J38 | Macro Paper Warehouse

Supply, Demand, Institutions, and Firms: A Theory of Labor Market Sorting and the Wage Distribution

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research question. How do workforce composition (labor supply), labor demand, and minimum wage policy jointly determine the wage distribution in imperfectly competitive labor markets, and what were the quantitative contributions of each force to the dramatic decline in Brazilian wage inequality between 1998 and 2012?

Motivation. Brazil’s formal-sector wage inequality fell sharply over this period. Three candidate shocks are well-documented: (1) a large increase in educational attainment — the share of adults completing at least secondary school rose by 20 percentage points (a 68 percent increase) between 1998 and 2012; (2) labor demand shocks, primarily the commodities boom of the 2000s; and (3) a 93.7 percent (66.1 log point) real increase in the federal minimum wage. Existing frameworks analyze these shocks separately — competitive supply/demand models on one side and imperfectly competitive minimum wage models on the other — and therefore cannot detect interactions or jointly explain all observed patterns, including the novel finding that assortative matching between high-wage workers and high-wage establishments rose in 104 out of 151 microregions, a fact inconsistent with the predictions of leading minimum wage models.

Data. The paper uses the RAIS (Relação Anual de Informações Sociais), a confidential linked employer-employee dataset covering the Brazilian formal sector, together with Brazilian Census data for 1991, 2000, and 2010. Statistics are computed for 151 microregions (analogous to US commuting zones) with at least 15,000 workers in RAIS in both base years and at least 1,000 formal workers per educational group. The final sample covers 73 percent of the adult population. Firm wage premiums and assortative matching are measured via AKM two-way fixed effects regressions using the bias-corrected KSS (Kline, Saggio, Sølvsten 2018) estimator, run separately for each microregion and period on three-year panels.

Theoretical framework. The paper develops a unified general-equilibrium model featuring: (i) a task-based production function with distance-dependent complementarity between worker types; (ii) monopsony power arising from idiosyncratic worker preferences for firms, generating constant firm-level labor supply elasticity β (calibrated at 4, implying markdowns of 20 percent); (iii) heterogeneous firms differentiated by their production “blueprints” (the complexity of tasks they require), with blueprint shape parameterized as a Gamma distribution; and (iv) free firm entry, endogenous participation, and goods market general equilibrium with CES consumer preferences (elasticity σ). A key result is that firms with different blueprints exhibit different within-firm substitution patterns: worker types that are substitutes at low-skill, low-wage firms may be complements at high-skill, high-wage firms.

Estimation. A parsimonious parameterization is estimated by simultaneous-equation nonlinear least squares, targeting 26 endogenous outcomes per region (13 per period) including between- and within-group wage inequality, variance of establishment effects, covariance of worker and establishment effects, formal employment rates by education, and minimum wage bindingness. The model requires solving for equilibrium more than 15,000 times per optimization step (151 regions × 2 periods × 53 Jacobian columns). The elasticity of substitution between goods is estimated at σ = 8.36 (significantly above 1), and the aggregate labor supply parameter λ implies formal-sector elasticities of approximately 0.6–0.7 for college workers and around 1.1 for less-than-secondary workers. The model fits the data well, with R² above 0.5 for most targeted moments and perfect fit for the six moments used in the inversion procedure.

Main findings.

Demand shocks and the minimum wage are the primary drivers of falling inequality. In counterfactual simulations, the minimum wage alone (a 66.1 log point increase) reduces the variance of log wages by 0.13. Demand shocks reduce it by a further 0.18. Supply shocks (rising education) increase the variance by 0.04, leaving their net inequality-reducing contribution negligible.
Supply shocks increase assortative matching despite compressing within-firm skill premiums. Within-firm task reassignment would reduce the variance of log wages by 0.221 and the correlation between worker and establishment effects by 0.165, holding production levels and firm entry fixed. However, scale, entry, and price adjustments — driven by the large estimated σ = 8.36 > β + 1 = 5 — reallocate skilled labor toward high-wage, skill-intensive firms, counteracting within-firm compression and raising assortative matching by 0.189. These two channels largely offset each other.
Concurrent supply and demand changes attenuate minimum wage impacts by roughly half. When the minimum wage is the only shock, it would have reduced the variance of log wages by 0.13; in the presence of supply and demand changes, its incremental contribution is approximately 0.07. Minimum wage effects on sorting (which would reduce assortative matching when acting alone) disappear when accompanied by supply and demand transformations.
Minimum wage effects are concentrated in the bottom two productivity deciles. Wage effects for workers in productivity deciles three through ten from the minimum wage are approximately 1 percent or less once all channels are considered. Strong wage gains are concentrated at the bottom, primarily through the monopsony channel. The wage-posting channel (within-firm returns to skill) reduces wages for low- and middle-skill workers and raises them at the top two deciles due to the reallocation of low-skilled workers toward high-wage firms, which reduces those workers’ marginal products there.
Cross-firm differences in substitution patterns generate non-standard minimum wage spillovers. Conditional on the task demands of the firm employing them, a pair of worker types may be substitutes in low-skill firms and complements in high-skill firms. This firm-heterogeneity channel causes minimum wage impacts to be non-monotone across the productivity distribution, contrasting with the smooth inequality-reducing effects predicted by both competitive task-based models and frictional minimum wage models.

Layer 2 — Q&A

Q1: What is the novel empirical fact that motivates the unified framework? A: Using KSS bias-corrected AKM decompositions performed separately for each of 151 microregions, the paper documents that assortative matching — measured as the correlation between worker and establishment fixed effects — rises in 104 out of 151 regions between 1998 and 2012. The covariance term accounts for less than 7 percent of the average decline in the variance of log wages. This finding is inconsistent with the leading imperfectly competitive minimum wage model (Engbom and Moser 2022), in which minimum wages reduce assortative matching. It is also inconsistent with purely competitive supply/demand models, which have no role for firm wage premiums or sorting. The divergence from prior national-level studies (which do not find rising sorting) is explained by the fact that national-level sorting conflates geographical sorting with supply-demand dynamics.

Q2: What is the key mechanism through which the task-based production function generates cross-firm differences in substitution patterns? A: In the task-based production function, each firm assigns workers to tasks assortatively — lower types handle lower-complexity tasks, higher types handle higher-complexity tasks, with cutoff thresholds determined by the firm’s blueprint. When a firm has a blueprint concentrated in complex tasks (a high-skill, high-wage firm), adjacent worker types are more differentiated in the tasks they perform, making them complements. When a firm has a blueprint concentrated in simple tasks (a low-skill, low-wage firm), adjacent worker types are assigned to a narrow, similar range of tasks and are therefore closer substitutes. The elasticity of complementarity between any pair of worker types is thus endogenous, depending on which tasks the firm uses and, in the monopsony case, on the firm’s skill intensity — a prediction validated empirically using nonroutine cognitive task content data for Brazilian occupations.

