J42 | Macro Paper Warehouse

Bargaining and Inequality in the Labor Market

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

Layer 1 — Overview

Research Question. How prevalent is individual wage bargaining in the labor market, what determines firms’ bargaining strategies, how do bargaining encounters unfold for workers, and does heterogeneity in bargaining behavior translate into wage inequality—including the gender wage gap?

Data and Setting. The paper develops and validates novel linked survey data for Germany. A firm survey was fielded by the ifo Institute to senior HR professionals and managers in two waves (September 2021 and January 2022), yielding 772 complete responses across all major sectors and regions. These responses were linked—with consent obtained from 72% of firms—to German Social Security records (the Integrated Employment Biographies, IEB) covering 416,821 full-time employees at matched firms in 2020, and to Orbis balance sheet data for firm productivity proxies. A separate worker survey was fielded by the IAB to 135,000 full-time German workers, with 9,756 completing it; nearly 10,000 responses were used for analysis, with 7,079 workers employed at surveyed firms. The worker survey elicited detailed bargaining histories for workers who had received an outside offer in the prior six months, bargaining at the start of current employment (for workers with tenure of three years or less), and responses to a hypothetical salary expectation scenario.

Definition of Individual Bargaining. The authors define a firm as having a “bargaining strategy” if it differentiates pay between workers in the same position it perceives to have similar productivity—encompassing both variation in initial offers (which may reflect firms using information on workers’ salary expectations) and back-and-forth negotiation. Elicitation distinguishes four employee groups (recent labor market entrants, experienced non-managers, managers, and bottleneck-occupation workers) and two contexts (new external hires and incumbent workers who receive an outside offer).

Prevalence of Bargaining. Approximately 50% of surveyed firms are willing to differentiate base wages for recent labor market entrants, more than 80% for experienced non-managers and managers, and nearly all for workers in bottleneck occupations they are struggling to fill. For incumbent workers facing outside offers, 57% of firms would increase pay for recent entrants, and more than 80% for experienced incumbents, managers, and bottleneck workers. In total, 80% of workers in the sample are in positions where individual bargaining is possible.

Magnitude of Wage Differentiation. For new external hires, the typical firm expects a gap between the highest and lowest offers of 3% for recent entrants, 5% for experienced non-managers, and 10% for managers (conditional on a gap: 6%, 10%, and 12% respectively). For incumbent workers responding to outside offers, the typical firm will adjust pay by 3% for recent entrants, 6% for experienced non-managers, and 10% for managers (conditional on responding: 6%, 7%, and 14% respectively). Forty-four percent of firms report that variation in initial offers is at least as important as back-and-forth negotiation in determining workers’ final pay.

Predictors of Firm Bargaining Strategies. Contrary to models predicting more productive firms are more likely to bargain (Doniger 2015; Postel-Vinay and Robin 2004; Flinn and Mullins 2021), firms that bargain are not more productive—as proxied by firm age, size, or assets per employee—nor do they pay higher mean wages. A variance decomposition shows that employee-group dummies alone explain 33% of variation in bargaining strategies for new hires, comparable to more than 500 firm dummies. Labor market factors—particularly whether a position is hard to fill—are systematically associated with bargaining willingness. Collective bargaining agreement (CBA) coverage and East German location are negatively correlated with bargaining flexibility.

How Bargaining Unfolds. In 57% of worker-firm interactions, the worker provides salary expectations before the firm makes its initial offer; 29% of firms require this information. About one-third of applicants ask for more after the initial offer, requesting on average a 3% increase; conditional on asking, about half of firms raise the offer, but fewer than one-third match what was requested, with the typical worker improving the offer by 1.5%. The majority of outside offers are rejected: only 9% of workers who received an outside offer in the prior six months chose to move to a new firm. Of the 91% who remained at their incumbent firm, 13% successfully renegotiated their pay. Back-and-forth dynamics—where offers are accepted or rejected only after multiple rounds—are consistent with models of two-sided incomplete information.

Worker Heterogeneity and Wage Inequality. Workers with better self-assessed outside options are 9 percentage points more likely to ask for an increase after the initial offer and 7 percentage points more likely to successfully negotiate a raise, relative to same-occupation coworkers with worse outside options. Women are 6 percentage points less likely to successfully negotiate their pay upward and show lower salary expectation provision rates, including in a hypothetical scenario in which pay range information is equalized. These gender differences in bargaining are not explained by women negotiating more over non-wage amenities; controlling for outside options and risk tolerance shrinks the female coefficient by at most 15%. Among surveyed workers, after controlling for occupation-establishment fixed effects, there is no gender wage gap at firms that do not bargain, but a 4–5 percentage point gender wage gap at firms that do bargain. Across specifications, firms that engage in individual bargaining have a 3 percentage point higher gender wage gap. A simple decomposition suggests that at surveyed firms, 44% of the residual gender pay gap can be attributed to bargaining. For workers at bargaining firms, a 10 percentage point higher pay premium at the prior firm is associated with 0.5 percent higher pay at the current firm, conditional on occupation-establishment fixed effects; this relationship is statistically insignificant for workers at non-bargaining firms.

Scope Conditions. Results apply to full-time private-sector workers in Germany between ages 25 and 50, with the firm sample over-representing medium and large firms (median size 50–249 employees). CBA coverage in the sample (41%) reflects Germany’s institutional context where firms retain the right to pay above CBA floors. Results are robust to re-weighting to match the overall distribution of German firm size and sector.

In depth

Q1. How do the authors define “individual bargaining” and why is this definition broader than standard labor economics usage?

The authors define a firm as having a bargaining strategy if it differentiates pay between workers in the same position it perceives to have similar productivity, covering both tailoring of initial offers and back-and-forth negotiation. Standard labor economics definitions typically condition on wages being set ex post once outside options are revealed, and focus on back-and-forth negotiation alone. The authors’ definition is most analogous to standard definitions of price discrimination. Empirically, the vast majority of firms that differentiate initial offers (93%) are also willing to engage in back-and-forth negotiation.

Q2. How was the firm survey designed to elicit bargaining strategies reliably, and what is the “protocol question”?

The protocol question asked: “How much more could a person maximally receive compared to the fixed compensation you would have offered based on the person’s qualification/fit for the position alone?” with options ranging from “0%/no adjustments possible” to “more than 40%.” Wording was developed through over 100 conversations with HR professionals; “qualifications and fit” was the phrase most closely aligned with HR professionals’ concept of productivity. The survey was fielded by the ifo Institute—an organization with decades of experience surveying this population—with a 51% response rate, 83% completion rate, and median response time of 11 minutes.

Q3. What validation exercises support the reliability of the elicited firm bargaining measures?

Four exercises are reported. First, intra-respondent reliability: the cross-tabulations between the protocol and incidence questions show most mass on or below the diagonal (incidence-implied spread no greater than the protocol-implied flexibility). Second, inter-respondent reliability: among 37 firms with multiple respondents, there is significant overlap in independently provided answers. Third, external validity using publicly available data: for 90% of firms reporting no CBA, no CBA evidence is found; for 99% reporting no pay information in job ads, none is found in online postings; for 82% reporting no salary expectation elicitation, no evidence of it appears in online application forms. Fourth, the elicited firm strategies are highly correlated with the matching workers’ survey responses—e.g., workers at firms stating they elicit salary expectations are significantly more likely to report having provided these expectations.

Q4. Is firm productivity associated with whether a firm engages in individual bargaining?

No. Firms that bargain and those that do not are similar with respect to firm size, firm age, and total assets per employee, and they also do not differ significantly in their AKM wage premium. These findings are inconsistent with theoretical models predicting that more productive firms are more likely to set pay via bargaining (Doniger 2015; Postel-Vinay and Robin 2004; Flinn and Mullins 2021). The result holds for both binary and continuous measures of bargaining, and is not overturned by machine learning prediction attempts.

Q5. What firm characteristics other than productivity predict bargaining strategies?

CBA coverage is negatively correlated with wage flexibility—CBA-covered firms report less flexibility even for managers who are typically exempt from CBAs and for groups not covered by CBAs, suggesting institutional norms or culture matter. Firms headquartered in East Germany are less likely to bargain with workers in all groups. Publicly traded firms (stock-based corporations) are more likely to set wages flexibly. These correlations are consistent with the view that managerial style and firm culture (rather than productivity) shape wage-setting strategies.

Q6. What does the variance decomposition say about the relative importance of firm versus market factors in predicting bargaining strategies?

Employee-group dummies alone explain 33% of the variation in bargaining strategies for new hires. After adjusting for the number of fixed effects used, four employee-group dummies explain as much variation as more than 500 firm dummies. Adding firm characteristics or coarse industry dummies does not significantly improve the adjusted R-squared relative to a model containing only group dummies. This supports models emphasizing market-level factors (worker replaceability, labor market tightness) over firm-level factors.

Q7. How common is it for workers to provide salary expectations before receiving an initial offer, and what do firms do with this information?

In 57% of worker-firm interactions, the worker provides salary expectations before the firm makes its initial offer. Twenty-nine percent of firms require this information; most ask for it. Forty-four percent of firms report that variation in initial offers is at least as important as subsequent back-and-forth negotiations in determining workers’ final pay. HR professionals and prior research indicate firms interpret variation in stated expectations as reflecting outside options rather than productivity.

Q8. What fraction of outside offers are rejected, and what happens when workers stay at the incumbent firm?

Only 9% of workers who received one or more outside offers in the prior six months chose to move to a new firm. Of the 91% who remained at the incumbent firm, 13% successfully renegotiated their pay at the incumbent. A follow-up survey fielded in spring 2024 corroborates this finding, showing approximately 80% of workers who received an outside offer remained at the incumbent firm; even recoding all job-to-job transitions as accepted offers implies no more than 26% of offers lead to a transition.

Q9. What do the back-and-forth dynamics imply for appropriate theoretical models of wage bargaining?

That many offers are accepted or rejected only after multiple rounds of negotiation is difficult to rationalize with models assuming either firms or workers have perfect information, which typically predict immediate acceptance or rejection. The patterns are consistent with models of two-sided incomplete information (Perry 1986; Chatterjee and Samuelson 1983). Sixty-nine percent of HR professionals in the survey report that decision-makers at their firm only have market-level information on wages, not specific information on what competitors pay.

Q10. How do outside options predict worker bargaining behavior and outcomes, controlling for occupation-establishment fixed effects?

Workers who rated it “easy” or “very easy” to obtain a better outside offer are 9 percentage points more likely to ask for an increase after the initial offer and 7 percentage points more likely to successfully negotiate a raise relative to same-occupation-establishment coworkers who rated it “difficult” or “very difficult.” The same pattern persists during the employment spell: workers with better outside options are 9 percentage points more likely to initiate and 8 percentage points more likely to succeed in renegotiation. These workers are not more likely to receive raises without asking.

