Equal Pay for Similar Work

Layer 1 — Overview

Research Question

This paper studies the labor market effects of “Equal Pay for Similar Work” (EPSW) policies — laws that require firms to pay equal wages to workers of different protected-class identities (e.g., different genders) who perform “similar” work within a firm. EPSW has become increasingly prevalent: as of January 2023, more of the U.S. workforce falls under state EPSW laws than state “Equal Pay for Equal Work” (EPEW) laws. Despite this spread, the equilibrium consequences of EPSW were previously unknown.

Theoretical Framework

The authors develop two theoretical models. The first is a static cooperative game (whose outcomes coincide with the Nash equilibria of a non-cooperative simultaneous-wage-offer game). Homogeneous firms with constant-returns-to-scale production compete for a continuum of heterogeneous workers. Workers belong to one of two groups A or B (e.g., men and women), with group A constituting a β ≥ 1 majority. Each worker’s productivity v is drawn from a group-specific distribution (FA or FB); firms’ willingness to pay equals each worker’s productivity, but can embed taste-based discrimination. The analysis is framed as applying “within job” in a local labor market — only workers performing “similar” work in the eyes of the law.

The second model is a dynamic search-and-bargaining framework with an arbitrary number of firms, search frictions, reallocation frictions, and Nash-in-Nash bargaining. EPSW is introduced as a surprise, and constrained firms choose whether to segregate for one group or remain desegregated (paying a common wage to all workers).

Main Theoretical Findings

Without EPSW, Bertrand competition among firms drives every worker’s wage to equal her productivity; any wage gap between groups A and B exactly reflects the difference in average productivities (EA(v) − EB(v)), whether or not those productivity differences stem from discrimination.

With EPSW, the equilibrium is qualitatively transformed. In the static model (Proposition 2), firms generically fully segregate their workforces: one firm hires all A-group workers and the other hires all B-group workers. EPSW functions as an enforcement mechanism for this segregation analogous to location choices in Hotelling’s model — poaching a worker from the competing firm is costly because EPSW then requires the poaching firm to pay equal wages to all workers it employs. In the core with EPSW (Proposition 3), the wage gap moves in favor of the majority group (A-group, β > 1) in the sense that all core outcomes except one strictly increase the A-group wage advantage. Moreover, firm profits and the magnitude of the wage gap co-move: firms benefit from selecting equilibria with larger wage gaps. The directional conclusion — EPSW benefits the majority group — holds regardless of the distributions of the two groups’ productivities, conditional only on β > 1 for the wage gap; for the log wage gap the additional regularity condition βEA[v] > EB[v] is required.

In the dynamic search model (Proposition 4), all firms eventually segregate under any equilibrium, with the long-run wage ratio moving in favor of the group toward which more firms segregate. Under equitable search and sufficiently low reallocation frictions (Proposition 5), more firms segregate toward the majority group when βEA[v] > EB[v]. Firms that are nearly segregated at the time of EPSW enactment segregate sooner than others (Proposition 6).

Empirical Setting and Design

The authors test these predictions using Chile’s 2009 EPSW (Law 20.348), the country’s first equal pay law, which prohibited paying women less than men (or vice versa) for similar work. Firms with 10 or more long-term workers at the time of announcement (June 2009) face formal grievance procedures and financial penalties (69–1,384 USD per worker-month of violation); firms below this threshold face no financial penalty, providing a clean threshold-based treatment assignment.

The data are matched employer-employee administrative records from the Chilean unemployment insurance system covering January 2005 – December 2013, a random sample of approximately 4% of all firms stratified by size. The main estimation sample restricts to firms with 6–13 total workers at announcement (41% of active firms), and the design is a difference-in-differences (event study) comparing treated (≥ 10 long-term workers) to control (< 10 long-term workers) firms. The identifying assumption is parallel trends between similarly sized firms.

Main Empirical Findings

First, EPSW increases full gender segregation across firms. The share of fully gender-segregated firms increases by 4.4 percentage points (baseline: 34.3% of firms were fully segregated at announcement). Simultaneously, the share of nearly-but-not-fully segregated firms (majority gender share ∈ [0.8, 1)) declines by 4.0 percentage points — a “missing mass” of near-segregated firms consistent with the search model’s prediction that firms on the margin of full segregation segregate most readily (e.g., by separating the sole worker of the “wrong” gender). Moreover, firms that are nearly segregated at announcement experience an 8.7 percentage point increase in full segregation post-EPSW, compared to 2.8 percentage points for firms not nearly segregated at announcement.

