results – Equations (11) through (20)

The return to another year of education in 2000 is estimated to be approximately 6%.

The change in the return to education is positive for all periods except that from 2000 to 2007

where it is slightly lower. Using the same null and alternative hypothesis as previously, there is

no evidence that the change in the return to education is statistically different from 0 in any year

except 2007. In 2007 the return falls by approximately 0.7 percentage points, at a 7%

significance level. This indicates that the return to education is essentially flat throughout the

periods of study. The only statistically significant change is in 2007, but even this is a change of

less than 1 percentage point.

Turning to the findings on male-female wage disparity, in 2000, other things being equal,

a woman is estimated to have earned approximately 25% less than a man in ln(wage). By

computing the exact percentage difference in predicted wages per the formula J{−.252{ −

1 ≈ −.22, we estimate that a woman’s wage is, on average 22% below a comparable man’s

wage. The estimated coefficients indicate that the gender gap appears to fall in all periods.

Testing that the change in the gender gap is statistically significant, we again test the null

hypothesis H" : $ = 0 against the alternative hypothesis H# : $ > 0. There is no evidence that

the change in the gender gap is statistically different from 0 in the periods 2000 to 2001 or 2002

at significance levels of 10% or below. In the period from 2000 to 2006, the gender gap is shown

to have fallen by about 3 percentage points and it is significant at an 8% significance level

against the positive one-sided alternative. In the period from 2000 to 2008, the gender gap fell

approximately 4 percentage points and is significant at a 2% significance level. The fall in the


gender gap is most significant in the periods 2000 to 2003, 2004, 2005, 2007, 2009 and 2010

where the fall was approximately 5, 4, 5, 5, 5, and 7 percentage points respectively. All are

significant at less than a 1% significance level. This indicates that the gender gap has been

narrowing in recent years, even in the recessionary period of 2008 as opposed to the previous

results. Unlike in the larger, less controlled samples, here the gender gap is seen to initially not

change, but then narrow throughout the decade. The wage gap has seen a larger change than the

return to education in the revised samples just as it did in the initial samples. By computing the

exact percentage difference in predicted wages per the formula J{−.252 + .069{ − 1 ≈ −.17,

we estimate that a woman’s wage is, on average 17% below a comparable man’s wage in 2010, a

narrower gap than in the initial data, but one must recall the initial gap was estimated to be

smaller in the revised samples. The narrowing is estimated to be approximately 5 percentage

points, which is the same as in the larger sample.

Monte Carlo Simulation

To test the veracity of the OLS estimators, a Monte Carlo simulation was conducted on

both sets of equations. The process for this study involved producing ten random error terms

with a normal distribution of mean 0 and variance the square of the mean standard error of the

original regression. This was done for each of the years of study. Using the coefficients

previously estimated, the data used for the original regressions and the new random errors

generated, ten new dependent variables were generated for each year. The coefficients were then

re-estimated using the new dependent variables generated. The mean of the estimated

coefficients from the regressions involved in the Monte Carlo simulation are indicated in italics

below the original estimated coefficients in Table 5 in Appendix A for the initial equations and


in Table 8 in Appendix A for the revised equations. The full results of the regressions may be

obtained by request, but have not been included in this paper due to the quantity of results.

All of the mean estimated coefficients from the Monte Carlo simulations for both sets of

equations are within the 95% confidence intervals of the estimated coefficients from the original

regressions. In fact, many of the mean estimated coefficients are the same as those from the

original regressions. The standard errors of the simulated coefficients are all similar to those of

the original estimated coefficients. There is some variation as to the significance of the

simulated coefficients from the original coefficients; however a larger number of simulations

may provide a different result. Based on the values of the estimated coefficients alone, the results

of the simulations indicate the estimated coefficients are reliable.

