Colleen P Cahill Writing Sample Econometrics II Select Pages

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  • 1. Running head: CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 1A 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
  • 2. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 2 AbstractThis paper takes a simplistic view of the issues of the wage gap and the return to education. Itdoes not attempt to explain why the persistence of the wage gap remains or why more educationand experience is viewed as positively correlated with higher income. The first goal of the paperis 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 educationcontributes to higher income in a statistically significant way for these same periods. The processis then repeated with a wage equation with more controls added to it per the literature to see ifthe results vary at all from the original regressions.
  • 3. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 3 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 referredto as the gender gap, has declined over the past half century in the United States from just over60 percent in 1960 (National Committee on Pay Equity, 2011), it still exists and women’searnings 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 muchresearch, especially since women have surpassed their male peers in educational expectationsand degree attainment since the 1990s (Peter, Horn, & Carroll, 2005). That the wage gap stillexists is a somewhat puzzling dilemma since there is a general expectation that more educationand experience equals higher income. This paper takes a simplistic view of the issues of the wage gap and the return toeducation. In no way does it attempt to explain why the persistence of the wage gap remains orwhy 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 thispaper takes these observations as given and instead has several straight forward goals. The firstgoal is to utilize a basic wage equation to see if a change in the wage gap occurs, what thatchange is, and if it is statistically significant. The second goal is to utilize that same basic wageequation to see if the return to education contributes to higher income in a statistically significantway. The process is repeated with a wage equation with more controls added to it per theliterature. The period of study is each year of the most recent decade, 2001 through 2010, ascompared to the year 2000. I have chosen this period primarily because it occurs after women
  • 4. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 4surpassed men in educational attainment in the 1990’s. I have also chosen to compare a ten yearperiod in order to ascertain differences between individual periods, especially those containingrecessionary years. In addition, the ranking of U.S. education compared to other OECDcountries has fallen during this time (Liepmann, 2011). It is of interest to see if the return toeducation has any corresponding decline as well. In order to conduct the study, data from the Current Population Survey (CPS), availablefrom the U.S. Census Bureau (U.S. Census Bureau, 2000-2010), is utilized. The basic wageequation used is modified from one found in Wooldridge (2009, p. 447). Admittedly, the wageequation is quite simplistic, as will be seen from a review of the literature. But for the goals ofthis 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 toeducation in the literature. The studies I surveyed which focus on the wage gap, are primarilyconcerned with the issue of what factors contribute to the disparity. There are several broadcategories that these factors fall into. One category involves personal choices made by women inregard to participation in the labor force (Korenman & Neumark, 1992; Welch, 2000). Anotherfocuses on male-female differences in skills, and yet a further centers on differences in thetreatment of equally qualified men and women (Blau & Kahn, 1994). The studies I surveyed onthe 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, anumber specifically address a male-female disparity of this return. This is also the case in a fewof the papers which are primarily concerned with the wage gap, as the disparity in the return toeducation is seen as a contributing factor. In addition, several of the studies present potential
  • 5. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 5problems with using the basic wage equation, including endogeneity of variables and bias. All ofthese issues are briefly addressed below. Lower participation rates and career disruptions of women as compared to men are seento 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 awoman has more than two children (Fleisher & Rhodes, 1979; Korenman & Neumark, 1992).This is because the associated “human capital depreciation” and decline of experience and tenurerelative to men has a negative impact on women’s wages (Mincer & Ofek, 1982). Exasperatingthis negative impact of career disruptions, may be an observed increase in the return toexperience. Since women, on average, are reported to have less experience relative to men, asthe 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 beenfound to be, on average, three times that of a married man’s (Hersh & Stratton, 1997). Thislowers a woman’s working time relative to a man’s and in turn has a negative impact on herwages. Another factor is that of wives who follow their husbands to a particular geographiclocation (Frank, 1978). A negative impact on the wife’s income is often observed because thegeographic 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 findingabout the return to education between husbands and wives is that it has been found that awoman’s education may be positively correlated with her husband’s income (Lefgren &
  • 6. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 18below a comparable man’s wage in 2010. Recall, the difference in 2000 was estimated to be34%, 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 2007where it is slightly lower. Using the same null and alternative hypothesis as previously, there isno evidence that the change in the return to education is statistically different from 0 in any yearexcept 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 theperiods of study. The only statistically significant change is in 2007, but even this is a change ofless 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). Bycomputing 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’swage. 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 nullhypothesis H" : $ = 0 against the alternative hypothesis H# : $ > 0. There is no evidence thatthe change in the gender gap is statistically different from 0 in the periods 2000 to 2001 or 2002at significance levels of 10% or below. In the period from 2000 to 2006, the gender gap is shownto have fallen by about 3 percentage points and it is significant at an 8% significance levelagainst the positive one-sided alternative. In the period from 2000 to 2008, the gender gap fellapproximately 4 percentage points and is significant at a 2% significance level. The fall in the
