Evaluating Gender Wage Inequality in Academia using Causal Inference Methods for Observational Data

Using causal inference methods on a dataset of 12,039 UNC faculty members, this study estimates that female tenure-track professors earn approximately 6% less than comparable male colleagues, with the wage gap varying across career stages and research productivity levels.

The Gist

Imagine a massive, bustling university campus where thousands of professors work. For years, people have noticed that the men in the building seem to be paid more than the women. But here's the tricky part: Why?

Is it because women are paid less for doing the exact same job? Or is it because women tend to hold different titles, work in different departments, or have different amounts of experience? It's like trying to figure out why two cars are going at different speeds—are they driving slower because of the engine, or because one is stuck in traffic while the other is on a highway?

This paper is like a team of detectives (statisticians) who decided to solve this mystery using a special set of tools called Causal Inference. Instead of just looking at the raw numbers, they tried to create a "fair fight" to see what happens when you compare apples to apples.

Here is the story of their investigation, broken down simply:

1. The Crime Scene: The Data

The detectives gathered records from 12,000 professors across the entire University of North Carolina system. They looked at:

• Who they are: Men vs. Women.
• What they do: Their job title (Assistant, Associate, Full Professor), their department (Medicine, History, Engineering), and how long they've worked there.
• Their "Scorecard": How famous their research is (measured by how many times other scientists cite their work).

2. The Problem: The "Apples and Oranges" Trap

If you just compare the average salary of all men vs. all women, you get a gap of about 11.7%. But that's a bad comparison.

• Analogy: Imagine comparing the salary of a Junior Chef in a food truck to a Head Chef in a 5-star restaurant. Of course, the Head Chef makes more! But that doesn't mean the Junior Chef is being underpaid for their specific role.
• In the university, women are often in different roles, different departments, or at different career stages than men. If we don't fix this, we can't tell if the pay gap is real or just a mix-up of different jobs.

3. The Detective's Toolkit: Making a "Fair Fight"

To solve this, the researchers used two main tools to create a "virtual reality" where every woman is compared to a man who is exactly like her in every way except for gender.

• Tool A: The Matchmaker (Propensity Score Matching)
  Imagine a dating app, but instead of finding a partner, it's finding a "twin." The computer looks at a female professor and finds a male professor who has the exact same job title, works in the exact same department, has the exact same number of years of experience, and has the exact same research score.

  • Once they are matched, they compare their salaries. If the man still makes more, that's the "unfair" part.

• Tool B: The Crystal Ball (Causal Forests)
  This is a more advanced AI tool. Instead of just finding one twin, it builds a complex map of the entire university. It asks: "How does the pay gap change for a young professor vs. an old one? How does it change for a medical researcher vs. a history teacher?"

  • Analogy: Think of this like a weather map. A simple map just says "It's raining." A weather map with layers shows where it's pouring, where it's drizzling, and where it's sunny. This tool showed that the "rain" (the pay gap) isn't the same everywhere.

4. The Verdict: The Gap is Real (and Uneven)

After all the matching and adjusting, the detectives found a clear answer:

• The Result: Even when you compare a woman to a man who is identical in every way (same job, same experience, same research), the woman still earns about 6% less.
• The "Hidden" Gap: The original 11.7% gap shrank to 6% once they accounted for the fact that women often work in lower-paying departments or have less experience. But that remaining 6% is the "unexplained" gap—the part that looks like pure bias or structural inequality.

5. The Twist: It's Not the Same Everywhere

The "Crystal Ball" (Causal Forest) revealed something fascinating: The gap isn't uniform.

• The Medical & Health Sciences: This is the "storm zone." Here, the gap is the worst (around 7%). Even highly productive female doctors and researchers are paid significantly less than their male counterparts.
• The "Sunny" Spots: In fields like Natural Sciences and Social Sciences, the gap is smaller (around 5.5%), though it still exists.
• The Career Stage: The gap doesn't just stay the same; it shifts. In some fields, the gap gets wider as you get more experienced, suggesting that the longer you stay in the system, the more the inequality piles up.