Conclusion

The return to education was expected to be positive for the year 2000 per the literature,

and it was found to be statistically significantly so at less than a 1% significance level for all

equations. I expressed doubt as to whether the change to the return to education would be

positive and significant for all years observed. This played out in the data, but the surprise in the

initial estimations is that the largest positive and most significant changes occurred in the most

recent years. This indicates that the return to education continued to rise even as the educational

ranking of the U.S. compared to other OECD countries has been declining. In the revised

estimations, the return to education is essentially unchanged with the exception of a slight

reduction in the year 2007. As pointed out previously, note that the increase in the return to

another year of education is small, at less than 1 percentage point for any period, for all of the

estimations.


I expected the ln{ I { differential between men and women in 2000 to be significant

and this was true in the regressions. I also expected the differential to persist in the periods of

study but narrow as the 2010 period approached. This did occur. In the original estimations, the

change was insignificant in general as expected early in the study and more significant in the

later periods. One unexpected result was the significant narrowing which occurred in 2001,

which is one of the recessionary periods. As expected, the period from 2000 to 2008, another of

the recessionary periods, did not narrow. In the revised estimations, the wage differential initially

did not narrow, but then did as the decade proceeded. The recessionary periods did not appear to

affect the revised estimations. As noted, unlike the return to education, the wage gap has seen a

larger change in the period studied. In the larger samples, from an estimated difference of a

woman’s wage being 34% below a comparable man’s wage in 2000, the percentage narrowed to,

on average, 29% in 2010. The smaller samples saw the same 5% narrowing, but started from a

22% difference, which is slightly lower than that seen in the actual population. The gap was

seen to have narrowed by 4% by 2010 in the population, so the estimated change is slightly

higher.

Estimating the equations with the basic wage equation and then again with more controls

saw some changes in the results. These changes however were not statistically significant.

Although the initial review of the estimations appears to produce different results, when the

significance levels are taken into account, the results are generally similar. This indicates that

for the basic purposes of this paper, a simplistic wage equation is most likely sufficient.

As stated in the introduction, this paper takes a simplistic view of the issues of the wage

gap and the return to education. It does not attempt to explain why the persistence of the wage

gap remains or why more education and experience is viewed as positively correlated with


higher income. As stated, the first goal of the paper was to utilize a basic wage equation to see if

a change in the wage gap occurs, what that change is, and if it is statistically significant. The

second goal was to utilize that same basic wage equation to see if the return to education

contributes to higher income in a statistically significant way. The process was then repeated

with a wage equation with more controls added to it per the literature. Because the premise of the

paper is not empirically demanding, I believe that the basic equation, although simplistic, is

adequate for the proposed investigation.


Table 1 (cont.): Summary Data (Recessionary Periods are in Gray)


Table 2: Variable Descriptions

Table 3: Recoding of the Education Variable


Table 4: OLS Coefficient Estimation Results: 2001-2010

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Year / 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Coefficient
(variable)
" -0.033 0.026 0.045 0.092 0.035 0.148 0.239 -0.154 0.116 0.086
( II) (0.045) (0.041) (0.044) (0.045) (0.045) (0.045) (0.044) (0.046) (0.046) (0.047)
# 0.117 0.118 0.116 0.116 0.117 0.117 0.117 0.116 0.117 0.117
( I) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002)
# 0.005 0.001 0.002 -0.0002 0.005 -0.0003 -0.005 0.008 0.006 0.007
( II ∙ I) (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) (0.003)
$ 0.063 0.066 0.067 0.068 0.067 0.068 0.065 0.068 0.065 0.064
( J J) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
% -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001
( J J $) (0.00002) (0.00002) (0.00003) (0.00003) (0.00003) (0.00003) (0.00003) (0.00003) (0.00003) (0.00003)