Q3: Under what conditions can a positive supply shock (rising educational attainment) widen the aggregate skill wage premium rather than compress it? A: The paper’s Proposition 4 and Corollary 2 show that a supply shock that increases the relative supply of skilled workers can widen the aggregate skill wage premium when the elasticity of substitution between goods (σ) exceeds the firm-level elasticity of labor supply plus one (β + 1). Intuitively, when σ is large, the reduction in prices for skill-intensive goods generated by the supply shock shifts consumption toward those goods, causing net entry of skill-intensive firms. If the gains in firm wage premiums earned by skilled workers reallocated to those firms outweigh the compression in within-firm productivity differentials, the aggregate skill premium can rise. This mechanism does not require non-convexities from endogenous innovation; it operates through imperfect competition and firm entry alone. In the estimated Brazilian model, σ = 8.36 substantially exceeds β + 1 = 5, so this condition holds, explaining why rising education increases rather than compresses assortative matching in the data.

Q4: How does the model generate positive employment effects from minimum wages, and how do these interact with reallocation? A: In the monopsonistic baseline without a minimum wage, firms post wages below workers’ marginal revenue products, causing some workers to choose non-employment. A minimum wage increase raises posted wages at constrained firms, shifting some workers from non-employment (or home production) to formal employment, generating positive employment effects at the margin where the minimum wage binds. Simultaneously, minimum wages price out the least productive workers at low-wage firms (disemployment), while workers in the intermediate productivity range reallocate from low- to high-wage firms, because high-wage firms have higher revenue productivity and can profitably hire workers that low-wage firms can no longer afford. The net employment elasticity for the lowest productivity decile with respect to the log minimum wage is −0.61 (Table 7), while the mean wage for that decile rises substantially through the monopsony channel.

Q5: What are the three channels through which the minimum wage affects wages and employment in the model, and what does each channel contribute? A: The paper decomposes minimum wage effects into three channels. Channel 1 (monopsony): mechanical wage increases, positive employment effects at firms where the minimum wage binds, disemployment of very low-productivity workers, and reallocation from low- to high-wage firms, holding posted wage schedules, prices, and entry fixed. This channel accounts for nearly all of the strong wage effects at the bottom two productivity deciles. Channel 2 (wage posting): firms reoptimize earnings schedules following changes in worker composition and marginal products induced by Channel 1, holding prices and entry fixed. This channel reduces wages for low- and middle-skill workers (productivity deciles 1–7) by approximately 0.01–0.02 log points and increases wages for top deciles (decile 9: +0.04, decile 10: +0.11), because reallocation of low-skill labor to high-wage firms lowers those workers’ marginal products there. Channel 3 (general equilibrium): firm entry and price responses. The fall in low-wage-firm profits causes entry of high-wage, skill-intensive firms, while the price of low-skill goods falls. General equilibrium effects generate modest positive wage effects for most workers but negative effects for very low-productivity workers due to reduced aggregate demand for low-skill labor.

Q6: Why do the minimum wage’s inequality-reducing effects diminish when accompanied by concurrent supply and demand changes? A: The paper documents that, under concurrent supply and demand transformations, the minimum wage’s reduction of the variance of log wages is approximately 0.07, roughly half the 0.13 reduction it would achieve acting alone. The attenuation occurs through interactions: supply and demand shocks raise the average productivity level of the labor market and shift workers toward high-wage, skill-intensive firms. In this altered equilibrium, the minimum wage binds less tightly (or hits a different part of the distribution), and the reallocation effects of the minimum wage that would normally reduce assortative matching are offset by the sorting-increasing effects of supply and demand changes. The estimated model shows that interactions between the minimum wage and supply/demand changes (columns 6, 7, 8 of Table 5) are economically meaningful, something undetectable without a unified framework.

Q7: How does the model’s prediction regarding minimum wage spillovers differ from Engbom and Moser (2022), and what explains the difference? A: Engbom and Moser (2022) find that the Brazilian minimum wage hike had significant wage effects extending far up the worker productivity distribution, while this paper’s model finds negligible effects (approximately 1 percent) beyond the bottom two productivity deciles. Two structural differences explain this divergence. First, Engbom and Moser (2022) assume perfect substitutability between worker types within firms, so a minimum wage increase at low-wage firms mechanically raises posted wages at all other firms to maintain relative competitiveness. In this paper’s framework, wage-posting responses at high-wage firms can be negative for low-skill workers because the inflow of reallocated low-skill workers reduces their marginal products — a channel absent under perfect substitution. Second, Engbom and Moser (2022) use a national model, allowing displaced low-skill workers to reallocate to top-productivity firms anywhere in the country, dampening disemployment; this paper’s local labor markets approach restricts reallocation to within-region boundaries, consistent with low rates of interregional migration documented for Brazil by Dix-Carneiro and Kovak (2017).

Q8: How are firm wage premiums generated in the model, and why do differences in physical productivity between firms not generate wage differentials? A: Proposition 3 establishes that wage dispersion for similar workers across firms requires either (i) differences in blueprint shapes (firm heterogeneity in skill intensity) or (ii) differences in entry costs. Differences in physical productivity (z_g) or consumer taste parameters alone are insufficient, because with equal entry costs, differences in productivity lead to additional firm entry until the marginal revenue product of labor is equalized across firm types. Wage premiums proportional to entry costs arise because optimal firm creation requires larger-scale operation for higher-entry-cost firms, and hiring more workers forces those firms to post higher wages. Additionally, skill-intensive firms (firms with blueprints tilted toward complex tasks) pay relative wage premiums for the worker types they use most intensively, and if skill intensity and entry costs co-vary, all workers at high-skill firms may receive a wage premium.

Q9: How does the estimation procedure handle unobserved regional heterogeneity in labor demand? A: Demand shocks are not directly observed; they are inferred as a residual from changes in targeted outcomes after accounting for observed supply (education shares from Census) and minimum wage changes. Five region-time-specific demand parameters — TFP (z), blueprint complexities (θ₁, θ₂), relative entry costs (F₂/F₁), and relative consumer preferences (γ₂/γ₁) — are modeled as linear functions of 1998 regional covariates (educational shares, agricultural share, manufacturing share, and initial minimum wage bindingness) with time-specific coefficients. This formulation allows unobserved demand shifters to correlate with initial educational levels, preventing incorrect attribution of demand-supply correlations to causal supply effects. Region-specific parameters (TFP in each period, education-group-specific formal employment shifters) are inverted exactly from six targeted moments within each region, eliminating incidental parameter bias.

Q10: What micro-level empirical validations does the paper conduct for the task-based model’s mechanisms? A: The paper tests four micro-level predictions using nonroutine cognitive task content data for Brazilian occupations. First, skill-intensive firms have greater demand for complex tasks (consistent with Figure 1 of the model). Second, within firms, more skilled workers are assigned to more complex tasks (Lemma 1). Third, workers who move to more skill-intensive firms are assigned more complex tasks (Lemma 2, consistent with the monopsony model’s mismatch prediction). Fourth, wage gaps between high- and low-skill firms are larger for skilled workers (Proposition 3). The paper reports finding strong support for all four predictions in the data, lending credibility to the theoretical structure and quantitative results.

Key Concepts

Task-based production function (paper’s definition): A production function in which a firm produces output by assigning workers of different types to tasks indexed by complexity. The assignment is assortatively optimal: lower-type workers handle lower-complexity tasks, with unique threshold complexities separating adjacent worker types. The critical property is distance-dependent complementarity — any pair of worker types that are “close” in skill rank are substitutes, while pairs distant in skill rank are complements. This differs from CES production functions where the elasticity of complementarity is the same for all pairs; in the task-based version, substitutability depends on endogenous assignment and thus on the firm’s blueprint.

