Problem 5 (a) Data Description Section Mean hourly wages for men and women Men $13.14 Women $ 9.42 Other differences between men and women Factor Men Women --------------------------------------------------------------- Education (mean) 13.2 years 13.2 years Age (mean) 37.5 years 37.1 years Potential Experience (mean) 24.3 years 24.0 years (note: exp = age - education) Hours (mean) 43.1 hrs/week 36.9 hrs/week Full Time 93.0% 77.7% Covered by union contract 18.6% 9.7% Union member 17.3% 8.6% Lives in central city 22.4% 22.6% Veteran 23.8% 1.0% White 82.9% 80.7% Married 68.8% 60.0% Many of the differences in personal characteristics between men and women are fairly insignificant; in particular, men and women on average have roughly the same level of schooling, age, and potential experience. Men are almost 10% more likely to be married than women, and, of course, are much more likely to be veterans; these differences are unlikely to account for the difference in wages, though. However, men are twice as likely to be covered by a union contract as women, which could have a significant effect on their wages. On the other hand, only a fairly small proportion of workers overall are unionized, which makes it doubtful that this effect is enough to account for the totality of the gap between male and female wages. Mean educational attainment by old vs. young Less than 40 years of age: 13.3 years 40 years or more of age: 13.0 years There is a slight tendency for younger people to get more schooling than older people did; thus, there is a slight trend towards more schooling over time. (b) Simple Regression Models Regression of log(wage) against female shows that females have approximately 31.1% lower wages than males. If we take education and experience into the regression, then the mere fact of being female still results in 30.0% lower wages. If we include various other factors into the regression, the percentage difference in wage associated with being female decreases, because some of that difference was due to other factors correlated with being female (for example, being married). The following table gives a list of such factors, and the percentage difference in wage due to being female after that factor is accounted for. Factor % diff % diff due to factor due to being female after correction for factor ------------------------------------------------------------ Being white + 6.0% -29.9% Being white, +10.9% asian, +13.6% hispanic, + 7.8% black, - 0.8% other + 8.1% -29.7% (after correction for all) Covered by union contract +23.7% -28.0% Full-time +28.8% -25.7% Live in central city + 2.9% -30.1% Married + 9.1% -29.3% Veteran + 2.0% -29.6% < 40 years old + 6.9% -30.0% This table gives us a pretty good idea of which factors most account for the wage differential between women and men: they are those for which the percentage difference in wage due to being female after correction for the factor, is least. Thus, in particular, being full-time and union coverage are significant parts of why females get lower wages on average. I then performed regressions based on combinations of the most likely factors from above, to test this hypothesis. As one would expect, the direct correlation between being female and wages decreased with every factor added. The most interesting result is the percentage differences associated with the regression including the following factors: female, covered by union contract, full-time, married, and white or asian. The results are below: Factor % diff in wage due to factor ------------------------------------------------------------- Being female -22.7% Covered by union contract +22.9% Full-time +28.6% Married + 9.6% White or Asian + 8.5% As is easy to see, the latter four factors account for 7.3% of the 30.0% wage differential between men and women. The remaining 22.7% cannot be easily explained by the data in this sample; it may represent a fundamental cultural bias of employers against women workers. I hypothesize that part of the remaining 22.7% is due to a signaling-like effect: because males are, on average, more productive than females (or at least the 7.3% we accounted for above would seem to indicate so), employers are likely to statistically discriminate against females. In other words, maleness would be a "signal" of ability (except for the fact that it cannot be acquired, and so cannot be a signal per se). (c) Models that Allow the Female Differential to Vary Each time bucket is 5 years long; the percentage differential in wage associated with each time slot, when the regression includes education, experience, and female1-female11, is in the table below. time slot % difference wage between females and males female# of same experience level ----------------------------------------------------------- 1 -14.6% 2 -18.0 3 -21.5 4 -28.9 5 -33.9 6 -43.3 7 -40.4 8 -47.3 9 -43.1 10 -30.1 11 +35.8 The last three categories represent females with more than 40 years of experience, and thus represent a very small portion of the population; the results from those should probably be ignored. Otherwise, there is a very striking increasing trend in the wage differential between males and females at the same experience level. If one takes into account various other factors, the increasing trend is not affected; in particular, even if one takes into account all of the factors from the final regression of part (b), the trend is hardly changed at all (although the whole curve is shifted down by a nearly constant factor). This would imply that this trend is not easily explainable by other data in this dataset. I hypothesize that this result can be explained by the human capital model: females derive less benefit from experience because they do not partake in on-the-job training as much as males. This might be due to concerns on the part of both the employers and the workers: for example, they may worry that the payoff period will be short due to females getting married or pregant and quitting their jobs. It may also be partly due to cultural factors that prevent females from engaging in the same sort of informal mentoring or formal on-the-job training as males.