Q11. How does risk tolerance predict bargaining, and how does it compare to outside options?

Workers with greater risk tolerance (those rating themselves 7 or above on a 10-point scale) are more likely to engage in wage negotiations and more likely to succeed both at the start of and during employment spells. Gaps in successful negotiations are somewhat larger than gaps in attempted negotiations, suggesting risk-tolerant workers also negotiate more effectively. However, outside options explain more of the between-worker variation in bargaining behavior than risk tolerance does.

Q12. What are the gender differences in bargaining behavior, and can they be explained by differences in outside options or risk tolerance?

Women are less likely to engage in back-and-forth negotiations and are 6 percentage points less likely to successfully negotiate pay upward during an employment spell. Women are also less likely to provide salary expectations and provide lower expectations as a fraction of their current salary in the hypothetical scenario, including when the salary range is provided—women are 6 percentage points less likely to provide expectations above the top of the stated range. Controlling for outside options and risk tolerance shrinks the female coefficient by at most 15%. There is no evidence that women substitute toward negotiating for non-wage amenities. The pattern is most consistent with women finding negotiation uncomfortable, not with a belief that it will not pay off or fear of backlash.

Q13. What is the estimated gender wage gap attributable to individual bargaining?

Among surveyed workers, after controlling for occupation-establishment fixed effects, there is no gender wage gap at firms without individual bargaining (coefficient closes to zero), while a 4–5 percentage point gender wage gap persists at firms with individual bargaining. This difference is robust across measures of pay (total daily pay, base pay, pay conditioning on hours worked), alternative fixed effect specifications, and to including non-surveyed workers at surveyed firms. A simple decomposition suggests 44% of the residual gender pay gap at surveyed firms can be attributed to bargaining. Across the interaction specifications, bargaining firms have a 3 percentage point higher gender wage gap and—in one key specification—a 6 percentage point difference between the gender gaps at bargaining and non-bargaining firms.

Q14. How does a worker’s prior firm wage premium affect current wages, and does bargaining status matter?

In a regression of log current wages on the AKM wage premium of the prior firm (conditional on occupation-establishment fixed effects), a 10 percentage point higher pay premium at the prior firm is associated with 0.5 percent higher pay at the new firm for workers at bargaining firms. For workers whose pay is not set via individual bargaining, the relationship between the prior firm’s pay premium and current pay is statistically insignificant. The result is consistent with the idea that during negotiations with a new firm, workers use their prior firm’s pay policy as an outside option.

Q15. How do AKM person effects relate to bargaining behavior?

Higher-person-effect individuals are more likely to have provided salary expectations when applying to their current firm and ask for a larger fraction of their current salary in the hypothetical scenario (conditional on their wage). These differences persist when controlling for occupation-establishment fixed effects and age and experience. Higher-person-effect workers are not more likely to receive raises without asking. These results are inconsistent with AKM person effects reflecting only productivity differences and instead suggest that fixed differences in individual bargaining behavior contribute to the variance in person effects—which Card, Heining, and Kline (2013) estimated explains a large share (40%) of the growth in German wage inequality.

Q16. Are the bargaining patterns found at surveyed firms representative of bargaining more broadly?

Two robustness exercises support broader representativeness. First, similar bargaining dynamics are found when including a random sample of German workers employed at non-surveyed firms. Second, re-weighting the sample to match the overall distribution of firm size and sector in Germany yields similar results. Because medium and large firms are over-represented in the firm sample, and because small firms hire infrequently and are less likely to have formal bargaining strategies, the true prevalence of individual bargaining among all German firms may be somewhat lower.

Key Concepts

Individual Bargaining Strategy (firm-level). A firm has an individual bargaining strategy if it differentiates pay between workers in the same position that it perceives to have similar productivity. This definition encompasses both tailoring of initial offers (based on, e.g., workers’ stated salary expectations) and back-and-forth negotiation. It is analogous to price discrimination rather than to the standard labor economics distinction between wage posting and Nash bargaining.

Protocol Question. The main survey measure of firm bargaining strategies: firms are asked the maximum percentage by which pay could be increased for a new hire above the fixed compensation the firm would have offered based on qualifications and fit alone, with response bins from “0%/no adjustments” to “more than 40%.” A zero response is used to classify a firm as not bargaining.

Incidence Question. A supplementary survey measure eliciting the expected spread (between highest and lowest offers) that the firm would make to ten candidates with identical qualifications and fit but differing stated salary expectations and competing offers. Used to validate the protocol question and to quantify the importance of initial-offer differentiation relative to back-and-forth negotiation.

Bottleneck Occupation. A firm-defined category of workers in positions that are particularly difficult to fill, drawing on an official German Federal Employment Agency designation. In the paper, bargaining willingness is systematically higher for workers in these positions than for other workers at the same firm, providing evidence that labor market tightness drives bargaining strategies.

Outside Offer Renegotiation. Wage renegotiation at the incumbent firm triggered by a worker receiving an outside offer, without a change in job tasks. The paper documents this is empirically more common than actual job-to-job transitions: of workers receiving outside offers, 91% remain at the incumbent firm, and 13% of those who remain successfully renegotiate their pay.

AKM Person Effect. A worker fixed effect estimated from a two-way fixed effects regression of log wages on worker and firm fixed effects (following Abowd, Kramarz, and Margolis 1999). In this paper, AKM person effects are taken from Bellmann et al. (2020), estimated over 2010–2017 German population data. The paper provides evidence that these effects capture, in part, fixed differences in individual bargaining behavior rather than solely differences in productivity.

AKM Firm Effect (Wage Premium). The firm fixed effect from the same two-way fixed effects regression, representing the pay premium a firm pays relative to what would be expected given its workforce composition. The paper uses the prior firm’s AKM effect as a measure of a worker’s outside option quality when testing whether prior-firm pay policy influences current pay under individual bargaining.

Salary Expectations (Gehaltsvorstellungen). The wage figure a worker provides to a prospective employer, typically before the firm’s initial offer. Legally, German firms (like most US states) cannot ask for salary history but can ask for salary expectations. In the paper, 57% of worker-firm interactions begin with the worker providing expectations; firms report using these to tailor initial offers, interpreting variation in stated expectations as reflecting outside options rather than productivity.

Firm Responses and Wage Effects of Foreign Demand Shocks with Fixed Labor Costs and Monopsony

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

Layer 1 — Overview

Research Question. The paper asks three related questions in the context of Belgium, a small open economy: (1) What do firms’ responses to demand shocks reveal about their cost structures? (2) What are the worker and wage impacts of foreign demand shocks? (3) How sensitive are the aggregate wage effects of foreign demand shifts to firms’ cost structures and imperfect competition in the labor market?

Data. The analysis combines administrative micro-data from Belgium for 2002–2014, provided by the National Bank of Belgium. The linked dataset covers 995,739 firm-year observations from private, non-financial firms with at least one FTE employee, and integrates: (a) a Business-to-Business (B2B) VAT transactions registry capturing all annual domestic firm-to-firm sales above €250; (b) customs records and intra-EU declarations for imports and exports at the 8-digit product level; (c) annual accounts containing data on sales, labor costs, intermediate inputs, capital, and firm characteristics; and (d) employer-employee matched data from the Belgian social security administration (BCSS) for a random sample of 500,000 workers in firms with 10 or more FTE employees, covering 2003–2014.

Identification Strategy. To isolate variation in firms’ sales driven by foreign demand rather than supply-side factors, the authors construct a firm-specific foreign demand instrument following Hummels et al. (2014) and Dhyne et al. (2021). The instrument is the weighted average of changes in world import demand facing a firm, using lagged export shares as weights and excluding Belgian imports from the world import measure. Crucially, the instrument captures both direct foreign demand exposure (for exporters) and indirect exposure through the domestic production network — including the foreign demand shocks passing through to upstream domestic suppliers via buyer-supplier links. Firm and industry-year fixed effects control for time-invariant heterogeneity and industry-level trends.

Key Empirical Facts. Within-firm analysis over four-year windows finds that intermediate input purchases respond nearly proportionally to changes in sales (slope coefficient 0.82), while labor costs respond less than proportionally (slope coefficient 0.57). The less-than-proportional response of labor costs — with the employment slope of 0.48 and the average wage slope of 0.09 — is consistent with sizable fixed overhead costs in labor inputs and upward-sloping labor supply curves. Output prices co-move more with input prices than with average wages, consistent with labor constituting a smaller share of variable costs than intermediate inputs.

IV Estimates of Firm Responses. In response to a foreign demand shock inducing a 10 percent instantaneous increase in a firm’s sales, the firm’s cumulative sales over four years increase by approximately 7.6 percent (balanced panel). Over the same four-year horizon, total input purchases increase by about 7.0–7.8 percent, while labor costs increase by only 3.5–4.1 percent — a substantially less-than-proportional response. Roughly one-quarter of the labor cost change comes from changes in average wages rather than employment changes. Domestic input purchases increase by 5.3–6.0 percent, indicating that firms pass on a large share of foreign demand shocks to their domestic suppliers.

Structural Parameters. The implied IV estimate of the labor cost elasticity with respect to sales is 0.53 (standard error 0.08), statistically significantly below one. The implied elasticity of total input purchases is 1.05 (standard error 0.15), close to one, so the fixed share of intermediate inputs is approximately zero. The labor supply elasticity estimated from the ratio of wage and employment responses is approximately 3.9 in the full sample and 2.3 in the stayer subsample; the implied wage markdown is 21 percent and 30 percent respectively. Incorporating upward-sloping labor supply into equation (15), the estimated share of total labor inputs that is fixed overhead is approximately 53 percent. By comparison, the fixed share of total costs (labor and intermediate inputs combined) is approximately 29 percent in Belgium — higher than the 18–22 percent found in U.S. data (De Loecker et al. 2020) and the 20 percent found in U.S. manufacturing plants (Ederhof et al. 2021).

General Equilibrium Counterfactuals. The authors parameterize and solve a small open economy general equilibrium model with monopsonistic competition in labor markets, monopolistic competition in product markets, and fixed and variable labor and intermediate input costs. Using the Dekle-Eaton-Kortum (2007) “hat algebra” technique, they simulate a 5 percent increase in foreign tariffs on all Belgian exports and compare four counterfactual economies: (1) baseline Belgium with fixed costs and imperfect labor market competition (ε = 3.9); (2) fixed costs and perfectly elastic labor supply (ε = ∞); (3) no fixed costs with imperfect competition; (4) no fixed costs and perfectly competitive labor markets.