Blueprint (paper’s definition): A function b_g(x) that specifies the density of tasks of each complexity level x required to produce one unit of good g. It is the fundamental source of firm heterogeneity in the model: firms producing goods with blueprints tilted toward complex tasks are more skill-intensive, hire workers of higher average type, and pay higher wages. The paper parameterizes blueprints as Gamma distributions with shape parameter θ_g indexing average task complexity; firms with higher θ_g are more skill-intensive.

Firm wage premium (paper’s definition): The component of wages at a given establishment that accrues equally to all workers at that firm regardless of their type, measured as the establishment fixed effect ψ_j in AKM two-way fixed effects regressions. In this model, firm wage premiums arise from heterogeneity in blueprints (skill intensity) and entry costs, not from differences in TFP or consumer tastes. Under monopsony, firms with higher entry costs must operate at larger scale and post higher wages; blueprint heterogeneity generates differential wage premiums by skill type.

Sorting / assortative matching (paper’s definition): The correlation between the worker fixed effect (ν_i,r capturing worker skill) and the establishment fixed effect (ψ_j capturing firm wage premium) in the AKM decomposition, measured as Cov(ν_i,r, ψ_{J(i,r,τ)} | r). In this paper’s framework, sorting arises because firms with blueprints demanding complex tasks (high-wage firms) have a comparative advantage in employing high-skill workers; labor market sorting can therefore change over time due to supply, demand, or minimum wage shocks, even without changes in search frictions.

Monopsony power / markdown (paper’s definition): Arising from idiosyncratic worker preferences for firms (modeled as a nested logit), firms face upward-sloping labor supply curves with constant firm-level elasticity β. Optimal posted wages equal a constant markdown β/(β+1) of the marginal revenue product of labor, set to β = 4 (implying a 20 percent markdown). The macro elasticity of formal sector labor supply is governed by a separate parameter λ, estimated from the data, yielding aggregate formal-sector supply elasticities of approximately 0.6–0.7 for college workers and around 1.1 for less-educated workers.

Wage posting responses (paper’s definition): The second channel of minimum wage effects, in which firms reoptimize their entire earnings schedule following the wage-composition changes induced by the minimum wage’s mechanical and reallocation effects (Channel 1), while keeping goods prices and firm entry fixed. Because task-based production functions are concave, changes in factor proportions (due to reallocation of low-skill workers to high-wage firms) alter marginal products of all worker types within those firms, causing firms to adjust all posted wages — not just those directly constrained by the minimum wage.

Distance-dependent complementarity (paper’s definition): The property, proven as a Corollary to Proposition 1, that for a fixed worker type h, the partial elasticity of complementarity between h and any other type h’ is strictly increasing in h’ for h’ ≥ h (more distant high types are stronger complements) and strictly decreasing in h’ for h’ ≤ h (more distant low types are weaker substitutes / stronger complements). This pattern results from the division of labor: adding a very different worker type allows specialization gains that do not arise when adding similar-type workers competing for the same tasks.

Unemployment Insurance, Starting Salaries, and Jobs

Mon, 01 Jan 0001 00:00:00 +0000

Seven U.S. states permanently cut unemployment insurance (UI) benefits by 30–64 percent between 2011 and 2014, providing the study’s quasi-experimental variation. North Carolina enacted the largest reform: maximum duration fell from 26 weeks to 12–20 weeks and maximum weekly benefits fell from $535 to $350, an average total reduction of 64 percent. Six “moderate reform” states (FL, GA, KS, MI, MO, SC) cut duration only, by an average of 30 percent (26→18 weeks). Using a multi-state firm identification strategy — comparing establishments of the same firm operating in reform states against the same firm’s establishments in non-reform states, with establishment and firm×year fixed effects — the paper estimates causal effects of UI cuts on employment (EEOC, 946K–1.4M establishment-years), starting salaries (Glassdoor, 500K–942K person-years), and posted wages (Burning Glass Technologies, 709K–1.18M establishment-job-quarters). The main results: NC establishments gain +1.3% employment on average relative to same-firm establishments in other states (ATT), reaching +2.1% by year 2; moderate reform states gain +0.8% (ATT). Starting salaries of new hires fall −5.5% in NC and −1.2% in moderate states. Posted wages for the same job within the same firm fall −3.5% in NC and −3.2% in moderate states. The negative co-movement of employment and wages identifies a labor supply shock: workers lower reservation wages in response to reduced outside options; firms take advantage by hiring more at lower wages. Labor demand elasticity: −0.36 (SE 0.21) for NC, −0.42 (SE 0.18) for moderate states. The larger effects in NC relative to moderate reform states are consistent with the larger total benefit reduction; effects are robust to controlling for concurrent right-to-work laws, minimum wage changes, Medicaid expansions, and corporate/personal tax reforms. The paper concludes that large, permanent UI reductions can raise employment but at the cost of lower starting wages.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. How does the multi-state firm design separate UI effects from aggregate and local shocks?

The key innovation is including firm×year fixed effects alongside establishment fixed effects: within any given firm and year, the only remaining variation is which state the establishment is in — absorbing all firm-wide demand trends, management strategies, and capital-allocation decisions that would otherwise confound cross-state comparisons. Standard difference-in-differences compares reform states to non-reform states at the level of geographic unit or industry; this approach confounds UI changes with the economic conditions that prompted them. The multi-state firm design eliminates this confound because firms’ nationwide operational decisions are held constant. The identification concern is policy endogeneity — whether reform states had weaker economies motivating both the UI cuts and slow hiring. This is addressed in three ways: (1) the 27 other states whose UI trust funds became insolvent in the early 2010s did NOT cut benefits, ruling out insolvency per se as the trigger; (2) restricting the control group to only the insolvent states (Table 3 cols 2 and 5) leaves estimates nearly unchanged; (3) restricting further to insolvent states that experienced a Great Recession unemployment shock within ±2 percentage points of the reform states (Table 3 cols 3 and 6) again leaves estimates unchanged, ruling out mean reversion. The mean reversion hypothesis is additionally ruled out by the wage results: mean reversion predicts faster wage growth in reform states, but wages fall.

Q2. What are the quantitative employment effects, and how do they compare across specifications?

In the baseline specification (Table 3, column 1), NC establishments gain +1.26% employment on average over the post-reform period (ATT, SE 0.0052, p<0.05), with the effect growing from +1.2% in year 1 to +2.1% in year 2 (both p<0.01); moderate reform states gain +0.83% (ATT, SE 0.0022, p<0.01), reaching +1.5% by year 2. Alternative specifications (Table 5) using less-saturated fixed effects (firm+state+year FEs or establishment+year FEs only) produce estimates roughly twice as large — +2.5% for NC — confirming that firm×year fixed effects absorb a substantial share of cross-state employment variation that is not attributable to UI. This amplification underscores why controlling for firm-level trends matters: firms simultaneously expanding in many states would appear in the unconditioned data as UI-reform effects. Robustness to policy confounders (Table 4): excluding states with RTW law changes, minimum wage changes, Medicaid expansions, major corporate or personal tax reforms all leave ATTs statistically significant and economically similar (0.80%–1.25% for NC; 0.82%–1.18% for moderate states). A Fisher exact test places NC’s t-statistic in the top 2/42 (4.8%) of placebo assignments, consistent with a one-sided 5% test. Controlling for NC’s concurrent corporate tax cut, which bounds the maximum tax-driven employment effect at 0.76pp (Giroud and Rauh 2019), implies the UI reform accounts for between 0.5% and 1.26% of NC’s employment increase — broadly consistent with the 0.83% moderate reform estimate.

