Critique on Catherine Weinberger’s “mathematical College Majors and the Gender Gap in Wages”

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math Test score ≠ math skills

To come up with a proxy for mathematical content of college majors, Dr. Weinberger intended to measure the math skills of graduates with GRE math test scores. This is a fair assumption, but it is argued that “caution is needed when using test scores to infer gender differences in skills”(Niederle and Vesterlund 2010). In the paper “Explaining the Gender Gap in Math Test Scores: The Role of Competition”, Niederle and Westerlund assert that gender differences in competitive attitudes may cause mathematics test scores to give a biased representation of the underlying gender differences in math skills. They stated “boys are more overconfident than girls conditional on math performance”, and this gender difference is especially large among the most gifted children. They pointed out the strong stereotype of male is better at math can explain a significant portion of this differential in confidence in math. Data from National Assessment of Educational Progress (NAEP) was used to support their opinion as less gender disparities of math test are detected in regions where gender equality is well adopted. Overall, it is claimed by Niederle and Westerlund that women tend to be less confident in math compared to men, and if this is true, this attribute can be a potential candidate for the measurement error term, e1.

Measurement of self-confidence in math

Similar to mathematical content, self-confidence is also an abstract term that is complicated to measure. Naturally, a proper proxy variable for it is required. Self-confidence in math can be interpreted as the satisfaction with one’s math skill. Anyone who is confident in math is likely to enjoy math more, and thus would get more involved in math-related activities. One of the easiest things to do is to take high level math classes. The willingness to learn high level math is a straightforward reflection of self-confidence in math. Therefore, number of high level math classes taken during undergraduate years can be an effective proxy here. Since the original dataset does not include much information on the graduates’ attitude on math, outside data needs to be to employed for testing.

The dataset “Longitudinal Study of American Youth, 1987-1994, 2007-2011”(LSAY) is used here to capture this math class variable(National Science Foundation 1985). This is a project that sent out survey to 7th and 10th grade students in public schools in the United States in 1987 as well as those same students that could be recontacted again in 2007-2011 with a follow-up questionnaire. The relevant variable is included in the 2007 questionnaire, when the original participants of the survey is middle-aged. The data set is preprocessed to resemble the one used in Dr. Weinberger’s paper. A sample of size 571 was generated with only full-time graduates with B.A. degree from 4-year universities or colleges. The variable name is “number of calculus or high level math classes taken during 4-year university or college”, and the result for different gender is shown in Table 1.

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TABLE 1

AVERAGE NUMBER OF HIGH LEVEL MATH TAKEN BY COLLEGE MAJORS

Major Category

Average Number of High Math Course Female Took

Average Number of High Math Course Male Took

Business

1.1304348

1.2318841

Communication

.46153846

0.5

Computer Science

4.3333333

4.3

Economics

1.75

3.5714286

Education

0.73684211

1.5714286

Engineering

3.8888889

4.9555556

Humanities

0.42424242

0.43478261

Mathematics

8

15

Nursing

0.25

0.5

Science

1.9354839

2.4468085

Social Science

0.46875

0.8125

Health Professions

0.79411765

0.75

Others

0.81818182

1

From the statistics above, it is easy to see that men in average took more high level math classes for almost all the major categories. Consequently, it is validated that men surpass women in self-confidence in math.

Apart from the variation in self-confidence, there are other aspects that may influence men and women differently. For example, female tend to be more sensitive to competitive pressure (Niederle and Vesterlund 2010). Hence, in our problem, the “e1” term is likely be negative for female because the use of GRE Quantitative score underestimates the “true” math quality, in other words, the “true” mathematical content of their college majors.

New measurement of math content

Solving measurement error requires the use of instrumental variable, which is beyond my current knowledge. The shortcut is to find a better variable that can potentially function better. Equipped with the data obtained from LSAY, I managed to select a new proxy for mathematical content for

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college