Main Findings on Wages. In the baseline Belgian economy, a 5 percent increase in foreign tariffs produces a 4.9 percent fall in the average real wage. With fixed costs but perfectly elastic labor supply, the real wage falls by 4.8 percent — nearly identical. With upward-sloping labor supply but no fixed costs, the real wage falls by only 3.0 percent; without fixed costs and with perfectly competitive labor supply, the fall is only 2.8 percent. The paper concludes that fixed overhead costs in labor substantially amplify real wage declines, while incorporating upward-sloping labor supply appears quantitatively less consequential for aggregate wage outcomes. Standard models that assume no fixed costs and perfectly elastic labor supply — the typical modeling choice in the trade literature — may substantially understate (by roughly 43–75 percent of the true effect) the aggregate wage decline from a negative foreign demand shock.

Mechanism. Fixed overhead costs reduce labor’s share of variable costs. When labor is a smaller share of variable costs, output prices are less sensitive to changes in wages. With a fixed aggregate labor supply, the economy must lower prices through wage reductions to restore equilibrium after a negative demand shock; the required wage decline is larger when fixed labor costs are taken into account. The findings are robust to adjustment cost specifications, a nested logit extension of the labor market model, and controlling for location-year fixed effects and import price changes.

In depth

Q1. What two motivating empirical facts about Belgian firms does the paper establish?

A1: First, within-firm four-year changes show that intermediate input purchases respond nearly proportionally to changes in sales (slope coefficient 0.82), while labor costs respond less than proportionally (slope coefficient 0.57). The labor cost response decomposes into an employment slope of 0.48 and a wage slope of 0.09. Second, output prices co-move more strongly with input (intermediate goods) prices than with average wages, consistent with labor constituting a smaller share of variable costs than intermediate inputs.

Q2. How does the instrument for foreign demand shocks capture indirect exposure through production networks?

A2: The instrument for firm k is a weighted average of changes in world import demand, where the weights reflect both the firm’s own direct export shares across countries and products and the firm’s indirect export exposure through its domestic buyers’ export shares. The term H̃_{kn,t-1} captures the share of firm k’s total sales purchased by firm n directly and indirectly through all upstream chains. This means even non-exporting firms receive a non-zero instrument through their sales to directly-exporting firms. In fact, non-directly-exporting firms sell on average nearly 10 percent of their output indirectly to foreign markets.

Q3. What is the estimated magnitude of the labor supply elasticity facing Belgian firms, and what does it imply for wage markdowns?

A3: In the full main estimation sample (balanced panel), the IV estimate of the firm-specific labor supply elasticity is approximately 3.9, implying a wage markdown of about 21 percent relative to the marginal revenue product of labor. In the stayer subsample (incumbent workers only, holding workforce composition fixed), the estimated labor supply elasticity is approximately 2.3, implying a markdown of about 30 percent. The paper can reject perfect competition (infinite elasticity, zero markdown) at a significance level of 0.06 in the full sample and 0.001 in the stayer sample using the closure method.

Q4. What is the estimated labor cost elasticity with respect to demand-driven sales changes, and what does it imply about fixed labor costs?

A4: The IV estimate of the labor cost elasticity with respect to sales is 0.528 (standard error 0.085), statistically significantly below one. If labor supply were perfectly elastic, this would directly imply a fixed labor cost share of approximately 47 percent. Incorporating the estimated upward-sloping labor supply curve through equation (15), the model implies that approximately 53 percent of total labor inputs are fixed overhead. For context, occupational data from Belgium’s 2014 Structure of Earnings Survey shows that clerical support workers and managers together account for 21 percent of total earnings, and adding professionals raises this to 51 percent — broadly consistent with the estimated fixed share.

Q5. What does the estimated elasticity of input purchases with respect to sales imply about fixed intermediate input costs?

A5: The IV estimate of the elasticity of total input purchases with respect to sales is 1.050 (standard error 0.150), close to one. The implied fixed share of total intermediate inputs is therefore approximately zero. However, there is substantial heterogeneity by input type: purchases from the manufacturing sector (roughly half of all input purchases) have an elasticity close to one, whereas service-sector inputs (roughly 30 percent of total input purchases) have an implied fixed cost share of approximately 36 percent, with a size-weighted average cumulative response of 4.3 percent against a total cumulative sales increase of 6.7 percent.

Q6. How does the paper rule out alternative explanations for the less-than-proportional response of labor costs?

A6: The paper considers three main alternatives. First, adjustment costs: even in the presence of labor adjustment costs, under a homothetic constant-returns production function a permanent shock should eventually produce a proportional labor response. The paper focuses on four-year cumulative responses where firm responses change little after the first couple of years, and shows identification of fixed costs holds even in models with quadratic or Calvo-style adjustment costs. Second, a non-homothetic CES production function without fixed costs: Appendix B.3 shows that such a specification predicts that if the labor cost elasticity is below one, the input purchase elasticity must be above one — at odds with the data, which shows the input purchase elasticity is close to one while the labor cost elasticity is well below one. Third, variable markups: a uniform markup change would reduce both elasticities proportionally, not create the large gap between labor cost and input purchase elasticities observed.

Q7. Why are firms’ domestic suppliers affected by foreign demand shocks, and how large are the pass-through effects?

A7: Firms pass on foreign demand shocks to their domestic suppliers through buyer-supplier production network links. When a foreign demand shock increases a firm’s sales by 10 percent instantaneously, its domestic input purchases increase cumulatively by approximately 5.3–6.0 percent over four years. Total input purchases increase by 7.0–7.8 percent over the same period; the difference between total and domestic input purchases reflects service inputs (which have smaller responses) and the composition of imported versus domestic inputs.

Q8. What is the aggregate real wage effect of a 5 percent increase in foreign tariffs on Belgian exports in the baseline model?

A8: In the baseline counterfactual representing the actual Belgian economy (with fixed overhead costs and labor supply elasticity ε = 3.9), a uniform 5 percent increase in foreign tariffs on all Belgian exports produces a 4.9 percent fall in the average real wage. The median firm reduces output by 3.8 percent, marginal costs by 4.8 percent, and wages by 7.9 percent. The fall in wages is driven by a general equilibrium mechanism: since the foreign price is exogenous and trade balance must hold, wages are the key adjusting margin.

Q9. How much does the modeling of fixed overhead costs versus imperfect labor market competition matter for the aggregate wage counterfactual?

A9: Fixed overhead costs account for nearly all of the amplification relative to the standard model. With fixed costs but perfectly elastic labor supply, the real wage falls 4.8 percent — almost identical to the 4.9 percent in the baseline. Without fixed costs but with the estimated upward-sloping labor supply, the fall is only 3.0 percent. Without either, the fall is 2.8 percent. Thus, incorporating fixed overhead costs in labor raises the estimated wage decline by approximately 1.9 percentage points, while incorporating imperfect labor market competition adds only about 0.1 percentage points. The paper concludes that fixed overhead costs, not monopsony, are the essential feature for accurately predicting tariff impacts on wages.

Q10. What is the mechanism by which fixed overhead costs amplify the aggregate wage decline from a negative demand shock?

A10: Fixed overhead costs reduce the share of labor in firms’ total variable costs. When labor constitutes a smaller fraction of variable costs, output prices are less sensitive to changes in wages. With aggregate labor supply fixed, the economy restores equilibrium after a negative demand shock by reducing prices through wage cuts. To achieve the same magnitude of price reduction when labor is a smaller fraction of variable costs, wages must fall by a larger amount — amplifying the aggregate wage impact. Fixed overhead costs in labor also make foreign inputs relatively more important in variable costs, as shown empirically in Appendix D.1.

Q11. Is the conclusion about the relative importance of fixed costs versus labor market imperfections robust to alternative specifications of the labor market?

A11: Yes. The paper extends the model to a nested logit structure for worker preferences (following Lamadon et al. 2022), which allows Belgium to contain multiple labor markets (defined as industry-region nests), permits heterogeneous markdowns across markets, and is still identified from the data. Empirically, incorporating multiple labor markets and heterogeneous markdowns does not quantitatively alter the aggregate counterfactual predictions for the wage effects of foreign demand shocks.

Q12. Are heterogeneous responses to the foreign demand shock observed across exporters, importers, and domestic-only firms?

A12: The paper finds no systematic differences in the elasticities of labor cost and input purchases between firms that trade internationally and those that do not. This implies that exporters and importers have higher absolute fixed costs (consistent with fixed export and import costs) but comparable fixed cost shares — since these firms tend to be larger and thus spread higher absolute fixed costs over larger output volumes.

Q13. Do the findings about fixed overhead costs extend beyond foreign demand shocks?

A13: Yes. The paper shows in Appendix D.4 that a uniform 5 percent reduction in the productivity of all Belgian manufacturing firms generates qualitatively and quantitatively similar conclusions: fixed overhead costs amplify the predicted wage effects of domestic productivity shocks, while imperfect competition in the labor market matters to a lesser but still meaningful extent.

Key Concepts

Fixed Overhead Costs (Fixed Labor Costs / Fixed Intermediate Input Costs): In the paper’s model, each firm has firm-specific fixed overhead input requirements for labor (denoted ℓ̄_k^f) and intermediate inputs (denoted q̄_k^f) that must be satisfied regardless of the firm’s output level. These fixed requirements are separate from the variable inputs used in production. Fixed labor costs may reflect administration, worker management, facility maintenance, and other tasks that do not directly translate into output. Fixed intermediate input costs include waste management, accounting services, and electricity payments that occur irrespective of sales. The share of total labor inputs that is fixed is identified by how much less than proportionally labor costs respond to demand-driven changes in sales.

Monopsonistic Competition in the Labor Market: The paper models each firm as facing an upward-sloping firm-specific labor supply curve arising from workers’ heterogeneous idiosyncratic preferences over non-wage firm attributes (amenities). Because workers’ idiosyncratic tastes are private information, firms cannot price-discriminate and thus face an increasing marginal cost of labor. Each firm is infinitesimal within the aggregate labor market but has wage-setting power at the firm level. This gives rise to a constant-elasticity firm-level labor supply curve ℓ_k = A_k w_k^ε, where ε is the labor supply elasticity facing the firm.

Wage Markdown: The firm’s equilibrium wage is marked down relative to the marginal revenue product of labor by the factor ε/(1+ε), which is less than one when ε is finite. With a labor supply elasticity of 3.9, the implied markdown is approximately 21 percent; with a supply elasticity of 2.3 (stayer sample), the markdown is approximately 30 percent. Perfect competition corresponds to ε = ∞ and a markdown of zero.