6. Why This Matters

This paper is important because it stops us from guessing.

• Before: We knew women made less, but we didn't know if it was because they chose different jobs or because the system was unfair.
• Now: We know that even when women do the exact same job as men, they get paid less. It's like two runners running the same track at the same speed, but one is given a heavier backpack.

The Takeaway

The authors are saying: "We have the proof. The system has a leak."
They suggest that universities need to stop just looking at the average numbers and start looking at the specific "weather patterns" of each department. They need to fix the "backpacks" in the Medical fields and ensure that research productivity is rewarded fairly, regardless of gender.

In short: The playing field isn't level, and now we have the map to show exactly where the hills and valleys are.

Technical Summary

1. Problem Statement

The paper addresses the persistent gender wage gap in academia, a phenomenon where female faculty earn less than their male counterparts even after controlling for observable factors like rank, discipline, and research output.

• Limitations of Existing Literature: Prior studies largely rely on associational methods (e.g., Oaxaca–Blinder decompositions, pooled regressions) which cannot estimate counterfactual outcomes or fully account for unobserved confounding (e.g., career interruptions, service burdens). They often fail to capture treatment effect heterogeneity (how the gap varies across subgroups).
• Objective: To estimate the causal effect of gender on faculty salaries within the University of North Carolina (UNC) system using modern causal inference techniques. The study aims to move beyond descriptive associations to isolate the "gender penalty" while accounting for complex interactions between institutional, disciplinary, and career-related covariates.

2. Data and Variables

• Dataset: A comprehensive dataset of 12,039 tenure-track faculty (Assistant, Associate, and Full Professors) across all 16 campuses of the UNC system for the year 2022.
• Data Sources:
  • Salaries: Publicly disclosed annual salaries from UNC Digital Measures.
  • Productivity: Bibliometric data (i10-index, citations, h-index) matched via Google Scholar API (41.4% match rate).
  • Gender: Inferred via the genderize.io API (confidence $\ge$ 60%) and manual verification for ambiguous cases.
• Key Variables:
  • Outcome: Log-transformed annual salary ($\log_{10}(\text{Salary})$) to handle right-skewness and interpret results as percentage changes.
  • Treatment: Binary gender indicator (Female = 1, Male = 0).
  • Covariates ($X_i$): Academic rank, years of experience, university classification (Carnegie: R1, R2, Master's/Bachelor's), department (6 broad fields), and research productivity (log-transformed i10-index).
• Preprocessing: Non-faculty staff were removed; low-salary outliers (<$27k) were excluded. Missing Google Scholar IDs were imputed using mean values from similar faculty profiles.

3. Methodology

The authors employ a multi-method causal inference framework to ensure robustness, combining parametric and non-parametric approaches.

A. Causal Framework

The study targets three estimands:

1. ATE (Average Treatment Effect): The expected salary difference if the entire population were female vs. male.
2. ATT (Average Treatment Effect on the Treated): The effect specifically for female faculty.
3. CATE (Conditional Average Treatment Effect): How the gender effect varies based on specific covariates (heterogeneity).

Assumptions: Unconfoundedness (conditional on $X_i$), Positivity (overlap), and SUTVA. Sensitivity analysis (Cinelli and Hazlett framework) was used to assess robustness against unobserved confounding.

B. Parametric Methods (Propensity Score-Based)

To address covariate imbalance, the authors estimated a propensity score ($P(Z=1|X)$) using logistic regression with high-order interaction terms (University $\times$ Department $\times$ Productivity; Rank $\times$ Experience).

1. Propensity Score Matching (PSM): Nearest-neighbor matching (caliper 0.2) to create a balanced sample of treated (female) and control (male) units, followed by OLS regression on the matched sample to estimate ATT.
2. Inverse Probability Treatment Weighting (IPTW): Reweighting the full sample to create a pseudo-population where treatment is independent of covariates, estimating ATE.
3. Regression Adjustment with Propensity Score: Including the estimated propensity score as a covariate in the outcome regression.