Second, EPSW shifts the gender wage gap in favor of the local labor market majority group. In male-majority local labor markets (defined by industry × county), EPSW increases the gender wage gap in favor of men by 4.3 percentage points. In female-majority local labor markets, EPSW decreases the gender wage gap (i.e., in favor of women) by 6.2 percentage points. The wage gap change is primarily driven by reductions in minority-group wages: women’s average wages in male-majority markets fall by 3.3 percentage points, and men’s average wages in female-majority markets fall by 4.5 percentage points; there are no statistically significant changes in majority-group wages. Because men dominate Chile’s overall labor market (approximately 5/6 of all workers are employed in majority-male local labor markets), the overall effect of EPSW is to increase the gender wage gap (in favor of men) by 2.7 percentage points. Pre-treatment coefficients are statistically indistinguishable from zero across all specifications, supporting the parallel trends assumption. These findings are robust across six alternative specifications covering different samples, fixed-effect structures, and controls.

Scope Conditions

Theoretical results apply within a set of “similar” workers in a given local labor market — the paper does not predict differential effects across job types within a firm (e.g., custodians vs. lawyers) that do not perform similar work. Empirical results are identified for firms with 6–13 workers and pertain to Chile’s formal sector (informal labor share ~25% in 2009). Predictions on the wage ratio (log wage gap) require the additional regularity condition βEA[v] > EB[v], which is consistent with the Chilean data.

Layer 2 — Q&A

Q1: What is the core mechanism by which EPSW leads firms to fully segregate in the static model?

A: EPSW makes cross-group poaching prohibitively costly. If a firm that hires only A-group workers were to hire even a positive measure of B-group workers, EPSW would — by transitivity — require it to pay the same wage to all workers. This eliminates the firm’s ability to exploit productivity heterogeneity across workers; it would have to raise all wages to match the highest worker, destroying profit. As a result, firms segregate in equilibrium to avoid the bite of EPSW entirely: each firm caters to one group, and the within-group wage schedule remains unconstrained. The mechanism is analogous to Hotelling’s location model: segregation serves as the enforcement device for avoiding the equal-pay constraint.

Q2: How does the equal profit condition generate a wage gap in favor of the majority group?

A: In any core outcome under EPSW (Proposition 3), the Equal Profit Condition requires both firms to earn the same total profit. When there are β > 1 A-group workers (more than B-group workers), the firm serving A-group workers must pay higher average wages per worker to extract the same total profit from a larger pool, relative to the firm serving a smaller B-group. This mechanically raises A-group average wages relative to B-group average wages. Crucially, this directional conclusion — EPSW widens the majority-group wage advantage — holds regardless of the shapes of FA and FB, meaning it is robust to any underlying discriminatory or non-discriminatory productivity differences.

Q3: What is the baseline (without-EPSW) wage gap, and how does EPSW change it?

A: Without EPSW, Proposition 1 establishes that every worker is paid exactly her productivity in any core outcome (full employment, wages = productivity). Therefore, the wage gap equals EA(v) − EB(v) and the wage ratio equals EA(v)/EB(v): any gap reflects only productivity differences (including discrimination embedded in willingness to pay). Under EPSW, Proposition 3 shows that all core outcomes except a single (measure-zero) one strictly widen the wage gap beyond this level. The wage ratio result (Proposition 3, Part 4) requires the additional condition βEA[v] > EB[v] — that the majority group is not sufficiently less productive or more discriminated against to reverse the direction.

Q4: How does the dynamic search model modify the static predictions?

A: In the dynamic model (Proposition 4), full segregation is achieved in finite time T in any equilibrium, not instantaneously. Prior to T, firms make sequential segregation decisions; workers displaced by firm desegregation choices are replaced at rate ρ ∈ [0,1]. The long-run wage ratio is determined by the ratio nA/nB — the number of firms segregating toward group A versus B. If nA > nB, the long-run wage ratio moves in favor of A; if nA = nB, the policy has no long-run effect on the wage ratio. The key departure from the static model is that this outcome depends not only on the majority group size but also on search intensities and reallocation frictions (high firm tenure/low d can make segregating toward the majority costly if the firm already employs many minority-group workers).

Q5: Under what conditions does the dynamic model predict that more firms segregate toward the majority group?

