Essay About Mathematical College Majors And Multivariate Linear Regression Models

Critique on Catherine Weinberger’s “mathematical College Majors and the Gender Gap in Wages”
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Critique on Catherine Weinberger’s “Mathematical College Majors and the Gender Gap in Wages”Jingyao ZhanStudent ID: 28279617Section: 2:00-3:15pmSummary of the PaperSocial inequality has always been the point of attention by researchers. Gender based discrimination, among all forms of inequality, is one of the most prevalent ones. Gender wage gap exists persistently for decades, and numerous researches have been done to figure out what accounts for this differential. Paglin and Rufolo(1990) argues the gender wage differential among college graduates is solely due to the choice of majors as women are less willing to choose mathematical majors. However, Catherine Weinberger casts doubt on this point in the paper “Mathematical College Majors and the Gender Gap in Wages”. By pointing out graduates with mathematical college majors tend to have higher wage consistently, Dr. Weinberger attempts to evaluate how much of the gap that is due to the choice of major is actuallydue specifically to the mathematical content of the major.The dataset the author used is “1985 Survey of Recent College Graduates”. For this particular analysis, she constrained the data only to white men and white women with Bachelor degree, younger than 30, employed full time or involuntarily part time, not full time student, having a salary greater than 1 dollar per hour, and having no missing data on earnings, work experience, weekly working hours, and grades. In doing so, many potential confounders, such as racial discrimination and degree difference, are eliminated. Since “mathematical content” of college majors are hard to measure and more likely to be unobservable, the author uses the average GRE Quantitative score earned by graduates from different categories of majors as proxy.The author employed the Ordinary Least Squares(OLS) estimators and constructed several multivariate linear regression models. Firstly, the author introduced the controls she made for this analysis. There are two college major controls. One is a set of dummy variables for individual majors, and the other is a single variable measures mathematical content of each college major using GRE Quantitative score. In addition, she included a technical major indicator, that is an interaction term of gender and technical major. Secondly, the author established four models with mathematical content of majors as independent variable and log of hourly wage as dependent variable. The models differ in the controls included. Model 1 has no college major control and it quantifies the wage gap between white men and women. Model 2 uses the complete set of college major variables as control to quantify the wage gap between white men and women with the same major. Model 3 uses mathematical content of individual college majors as control to quantify the wage gap between white men and women with majors of same level of math content. Model 4 is an extension of Model 3 as it adds the technical major indicator to Model 3 to compare the gender wage gap for technical and non-technical majors. All four models have the same human capital controls: predegree work experience, postdegree experience, college grade-point average, and hours worked per week. The regression for Model 4, for example, is

log(w) = β0 + β1MC + β2ww + β3ww ∗ TCM + β4H + β5P rE + β6P oE + β7GrP A + εThe results are drawn from comparing the coefficients on the variable of gender. Model 1 shows the gender wage gap is 17% when no college major controls applied. Model 2 and 3 give the same coefficient, 0.09, on gender, meaning that mathematical content of college majors can explain as much of the gender wage gap as the college major alone can. In other words, almost all the gap caused by majors is explained by math content of majors. The coefficient on mathematical content, 0.0017, in Model 3 and 4 implies higher mathematical contents indeed leads to higher earnings in general. The technical major indicator in Model 4 has a coefficient of 0.02, which means that women in technical major may face a slightly smaller wage disadvantage compared to women in non technical major. However, this coefficient is insignificant, so the author contends women in technical major and non technical major face similar gender wage gap. This result also demonstrates the assumption of exogenity is satisfied as the unexplained gender differential is likely to be the same for the two groups. In the end, the author argues that policies that encourage female involvement in technical college majors will effectively mitigate the gender wage disadvantage.CritiqueBy restricting the sample, Dr. Weinberger managed to avoid many potential confounders in this analysis. Also, the controls were carefully chosen so that near-multicollinearity is avoided. However, some of the limitations do affect the validity of this research. The aspect I focus on is measurement error in independent variable. Measurement error is defined as all forms of mis-measurement in the variables in the model. Suppose the true variable is x1*(the “latent variable”), the term we observe is a measurement x1, which may be wrong. Regression models that account for measurement errors in the independent variables is known as error-in-variables model(CEV model). I would argue the models introduced in this paper are CEV models. In the paper, the author used GRE Quantitative score as the proxy for mathematical content of college majors. Using only GRE Quantitive score of the graduates to measure the math content of majors is inadequate. The true independent variable here is mathematical content(MC*), but the author included here is GRE Quantitative-score. And there exists GRE = MC* + e1, where e1 is independent of all the regressors x1*…xk*. Here, we assume only GRE has measurement error, so the other explanatory variables, such as gender, weekly working hours, work experience, equal to their true values. For example for model 4, the true model here is: log(w) = β0 + β1MC* + β2ww + β3ww ∗ TCM + β4H + β5P rE + β6P oE + β7GrP A + uSubstitute the wrong measurement term would give:log(w) = β0 + β1MC + β2ww + β3ww ∗ TCM + β4H + β5P rE + β6P oE + β7GrP A + u – β1e1The error term now is u – β1e1. ThusE[u – β1e1] = E[u|MC, ww, …, GrP A] – β1E[e1|MC, ww, …, GrP A]Although the paper assumes exogenity, which implies E[u|MC, ww, …, GrP A] = constant, E[e1|MC, ww, …, GrP A] is very likely not zero because E[e1|MC, ww, …, GrP A] = E[e1|MC*+e1, ww*, …, GrP A*], and e1 is not independent on MC* + e1. As a result, the model still suffers from the problem of endogenity because the expected value of the error term overall is not a constant. In this context, I believe there are other factors hide in the measurement error term e1 that worth noticing. My research is done on discovering what this e1 might be.