Labor Market Concentration

A. Data

We use proprietary data from CareerBuilder, which is the largest online job board in the United States. The site received approximately 11 million unique job-seeker visits in January 2011. Job-seekers can use the site for free, while firms seeking to hire workers must pay a fee of several hundred dollars to post a job opening for one month. According to CareerBuilder rules, a job posting corresponds to one vacancy, but in practice employers may sometimes hire more than one worker for a given job posting. In what follows, we refer to job postings and vacancies interchangeably. The total number of vacancies on CareerBuilder.com represents 35 percent of the total number of vacancies in the United States in January 2011 as counted in the Job Openings and Labor Turnover Survey. The data set used here was first used in Davis and Marinescu (2017). Occupations were selected based on counts of jobs posted between 2009 and 2012 on CareerBuilder: at the broad SOC level, that is, SOC-5 digits, the 13 most frequent occupations were selected. We also added the three most frequent occupations in manufacturing and construction (17-2110, 47-1010, 51-1010). The full list of SOC-6 occupations can be found in Table 1; the total number is 26 because each SOC-5 may correspond to a couple of SOC-6 occupations, such as Legal Secretaries (43-6012) and Medical Secretaries (43-6013).

Our data include, for each vacancy, the number of applicants. This allows us to calculate labor market tightness at the occupation by local labor market level as (number of vacancies)/(number of applications).

Only about 20 percent of the CareerBuilder vacancies post salary information. The posted wage is converted into an annual salary if it is hourly. The posted wage is defined as the middle of the range if the vacancy posts a range rather than a single value. We estimate posted wages for a given market and year–quarter as the simple average of the posted wage in the wage-posting vacancies. Figure 1 shows the distribution of log real wages across markets and year–quarters. The distribution is tri-modal. For comparison, the figure also plots the distribution of occupational wages for the same markets from the BLS Occupational Employment Statistics. The distribution of posted wages is overall similar to the distribution of occupational wages. Posted wages have more mass in the left tail of the distribution, consistent with starting wages being lower.

Figure 1

Log Real Wages across Markets in CareerBuilder and BLS

Notes: This figure shows a kernel density plot of the log real wage for labor markets for the period 2010Q1–2013Q4 on CareerBuilder.com. The real wage is defined as the average wage across wage-posting vacancies in a given market and year–quarter, divided by the consumer price index for that year–quarter. The BLS plot corresponds to the log average wages from the Occupational Employment Statistics.

B. Labor Market Definition

Given that monopsony power in labor markets has not been a focus of antitrust policy, the crucial question of how to define the relevant market for antitrust analysis is relatively unexplored in the literature. The twin imperatives contained in the Horizontal Merger Guidelines are that markets be defined in terms of “lines of commerce” and “section of the country.”

Marinescu and Rathelot (2018) show that applications to a job decline rapidly with distance, although most applications are still outside the applicant’s zip code. It is therefore key to define labor markets geographically to obtain meaningful measures of market concentration. For our baseline analysis, we use commuting zones (CZs) to define geographic labor markets. Commuting zones are geographic area definitions based on clusters of counties that were developed by the United States Department of Agriculture (USDA) using data from the 2000 Census on commuting patterns across counties to capture local economies and local labor markets in a way that is more economically meaningful than county boundaries. According to the USDA documentation, “commuting zones were developed without regard to a minimum population threshold and are intended to be a spatial measure of the local labor market.” Marinescu and Rathelot (2018) also show that 81 percent of applications on CareerBuilder.com are within the commuting zone, and Manning and Petrongolo (2017) similarly find that labor market searches are local in UK data. Bartik (2018) finds evidence against full worker mobility across commuting zones. We conduct robustness checks using single counties for our geographic market definition instead of commuting zones.