Q3. What do the wage results show, and how do posted wages rule out compositional explanations?

Table 7 (Glassdoor starting salaries, job and firm×year FEs): NC ATT = −5.5% (SE 0.021, p<0.01), moderate states ATT = −1.2% (SE 0.0051, p<0.05); the effect is concentrated in jobs with starting salaries at or below $100,000, where UI replacement rates are meaningfully binding, and is statistically insignificant for higher-wage jobs. Starting salary declines could in principle reflect worker composition (lower-skilled workers drawn into the labor force) or worse job matches (workers accepting jobs below their productivity) rather than firms lowering offer wages. Burning Glass Technologies (BGT) posted wages, which measure the wage advertised for the same job within the same firm over time (establishment-job and firm×year FEs), rule out both channels: Table 8 shows NC posted wage ATT = −3.5% (SE 0.013, p<0.01) and moderate states = −3.2% (SE 0.0071, p<0.01). The near-equality of posted and realized wage effects implies the wage decline is driven by firms lowering their wage offers — not by changes in worker composition or match quality. Occupational heterogeneity confirms the mechanism: high-exposure occupations (above-median fraction of workers with unemployment spells or employment tenures exceeding 20 weeks) exhibit NC posted wages −3.5% and moderate states −4.1%; low-exposure occupations show near-zero insignificant effects (Table 9). Posted wages also provide additional evidence against mean reversion: if reform states had faster-growing underlying wages, posted wages would rise relative to controls, but the opposite occurs.

Q4. How does the negative co-movement of employment and wages identify a labor supply shock and discipline the theoretical mechanism?

The simultaneous rise in employment (+1.26% NC, +0.83% moderate) and fall in posted wages (−3.5% NC, −3.2% moderate) is the signature of a labor supply shock under the standard Mortensen-Pissarides (1994) framework: when workers’ outside option (the value of UI) falls, their reservation wages fall, inducing firms to post more jobs at lower wages. A positive demand shock would raise both employment and wages; a positive supply shock raises employment while lowering wages. The posted wage channel further implies that firms’ labor demand responds to the wage reduction (not just to the supply expansion): if firms were passive price takers, posted wages would not change. The data imply that firms internalize workers’ changed outside options and lower their wage offers accordingly, consistent with the monopsonistic wage-setting in Mortensen-Pissarides with free entry. The labor demand elasticity calculated as (Δlog employment / Δlog posted wage) = 1.26/3.5 ≈ −0.36 (SE 0.21) for NC and 0.83/3.2 ≈ −0.26 or using preferred specification −0.42 (SE 0.18) for moderate states; these fall in the middle of the distribution of prior estimates from cross-country labor demand elasticity studies (Hamermesh 1996; Acemoglu et al. 2004). A Chodorow-Reich et al. (2019) decomposition suggests that if labor market tightness increased (fewer unemployed and more vacancies), the reservation wage (opportunity cost) effect dominates the tightness effect — since we observe posted wages falling.

Q5. What do the CPS results add, and how do employment duration effects inform the mechanism?

Using individual-level CPS data with state and year fixed effects (no within-firm comparison), combining all reform states: employment probability +1.0pp (SE 0.43pp, a 1.5% increase relative to the 65% baseline) [Table 10 col 1]; new-hire wages (tenure <1yr) −6.3% [col 2]; unemployment duration −2.8 weeks/year ATT (relative to 33.48-week control mean, an 8% reduction) [col 3]. The CPS results are qualitatively consistent with the multi-state firm findings and use an entirely different data source, sampling frame, and identification approach. The unemployment duration effects are instructive about timing and mechanism: the ATT is negligible in the first two post-reform years (−1.0 and −1.2 weeks, insignificant), rises to −1.7 weeks in year 3, −3.6 in year 4, −4.2 in year 5, and −5.6 in year 6 — consistent with gradual stock-flow dynamics (the stock of workers who began unemployment before the reform exhausts gradually, so average duration in the reform states drifts lower over time as a larger share of the unemployed pool faces the new rules). This pattern helps interpret the gradual employment growth in the event studies.

Q6. How does the paper explain divergence from prior literature finding small UI effects?

The paper argues that prior work finds small effects because reforms studied were smaller in size, temporary, and enacted during deep recessions — all conditions where the job creation channel from lower reservation wages is muted. Schmieder et al. (2010), Rothstein (2011), Farber-Valletta (2015), Chodorow-Reich et al. (2019) and others study UI extensions/expirations that are often 13–20% changes in duration (versus NC’s 44% duration cut and 64% total benefit cut), enacted during high unemployment (when moral hazard is lower) or temporary (so workers discount the change in outside options). A 13-week contrast off a high base of 83 weeks (the EUC expansions) differs fundamentally in moral hazard intensity from an 11.5-week cut off a low base of 26 weeks plus a benefit level reduction — the effective present value of UI falls far more in the NC reform. Additionally, the border county-pair design used in much prior work (Chodorow-Reich et al. 2019, Hagedorn et al. 2025) compares establishments on opposite sides of a state border within the same labor market; these competing establishments cannot fully exploit lower reservation wages because they compete for the same workers — suppressing both the employment and wage responses. Notable exceptions that do find sizable effects — Johnston-Mas (2018) and Karahan et al. (2025), both studying large permanent post-recession reforms — corroborate this paper’s findings.

Key concepts

multi-state firm design : the identification strategy that compares establishments of the same firm operating in reform states against the same firm’s establishments in non-reform states; with establishment and firm×year fixed effects, this absorbs firm-wide demand trends, product market shocks, and management decisions that affect all of a firm’s establishments equally, isolating state-level UI variation as the sole source of identification.

reservation wage : the minimum wage at which an unemployed worker is willing to accept a job offer, determined by the outside option value (UI benefits plus expected future wages from continued search); UI cuts reduce the outside option value, lowering the reservation wage and enabling firms to post and fill vacancies at lower wages.

posted wage : the wage listed in a job advertisement before any worker-firm negotiation or match quality sorting; measured here using Burning Glass Technologies (BGT) data at the establishment-job level, controlling for the same job across time within the same firm; distinct from realized starting salary in that it reflects the firm’s wage-setting decision independent of which worker accepts.

labor supply shock : an exogenous change in the willingness of workers to supply labor at given wages; identified here by the negative co-movement of employment (up 1.3–0.8%) and wages (down 3.5–3.2%), which is the opposite of what a positive labor demand shock would predict, ruling out confounding from corporate tax cuts or mean-reverting demand.

outside option : the payoff available to an unemployed worker from continued search rather than immediate job acceptance; UI benefits are the dominant component; when UI generosity falls, the outside option value falls and firms can hire more workers at lower wages — the core mechanism linking permanent UI cuts to simultaneous employment gains and wage reductions.

What's My Employee Worth? The Effects of Salary Benchmarking

Mon, 01 Jan 0001 00:00:00 +0000

This paper studies how salary benchmarking tools — products that reveal aggregate market pay statistics for specific job titles — affect employee compensation. The research question is whether firms’ access to such tools causally changes how they set salaries, and what this implies about information frictions in labor markets and the policy debate over benchmarking regulation.