A: Proposition 5 states that for sufficiently large d (fast worker turnover / low reallocation frictions) and equitable search (equal search intensity across firms within a group), the number of firms segregating toward A satisfies nA ∈ [xA−1, xA+1], where xA is defined by an equal-profit condition. Moreover, if βEA[v] > EB[v] (the majority group is collectively more valuable), then nA ≥ nB. Without equitable search, the conclusion holds under more stringent conditions: for any search intensity vector r, there exist d* and β* such that for d > d* and β > β*, any equilibrium yields nA > nB. Empirically, 94% of local-labor-market-by-month units in Chile exhibit more firms segregating toward the majority gender post-EPSW, consistent with these conditions being met.

Q6: Why do firms that are nearly segregated at announcement respond most strongly to EPSW?

A: Proposition 6 establishes that firms with a low ratio of minority-group to majority-group search intensity (i.e., nearly segregated in employment) segregate earliest, provided the discount rate is sufficiently low. The intuition is that for a nearly segregated firm, the cost of segregating — separating the few minority-group workers — is small relative to the costs of remaining desegregated (paying a common wage that compresses profit, and being unable to poach new workers). Empirically, firms nearly segregated at announcement (majority gender share ∈ [0.8,1) at announcement) show an 8.7 percentage point increase in full segregation post-EPSW, roughly three times larger than the 2.8 percentage point effect for firms not nearly segregated at announcement. This “missing mass” pattern (decline in near-segregation matched by increase in full segregation) is also consistent with Proposition 6.

Q7: What is the heterogeneous effect of EPSW on the wage gap by local labor market type?

A: The empirical design allows the wage gap effect to differ by local labor market (LLM) majority type (male vs. female). In male-majority LLMs (firm industry × county pairs where males comprise more than 50% of workers in June 2009), EPSW increases the gender wage gap in favor of men by 4.3 percentage points (SE = 0.0116). In female-majority LLMs, EPSW decreases the gender wage gap (in favor of women) by 6.2 percentage points (SE = 0.0234). These findings precisely match the theoretical prediction that EPSW benefits whichever group is in the majority of the local labor market. The dynamic event studies show no pre-trends in either subsample; effects begin at announcement (τ = 0) and grow over time.

Q8: What drives the wage gap change — majority wages rising or minority wages falling?

A: The change is primarily driven by a reduction in the minority group’s average wages, not an increase in majority wages. Women’s average wages in male-majority labor markets fall by 3.29 percentage points (SE = 0.0111) in treated versus control firms post-EPSW. Men’s average wages in female-majority labor markets fall by 4.45 percentage points (SE = 0.0178) in treated versus control firms post-EPSW. There are no statistically significant changes in the average wages of the majority group of workers within any LLM type. This is consistent with the model’s mechanism: segregation reduces competition for minority-group workers (fewer firms competing for them), depressing their wages.

Q9: What is the aggregate (economy-wide) effect of EPSW on the gender wage gap in Chile?

A: Because approximately 5/6 of all Chilean workers are employed in male-majority local labor markets (men have higher labor force participation, with female labor force participation at roughly 30% in 2009), the overall effect of EPSW is to increase the gender wage gap in favor of men by 2.74 percentage points (SE = 0.0102). This is a net effect that averages the positive (pro-male) gap increase in male-majority markets and the negative (pro-female) gap decrease in female-majority markets, weighted by market sizes.

Q10: How does the identification strategy deal with anticipation and compositional changes?

A: Treatment status is assigned based on firm size at the time of policy announcement (June 2009) rather than enactment (November 2009), creating an intent-to-treat framework: some “treated” firms may fall below the threshold by enactment, and some “control” firms may rise above it, both attenuating the estimates (implying estimated effects are plausible lower bounds). The no-anticipation assumption is supported by the absence of statistically significant pre-trends in either the segregation or wage-gap specifications. To address compositional changes in worker characteristics across LLMs induced by EPSW itself, the wage regressions include time fixed effects interacted with human capital dimensions (education, contract type, age decade) and firm comparison groups, controlling for observable composition shifts. Placebo tests at alternative firm-size thresholds find no statistically or economically meaningful effects, supporting the causal interpretation.

Q11: How does EPSW in Chile compare to EPEW theoretically and in the literature?

A: EPEW requires equal pay only for workers doing exactly equal work, which creates an easily exploitable loophole: firms can proliferate job titles or marginally differentiate duties to avoid compliance. EPSW closes this by requiring equal pay across a coarser “similar work” category, making evasion harder. Theoretically, the prior EPEW literature (Bhaskar et al. 2002, Kaas 2009, Lagerlöf 2020, Lanning 2014) generated ambiguous directional predictions — equal pay laws could either increase or decrease wage disparities within the same paper. The authors attribute this ambiguity to EPEW models’ requirement that workers be exactly equally productive. By contrast, EPSW applies across workers with heterogeneous productivities, and the authors derive unambiguous predictions: full segregation and a wage gap shift toward the majority group, both of which are confirmed empirically.