When it comes to defining the analog to “line of commerce” in labor markets, the economic literature shows that there are substantial frictions associated with transitioning between jobs (Artuc, Chaudhuri, and McLaren 2010; Dix-Caneiro 2014; Artuc and McLaren 2015; Traiberman 2019; Macaluso 2017). No work, to our knowledge, attempts to define labor markets in the education space. Macaluso (2017) defines the concept of “skill remoteness” on the supply and demand sides of a labor market and finds that workers whose skills are further away from the available jobs in their local labor market (defined by city and occupation) are more likely to either move or exit the labor force in response to a layoff. Hershbein and Kahn (2016) and Modestino, Shoag, and Ballance (2016) characterize the skill distribution of job vacancies as changing in response to the severity of local labor market recessions. But the extent to which workers confine their job searches to an education- or skills-delimited segment of available jobs has not yet been systematically explored (but some evidence on search across occupations is available in Marinescu and Rathelot 2018).

Using the vacancies data set from the same source as the one used in this paper, Marinescu and Wolthoff (2020) show that, within a six-digit SOC, the elasticity of applications to a given job posting with respect to posted wages is negative. Therefore, the six-digit SOC is likely too broad to be a labor market, since we would expect applications to increase in response to posted wages in a frictional labor market (see Section III.C below). Nonetheless, we consider SOC-6 occupation to be a conservative benchmark, with the understanding that concentration measured within labor markets defined that way is likely to be an underestimate.

We calculate labor market concentration using posted vacancies and applications to those vacancies. Concentration could also be computed using observed employment (albeit not with this data set). The concentration of employment is almost certainly lower than the concentration of vacancies—only a subset of the firms in a given labor market (defined by geography and occupation) will be hiring at any given time. But our measure of concentration based on vacancies is more relevant for active job-seekers, especially in light of evidence of lengthening job tenures, which implies that a given position will remain filled for longer (Hyatt and Spletzer 2016). Moreover, our results about the effect of concentration on wages are estimated from variation in concentration over time within a labor market, and in our robustness checks we aggregate vacancy postings over time, which reduces observed concentration levels, toward what we would probably observe if concentration were computed from firm-level employment.

We perform our analysis at the quarterly level in the baseline specification, since the median duration of unemployment was about ten weeks in 2016 (BLS 2017). For our market share calculations we consider all vacancies or applications that occur within a given quarter, including vacancies with missing wages.

C. Measuring Concentration

We keep an unbalanced panel of 61,017 CZ–occupation–year–quarter observations, covering the period 2010Q1–2013Q4, 681 commuting zones, and 26 SOC six-digit occupations. These markets all include at least one vacancy with a posted wage.

Our baseline measure of market power in a labor market is the Herfindahl–Hirschman index (HHI), calculated based on the share of vacancies of all the firms that post vacancies in that market. By confining this investigation to only the largest online job board, CareerBuilder, we add another dimension to market definition, that of the search platform. If firms post all of their jobs on CareerBuilder, we accurately measure concentration, even if firms also post their jobs on other platforms. If workers who search on CareerBuilder only use that platform, we are accurately measuring concentration for those workers. To the extent that workers search for jobs across multiple platforms and firms do not post all of their jobs on CareerBuilder, our data might yield an excessive concentration estimate.

The HHI is widely used as a measure of market concentration in the industrial organization literature and in antitrust practice. An advantage of this measure of market concentration is that there are guidelines for what represents a high level of market concentration. According to the DOJ–FTC guidelines: an HHI above 1,500 is “moderately concentrated,” and above 2,500 is “highly concentrated.” An HHI of 2,500 occurs when four employers have equal shares of the vacancies in a labor market. A merger that increases the HHI by more than 200 points, leading to a highly concentrated market, is “presumed likely to increase market power.”

While these measures and thresholds are generally used to evaluate market concentration in product markets, the antitrust agency guidelines state that “[t]o evaluate whether a merger is likely to enhance market power on the buying side of the market, the Agencies employ essentially the framework described above for evaluating whether a merger is likely to enhance market power on the selling side of the market.” This implies that adverse effects of mergers on the inputs market, including the labor market, are part of the legal framework for evaluating mergers.

These DOJ–FTC HHI thresholds give some guideposts to evaluate the level of concentration, but they have no precise economic meaning beyond that given to them by the historical practice of antitrust enforcement in product markets. Labor markets are different from product markets in a number of ways, and different thresholds for the labor market might make sense. For example, labor markets are two-sided: both employers and workers must agree to the employment contract, while in the product market consumers can buy without an explicit agreement by sellers. This feature of labor markets arguably makes them thinner, so reasonable HHI thresholds for the labor market might be lower than for the product market.