The authors collaborated with the largest U.S. payroll processing company (serving 650,000 firms and 20 million workers), exploiting the staggered roll-out of a proprietary Compensation Benchmark Tool. The tool aggregates payroll data into salary benchmarks by standardized job title, with the median base salary as its most prominent statistic. The study draws on three linked administrative datasets: payroll records (January 2017 to July 2021), tool usage logs (September 2019 to August 2021), and historical benchmark snapshots. The main analytical sample covers new hires at 586 treatment firms that gained tool access and 1,419 matched control firms that did not, within a 10-quarter window around each firm’s onboarding date.

The identification strategy is difference-in-differences, exploiting three sources of variation: which firms gain access; the staggered timing of access (driven by the arbitrary order in which sales representatives introduced the tool); and within treatment firms, whether a specific position was actually searched in the tool. New hires are classified into Searched positions (5,266 hires at treatment firms for positions eventually looked up), Non-Searched positions (39,686 hires at treatment firms for positions not looked up), and Non-Searchable positions (156,865 hires at control firms). Event-study analyses confirm flat pre-trends across all groups, supporting causal interpretation.

The primary finding is that benchmark access reduces salary dispersion around the median market benchmark by 25%. Before onboarding, the average absolute deviation of offered salaries from the median benchmark in Searched positions was 19.8 percentage points (pp). After onboarding, this fell to 14.9 pp — a drop of 5.0 pp using Non-Searched positions as control (p-value < 0.001) and 6.2 pp using Non-Searchable positions as control (p-value < 0.001). Compression runs in both directions: firms previously paying above the benchmark reduce salaries toward the median, and firms previously paying below raise salaries toward the median. The probability of setting a salary within 2.5% of the median benchmark nearly doubled, from 11.6% to 22.1% after onboarding.

Effects are heterogeneous by skill level. For low-skill positions (approximately 42% of the sample, e.g., bank teller, receptionist), dispersion falls from 14.5 pp to 8.7 pp — a 40% reduction. For high-skill positions (e.g., software developer), dispersion falls from 24.0 pp to 20.5 pp — a 14.6% reduction. For low-skill positions, compression from below dominates, producing a net average salary increase of +5.0% to +6.7% (p-values 0.014 and 0.001 depending on control group). For high-skill positions, the average salary effect is small and statistically insignificant overall. Twelve-month retention rates for low-skill workers increase by 6.6 to 6.8 pp after benchmarking, and the implied retention elasticity is consistent with prior literature estimates.

The authors propose a theoretical model to rationalize these findings. Firms are assumed uncertain about the wage distribution (aggregate uncertainty), with private information about their own value of filling a position and affiliated valuations across firms. In equilibrium, firms with higher values make higher offers — generating wage dispersion among identical workers without monopsony power, efficiency wages, or amenity differences. When a firm gains benchmark access, it adjusts its offer toward the threshold wage needed to hire, compressing offers from both sides. In the full-information equilibrium where benchmarks are common knowledge, the mean salary is weakly higher than without benchmarks, because the marginal firm had previously underestimated labor market tightness and offered too little, capturing extraordinary profits. Benchmarking eliminates these informational rents, intensifying competition and raising average pay.

The scope of the empirical findings is restricted to new hires at firms in the top quartile of U.S. firm size by employment, across all industries and U.S. states, over 2017–2020. The estimated effect is the incremental causal impact of one additional high-quality benchmarking source, since most firms already had access to some pay information through other channels.

Q: What is the main causal finding of the paper? A: Access to the salary benchmarking tool reduces the absolute deviation of new-hire salaries from the median market benchmark by approximately 25%. Specifically, average dispersion in Searched positions falls from 19.8 pp before onboarding to 14.9 pp after, a drop of 5.0 pp (using Non-Searched controls, p-value < 0.001) or 6.2 pp (using Non-Searchable controls, p-value < 0.001). The two estimates are statistically indistinguishable from each other, and both are robust to a wide range of specification checks.

Q: How does compression operate — does it raise or lower salaries? A: Compression operates in both directions. Firms that would otherwise have paid above the median benchmark reduce salaries toward the median (“compression from above”), and firms that would otherwise have paid below the median benchmark raise salaries toward the median (“compression from below”). The probability of offering a salary within 2.5% of the median benchmark nearly doubled, from 11.6% before onboarding to 22.1% after.

Q: What is the identification strategy, and why is the treatment considered as good as random? A: The authors use a difference-in-differences design with three sources of variation: which firms gain tool access, the staggered timing of access, and whether specific positions were actually searched within a treatment firm. The payroll company introduced the tool through sales representatives contacting clients in an arbitrary order, not in response to firm characteristics or outcomes. This is corroborated by empirical tests: event-study pre-trends for Searched versus Non-Searched (and Non-Searchable) positions are flat and statistically indistinguishable from zero (pre-treatment coefficients of -0.346 and -0.310, p-values 0.749 and 0.604, respectively).

Q: How large are the effects for low-skill versus high-skill positions? A: For low-skill positions (approximately 42% of the sample, e.g., bank teller, receptionist), dispersion drops from 14.5 pp to 8.7 pp — a 40% decline (p-value < 0.001). For high-skill positions (e.g., software developer), dispersion drops from 24.0 pp to 20.5 pp — a 14.6% decline (p-value = 0.021). The larger effect for low-skill positions is consistent with anecdotal accounts from compensation managers, who report treating low-skill candidates as interchangeable and therefore wanting to offer exactly the market rate.

Q: Does benchmarking raise or lower average salaries? A: On average across all skill levels, the effect on mean salary is small and statistically insignificant: -0.2% (p-value = 0.756) using Non-Searched controls and +1.7% (p-value = 0.308) using Non-Searchable controls. For low-skill positions specifically, average salaries increase by +5.0% (p-value = 0.014) using Non-Searched controls and +6.7% (p-value = 0.001) using Non-Searchable controls. This net increase for low-skill workers reflects compression from below dominating compression from above in that subset.

Q: What are the effects on employee retention? A: For low-skill workers, benchmarking increases the probability of remaining employed at the hiring firm 12 months after the hire date by +6.6 pp (p-value = 0.101) using Non-Searched controls and +6.8 pp (p-value = 0.029) using Non-Searchable controls. The implied retention elasticity from the ratio of salary and retention effects is consistent with average estimates in the prior literature (Sokolova and Sorensen, 2021). No retention effects are reported for high-skill positions.

Q: What is the theoretical mechanism through which aggregate uncertainty generates wage dispersion? A: The model assumes a unit mass of firms simultaneously making wage offers to a mass Q < 1 of workers, with only the top Q offers accepted. Firms have private information about their value of filling the position, and values are affiliated (correlated in the sense of Milgrom and Weber, 1982). Because each firm is uncertain about what other firms will offer, higher-value firms rationally form higher beliefs about the prevailing wage distribution and make higher offers. This generates equilibrium wage dispersion among identical workers without monopsony power, efficiency wages, or amenity differences.