Labor Cost Elasticity: The elasticity of a firm’s total labor cost with respect to a demand-driven change in the firm’s sales, as derived from the model’s comparative statics (equation 15). This elasticity depends on both the variable share of labor inputs (ℓ_k^v / ℓ_k) and the labor supply elasticity ε. It lies strictly between zero (all labor fixed) and one (all labor variable), and is declining in ε for a given variable share. The paper estimates this elasticity at 0.528 via IV, implying substantial fixed overhead in labor.

Total Foreign Demand Shock: The firm-level measure of foreign demand used as an instrument, defined as the weighted average of changes in world import demand (excluding Belgium) across country-product pairs, where the weights reflect both the firm’s own lagged direct export shares and its indirect exposure through the domestic production network (via the Leontief inverse matrix H̃). This measure captures both direct exporter exposure and indirect upstream exposure for non-exporting firms that supply to exporters.

Indirect Export Exposure: The share of a firm’s output that reaches foreign markets indirectly through sales to domestic buyers who subsequently export. Defined recursively: the total export share of firm k equals its direct export revenue share plus the sum over all domestic buyers of the product of k’s revenue share from that buyer and the buyer’s own total export share. Even non-direct-exporting firms sell on average approximately 10 percent of their output indirectly to foreign markets in the Belgian data.

Dekle-Eaton-Kortum Hat Algebra: A technique for solving general equilibrium counterfactuals in trade models by expressing all outcomes as proportional changes (“hats”) relative to the observed equilibrium, without needing to recover the underlying structural parameters. The paper uses this approach to compute counterfactual wages under alternative tariff scenarios, holding fixed the observed firm-level expenditure shares from the reference year (2012) while allowing parameters such as productivity and technology weights to vary across counterfactual economies to rationalize identical observed firm-level observables.

Worker Rents: In the monopsony model, inframarginal workers earn rents defined as the excess return over what would be required to make them indifferent between employers. These rents arise because firms cannot price-discriminate across workers with heterogeneous amenity valuations. The additional rents accruing to workers from a demand-driven increase in firm sales decompose into: (1) wage increases for incumbent workers multiplied by current employment, (2) rents for new hires (the excess of their wage bill over the amount required to induce them to switch to the expanding firm), and (3) a correction term related to the fraction of the labor cost increase borne by expanding employment rather than wages.

Minimum Wages, Efficiency, and Welfare

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

Overview

Research question. Can minimum wages improve welfare through efficiency — by correcting monopsony-driven under-employment — and, if so, by how much? What is the optimal minimum wage, and how much of the welfare gain from a higher minimum wage comes from efficiency versus redistribution?

Model and methodology. The paper develops a tractable general equilibrium oligopsony model with heterogeneous workers (four types: non-high-school, high-school, college workers, and capital owners) and heterogeneous firms (varying in total factor productivity), embedded in a continuum of local labor markets where firms compete strategically in Cournot fashion. Firms face downward-sloping labor supply curves; their market power generates wages below the marginal revenue product of labor (markdowns). The model is calibrated to US data using the Census Longitudinal Business Database (LBD, 2014), the Bureau of Labor Statistics Current Population Survey (CPS, 2019), and the Survey of Consumer Finances (SCF). Key calibration targets include: average firm size of 22.83 workers (LBD), 29 percent of workers earning below $15/hr (CPS), labor and capital income shares, and household-level earnings and capital income ratios. The model is validated by quantitatively replicating four strands of empirical evidence: (i) reallocation effects of the German minimum wage introduction (Dustmann et al., 2021); (ii) employer spillover responses to Amazon’s voluntary $15 minimum wage (Derenoncourt et al., 2021); (iii) wage distribution compression evidence from Brazil (Engbom and Moser, 2021); and (iv) heterogeneous employment effects by market concentration (Azar et al., 2019).

Three channels for efficiency gains. The model identifies three mechanisms through which a minimum wage can improve efficiency under oligopsony: (1) a direct effect in which constrained firms with monopsony markdowns increase wages and expand employment toward the competitive level (Region II firms); (2) a spillover effect in which unconstrained competitor firms narrow their own markdowns in response to constrained firms’ increased wages and market shares; (3) a reallocation effect in which employment is shifted away from low-productivity firms (which enter Region III — constrained on labor demand) toward more productive firms.

Main findings on efficiency versus redistribution. Under the $15.12/hr minimum wage that maximizes social welfare under utilitarian weights (population-share weights), less than 5 percent of the welfare gains come from improved efficiency, while more than 95 percent come from redistribution. When the government is additionally given access to budget-neutral lump-sum transfers that fully address redistribution goals, the efficiency-maximizing minimum wage narrows to a range of approximately $7.50–$10.00 per hour, which is robust across social welfare weight specifications. The welfare gains attributable to efficiency alone are approximately 0.16–0.20 percent in consumption-equivalent terms, representing only about 1–2 percent of the welfare gains achievable in an economy with no labor market power at all (which would be 15.26 percent in consumption-equivalent terms under the same conditions with optimal transfers).

Why efficiency gains are small. Three structural reasons limit efficiency gains: (i) low-productivity firms — which are the firms most affected by a binding minimum wage in Region II — have endogenously narrow markdowns even absent a minimum wage, because they face more elastic labor supply and command small market shares; (ii) the calibrated production function has relatively flat marginal revenue product of labor schedules (decreasing returns parameter α = 0.940), so once firms enter Region III, employment rationing occurs rapidly; (iii) the large, high-productivity firms with the widest markdowns are not materially affected by the minimum wages of their small, low-wage competitors because those competitors have small market shares — making spillovers quantitatively negligible even though the model matches empirical cross-employer wage elasticities.

Optimal minimum wages under alternative frameworks. Without transfers and under utilitarian weights, the optimal minimum wage is $15.12. Without transfers but under Negishi weights (which rationalize the observed competitive equilibrium and load approximately 62 percent of weight on college workers and owners versus their 35 percent population share), the optimal is $6.97. Under a 97 percent weight on high-school graduates, the optimal rises to $18.32. With optimal lump-sum transfers, the optimal collapses to $7.76–$10.11 regardless of social welfare weights — a range robust across Frisch elasticity variants (ϕ ∈ {0.30, 0.62, 0.86}), regional decompositions (low, medium, and high income US states), short-run capital-fixed scenarios (where the optimum declines by approximately $1 under utilitarian weights), and the removal of household heterogeneity entirely (which yields an optimum of $7.74).

Distributional proxies versus welfare. Wage inequality (college–non-college log wage premium, cross-sectional variance of log wages) and the labor income share are monotonically improving as the minimum wage rises, even as welfare is hump-shaped and eventually declining. A rise in the minimum wage from $7.50 to $15 reduces the college–non-college log wage premium from 0.53 to 0.43 (roughly one-fifth), reduces the cross-sectional variance of log wages by nearly half, and raises the aggregate labor income share by approximately 3 percentage points — all while welfare (under utilitarian weights with no transfers) reaches its maximum at $15.12 and then declines. These standard proxies therefore do not reliably indicate welfare.

Scope conditions. All results are long-run steady-state comparisons unless otherwise noted. Results assume no price passthrough and a unit elasticity of substitution between capital and labor. The paper abstracts from capital–labor substitution responses and occupational choice. The redistribution channel quantified here is specific to the utilitarian welfare criterion and to the existing distribution of capital and profit income, in which owners (6 percent of households) earn 92 percent of dividends.

In depth

Q1. What are the three regions of firm behavior in response to a binding minimum wage, and what are their efficiency implications?

A: A firm can be in one of three regions. In Region I the minimum wage is not binding: the firm pays its optimal monopsony wage and employment is inelastically below the competitive level. In Region II the minimum wage binds and exceeds the firm’s optimal monopsony wage, but labor supply at the minimum wage still falls short of labor demand: employment and efficiency improve as the shadow markdown narrows. In Region III the minimum wage exceeds the competitive wage, so unconstrained labor supply would exceed demand: the firm rations employment and the rationing constraint binds, reducing efficiency. At the boundary of Region II and Region III, the shadow markdown equals one and the firm is at its efficient employment level. Only a firm-specific minimum wage targeting each firm’s competitive wage could deliver economy-wide efficiency.

Q2. How does the paper define and use “shadow wages” to characterize equilibrium?

A: The shadow wage for a firm is the effective wage that rationalizes equilibrium employment given rationing constraints. Formally, when a firm rations employment (Region III), households act as if facing a shadow wage equal to the actual minimum wage multiplied by a rationing factor p < 1 (the Lagrange multiplier on the rationing constraint, normalized as a fraction). Shadow wages aggregate across firms into market- and type-level shadow wages via CES aggregation. The key insight is that shadow wages, not observed wages, are allocative: aggregate labor supply for each worker type is determined by the type-level shadow wage, not by the minimum wage that firms actually pay. This allows the paper to express aggregate efficiency via two wedges — the aggregate shadow markdown (capturing average market power) and a misallocation term — without tracking all firm-specific constraints individually.

Q3. What are the two aggregate efficiency wedges and how do they behave as the minimum wage rises?

A: The two wedges are: (i) the aggregate shadow markdown µ̃, which is a productivity-weighted average of firm-level shadow markdowns and measures the extent to which aggregate wages fall short of marginal revenue products; and (ii) the misallocation term ω, which measures whether employment is allocated toward more productive firms and equals one when all shadow markdowns are identical. As the minimum wage rises from zero, µ̃ initially narrows (improving efficiency) because firms in Region II expand toward their competitive employment level and constrained firms’ market shares rise, tightening the residual labor supply of unconstrained competitors and narrowing their markdowns. But as the minimum wage rises further, Region III rationing causes shadow markdowns to widen rapidly — first for low-productivity firms and then progressively for more productive ones — so µ̃ turns back downward. The misallocation term ω first improves as low-productivity firms are pushed out, but then worsens because rationing at intermediate-productivity firms redirects employment from high- to medium-productivity firms.

Q4. What does the model validation exercise on the German minimum wage (DLSUB 2021) show?

A: The paper calibrates the model to the German context by setting a minimum wage of $8.95/hr equivalent to 48 percent of the pre-reform median wage — matching Germany’s 8.50 euro introduction in 2015, where 15 percent of workers earned below the threshold. The model produces employment effects that are slightly positive (consistent with empirical findings of no disemployment), average wage increases consistent with both constrained and unconstrained firms raising wages, a negative elasticity of the number of operating firms with respect to minimum wage exposure (correctly signed, moderately smaller than data), and a positive elasticity of average firm size with respect to exposure (slightly larger than the data). The reallocation direction — small unproductive firms shrinking and workers moving to larger, more productive firms — matches the data qualitatively and within the range of data estimates across specifications.