The formula for the HHI in market m and year–quarter t is 1where s_j,m is the market share of firm j in market m. For the HHI based on vacancies, the market share of a firm in a given market and year–quarter is defined as the sum of vacancies posted in CareerBuilder by a given firm in a given market and year–quarter divided by total vacancies posted in the website in that market and year–quarter. We treat all vacancies posted by a recruiting or staffing firm as belonging to the same firm, since we cannot observe for which firm the recruiting or staffing firm is hiring.

In addition to calculating HHIs for each labor market based on shares of vacancies, we also calculated HHIs based on shares of applications (more specifically expressions of interest, that is, clicking on the button “Apply now”). For the HHI based on applications, we define the market share of a firm in a given market and year–quarter as the sum of applications to a given firm in a given market and year–quarter divided by the total number of applications to all firms in that market and year–quarter.

Table 2 shows summary statistics of the main variables used in our analysis. The average real wage was 41,547 USD (in 2009 dollars). The average market in our sample had 20 firms, 83 vacancies, 441,156 searches, and 3,613 applications. The average HHI based on vacancies was 3,157. The average HHI based on applications was somewhat higher at 3,480, reflecting the fact that not all vacancies received the same level of interest from job-seekers.

Table 2 also shows that the average HHI calculated using shorter time periods than the quarter is higher, and the HHI using longer time periods is lower but still highly concentrated. The population-weighted quarterly HHI is lower and moderately concentrated. The population-weighted HHI is lower than the unweighted HHI because large cities tend to be less concentrated (Figure 2). The population-weighted HHI is relevant to understand the experience of the average worker, while the unweighted HHI represents the average labor market. That many labor markets are highly concentrated is policyrelevant because a merger review by antitrust authorities asks whether anticompetitive effects are likely in any one market (Marinescu and Hovenkamp 2019).

Figure 2

Average HHI by Commuting Zone, Based on Vacancy Shares

Notes: This figure shows the average of the Herfindahl–Hirschman index by six-digit SOC occupation code for labor markets for the period 2010Q1–2013Q4. The categories we use for HHI concentration levels are: “Low”: HHI 0–1,500; “Moderate”: HHI 1,500–2,500; “High”: HHI 2,500–5,000; “Very High”: HHI 5,000–10,000. These categories correspond to the DOJ–FTC guidelines, except that we add the additional distinction between high and very high concentration levels around the 5,000 HHI threshold. Market shares are defined as the sum of vacancies posted in CareerBuilder.com by a given firm in a given market and year–quarter divided by total vacancies posted in the website in that market and year–quarter.

As would be expected, county-level HHIs are higher than CZ-level HHIs, and statelevel HHIs are lower than CZ-level HHIs. With the exception of a state-level definition of the labor market, all alternative definitions still show moderate to high concentration.

Figure 2 shows a map of all the commuting zones in the United States color-coded by the average HHI, based on vacancy shares. Commuting zones around large cities tend to have lower levels of labor market concentration than smaller cities or rural areas. This suggests a new explanation for the city wage premium (Yankow 2006; Baum-Snow and Pavan 2012): cities, and especially large cities, tend to have less concentrated labor markets than rural areas.³ Consistent with this interpretation, Hirsch et al. (2022) find that the urban wage premium in Germany is partly explained a higher labor supply elasticity in more densely populated cities.

Figure 3 shows the distribution of the HHIs based on vacancies and of the HHI based on applications in our sample. Under both definitions for market shares, the median market is moderately concentrated, while the average market is highly concentrated.

Figure 3

Histogram ofHHIs Based on Application Shares and Vacancy Shares

Notes: This figure shows a histogram of the Herfindahl–Hirschman index for labor markets for the period 2010Q1–2013Q4. Market shares are defined as either the sum of vacancies posted in CareerBuilder.com by a given firm in a given market and year–quarter divided by total vacancies posted in the website in that market and year–quarter, or as the sum of applications (EOI) through the website to a given firm in a given market and year–quarter divided by the total number of applications to all firms in that market and year–quarter.