  • 7. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 19gender gap is most significant in the periods 2000 to 2003, 2004, 2005, 2007, 2009 and 2010where the fall was approximately 5, 4, 5, 5, 5, and 7 percentage points respectively. All aresignificant at less than a 1% significance level. This indicates that the gender gap has beennarrowing in recent years, even in the recessionary period of 2008 as opposed to the previousresults. Unlike in the larger, less controlled samples, here the gender gap is seen to initially notchange, but then narrow throughout the decade. The wage gap has seen a larger change than thereturn to education in the revised samples just as it did in the initial samples. By computing theexact 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, anarrower gap than in the initial data, but one must recall the initial gap was estimated to besmaller in the revised samples. The narrowing is estimated to be approximately 5 percentagepoints, 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 onboth sets of equations. The process for this study involved producing ten random error termswith a normal distribution of mean 0 and variance the square of the mean standard error of theoriginal regression. This was done for each of the years of study. Using the coefficientspreviously estimated, the data used for the original regressions and the new random errorsgenerated, ten new dependent variables were generated for each year. The coefficients were thenre-estimated using the new dependent variables generated. The mean of the estimatedcoefficients from the regressions involved in the Monte Carlo simulation are indicated in italicsbelow the original estimated coefficients in Table 5 in Appendix A for the initial equations and
  • 8. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 20in Table 8 in Appendix A for the revised equations. The full results of the regressions may beobtained 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 ofequations are within the 95% confidence intervals of the estimated coefficients from the originalregressions. In fact, many of the mean estimated coefficients are the same as those from theoriginal regressions. The standard errors of the simulated coefficients are all similar to those ofthe original estimated coefficients. There is some variation as to the significance of thesimulated coefficients from the original coefficients; however a larger number of simulationsmay provide a different result. Based on the values of the estimated coefficients alone, the resultsof 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 allequations. I expressed doubt as to whether the change to the return to education would bepositive and significant for all years observed. This played out in the data, but the surprise in theinitial estimations is that the largest positive and most significant changes occurred in the mostrecent years. This indicates that the return to education continued to rise even as the educationalranking of the U.S. compared to other OECD countries has been declining. In the revisedestimations, the return to education is essentially unchanged with the exception of a slightreduction in the year 2007. As pointed out previously, note that the increase in the return toanother year of education is small, at less than 1 percentage point for any period, for all of theestimations.
  • 9. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 21 I expected the ln{ I { differential between men and women in 2000 to be significantand this was true in the regressions. I also expected the differential to persist in the periods ofstudy but narrow as the 2010 period approached. This did occur. In the original estimations, thechange was insignificant in general as expected early in the study and more significant in thelater 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 ofthe recessionary periods, did not narrow. In the revised estimations, the wage differential initiallydid not narrow, but then did as the decade proceeded. The recessionary periods did not appear toaffect the revised estimations. As noted, unlike the return to education, the wage gap has seen alarger change in the period studied. In the larger samples, from an estimated difference of awoman’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 a22% difference, which is slightly lower than that seen in the actual population. The gap wasseen to have narrowed by 4% by 2010 in the population, so the estimated change is slightlyhigher. Estimating the equations with the basic wage equation and then again with more controlssaw 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 thesignificance levels are taken into account, the results are generally similar. This indicates thatfor 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 wagegap and the return to education. It does not attempt to explain why the persistence of the wagegap remains or why more education and experience is viewed as positively correlated with
  • 10. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 22higher income. As stated, the first goal of the paper was to utilize a basic wage equation to see ifa change in the wage gap occurs, what that change is, and if it is statistically significant. Thesecond goal was to utilize that same basic wage equation to see if the return to educationcontributes to higher income in a statistically significant way. The process was then repeatedwith a wage equation with more controls added to it per the literature. Because the premise of thepaper is not empirically demanding, I believe that the basic equation, although simplistic, isadequate for the proposed investigation.
  • 11. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 35Table 1 (cont.): Summary Data (Recessionary Periods are in Gray)
  • 12. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 36Table 2: Variable DescriptionsTable 3: Recoding of the Education Variable
  • 13. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 37 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
  • 14. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 38 (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: Mens Schooling 12.4 Sample Mean: 12.2 Womens 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: Mens 20.5 Experience 20 Sample Mean: 19.5 Womens Experience 19 18.5 18
  • 15. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 39Figure 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 0Figure 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
  • 16. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 53 Appendix B Table 9: Estimation Results: Period from 2000 to 2001 Table 10: Estimation Results: Period from 2000 to 2002 Table 11: Estimation Results: Period from 2000 to 2003
  • 17. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 54 Table 12: Estimation Results: Period from 2000 to 2004 Table 13: Estimation Results: Period from 2000 to 2005 Table 14: Estimation Results: Period from 2000 to 2006
  • 18. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 55 Table 15: Estimation Results: Period from 2000 to 2007 Table 16: Estimation Results: Period from 2000 to 2008 Table 17: Estimation Results: Period from 2000 to 2009
  • 19. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 56 Table 18: Estimation Results: Period from 2000 to 2010 Table 19: Revised Estimation Results: Period from 2000 to 2001
  • 20. CHANGE TO THE RETURN TO EDUCATION AND GENDER GAP 57 Table 20: Revised Estimation Results: Period from 2000 to 2002 Table 21: Revised Estimation Results: Period from 2000 to 2003