Q5. What does the Amazon spillover replication (DNWT 2021) show, and what does it imply about the minimum wage spillover channel?

A: Derenoncourt et al. (2021) estimate a cross-employer wage elasticity of 0.26: when Amazon raised wages by approximately 18.1 percent, competitors raised wages by 4.7 percent on average. The model replicates this by treating Amazon as the largest (or second-largest) firm in each market, exogenously narrowing its markdown by a fraction ζ calibrated to deliver an 18.1 percent wage increase. Competitors in the model raise wages through the strategic interaction mechanism: Amazon’s higher wage and market share tightens competitors’ residual supply curves, inducing them to narrow their own markdowns. The model matches the 0.26 cross-employer elasticity when Amazon is the largest firm in markets with at least 36 competitors, or the second-largest in markets with at least 12. Critically, the authors note that this empirical evidence concerns responses to a large firm raising wages; for minimum wages the question is whether large firms respond to their small wage competitors, which the model shows they do not substantially, because small firms have negligible market shares.

Q6. How does the paper separate efficiency from redistribution, and what is the key methodological innovation?

A: The paper gives the government access to budget-neutral, unrestricted lump-sum transfers across households in addition to the minimum wage. With transfers available, the government can use them to meet any redistributive objective encoded in arbitrary social welfare weights. Whatever is left for the minimum wage to do must be purely efficiency-improving. The paper shows (via aggregation theorems) that optimal lump-sum transfers can be computed in closed form for any social welfare weights, and that the social welfare maximizing allocation subject to transfers can be decentralized by transfers that sum to zero across households. Under this framework, the efficiency-maximizing minimum wage lies between $7.50 and $10.00 per hour regardless of whether utilitarian, Negishi, or 97 percent high-school-weighted social welfare functions are used — collapsing the original $0–$31 range to a tight interval.

Q7. How are Negishi weights computed, and why are they important for interpreting the results?

A: The Negishi weights are the social welfare weights under which a planner would choose the observed competitive equilibrium with zero lump-sum transfers. They are computed by inverting the planner’s first-order conditions: for the competitive equilibrium to be optimal under some set of weights, the implied consumption ratios must match observed data. The calibrated Negishi weights assign a combined weight of approximately 62 percent to college workers and owners, who constitute only 35 percent of the population. This means the competitive equilibrium is disproportionately aligned with higher-income households. A utilitarian planner, which weights households by population shares, therefore sees large scope for redistribution toward non-college workers — which is exactly why the utilitarian-optimal minimum wage is $15.12 and why 94 percent of its welfare gains come from redistribution rather than efficiency.

Q8. What are the quantitative welfare gains from the efficiency-maximizing minimum wage, and how small are they relative to the potential gains from eliminating monopsony?

A: With optimal lump-sum transfers, the welfare gains from the efficiency-maximizing minimum wage are approximately 0.16–0.20 percent in consumption-equivalent terms, robust across social welfare weight specifications, Frisch elasticity variations, and regional decompositions. The welfare gains associated with an economy in which all firms’ markdowns are set to one (no labor market power at all), also evaluated with optimal transfers, are 15.26 percent in consumption-equivalent terms. The efficiency-maximizing minimum wage therefore recovers approximately 1–2 percent of the potential welfare gains from eliminating monopsony. Equivalently, the efficiency gains correspond to roughly a 0.1 percent increase in TFP. These gains are small despite the model matching all empirical evidence on the channels through which efficiency gains could occur.

Q9. How do employment effects of minimum wages vary by market concentration, and why?

A: In concentrated markets (upper tercile of HHI), firms have larger monopsony markdowns, so a binding minimum wage pushes them into Region II — where employment expands — over a wider range of minimum wage values before entering Region III. This produces large, positive employment effects in concentrated markets. In less concentrated markets, firms already have narrow markdowns (they are closer to competitive), so even small minimum wage increases push them into Region III, where employment contracts. The model replicates the statistically significant positive effects in high-concentration markets and negative effects in low-concentration markets documented by Azar et al. (2019), for initial minimum wages below approximately $8/hr. At higher initial minimum wages, however, even high-concentration markets exhibit negative employment effects as more firms enter Region III.

Q10. What does the robustness exercise for Mississippi reveal?

A: Mississippi has the lowest per capita income in the US, and a $15 minimum wage would bind for 41.3 percent of its workers (versus 29.4 percent nationally). Despite this, the model finds that Mississippi would benefit from a $15 federal minimum wage under utilitarian weights, and the Mississippi-specific optimal minimum wage is $14.89 — nearly identical to the national optimum. The reason is an offsetting compositional effect: while Mississippi has lower average wages (pushing toward a lower optimal), it has a larger share of high-school graduates (63 percent versus 52.8 percent nationally) who prefer higher minimum wages (around $17 in the model). These two forces wash out, producing a stable optimal close to the national figure.

Q11. What happens to common empirical proxies for inequality and worker power as the minimum wage rises?

A: The college–non-college log wage premium declines from 0.53 to 0.43 (a fall of roughly one-fifth) as the minimum wage rises from $7.50 to $15. The cross-sectional variance of log wages falls by nearly half over this range, driven equally by declining within- and between-type inequality. The aggregate labor income share rises by approximately 3 percentage points, and the share of output created in non-high-school jobs paid to non-high-school workers rises by 7 percentage points. All of these proxies are monotonically improving in the minimum wage throughout, even as aggregate welfare under the model’s social welfare function is hump-shaped and declining past the optimum. The paper concludes that observations of declining inequality or a rising labor share are consistent with falling welfare, so these proxies cannot serve as reliable welfare indicators.

Q12. How does the short-run (fixed-capital) analysis differ from the long-run baseline?

A: In the short run, capital at each firm is fixed at the type-specific level chosen under a zero minimum wage. This creates sharper decreasing returns in labor (parameter γα rather than α̃), overhead costs that can make operation unprofitable, and a narrower range of minimum wages over which firms remain in Region II. The result is that firms in the short run enter Region III at lower minimum wages than in the long run, limiting the range of efficiency gains. Quantitatively, the efficiency-maximizing optimal minimum wage declines by approximately $1 under utilitarian weights (from about $10 to about $9 in the short-run exercise) and by only about $0.20 under Negishi weights. The robustness conclusion is that the difference between short- and long-run optimal minimum wages is modest, and the main finding that efficiency gains are small is preserved.

Key Concepts

Shadow wage (w̃ᵢⱼ): The effective wage that rationalizes a firm’s equilibrium employment in the presence of a minimum wage. When labor is rationed at firm ij (Region III), the shadow wage equals the actual minimum wage multiplied by a rationing factor pᵢⱼ < 1, where pᵢⱼ is derived from the Lagrange multiplier on the household’s rationing constraint. The shadow wage is allocative — it determines labor supply decisions — while the observed minimum wage wage is not. When the rationing constraint is slack (Regions I and II), the shadow wage coincides with the observed wage.

Shadow markdown (µ̃ᵢⱼ): The ratio of a firm’s shadow wage to its marginal revenue product of labor. In Region I (unconstrained), this equals the standard monopsony markdown. In Region II (constrained, on the labor supply curve), the shadow markdown narrows as the minimum wage increases, moving the firm toward its efficient employment level. In Region III (constrained, on the labor demand curve), the shadow markdown equals the rationing multiplier pᵢⱼ and widens, reflecting efficiency losses from rationing. An aggregate shadow markdown µ̃ is computed as a productivity-weighted average of firm-level shadow markdowns across all firms in the economy.

Misallocation wedge (ω): A productivity-weighted measure of how well employment is allocated across firms. In an efficient allocation with identical shadow markdowns, ω = 1. When high-productivity firms have wider markdowns than low-productivity firms (the baseline oligopsony outcome), ω < 1 because employment is directed away from productive firms. A minimum wage can improve ω by shrinking low-productivity firms but worsens it when high-productivity firms enter Region III and are over-rationed relative to medium-productivity firms.

Oligopsony with Cournot competition: The specific form of labor market power in this model. In each local labor market (defined as a NAICS 3-digit industry × commuting zone cell), a finite number of firms compete strategically in employment quantities, taking their competitors’ employment levels as given (Cournot assumption). Each firm has an upward-sloping labor supply curve derived from nested CES household preferences, and exercises a markdown on the marginal revenue product of labor. This differs from monopsony (one firm) or perfect competition (infinitely many firms), and generates both direct effects and spillover effects of minimum wages.

Negishi weights: The vector of social welfare weights under which the observed competitive equilibrium allocation would be the solution to a social planner’s problem with zero lump-sum transfers. In this model, the calibrated Negishi weights assign roughly 62 percent combined weight to college workers and owners (who constitute only 35 percent of the population), reflecting the fact that the market equilibrium allocates a disproportionate share of consumption to high-income households. The Negishi weights are used both to identify the gap between market outcomes and utilitarian objectives (motivating redistribution) and as one alternative normative benchmark.

Efficiency-maximizing minimum wage: The minimum wage that maximizes social welfare when the government additionally has access to budget-neutral lump-sum transfers across households. Because transfers can be optimized to handle any redistributive objective encoded in any arbitrary social welfare weights, the minimum wage under this framework serves solely to improve productive efficiency. In the calibrated model, the efficiency-maximizing minimum wage is approximately $7.50–$10.00 per hour, robust to social welfare weight specifications, Frisch elasticity variations (ϕ ∈ {0.30, 0.86}), and regional income differences.

Rationing constraint (n̄ᵢⱼₖ): A firm-specific, type-specific upper bound on the labor a household may supply to a firm in equilibrium. These constraints are taken as given by households and determined in equilibrium by firms’ labor demand decisions. When the minimum wage is above the firm’s competitive wage (Region III), the firm’s labor demand is less than what households would want to supply at that wage, so the rationing constraint binds. The binding rationing constraint generates the shadow wage discount (pᵢⱼ < 1) and is the mechanism by which high minimum wages reduce efficiency in the model.

