Salary inequality in young professors: evidence from public U.S. economic department

ABSTRACT

The current literature provides little empirical evidence on the study of salaries for young faculty members in the economic department, possibly because effective recognition of their research productivity remains a difficult challenge. To address this research gap, we analyse the effects of gender, PhD graduation school rank and undergraduate major on the salaries of young economics professors with varying experience levels. We create a novel dataset by manually collecting detailed and time-varying research productivity measures and demographic information of young economics professors from the top 50 public research universities in the U.S. We use double machine learning to obtain consistent estimators, which allows us to account for non-parametric features associated with the high-dimensional control variable set. Our findings indicate that in experience years 4 to 8, which is the time most faculty tenured, the gender effect estimates are statistically significant and large enough in magnitude to have practical implications. For PhD graduation school rank and undergraduate major, the effects in experience years 7 to 9 are large in magnitude but do not have statistical significance.

KEYWORDS:

• Salary inequality
• productivity measures
• gender bias
• double machine learning
• young economic professors

JEL CLASSIFICATION:

• J31
• J70
• I23

Acknowledgements

This research was supported by Zhejiang Gongshang University “Digital+” Disciplinary Construction Management Project (SZJ2022B001) and the characteristic & preponderant discipline of key construction universities in Zhejiang Province (Zhejiang Gongshang University - Collaborative Innovation Center of Statistical Data Engineering Technology & Application). Qin Zhang was supported by Young Scholar Program of Zhejiang Gongshang University (QRK23026). Wei Kong’s research was supported by the National Natural Science Foundation of China (Grant No.72373095) and the Shanghai Pujiang Program (No. 2020PJC064). The authors are grateful for the comments and reviews made by the editor, anonymous reviewers, Professor David M. Kaplan and Professor Zhiguo He for their valuable advice and insightful comments.

Disclosure statement

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. We also declare that the work has not been published previously and it is not under consideration for publication elsewhere, that its publication is approved by all authors and tacitly or explicitly by the responsible authorities where the work was carried out, and that, if accepted, it will not be published elsewhere in the same form, in English or in any other language, including electronically without the written consent of the copyright-holder.

Notes

¹ Full list of variables shown in Table 4.

² See table-note of Table 4 for the criteria of journal tiers separation.

³ such as associate editors of top economic journals and econometrics society fellows.

⁴ Among these universities, 21.4% universities ranked at top 30, 25% universities ranked at top 30–50, 25% universities ranked at top 50–100, 21.4% universities ranked at top 100–200.

⁵ Considering the gap among different fields, this study examines the faculty members from the department of economics, excluding the departments that are in business schools.

⁶ To calculate total years of graduate education, we use time in Master’s degree programs, time pursuing degrees in ECON/non-ECON fields, and the total years spent pursuing a PhD.

⁷ https://ideas.repec.org/top/top.journals.all.html.

⁸ Tiered variables are continuous and partitioned by journal rank. Tier 1 includes journals ranked from 0 to 10; tier 2 includes journals ranked from 11 to 50; tier 3 includes journals ranked from 51 to 150; tier 4 includes journals ranked from 151 to 300; tier 5 includes journals ranked 301 and after. We take IDEAS 2015 journal rank here as the criterion.

⁹ The Equation (1)(1) $Y=D{\theta }_0+g_0(\mathbf{X})+U,\mathbb{E}[U|\mathbf{X},D]=0,$(1) , (2) and (3) corresponds to Equation (1.1), (5.1) and (1.2) in Chernozhukov et al. (2018) respectively.

¹⁰ The rank variable is continuous.

¹¹ In the Supplementary Material, we provide a short proof of how a partially linear model can be estimated by DML to obtain a consistent estimator.

¹² The control variable vector $\mathbf{X}$ mentioned in the rest of paper is the vector of the principal components.

¹³ Chernozhukov et al. (2018) Equations (2.9).

¹⁴ Introduced by Neyman (1959).