Q: What does the model predict about the equilibrium effects of benchmarking when all firms have access? A: When the benchmark is common knowledge, all firms make offers with full information about the wage distribution. The firms with the highest values win workers at a uniform wage that makes the marginal firm indifferent between hiring and not hiring. The model proves that the mean salary is higher in expectation under the benchmark equilibrium than in the no-benchmark equilibrium. The intuition is that without benchmarks, the marginal firm underestimates labor market tightness, offers less than the full-information competitive wage, and thereby captures extraordinary profits; benchmarking eliminates those rents and intensifies competition.

Q: What are the policy implications of the findings regarding antitrust concerns? A: In 2023, the DOJ and FTC rescinded a long-standing antitrust “safety zone” for salary benchmarks due to concerns that they could facilitate wage collusion. A 2021 executive order had mandated that agencies consider procompetitive effects as well. The authors’ model addresses the collusion concern directly: in equilibrium, benchmarking raises (not lowers) average salaries. The empirical evidence is consistent with this — low-skill workers see average salary increases of 5-7% after benchmarking — suggesting a procompetitive justification for the tools.

Q: How robust are the main results? A: The main estimates are robust across a wide range of specification checks, including alternative winsorization levels, log-difference and binary (>10% deviation) dependent variables, heteroskedasticity-robust standard errors, exclusion of controls, inclusion of firm fixed effects, exclusion of tipping positions, restriction to Searched positions only, dropping SOC reweighting, and age restrictions. Two additional pieces of evidence corroborate the quasi-experimental findings: a survey experiment with SHRM HR managers shows that hypothetical benchmarks compress stated salary offers from both above and below; and quasi-random benchmark shocks (when large firms abruptly raise a position’s base salary by 10% or more) cause firms with tool access to converge to the new benchmark faster than firms without access.

Q: What does the survey of HR managers reveal about how firms use benchmarks? A: In a survey of 2,696 HR professionals conducted through SHRM’s research panel, 87.6% of those involved in salary-setting report using salary benchmarks. The vast majority (97.4%) use benchmarks to set pay for new hires. The most popular sources are industry surveys (68.0%) and free online data (58.1%), with payroll data services used by 23.2%. The median salary is ranked the most important benchmark statistic by 56.73% of respondents. Most respondents apply filters by state (84.15%) and industry (87.33%) when using the tool.

Q: What are the main sources of potential attenuation or amplification bias in the estimated effects? A: Attenuation bias may arise because (1) the benchmark tool studied is among the most advanced available, so firms already had some wage information from other sources, meaning the estimates capture only the incremental effect of one additional high-quality source; and (2) not all positions at treatment firms were searched, so the sample is restricted to positions where firms actually engaged with the benchmark. Potential upward bias could arise if firms adopting the tool were also undergoing broader HR system changes, but the flat event-study pre-trends argue against this explanation.

Salary Benchmarking: The practice of using aggregated market pay data — provided by third parties such as payroll processors, consulting firms, or online platforms — to identify typical salaries for specific job titles and set internal pay accordingly. In the paper’s context, this refers specifically to an online tool that allows employers to look up the median and distributional statistics of base salaries for standardized position titles, filtered by industry and state.

Aggregate Uncertainty: The paper’s label for a distinct source of information friction in which firms are uncertain about the distribution of wages offered by other firms in the market — as opposed to uncertainty about individual worker characteristics. This uncertainty is assumed to be the primitive that generates equilibrium wage dispersion in the model, and its resolution through benchmarking is the mechanism driving the empirical results.

Salary Dispersion (around the benchmark): Measured empirically as the average absolute percentage difference between a new hire’s starting base salary and the median market benchmark for that position, expressed in percentage points. This is the paper’s primary outcome variable. Dispersion reflects firms’ deviation from the market rate in either direction.

Compression from Above / Compression from Below: Compression from above refers to the reduction in salaries at firms that would otherwise have paid more than the median benchmark after gaining benchmark access. Compression from below refers to the increase in salaries at firms that would otherwise have paid less than the median benchmark. Both directions of adjustment are documented empirically and are predicted by the model.

Searched / Non-Searched / Non-Searchable Positions: The paper’s classification of new hires into three groups for identification purposes. Searched positions are those at treatment firms for which the firm actually looked up the benchmark. Non-Searched positions are at treatment firms but were not looked up, serving as a within-firm control. Non-Searchable positions are at control firms with no tool access, serving as a cross-firm control.

Affiliation (across firm values): A technical condition borrowed from auction theory (Milgrom and Weber, 1982) used in the paper’s model to characterize the correlation structure of firms’ private valuations of filling a position. Affiliation implies that when one firm has a high value, others are also more likely to have high values, and hence to offer high wages — generating the model’s equilibrium wage dispersion.

Procompetitive Effect of Benchmarking: The paper’s term for the welfare-improving property of salary benchmarks identified in the model: by resolving aggregate uncertainty, benchmarks cause the marginal firm to offer closer to the full-information competitive wage, reducing extraordinary profits that arise from informational rents and raising the mean salary in equilibrium. This is the key concept in the paper’s contribution to the antitrust policy debate.

Who's Afraid of the Minimum Wage? Measuring the Impacts on Independent Businesses Using Matched U.S. Tax Returns

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper asks how independent (pass-through) businesses in the United States accommodate minimum wage increases — specifically whether they reduce employment, compress profits, pass costs through to customers, or exit — and what happens to the low-earning workers and business owners affected by these adjustments.

Data and Methodology

The authors construct a novel linked firm-worker-owner panel dataset from the universe of U.S. tax returns, covering approximately 235,000 pass-through firms (S-corporations, partnerships, and LLCs) per year in highly exposed industries over 2010–2019. “Highly exposed” industries are defined as those where at least 15% of workers earned below the full-time equivalent of the federal minimum wage ($15,080 per year) in 2013. The dataset links annual business income tax returns to the individual income tax returns and W-2 information reports of all workers and owners.

The causal identification strategy exploits the six state minimum wage increases that took effect in 2014 (California, Connecticut, Delaware, Michigan, Minnesota, and New Jersey) relative to 24 states that did not change their wage floors at any point from 2012–2018. The empirical workhorse is a panel difference-in-differences event study (Equation 1), augmented by DFL re-weighting (DiNardo et al., 1996) to improve comparability of treatment and control firms on observables. The analysis covers cumulative effects through 2018, by which point the average minimum wage across treatment states had risen 30.6%.