Monopsony Makes Firms Not Only Small but Also Unproductive: Why East Germany Has Not Converged

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

Layer 1 — Summary

When employers face a trade-off between growing large and paying low wages — that is, when they have monopsony power — some productive employers will decide to acquire fewer customers, forgo sales, and remain small; these decisions have adverse consequences for aggregate labor productivity beyond the standard monopsony result that firms are too small. The paper documents that East German plants (compared to West German ones) face a steeper size-wage curve, invest less into marketing, and remain smaller, with the share of employment at plants with more than 249 employees standing at roughly 25% in East Germany versus 39% in West Germany in 2014 (and 31% versus 55% in manufacturing specifically). The steeper size-wage curve in East Germany is traceable to the historically determined underrepresentation of collective bargaining and union membership in small East German plants — a legacy of communist-era labor organization that caused union membership to collapse after reunification. The authors combine this evidence with a heterogeneous-plant model in which plants have product market power and choose how many customers to acquire subject to an upward-sloping size-wage schedule; two channels reduce aggregate productivity: a love-of-variety loss (fewer active plants means consumers bundle from a smaller variety of suppliers) and a compositional reallocation loss (labor is shifted from more productive to less productive plants, an effect exacerbated by product market power). When the model is calibrated to West Germany and the steeper East German size-wage trade-off is imposed, it predicts 10 percentage points lower aggregate labor productivity in East Germany — and for manufacturing, where East-West differences in plant size and the size-wage trade-off are particularly pronounced, the model predicts 18 percentage points lower productivity; in both cases the compression of the plant size distribution accounts for the largest share of the predicted productivity loss. The paper thus offers an explanation for why, more than thirty years after reunification, labor productivity and wages remain roughly 25% lower in the East German private sector despite uniform legal institutions across the two regions.

In depth

Q1. What is the core mechanism by which monopsony power reduces aggregate productivity, and how does it differ from the standard “firms are too small” result?

In the standard monopsony account, firms face an upward-sloping labor supply curve and choose to employ fewer workers than the competitive optimum, so individual firms are below efficient scale. The paper identifies an additional, investment-distortion channel: plants must also decide how large a customer base to acquire, and doing so requires marketing expenditure as well as the labor to service additional customers — labor whose cost rises with plant size along the size-wage schedule. A steeper size-wage curve therefore makes customer acquisition more expensive at the margin, and some productive plants optimally choose to acquire fewer customers, forgo sales, and remain small. The new aggregate productivity loss stems from this distorted investment margin: plants that could generate high value added at large scale instead operate at sub-optimal customer networks, suppressing aggregate output through both a love-of-variety effect (fewer active large plants means consumers access a smaller product variety) and a misallocation effect (the compressed size distribution shifts employment toward less productive plants).

Q2. What empirical patterns do the authors document to link the East-West productivity gap to missing large plants and steeper size-wage curves?

The authors document three nested empirical facts using the German Structure of Earnings Survey (SES) pooled across 2006, 2010, and 2014, supplemented by administrative wage panel data (AWFP) and national accounts (VGR). First, East German labor productivity in the private non-primary sector is about 25% below West Germany’s and has not converged since roughly 1995. Second, the share of employment at large plants (>249 employees) is substantially smaller in the East, and this gap is present both cross-sectionally across survey years and conditionally: East German plants enter smaller and remain smaller over their life-cycles, so plant age does not explain the difference. Third, industries where missing large plants are most pronounced in East Germany relative to West Germany are also the industries with the largest East-West productivity and wage gaps — the employment-weighted correlation between the large-plant share gap and the productivity gap is 0.53 across industries. The steeper size-wage curve itself is documented using within-industry comparisons: on average the plant size elasticity of wages is one-fifth larger in East Germany, and those industries with a steeper East-West size-wage differential are also the industries with the most missing large plants and the lowest average wages in the East.

Q3. Why is the steeper size-wage curve specific to East Germany, and why does it persist decades after reunification?

In communist East Germany, trade unions did not have the role of representing worker interests; consequently, after reunification, union membership fell dramatically. The key institutional consequence is that collective bargaining coverage in East Germany is underrepresented specifically in small plants. Workers at small plants in East Germany are more likely to have individually rather than collectively bargained wages than their West German counterparts, whereas workers at large plants in both regions are more similarly covered. Because collective bargaining flattens the size-wage curve (larger plants pay a smaller premium over small plants’ wages when both are covered by the same bargaining agreement), its absence in small East German plants produces a steeper gradient of wages with plant size in the East. This is a persistent structural feature rather than a transitional one: government policies and their enforcement are essentially uniform across regions, so the asymmetric bargaining coverage, which originates in communist-era institutional history, has not been erased by market forces or policy since 1990.

Q4. How is the model structured, and what are the three decision stages for plants?

The model is a static, long-run heterogeneous-plant framework that yields closed-form solutions. Within a period, plants face a three-stage decision problem. First, they decide whether to enter the market. Second, after entry, they choose how many customers to acquire, trading off additional sales revenue against marketing costs and the labor cost of servicing a larger customer base — a cost that rises with the number of customers because the upward-sloping size-wage curve means each additional worker hired requires a higher wage for all infra-marginal workers. Third, taking into account their product market power (each plant is a monopolistic competitor with its own customers), plants set prices to each customer and thereby determine how many workers they need. The size-wage schedule enters the second stage directly, so a steeper schedule reduces optimal customer acquisition across all plants, with the distortion being largest for the most productive plants (which would otherwise grow the largest).

Q5. Through what two channels does the steeper size-wage trade-off reduce aggregate labor productivity in the model?

The first channel is a love-of-variety effect in the product market: because more productive plants acquire fewer customers and operate at smaller scale under a steeper size-wage schedule, the average consumer bundles goods from a smaller number of distinct plants, and aggregate efficiency falls through the standard CES love-of-variety mechanism. The second channel is a misallocation effect in the labor market: the steeper size-wage schedule compresses the employment distribution across plants, reallocating labor from more productive to less productive plants relative to the benchmark with a flatter schedule. The paper shows that this second channel is exacerbated by product market power, because plants with stronger pricing power respond more aggressively to the changed labor cost trade-off. In the model’s decomposition, the compression of the plant size distribution (the misallocation channel) accounts for the largest part of the predicted 10 percentage point productivity shortfall.

Q6. What quantitative predictions does the model make, and how does it perform in untargeted moments?

The model is calibrated to two moments for West Germany: average plant size and the share of large plants (>249 employees). When the steeper East German size-wage trade-off is imposed without re-calibrating other parameters, the model predicts 10 percentage points lower aggregate labor productivity in East Germany — accounting for at least 10 of the roughly 25 percentage point observed gap. For the manufacturing sector alone, where East-West differences in plant size, the size-wage trade-off, and aggregate productivity are particularly pronounced, the calibrated model predicts 18 percentage points lower productivity. As an untargeted validation, the model also replicates the plant size distribution in East Germany, matching both the smaller average plant size and the relatively small number of large plants. These untargeted predictions provide additional support for the mechanism.

Q7. What alternative explanations for East Germany’s non-convergence does the paper rule out or place in context?

The paper addresses several confounds. In Appendix A, the authors show that East-West aggregate labor productivity differences are driven by differences in aggregate total factor productivity, not by labor quality differences, capital intensity differences, or capital quality differences — confirming within-country the finding that TFP explains a large fraction of productivity dispersion. The TFP differences are shown to be unlikely the result of greater labor market flexibility in West Germany or differences in industry composition. Appendix B shows that the East-West plant size distribution gap is not driven by differences in urbanization (West Germany has more metropolitan areas). The paper also addresses plant age: East German plants enter smaller and remain smaller at every age and across entry cohorts, ruling out the hypothesis that the size gap is purely a transitional legacy of the restructuring that destroyed many large East German plants at reunification.

Q8. How does this paper relate to the Heise and Porzio (2021) finding that plant productivity differences, not worker quality differences, drive the East-West wage gap?

Heise and Porzio (2021) use matched employer-employee data to document that plant productivity differences (as opposed to worker quality differences) account for most of the East-West wage differential, and they explain why low worker mobility does not remove these differences. The present paper complements this by providing an explanation for why plant productivity is lower in East Germany in the first place and why firm-level convergence does not occur: the steeper size-wage curve induced by the legacy of missing collective bargaining coverage in small East German plants distorts the investment and customer acquisition decisions of productive plants, keeping them small and unproductive. The two papers are thus complementary: Heise and Porzio take the plant productivity gap as given; Bachmann et al. endogenize it through the size-wage mechanism.

Key Concepts

Size-wage curve: The empirical relationship between plant size (measured by employment) and wages paid to workers, conditional on worker characteristics. A steeper size-wage curve means that the wage premium for working at a large plant relative to a small plant is larger. In this paper’s model, plants internalize that expanding their customer base and workforce requires paying higher wages to all workers (not just the marginal hire), making growth more costly when the size-wage curve is steeper.

Monopsony power (monopsonistic competition): The market structure in which an individual employer faces an upward-sloping labor supply curve — i.e., it must raise wages to attract additional workers. The paper uses “monopsonistic competition” to describe a setting with many such employers, each with some wage-setting power, in contrast to oligopsony. The paper focuses on allocative effects of this power, not on normative efficiency questions.

Customer capital / customer acquisition: Plants must incur marketing expenses to build a customer base; each customer relationship generates a stream of sales but requires labor to service. The size of the customer network is a long-run investment decision. Under monopsonistic labor markets, the cost of expanding the customer base includes not only marketing expenses but also the higher wages that a larger workforce requires, making customer acquisition a margin that is distorted by labor market power.

Love-of-variety effect: A welfare loss that arises in models with monopolistic competition and CES preferences when the number of active product varieties declines. In this paper it applies to the product market: when plants remain small and acquire fewer customers, the effective number of distinct varieties consumed falls, reducing aggregate efficiency even holding plant-level productivity fixed.

Misallocation / compressed size distribution: A situation in which factors of production are not allocated to their highest-value uses. Here, the steeper size-wage curve induces productive plants to remain small, so labor that would otherwise be employed at high-productivity large plants is instead employed at lower-productivity small plants. The resulting compression of the plant size distribution — fewer very large plants, more mass in the middle — is both the key empirical fact and the primary quantitative driver of the predicted aggregate productivity shortfall.

Collective bargaining coverage: The fraction of workers whose wages are set by collective agreements between employers (or employer associations) and trade unions, rather than by individual negotiation. The paper establishes that collective bargaining flattens the size-wage curve by compressing wages across plants of different sizes. The historically low collective bargaining coverage among small East German plants — a legacy of communist-era labor relations — is the institutional root cause of the steeper East German size-wage schedule.

Summary based on IZA Discussion Paper 15293. AI-assisted, human review pending.

Voluntary Minimum Wages: The Local Labor Market Effects of National Retailer Policies

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

Layer 1 — Overview

Research Question

This paper studies the labor market effects of voluntary minimum wages (VMWs) — company-wide, publicly announced wage floors set by large private employers — in the U.S. low-wage retail and service sector from 2014 to 2023. The central questions are: (1) How do VMWs affect wages and employment at the adopting large retailers? (2) Do VMWs generate wage spillovers to other employers in shared local labor markets?