¹⁵ The score function must satisfy an additional condition that its Gateaux derivative $D_r[\eta -{\eta }_0]$ exists, and it is non-sensitive to the change of nuisance parameters $\eta$ towards any direction. The Gateaux derivative, which is defined as in Chernozhukov et al. (2018) the equation below (2.1).

¹⁶ Chernozhukov et al. (2018) Equations (2.3).

¹⁷ The quoted names are variables showed in Table 4.

¹⁸ Such that it’s called interactive model when we discuss DML results.

¹⁹ Wooldridge (2010) Assumption ATE.1 and a weaker version ATE.1’.

²⁰ Wooldridge (2010) Assumption ATE.2.

²¹ Wooldridge (2010) Proposition 21.1.

²² According to Wooldridge (2010), section 21.3, unobservables are allowed to be correlated with $D$ only when the unobservables are not correlated with $Y_0$ and $Y_1$.

²³ CIA condition, $\mathbf{X}$ includes all the other information except ‘Male’ and ‘Salary’ in Table 4.

²⁴ we use ‘PhD Graduation School Rank (IDEAS_2013)’ exclusively and omit ‘PhD Graduation School Rank (USnews_2013)’ and ‘PhD graduation School Score(USnews_2013)’ from the dataset and put other background and productivity measures in control set $\mathbf{X}$.

²⁵ In our study, undergraduate majors in Economics (Econ) and STEM are two dummy variables, not mutually exclusive to each other; individuals may possess either one, both, or neither of the two attributes. When analysing the effect of the undergraduate major in economics, the counterparts are people who do not have a major in economics. While the counterparts for Undergraduate STEM majors are those whose undergraduate major are not STEM. When we analyse the undergraduate Econ effect, we have the dummy variable indicating the young economic professors who are majored in STEM or not in the control variable set, and vice versa.

²⁶ More than 80 variables; approximately 100 observations for each experience year’s data set.

²⁷ In DML, only a partial of the data are used for causal parameter estimation after sample splitting.

²⁸ Post Lasso is a method originated by Belloni and Chernozhukov (2013). Lasso is not applicable at the same time with PCA, because after PCA the principle components are already orthogonal with each other.

²⁹ In the Supplementary Material, we also provide the coefficients obtained by OLS (Tables 17 to 23) for readers who are interested to compare the results by traditional econometrics method and DML.

³⁰ A result getting from choosing best methods for $g(.)$ and $m(.)$ separately.

³¹ Chernozhukov et al. (2018) Definition 3.3.

³² All salaries are log-transformed, so the effects can be explained in percentage.

³³ We are specifically interested in studying young economics professors who work at the top 50 research university economics departments on the tenure track. Therefore, individuals who have been offered a position from these universities but declined or individuals who have left the tenure track or moved to private schools after a few years of working in the system are not included in our analysis.

³⁴ Economically significant means the estimated coefficients are large in absolute values and the real effects cannot be ignored.

³⁵ We also explored the possibility of excluding promotion-related variables from the set of control variables, however as has been showed in Tables 24 to 27 in the Supplementary Material, there are significant differences between before and after promotion for the effects from all the key variables of interest we investigate. Clearly, the jump on the estimates are driven by promotion status if not being controlled. Therefore, promotion status is of importance when considered as a confounding factor.

³⁶ We do not include current year cumulative productivity information because we believe that next year’s cumulative productivity measures already contain the current year cumulative information. But current productivity is not representable by next year’s information.

³⁷ In the result tables, if NA shows up in the whole column, meaning this model does not work on this specific dataset and no results are reported; if NA shows up in se(median), meaning no ‘best’ result reported and we report a median value among all ML estimators and its corresponding se.

³⁸ 2 folds times 5 splits as explained in Section IV.

Additional information

Funding

The work was supported by the Shanghai Pujiang Program [2020PJC064]; Zhejiang Gongshang University [1330KU1622007,QRK23026,SZJ2022B001].