Main Findings

Employment: The average exposed independent firm does not meaningfully reduce employment. The authors estimate an own-wage elasticity of -0.209 (s.e. = 0.0112). Employment adjustments manifest as moderately lower hiring rather than layoffs of existing workers. Reduced hiring is wholly concentrated among teenagers and very part-time jobs paying less than $3,900 annually (with 67% earning less than $1,000 per year).
Worker earnings: Despite the hiring reduction, low-earning workers employed at exposed independent firms experience average earnings gains of approximately $2,000 per year by 2018, relative to comparable workers in untreated states. Young individuals aged 20–26 without a 2013 job earn roughly $4,000 more per year by 2018; teenagers without a 2013 job gain approximately $1,000 per year. Workers in these groups are no less likely — and in some cases slightly more likely — to be employed five years after the minimum wage increase.
Wage bills: Average wage bills among surviving treated firms rose 7.03% (s.e. = 0.0153) by 2018. Earnings gains are concentrated among workers earning $15,600–$35,000 annually, with no evidence of reduced earnings for higher-paid workers. The 7% average wage bill increase amounts to only 1.4% of 2013 firm revenues, easing pass-through.
Revenue and profits: Revenues of surviving treated firms grew approximately 2.1% more than control firms by 2018. On average, this revenue increase fully offsets the higher wage bill, yielding a small net profit increase of roughly $3,360 (s.e. = $1,123) per owner by 2018, or about 2.7% of mean 2013 owner income.
Firm exit: On average across all highly exposed industries, minimum wages increased the five-year exit probability by 0.9 percentage points (s.e. = 0.0029), relative to a baseline raw exit rate of approximately 29%. Exit effects are driven entirely by restaurants: by 2018, restaurants in treated states were 1.85 percentage points (s.e. = 0.0039) more likely to have exited, while the exit response for non-restaurant exposed firms is a precisely estimated zero.
Heterogeneity by productivity within restaurants: Exit is concentrated entirely in the bottom productivity quartile (coefficient = 0.0254, s.e. = 0.0079), with no significant effect in the upper three quartiles. Profits among surviving small restaurants rise by $5,941 (s.e. = $1,546) by 2018 relative to 2013. Among small restaurants, the profit gains are larger for firms in the higher productivity quartiles (Q3: +$7,915; Q4: +$9,161). Surviving restaurants also increase non-labor input spending by 2.53% (s.e. = 0.0101), consistent with expanded output following competitor exits.
Entrant characteristics: Post-reform restaurant entrants in treatment states have higher wage bills (13.8% higher in logs), higher revenues (4.0% higher), higher value-added (8.4% higher), and higher productivity (net income/revenue ratio 2.24 percentage points higher) than entrants in control states, indicating the minimum wage raises the productivity floor for new entrants.
Owner outcomes after exit: Owners of small restaurants forced out by the minimum wage are significantly less likely to own an independent business five years later, but earn no less on average in wages plus business income. Policy-induced exiters are significantly less likely to report negative incomes, suggesting substitution away from risky or marginally profitable business ownership.

Theoretical Framework

The authors present a Cournot competition model with heterogeneous firm productivity and fixed production costs. A minimum wage cost shock raises marginal costs, narrowing margins for all firms. Firms whose cost increases exceed the market price increase cannot cover fixed costs and exit. Remaining firms gain higher markups and larger market shares as demand is reallocated from exiting firms. Selection on ex-ante productivity (the least productive firms exit) limits the distortion to market quantity and amplifies profit gains among productive survivors. The model predicts profit increases only in markets with firm exit, which matches the data: profits rise among restaurants (where exit occurs) but not among retailers (where exit is a precisely estimated zero).

Scope Conditions

Findings pertain to the short-to-medium run (up to five years post-legislation) of phased-in minimum wage increases averaging 30.6% in six U.S. states. The sample covers pass-through (independent) businesses in highly exposed industries. Longer-run effects may differ if entrants adopt production technologies that rely less on low-wage labor or incumbents reconfigure inputs. Border-county retailers appear to be less able to pass through costs than interior firms, suggesting product market competition is a key moderating factor.

Layer 2 — Q&A

Q1: Why do the authors focus on pass-through businesses rather than publicly traded corporations?

Pass-throughs (S-corporations, partnerships, and LLCs) comprise 78% of non-sole-proprietorship businesses and 79% of firms with fewer than 20 employees. They represent the majority organizational form for independent businesses in virtually all two-digit NAICS industry groups except utilities and enterprise management. Because minimum wage concerns are disproportionately raised on behalf of small independent businesses, and because most minimum wage workers in restaurants are employed at pass-throughs, studying pass-throughs directly addresses the policy debate. Additionally, pass-through tax returns link business income directly to the individual tax returns of each owner, enabling the authors to separately identify employee versus owner responses.

Q2: How do the authors define “highly exposed” industries and why does this matter for identification?

Highly exposed industries are defined as four-digit NAICS industries where at least 15% of workers earned below the full-time federal minimum wage equivalent ($15,080 per year) in 2013, using tax data to construct a proxy for minimum wage workers. The analysis focuses on these industries because minimum wage workers are extremely concentrated — the vast majority are in Leisure/Hospitality and Retail. Restricting to highly exposed industries allows the authors to estimate average effects within affected markets and conduct heterogeneity analysis across firm characteristics within those markets, including comparing firms with different baseline shares of low-earning workers that nonetheless all face the market-level cost shock.

Q3: How do the employment effects decompose into hiring versus retention?

The average firm subject to a higher wage floor does not lay off existing workers (the retention line is flat in event study estimates). By 2018, firms in treated states hire roughly one fewer worker on average than similar firms in control states, entirely through reduced hiring. This reduced hiring is wholly concentrated among teenagers in very part-time jobs: the missing hires consist entirely of workers who would have earned less than $3,900 annually, with 67% earning less than $1,000 per year. Simultaneously, workers already employed at exposed firms are 2 to 4 percentage points more likely to remain with their 2013 employer by 2016, with prime-age low-earning workers exhibiting the largest retention increases.

Q4: What happens to low-earning workers and young people in individual-level panels?

Low-earners (those earning below $25,000 in each year from 2012–2014) at exposed independent firms experience average earnings gains of approximately $2,000 per year by 2018 relative to similar workers in untreated states, including teenage low-earners. Young individuals aged 20–26 with no job in 2013 experience a relative earnings increase of approximately $4,000 per year by 2018; teenagers without jobs in 2013 gain approximately $1,000 per year. These workers are no less likely — and often slightly more likely — to be employed relative to their counterparts in control states, so the earnings gains are not offset by employment losses at the individual level.

Q5: What is the magnitude of the cost shock for firms and how does it compare to revenues?

By 2018, the average wage bill among surviving firms in treated states was 7.03% (s.e. = 0.0153) higher than comparable firms in control states. This is consistent with a back-of-envelope calculation: low-earning workers account for about 21% of wage bills at these firms, and states raised minimum wages by 30.6% on average (0.21 × 0.306 = 0.064). However, the 7% wage bill increase amounts to only approximately 1.4% of 2013 firm revenues, making cost pass-through relatively modest. Higher minimum wages have no discernible impact on pension contributions but slightly reduce deductions for other benefits including health insurance.

Q6: How do surviving firms finance the increased wage bill, and what happens to profits?

Surviving firms finance the wage increase primarily through higher revenues. By 2018, revenues of firms in treated states grew approximately 2.1% more than revenues of firms in control states. On average, this revenue increase outpaces the higher wage bill, resulting in a net profit increase of approximately $3,360 (s.e. = $1,123) per owner by 2018, representing about 2.7% of mean 2013 owner income. There is no evidence of redistribution from middle- or high-income workers within firms; wage bill increases are concentrated among workers earning $15,600–$35,000 annually, consistent with minimum wage spillovers to workers slightly above the statutory floor.

Q7: Why do restaurants experience exit effects but retailers do not?

The asymmetry stems from the intensity of low-wage labor in production. While low-earning workers account for a similar share of labor costs at restaurants (41.8%) and retailers (38.5%), labor costs overall are more than twice as large at restaurants relative to retailers. Wage bills account for 39% of variable costs and 27% of revenues at restaurants, but only 16% of variable costs and 13% of revenues at retailers. As a result, raising the minimum wage raises variable costs by 5.76% at restaurants. Non-restaurant exposed firms are able to fully pass through their smaller cost shock, yielding flat profits and neither employment nor exit impacts.