Data and Setting

The authors use anonymized payroll data obtained from a large U.S. credit bureau, covering the wage distributions and employment of over 4,000 firms and approximately 18 million hourly workers (roughly 22–24% of the U.S. hourly workforce) from January 2013 to August 2023. The database is skewed toward retail and service sectors: over a third of covered workers are in retail, and over half in retail and services combined. Critically, the data also include worker flow information — records of individual workers moving between firms — enabling the authors to define shared labor markets via actual employment transitions rather than broad geographic or industry proxies.

The sample of VMW events consists of 20 voluntary minimum wage policies across 5 large retailers (each with over 150,000 employees nationally), restricted to events with no other major wage policy within six months before or after the focal event. Voluntary minimum wage announcements were identified from an inventory maintained by the National Employment Law Project and independently verified through media sources, then matched to anonymized companies using employer size, industry, and observed shifts in the wage distribution.

Identification Strategy

The authors adapt the gap design from the national minimum wage literature. For each company-by-commuting-zone (CZ) cell, the “gap” measures the percent increase in average hourly wages that would be required to bring all workers in the area up to the company’s new voluntary minimum. The gap is averaged over months −6 to −3 before the event (months −3 to −1 serve as a built-in placebo-in-time check). This variation in bite across CZs — arising because the same nominal VMW level implies different wage increases depending on local wage distributions — is combined with a stacked event study across 20 VMW events. Spillover effects are estimated by regressing log average wages at non-policy establishments on the large retailer’s CZ-level gap measure, progressively narrowing the definition of “labor market” from: (i) all non-policy establishments in the same CZ, to (ii) establishments in industries connected to the large retailer by worker flows (15 three-digit NAICS industries), to (iii) specific establishments with documented pre-event worker flows to or from the large retailer (“connected establishments”).

Main Findings

Own effects: For $15 VMW events, moving from a CZ gap of 0 to a gap of 1 is associated with an approximately 88 log point increase in average hourly wages in the six months after adoption. Given that the average establishment-level gap for $15 VMWs is 0.11, the implied average wage increase is approximately 10.45% (the authors’ estimate is 9–10%, consistent with small wage increases even in zero-gap comparison areas). Employment of workers earning under $30 per hour rose by 4.62% after $15 VMW events, 2.01% after major events (affecting ≥30% of workforce), and 1.25% across all 20 events. These employment increases are entirely attributable to reduced separations rather than new hiring: separation rates fell by 0.42, 0.57, and 1.09 percentage points after all, major, and $15 VMW events respectively — equivalent to reductions of 6.57%, 8.73%, and 15.33% relative to pre-period means. Separations specifically to other database companies fell by 0.07–0.19 percentage points (5.63–13.48% relative to base rates). If anything, new hiring fell modestly after VMW adoption. Total monthly base pay and gross compensation both rose after VMWs, indicating increased total take-home pay without compensatory reductions in hours or bonuses. The total employment elasticity with respect to wages ranges from approximately 0.35 to 0.45, while the quit elasticity is 2.20–2.38 (consistent with dynamic monopsony models in which the labor supply elasticity is twice the quit elasticity).

Spillover effects: Across all three definitions of the labor market, the paper estimates precise, economically negligible cross-employer wage spillovers in the six months following VMW events. Cross-employer wage elasticities are statistically indistinguishable from zero across all specifications. Among the most narrowly defined sample — establishments with documented pre-event worker flows to or from the large retailer — the upper bound of the confidence interval rules out spillovers greater than 0.2% of wages. No wage spillovers are detected for new hires at non-policy establishments either. These null results are confirmed over a 12-month post-event horizon for the subsample of events with no other major policy nearby.

Mechanism: The reason for negligible spillovers is that VMWs reduced labor market churn rather than expanding the large retailer’s total employment. Hiring away from large retailers by connected non-policy firms falls after VMW adoption — consistent with fewer separations to recruit from — but overall hiring by non-policy firms does not decline, as these firms substitute toward other hiring sources. This substitutability across new hire sources in a thick market is the proximate explanation for the absence of wage pressure on competitor firms.

Scope Conditions

Results pertain to large national retailers (>150,000 employees) operating in U.S. commuting zones during 2014–2023. The database covers only employers large enough to participate in credit bureau income verification; smaller employers (representing over 75% of U.S. hourly workers by the BLS comparison) are not observed, and the authors caution that spillover effects on smaller firms cannot be assessed. The authors also explicitly note that their null local spillover results do not rule out national-level strategic wage-setting dynamics — the rapid sequential adoption of VMWs across major retailers may reflect national-level competition rather than local market competition.

In depth

Q1. What exactly are “voluntary minimum wages” and how do they differ from statutory minimum wages?

Voluntary minimum wages (VMWs) are company-wide, publicly announced wage floors set unilaterally by private employers, typically well above the applicable statutory (federal, state, or local) minimum. Unlike statutory minimums, which bind all employers in a jurisdiction, VMWs apply only to the announcing company across all of its geographic operations in the U.S. The paper studies VMWs adopted by retailers with over 150,000 workers, which include wage floors at levels such as $9, $10, $12, and $15 per hour. $15 VMWs were adopted at a time when few states or localities had yet reached that threshold, meaning the policy bit into the company wage distribution far more deeply than prevailing statutory floors.

Q2. How were VMW events identified and matched to anonymized firms in the payroll database?

VMW events were identified from a database maintained by the National Employment Law Project and verified through an independent review of business news articles. These publicly reported announcements were then matched to the anonymized companies in the credit bureau payroll database using employer size, industry, and the timing of observed shifts in the firms’ wage distributions. An additional three events were identified directly from data: months where the share of workers earning below a given wage level dropped by at least 15 percentage points (for non-$15 events) or 10 percentage points (for $15 events) while the share at exactly that wage bin jumped by at least 10–20 percentage points. The final sample of 20 events was restricted to those with no other major wage policy in the six months before or after.

Q3. How does the gap design work and why does it improve on the fraction-affected approach?

The gap for a given company, commuting zone, and time period is defined as the total wage increase needed to bring all sub-$30 workers up to the company minimum, divided by total wage costs — formally a labor-share-weighted average shortfall from the new minimum across wage bins. The gap leverages more cross-sectional variation in treatment intensity than the simple fraction of workers below the minimum: for a $15 VMW, an area where all workers earn $10 has a gap of 0.50 while an area where all earn $12 has a gap of 0.25. The gap is averaged over months −6 to −3 before the event. The period months −3 to −1 then serve as a placebo window: genuine VMW effects should appear only after the policy’s adoption month, not during the period immediately after the gap is measured. If instead the regression picks up mean reversion in noisy wage data, spurious effects would appear in months −3 to −1 rather than at event time 0.

Q4. What is the magnitude of the wage effect on the large retailers themselves?

For $15 VMW events, the stacked event study estimates that moving from a gap of 0 to a gap of 1 is associated with an approximately 88 log point increase in average hourly wages beginning exactly in the month of policy adoption. Given the average establishment-level gap of 0.11 for $15 VMWs, this implies the average establishment raised wages by approximately 9–10% (the authors compute 10.45% from the average gap, consistent with a slight dampening because zero-gap CZs experienced marginally higher wages too). Wage increases are confirmed persistent at 12 months in robustness checks. For all 20 VMW events pooled, effects are somewhat smaller commensurate with the lower average bite.

Q5. How did VMWs affect total employment and its components at the large retailers?

After $15 VMW events, log total employment of sub-$30 workers rose by 4.62%; after major VMW events (≥30% bite), 2.01%; after all 20 events, 1.25%. The increases are entirely driven by retention gains. Separation rates fell by 1.09 percentage points after $15 VMWs, 0.57 p.p. after major events, and 0.42 p.p. after all events — translating to reductions of 15.33%, 8.73%, and 6.57% relative to pre-period means. Separations to other database companies specifically fell by 0.07–0.19 percentage points (5.63–13.48% relative to the base mean). New hiring — measured as year-on-year log change in hires to control for seasonality — fell after VMW adoption, consistent with a reduced need to replace departing workers.

Q6. What do the labor supply elasticities implied by the VMW results look like?

The total employment elasticity with respect to wages ranges from approximately 0.35 to 0.45 across the three event groupings. Under standard dynamic monopsony models, the labor supply elasticity facing the firm equals twice the quit elasticity in steady state (Manning, 2003). The quit elasticity — derived by dividing the proportional reduction in separations by the log wage increase — ranges from 2.20 to 2.38, consistent with the earlier monopsony-based case study of Ford’s $5 workday (Raff and Summers, 1987) and implying substantial firm-level wage-setting power.

Q7. Did VMWs increase total take-home pay or were wage gains offset by reductions in hours or bonuses?

The paper examines log average monthly base pay and log average gross compensation (which includes bonuses and overtime) as additional outcomes. Both measures rose after $15 VMW events, indicating that the wage floor increase translated into genuine improvements in total take-home pay without compensatory reductions in hours or other non-wage compensation. The monthly gross pay series is an average over calendar year-to-date months, so increases appear gradually rather than as a sharp jump at the adoption month; nevertheless the upward trend is evident and consistent.

Q8. What are the estimated spillover effects on wages at non-policy employers?

Across all three definitions of the labor market — all non-policy establishments in the same CZ, establishments in the 15 connected industries in the same CZ, and establishments with documented pre-event worker flows — the estimated cross-employer wage effects are precise zeros. The stacked event study in the post-period shows coefficients centered on zero with small confidence intervals. The difference-in-differences cross-employer wage elasticity (instrumenting the large retailer’s wage change with the gap) is also indistinguishable from zero. Among the most exposed connected establishments, the point estimate is slightly positive but economically negligible; the upper confidence interval bound rules out spillovers greater than 0.2%. Results are confirmed over a 12-month horizon for the clean-event subsample.

Q9. Could the null spillover result reflect mean reversion bias rather than a true zero?

The authors address this concern explicitly. For the policy-company gap design, they build in a placebo-in-time check by measuring the gap over months −6 to −3 and checking that no wage effects appear in months −3 to −1. For the non-policy spillover analysis, they also examine an alternative treatment variable — the gap between non-policy establishments’ wages and the large retailer’s new VMW — and find evidence of mean reversion: wages begin rising in the pre-period in the direction of this gap measure. They correct for this by detrending post-period estimates using a linear extrapolation of the pre-period trend. After detrending, spillover effects remain indistinguishable from zero.

Q10. Why are spillover effects so limited if the large retailer is drawing fewer workers away from competitors?