C. Non-Parametric Method: Causal Forests

To capture complex, non-linear interactions and heterogeneity without pre-specifying functional forms, the authors used Causal Forests (Athey & Imbens, 2016; Wager & Athey, 2018).

• Mechanism: An ensemble of decision trees using "honest" splitting (separate data for tree structure and effect estimation) and orthogonalization (double machine learning) to reduce bias from nuisance parameter estimation.
• Goal: To estimate individual treatment effects ($\hat{\tau}(X_i)$) and identify subgroups where the gender wage gap is most pronounced.

4. Key Results

A. Magnitude of the Gap

• Unadjusted Gap: Female faculty earn 11.71% less than males on average.
• Adjusted Causal Estimates: After controlling for rank, discipline, experience, and productivity, the gap persists but narrows:
  • PSM (ATT): 6.61% lower for females.
  • IPTW (ATE): 6.17% lower.
  • Regression Adjustment: 6.45% lower.
  • Causal Forest (ATE): 5.96% lower.
• Conclusion: Approximately half of the raw disparity is explained by observable characteristics, but a statistically significant structural gap of ~6% remains unexplained.

B. Heterogeneity Analysis (Causal Forests)

The gap is not uniform; it varies significantly by discipline and productivity:

• Disciplinary Variation:
  • Medical and Health Sciences (MHS): The largest disparity (~7%), which widens with experience and remains high even at high productivity levels.
  • Natural/Social Sciences: Smaller gaps (~5.5%).
  • Arts, Humanities, Business, Engineering: Gaps average around 6%.
• Productivity Interaction: In MHS, the gender penalty worsens at intermediate levels of research productivity before slightly improving at the highest levels, whereas other fields show more stable gaps.
• Contextual Nuance: In Business and MHS at R1 institutions, research productivity strongly correlates with higher salaries. Conversely, in Arts and Humanities, citation-based metrics show a negative association with salary, suggesting misalignment of evaluation metrics.

C. Methodological Comparison

• Consistency: All methods yield consistent results (6–7%), validating the robustness of the findings.
• PSM vs. Others: PSM estimates were slightly higher, likely because it targets the treated population (female faculty), who may face more severe structural barriers than the average population.
• Causal Forest: Provided the most granular insight, revealing that average estimates mask significant subgroup variations, particularly in MHS.

5. Key Contributions

1. Causal Identification: Moves beyond correlation to provide credible causal estimates of the gender wage gap in a large-scale public university system, addressing selection bias and confounding.
2. Heterogeneity Mapping: Utilizes Causal Forests to demonstrate that the gender penalty is not a monolithic average but varies systematically by discipline (especially MHS) and career stage.
3. Reproducible Framework: Integrates public salary data, bibliometrics, and modern causal inference (PSM + Causal Forests) into a reproducible workflow applicable to other academic systems for equity audits.

6. Significance and Implications

• Structural Inequity: The persistence of a ~6% gap after rigorous adjustment suggests deep-seated structural barriers (e.g., bias in negotiation, service loads, or promotion criteria) rather than just differences in productivity or rank.
• Targeted Interventions: The findings suggest that "one-size-fits-all" policies are insufficient. Interventions must be discipline-specific, with urgent attention needed in Medical and Health Sciences.
• Evaluation Metrics: The negative correlation between citations and salary in Arts/Humanities highlights the need to rethink how scholarly impact is measured and rewarded across different fields.
• Policy Recommendations: The authors advocate for salary transparency, standardized evaluation criteria across disciplines, and regular equity audits disaggregated by field and career stage.

Limitations

• Productivity Measure: Reliance on Google Scholar (i10-index) may underrepresent teaching, mentorship, and service contributions.
• Cross-Sectional: The study captures a single point in time (2022) and cannot track the evolution of the gap over a career.
• Generalizability: Findings are specific to the UNC public system and may not apply to private institutions or systems with different governance structures.