& -0.415 -0.406 -0.415 -0.415 -0.415 -0.415 -0.415 -0.415 -0.415 -0.416
( I ) (0.011) (0.012) (0.011) (0.011) (0.011) (0.011) (0.011) (0.011) (0.011) (0.011)
$ 0.026 0.014 0.032 0.011 0.021 0.022 0.049 -0.020 0.046 0.071
( II ∙ I ) (0.016) (0.016) (0.016) (0.016) (0.016) (0.016) (0.016) (0.017) (0.017) (0.017)
" 4.151 4.091 4.119 4.106 4.101 4.096 4.123 4.122 4.121 4.115
(Constant) (.033) (.031) (.033) (.033) (.033) (.033) (.033) (.033) (.033) (.033)
$ 0.3490 0.3451 0.3478 0.3511 0.3557 0.3603 0.3457 0.3466 0.3501 0.3482

N 26132 28547 28568 28304 27804 27631 27621 27660 26986 26876

Note: Standard errors are shown in parenthesis below the estimated coefficients.

Table 5: Mean Coefficients from Regressions for Monte Carlo Simulations: 2001-2010

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Year /
Coefficient 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
(variable)
" -0.033 0.026 0.045 0.092 0.035 0.148 0.239 -0.154 0.116 0.086
( II) -0.040 -0.035 0.047 0.086 0.031 0.163 0.250 -0.156 0.124 0.058
# 0.117 0.118 0.116 0.116 0.117 0.117 0.117 0.116 0.117 0.117
( I) 0.117 0.116 0.117 0.116 0.116 0.117 0.118 0.115 0.117 0.117
# 0.005 0.001 0.002 -0.0002 0.005 -0.0003 -0.005 0.008 0.006 0.007
( II ∙ I) 0.005 0.005 0.002 0.0002 0.005 -0.0008 -0.005 0.007 0.006 0.009
$ 0.063 0.066 0.067 0.068 0.067 0.068 0.065 0.068 0.065 0.064
( J J) 0.063 0.067 0.067 0.068 0.067 0.068 0.065 0.068 0.065 0.064
% -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001
( J J $) -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001
& -0.415 -0.406 -0.415 -0.415 -0.415 -0.415 -0.415 -0.415 -0.415 -0.416
( I ) -0.410 -0.419 -0.415 -0.415 -0.414 -0.414 -0.412 -0.421 -0.410 -0.421


(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Year /
Coefficient 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
(variable)
$ 0.026 0.014 0.032 0.011 0.021 0.022 0.049 -0.020 0.046 0.071
( II ∙ I ) 0.020 0.028 0.030 0.012 0.022 0.010 0.045 -0.010 0.037 0.075
" 4.151 4.091 4.119 4.106 4.101 4.096 4.123 4.122 4.121 4.115
(Constant) 4.143 4.126 4.105 4.098 4.107 4.088 4.111 4.129 4.110 4.125
Note: Mean coefficients from the regressions of the Monte Carlo Simulations are shown in italics
below the estimated coefficients from the original regressions.

Figure 5: Revised Sample - Average Educational Attainment of Men and Women: 2000-2010
13.2

13

12.8

12.6 Sample Mean: Men's
Schooling
12.4
Sample Mean:
12.2 Women's Schooling

12

11.8

Figure 6: Revised Sample - Average Experience Level of Men and Women: 2000-2010

23
22.5
22
21.5
21
Sample Mean: Men's
20.5 Experience
20 Sample Mean:
19.5 Women's Experience
19
18.5
18


Figure 7: Revised Sample - Average Weekly Wages of Men and Women: 2000-2010

800

700

600

500
Mean Weekly Wages -
400 Men
300 Mean Weekly Wages -
Women
200

100

0

Figure 8: Revised Sample - Ratio of Female to Male Average Weekly Wages: 2000-2010

1.05
1
0.95
0.9
0.85
0.8 Female-Male Ratio of
Mean Weekly Wages
0.75
0.7
0.65
0.6


Appendix B

Table 9: Estimation Results: Period from 2000 to 2001





Table 19: Revised Estimation Results: Period from 2000 to 2001

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