The paper’s mechanism analysis shows that while the probability of a non-policy firm hiring a worker from the large retailer falls after a VMW event (consistent with fewer separations to recruit from the large retailer), the overall rate of hiring by non-policy firms does not decline. Non-policy firms substitute toward other hiring sources — primarily other non-policy companies — rather than hiring fewer workers overall. This substitutability across recruiting sources in a thick labor market mutes the competitive pressure on competitor wages: since non-policy firms can replace the reduced flow from VMW companies with workers from other sources without changing total employment, they face no pressure to raise wages.

The authors test whether larger local market presence amplifies spillovers by splitting the sample at the median employment share of the large retailer in the CZ. They find no evidence of positive wage spillovers even in CZs where the large retailer’s employment share is above the median, confirming that neither local market size nor market concentration is a mechanism for spillover transmission in this setting.

Q12. How do these VMW spillover results compare to prior evidence on employer wage-setting spillovers?

The main prior U.S. evidence (Staiger et al., 2010) studied a federally mandated wage increase at Veterans Affairs hospitals and found a cross-establishment wage elasticity of approximately 0.19 for registered nurses at neighboring hospitals. The authors note two key differences: first, the VA policy increased both wages and employment at treated facilities, whereas VMWs primarily reduced separations without increasing hiring, so the supply of workers to competitor firms was not squeezed. Second, the market for low-wage retail and service workers is likely thicker (more potential hires available) than the market for registered nurses, allowing competitors to substitute hiring sources without bidding up wages.

Q13. What do the null local spillover results imply about national-level wage dynamics?

The authors explicitly caution against reading the null local spillover result as implying VMWs have no broader effect on the low-wage labor market. The rapid and successive adoption of VMWs across major retailers during 2021–2022 could reflect national-level strategic wage-setting competition — firms mimicking each other’s announcements in an arms-race dynamic during tight labor markets — rather than local competitive transmission. The paper does not test for national-level strategic interactions and calls for further research on this dimension.

Key Concepts

Voluntary Minimum Wage (VMW): A company-wide, publicly announced wage floor set unilaterally by a private employer, applying across all of the firm’s geographic operations in the U.S., typically well above applicable statutory minimums. Distinct from legally mandated minimum wages in that they bind only the announcing firm and arise from the firm’s own strategic or reputational motivations.

Gap Measure: Borrowed from the national minimum wage literature (Card, 1992; Draca et al., 2011), this is the percent increase in a firm’s average hourly wage that would be required to bring all workers in a given commuting zone up to the company’s new voluntary minimum. Formally the labor-share-weighted average shortfall from the VMW across sub-$30 wage bins. A gap of 0 means no workers fall below the new minimum; a gap of 1 means all workers would need to be raised to the minimum, doubling the average wage. Used as a continuous treatment variable capturing the local bite of the policy.

Stacked Event Study: An empirical design in which a separate 12-month panel (6 months pre- and post-event) is constructed for each of the 20 VMW events, these datasets are stacked, and the effect of the continuous gap treatment is estimated jointly across all events, with event-specific indicators interacting all regressors to allow each event to have its own intercept.

Placebo-in-Time Check: A robustness test built into the gap design by computing the gap over months −6 to −3 and verifying that wage effects do not appear in months −3 to −1 (the period between gap measurement and VMW adoption). Genuine policy effects should materialize at the adoption month; spurious effects driven by mean reversion in noisy wage data would appear in months −3 to −1 because the gap would mechanically predict wage reversion toward the mean in the period immediately following its measurement.

Connected Establishments / Poaching and Feeder Establishments: Specific firm-by-CZ cells identified as sharing a labor market with the large retailer via actual worker flows. “Poaching establishments” hired at least one worker from the large retailer in the 12 months before the VMW event. “Feeder establishments” had at least one worker subsequently hired by the large retailer in the same pre-period. These are the most narrowly defined and most economically relevant labor market competitors for testing spillover effects.

Quit Elasticity / Labor Supply Elasticity (Firm-Level): The quit elasticity is the percent change in the separation rate divided by the percent change in wages induced by the VMW. Under standard dynamic monopsony models (Manning, 2003), in steady state the recruit elasticity equals the quit elasticity, and the firm-level labor supply elasticity equals twice the quit elasticity. The authors estimate quit elasticities of 2.20–2.38, implying labor supply elasticities of 4.40–4.76 to the firm — consistent with meaningful but not extreme monopsony power.

Cross-Employer Wage Elasticity: The percent change in wages at a non-policy employer’s establishment associated with a 1% change in wages at the large retailer in the same commuting zone, instrumented using the large retailer’s gap interacted with the post-event indicator. Estimated to be a precise zero across all market definitions and event groupings in this paper.

J42 | Macro Paper Warehouse

Bargaining and Inequality in the Labor Market

Layer 1 — Overview

In depth

Q1. How do the authors define “individual bargaining” and why is this definition broader than standard labor economics usage?

Q2. How was the firm survey designed to elicit bargaining strategies reliably, and what is the “protocol question”?

Q3. What validation exercises support the reliability of the elicited firm bargaining measures?

Q4. Is firm productivity associated with whether a firm engages in individual bargaining?

Q5. What firm characteristics other than productivity predict bargaining strategies?

Q6. What does the variance decomposition say about the relative importance of firm versus market factors in predicting bargaining strategies?

Q7. How common is it for workers to provide salary expectations before receiving an initial offer, and what do firms do with this information?

Q8. What fraction of outside offers are rejected, and what happens when workers stay at the incumbent firm?

Q9. What do the back-and-forth dynamics imply for appropriate theoretical models of wage bargaining?

Q10. How do outside options predict worker bargaining behavior and outcomes, controlling for occupation-establishment fixed effects?

Q11. How does risk tolerance predict bargaining, and how does it compare to outside options?

Q12. What are the gender differences in bargaining behavior, and can they be explained by differences in outside options or risk tolerance?

Q13. What is the estimated gender wage gap attributable to individual bargaining?

Q14. How does a worker’s prior firm wage premium affect current wages, and does bargaining status matter?

Q15. How do AKM person effects relate to bargaining behavior?

Q16. Are the bargaining patterns found at surveyed firms representative of bargaining more broadly?

Key Concepts

Firm Responses and Wage Effects of Foreign Demand Shocks with Fixed Labor Costs and Monopsony

Layer 1 — Overview

In depth

Q1. What two motivating empirical facts about Belgian firms does the paper establish?

Q2. How does the instrument for foreign demand shocks capture indirect exposure through production networks?

Q3. What is the estimated magnitude of the labor supply elasticity facing Belgian firms, and what does it imply for wage markdowns?

Q4. What is the estimated labor cost elasticity with respect to demand-driven sales changes, and what does it imply about fixed labor costs?

Q5. What does the estimated elasticity of input purchases with respect to sales imply about fixed intermediate input costs?

Q6. How does the paper rule out alternative explanations for the less-than-proportional response of labor costs?

Q7. Why are firms’ domestic suppliers affected by foreign demand shocks, and how large are the pass-through effects?

Q8. What is the aggregate real wage effect of a 5 percent increase in foreign tariffs on Belgian exports in the baseline model?

Q9. How much does the modeling of fixed overhead costs versus imperfect labor market competition matter for the aggregate wage counterfactual?

Q10. What is the mechanism by which fixed overhead costs amplify the aggregate wage decline from a negative demand shock?

Q11. Is the conclusion about the relative importance of fixed costs versus labor market imperfections robust to alternative specifications of the labor market?

Q12. Are heterogeneous responses to the foreign demand shock observed across exporters, importers, and domestic-only firms?

Q13. Do the findings about fixed overhead costs extend beyond foreign demand shocks?

Key Concepts

Minimum Wages, Efficiency, and Welfare

Overview

In depth

Q1. What are the three regions of firm behavior in response to a binding minimum wage, and what are their efficiency implications?

Q2. How does the paper define and use “shadow wages” to characterize equilibrium?

Q3. What are the two aggregate efficiency wedges and how do they behave as the minimum wage rises?

Q4. What does the model validation exercise on the German minimum wage (DLSUB 2021) show?

Q5. What does the Amazon spillover replication (DNWT 2021) show, and what does it imply about the minimum wage spillover channel?

Q6. How does the paper separate efficiency from redistribution, and what is the key methodological innovation?

Q7. How are Negishi weights computed, and why are they important for interpreting the results?

Q8. What are the quantitative welfare gains from the efficiency-maximizing minimum wage, and how small are they relative to the potential gains from eliminating monopsony?

Q9. How do employment effects of minimum wages vary by market concentration, and why?

Q10. What does the robustness exercise for Mississippi reveal?

Q11. What happens to common empirical proxies for inequality and worker power as the minimum wage rises?

Q12. How does the short-run (fixed-capital) analysis differ from the long-run baseline?

Key Concepts

Monopsony Makes Firms Not Only Small but Also Unproductive: Why East Germany Has Not Converged

Layer 1 — Summary

In depth

Q1. What is the core mechanism by which monopsony power reduces aggregate productivity, and how does it differ from the standard “firms are too small” result?

Q2. What empirical patterns do the authors document to link the East-West productivity gap to missing large plants and steeper size-wage curves?

Q3. Why is the steeper size-wage curve specific to East Germany, and why does it persist decades after reunification?

Q4. How is the model structured, and what are the three decision stages for plants?

Q5. Through what two channels does the steeper size-wage trade-off reduce aggregate labor productivity in the model?

Q6. What quantitative predictions does the model make, and how does it perform in untargeted moments?

Q7. What alternative explanations for East Germany’s non-convergence does the paper rule out or place in context?

Q8. How does this paper relate to the Heise and Porzio (2021) finding that plant productivity differences, not worker quality differences, drive the East-West wage gap?

Key Concepts

Voluntary Minimum Wages: The Local Labor Market Effects of National Retailer Policies

Layer 1 — Overview

In depth

Q1. What exactly are “voluntary minimum wages” and how do they differ from statutory minimum wages?

Q2. How were VMW events identified and matched to anonymized firms in the payroll database?

Q3. How does the gap design work and why does it improve on the fraction-affected approach?

Q4. What is the magnitude of the wage effect on the large retailers themselves?

Q5. How did VMWs affect total employment and its components at the large retailers?

Q6. What do the labor supply elasticities implied by the VMW results look like?

Q7. Did VMWs increase total take-home pay or were wage gains offset by reductions in hours or bonuses?

Q8. What are the estimated spillover effects on wages at non-policy employers?

Q9. Could the null spillover result reflect mean reversion bias rather than a true zero?

Q10. Why are spillover effects so limited if the large retailer is drawing fewer workers away from competitors?

Q11. How do the results differ when focusing on CZs where the large retailer accounts for a larger employment share?