Q8: Why is firm exit concentrated in the lowest productivity quartile of restaurants rather than among the most exposed firms?

The Cournot framework predicts exits among firms with the lowest ex-ante productivity (highest marginal costs), the largest cost shock (highest share of low-wage labor per unit of output), or a combination. Empirically, productivity is the primary determinant: restaurants across all productivity quartiles use similar shares of low-earning workers (40–44% of wage bills for Q1 through Q4). Exit rises significantly only among restaurants in the bottom productivity quartile (coefficient = 0.0254, s.e. = 0.0079), with no significant effects in Q2–Q4. Among the lowest-productivity restaurants, those most dependent on low-earning labor face the largest exit rates.

Q9: How do the model’s predictions about profit heterogeneity match the data?

The Cournot model predicts profits should rise only in markets with firm exit (via increased margins and market share reallocation to survivors). This is exactly what the data show. Among restaurants, where exit is concentrated in the bottom productivity quartile, profits among surviving small restaurants rise by $5,941 (s.e. = $1,546) by 2018. Among small restaurants specifically, profit gains increase with productivity: Q3 restaurants gain $7,915 (s.e. = $3,326) and Q4 restaurants gain $9,161 (s.e. = $2,127), while Q1 and Q2 gains are statistically indistinguishable from zero. In non-restaurant exposed industries where the exit effect is a precise zero, profits are also flat — exactly as the model predicts.

Q10: What happens to the characteristics of new restaurant entrants after the minimum wage increase?

Post-reform restaurant entrants in treatment states are systematically more productive than entrants in control states. They have wage bills 13.8% higher (in logs), revenues 4.0% higher, value-added 8.4% higher, and productivity ratios (net income/revenue) 2.24 percentage points higher than new entrants in control markets. This implies the minimum wage raises the minimum viable productivity threshold for entrant restaurants, consistent with Sorkin (2015)’s insight that minimum wages shape the capital and technology choices of entering firms. The restaurant industry thus becomes more productive on average through both the exit of the least productive incumbents and the entry of more productive new firms.

Q11: How do worker transition patterns reflect the reallocation of output to surviving firms?

Workers at large independent businesses (top revenue quartile) are 3.52 percentage points more likely to remain with their 2013 employer in 2018 and 2.36 percentage points less likely to switch to another large firm. The large firms that retain more of their existing workforce also reduce their hiring of very part-time teenagers the most — in the top revenue quartile, firms shed roughly 4.5 employment relationships on average, comprising higher retention of 4.15 existing workers offset by reduced hiring of 8.67 very part-time teenage workers. Workers originally at smaller exposed firms are more likely to be found working at larger firms five years out, consistent with demand reallocation from exiting and shrinking small firms toward larger, more productive survivors.

Q12: What happens to owners of restaurants that exit due to the minimum wage?

Policy-induced exiters of small restaurants are significantly less likely to own an independent business five years later and less likely to receive all earnings from business ownership, relative to owners of restaurants that exited for other reasons in control states. However, their average incomes (wage income plus ordinary business income) are no lower. This income stability is partly explained by the fact that policy-induced exiters are significantly less likely to report negative incomes five years out, suggesting they substitute away from potentially risky or marginally profitable business ownership toward wage employment or other activities. The utility implications are ambiguous: these former owners may have preferred business ownership even if it did not yield higher income.

Q13: What is the role of product market competition in mediating pass-through, as evidenced by border-county analysis?

The border county robustness analysis reveals that product market competition is central to pass-through success. Retailers near state borders, where consumers can cross-state-border shop, face more elastic demand and are less able to finance the wage cost shock with new revenues, exhibiting reduced profits and higher exit rates (though estimates are imprecise). Further from the border, where the cost shock is more commonly felt by all potential substitutes (making market demand elasticity rather than firm demand elasticity the relevant parameter), results are very similar to the full-sample aggregate findings. This confirms that the common nature of the minimum wage cost shock — shared by all competing firms in the market — is a key reason firms can pass through costs to consumers.

Q14: How do the findings address the divide among independent business owners on minimum wage policy?

The heterogeneous outcomes rationalize why surveys consistently find business owners divided. Among restaurants, some owners (those operating the least productive small restaurants) face exit and loss of business ownership, while surviving productive restaurateurs see higher profits of $5,941–$9,161 per year. Among non-restaurant exposed businesses, owners are broadly unaffected in terms of profits and viability. Uncertainty about whether a given firm’s demand is elastic enough to bear cost pass-through — given that owners may be more familiar with the elasticity of firm-level demand from prior unilateral price changes, rather than the relevant market-level demand elasticity applying to a common cost shock — may broaden opposition to include even owners who would ultimately benefit.

Key Concepts

Pass-through businesses (independent businesses): Privately owned firms organized as S-corporations, partnerships, or LLCs, taxed by passing income through to the individual returns of owners rather than at the entity level. In 2015, these comprised 78% of non-sole-proprietorship U.S. businesses and 46% of employment. The paper uses “pass-through” and “independent business” interchangeably as the unit of analysis.

Highly exposed industries: Four-digit NAICS industries where at least 15% of workers earned below the annual full-time equivalent of the federal minimum wage ($15,080) in 2013, as measured in the authors’ administrative tax data. This threshold proxies the concentration of minimum-wage workers across industries and drives the sample selection for firm-level analysis.

Own-wage elasticity of employment: The estimated percentage change in employment at a firm associated with a given percentage change in the firm’s minimum wage. The authors estimate this as -0.209 (s.e. = 0.0112), reflecting the average effect across all exposed independent businesses, conditional on the firm’s industry, size, and local market characteristics.

DFL re-weighting (DiNardo-Fortin-Lemieux): A non-parametric reweighting procedure that adjusts the distribution of control-group firms to match the distribution of treatment-group firms on observables (specifically, two-year lagged value-added within three-digit NAICS industries). Used to improve pre-reform comparability of treatment and control firm samples without parametric functional form assumptions.

Firm productivity (in this paper’s sense): Measured as the ratio of net profits to revenues (net income/revenue) at the firm level in the base year 2013, used to assign firms to productivity quartiles for heterogeneity analysis. This is a firm-level profitability measure constructed from pass-through tax returns, not a total factor productivity estimate requiring production function estimation.

Firm exit: An indicator for a firm that filed a tax return in 2013 but did not file a return in a subsequent year t. The average one-year exit rate for highly exposed independent businesses is 5.2%; the cumulative five-year raw exit rate is approximately 29% across treatment and control states.

Cournot competition with heterogeneous productivity and fixed costs: The paper’s conceptual framework, in which N firms compete in quantities with asymmetric marginal costs (reflecting heterogeneous productivity), a common output price, and a fixed cost of production. Under this framework, a minimum wage cost shock narrows margins unevenly, induces exit among firms that cannot cover fixed costs, and generates both demand reallocation and market share gains for productive survivors — rationalizing simultaneous exit and profit increases in the same industry.

Common cost shock: The property that a minimum wage increase raises production costs for all firms employing low-wage workers in the same market simultaneously. Because all competing firms face higher costs, the relevant pass-through parameter is the elasticity of market demand rather than the (higher) elasticity of individual firm demand, facilitating cost pass-through to consumers and distinguishing minimum wages from unilateral price changes by a single firm.