Q12: What is the analogy to “best-price guarantees” in product markets?

A: The paper draws a methodological parallel to most-favored-customer (MFC) clauses in product markets. MFC clauses commit firms to rebating past consumers if prices fall, which directly equalizes payments across buyers but unintentionally raises firm market power. In the EPSW setting, the policy plays the role of a best-wage guarantee — but because firms compete for workers, the constraint binds off the equilibrium path. Firms segregate so that no firm is ever exposed to the equal-pay constraint in equilibrium, yet the threat of the constraint (if a firm deviates and hires from both groups) effectively differentiates labor costs across groups, driving the unintended wage effects. This is related to “artificial” switching costs that create local market power in consumer markets (Klemperer, 1987).

Key Concepts

Equal Pay for Similar Work (EPSW): A legal constraint requiring that within a firm, workers belonging to different protected-class identities (e.g., different genders) who perform “similar” work receive equal wages. Distinguished from “Equal Pay for Equal Work” (EPEW) by its coarser similarity standard, which cannot be evaded by minor job-title differentiation. In the model, this constraint is formalized as: a firm cannot hire positive measures of workers from two different groups such that all workers in one group receive strictly higher wages than all workers in the other group; by transitivity, a firm hiring from both groups must pay almost all workers the same wage.

Core Outcome: The solution concept used in the static model, drawing on cooperative game theory (Shapley–Shubik assignment game). An outcome (specifying which firm hires each worker and at what wage) is in the core if no firm and subset of workers can form a blocking coalition that makes both the firm and each worker in the coalition strictly better off. The paper uses this concept because its pure-strategy Nash equilibrium outcomes (in the associated non-cooperative simultaneous wage-offer game) exactly coincide with the core outcomes under the restriction that firms pay the same wage to all workers of the same type.

Full Segregation: A labor market outcome in which each firm employs workers from only one group (all A-group workers at one firm, all B-group workers at the other). The paper proves (Proposition 2) that EPSW generically forces full segregation in equilibrium, because any deviation to hire from both groups exposes the firm to the equal-pay constraint. Empirically measured as a binary indicator for whether all workers at a given firm in a given month are of the same gender.

Near Segregation: A firm-level state in which the majority gender constitutes 80–99% of the firm’s workforce (the majority gender share is in [0.8, 1)). The paper uses this as a complementary outcome to full segregation; theory (Proposition 6) predicts a decline in near segregation post-EPSW because firms in this state face the lowest cost of transitioning to full segregation. Empirically, the near-segregation share falls by 4.0 percentage points post-EPSW, mirroring the 4.4 percentage point rise in full segregation.

Local Labor Market (LLM): Defined in the empirical analysis as a firm’s geographic county interacted with its industry code, creating 321 × 21 potential cells. The LLM is classified as male-majority or female-majority based on the share of female workers across all firms in the industry-county pair in June 2009. This is the unit at which the “majority group” for Proposition 3’s wage gap prediction is defined, and the level at which the heterogeneous wage effects of EPSW are estimated.

Equal Profit Condition: A necessary condition of any core outcome (with or without EPSW): both firms must earn the same total profit in equilibrium. Under EPSW with full segregation, this condition determines the relative average wages of the two groups — because firm sizes differ (β A-group workers vs. 1 B-group worker), equal profit requires the firm serving the larger group to pay higher average wages, mechanically moving the wage gap in favor of the majority group.

Nash-in-Nash Bargaining: The bargaining protocol used in the dynamic search model, following Horn and Wolinsky (1988). Each bilateral worker-firm bargain splits the available surplus in proportion to exogenous bargaining power parameter Δ ∈ (0,1), taking as given the outcome of all other bilateral bargains. A worker’s disagreement point is the wage she would receive from bargaining with the next firm in her search order. This generates the result that a worker’s realized payoff is increasing in the number of segregated (non-EPSW-constrained) firms competing for her, connecting firm segregation decisions to wage determination.

Reallocation Friction: In the dynamic search model, represented by a low departure probability d ∈ (0,1) for existing employees. When d is low, firms retain a large fraction of their workforce across periods, making segregation costly because the firm must separate from any existing workers of the “wrong” group. The paper shows (Proposition 5) that for sufficiently large d (low frictions), the equal-profit condition approximately pins down the number of firms segregating toward each group, and for d above a threshold, the majority group attracts weakly more segregating firms.