Figure 4 shows the average HHI, based on vacancy shares, by six-digit SOC occupation. The occupations that are least concentrated on average are “Customer service representatives,” “Sales representatives, wholesale and manufacturing, technical and scientific products,” and “Registered nurses,” each with an average HHI of around 2,000. The occupations that are most concentrated on average are “Farm equipment mechanics,” “Rail car repairers,” and “Light truck or delivery services drivers,” each with an average HHI well above 5,000 (which is the level of concentration of a symmetric duopsony market).

Figure 4

Average HHI by Occupation, Based Vacancy Shares

Notes: This figure shows the average of the Herfindahl–Hirschman index by six-digit SOC occupation code for labor markets for the period 2010Q1–2013Q4. Market shares are defined as the sum of vacancies posted in CareerBuilder.com by a given firm in a given market and year–quarter divided by total vacancies posted in the website in that market and year–quarter.

In summary, we find that reasonably defined local labor markets are highly concentrated on average. Manning (2011) notes that monopsony power is due to two types of mechanisms: labor market frictions and idiosyncrasies, and collusion and institutions, with almost no evidence on the latter mechanism. High labor market concentration can facilitate collusion, so our findings start to fill in the gap on these types of mechanisms behind labor market power. A limitation of our analysis is that we only use vacancies posted on the CareerBuilder website.⁴ Given that CareerBuilder is the largest jobposting website in the United States, the high level of concentration was somewhat surprising to us.

A. Empirical Specification: OLS and IV

Our baseline specification is as follows: 2where log(w_m,t) is the log real wage in market m in year–quarter t, log HHI_m,t is the corresponding log HHI, X_m,t is a set of controls, α_t and δ_m are year–quarter and market (commuting zone–occupation) fixed effects, and ε_m,t is an error term.

We run a first specification with just year–quarter fixed effects (Table 3). We then add successively market (CZ by SOC-6) fixed effects and log tightness (defined as the number of vacancies divided by the number of applications in a labor market) in the commuting zone and occupation for a given year–quarter. We then run a fourth specification further controlling for year–quarter by commuting zone, and finally we also add year–quarter-by-SOC fixed effects in a fifth specification, to control for any possible changes in the characteristics of the commuting zone or the occupation over time. In a robustness test, we also control for the number of vacancies in the market, which can be interpreted as a measure of labor demand independent of the level of concentration. We cluster standard errors at the commuting zone-occupation level.

The key threat to identification is that there is a time-varying market-specific variable that is correlated with HHI and drives wages. The key confound according to the oligopsony theory discussed above is labor productivity. What other confounds are most likely? According to search and matching theory, posted wages are determined by labor market tightness, productivity, and the worker’s out-of-work benefit (Rogerson, Shimer, and Wright 2005). We already control for labor market tightness. Since unemployment benefits are determined at the state level, we are able to control for workers’ out-of-work benefits by controlling for market fixed effects, and, in some specifications, market-by-time fixed effects. Therefore, the main threat to identification remains timevarying, market-specific productivity changes.

To further address the issue of the endogeneity of HHI, we instrument the HHI with the average of log(1/N) in other commuting zones for the same occupation and time period (where N refers to the number of firms in the market). That is, for each commuting zone–occupation–time period combination, we calculate the average of log(1/N) for the same occupation for every other commuting zone. We use log(1/N) instead of HHI as the instrument because it is less likely to be endogenous, as it does not depend on market shares. This instrument provides us with variation in market concentration that is driven by national-level changes in the occupation, not by changes in the occupation in that particular local market. In particular, the instrument should be independent of the occupational productivity in the local labor market, which is likely to be the main confounding factor in the baseline OLS regressions. For example, if the productivity of customer service representatives falls in the Chicago area, this could both decrease wages and increase concentration, since fewer firms would likely be recruiting. By instrumenting with the number of firms posting vacancies for customer service representatives in other areas, we rule out a direct effect of productivity in Chicago on the HHI.

This type of instrumental variables strategy is commonly used in industrial organization to address the endogeneity of prices in a local product market. For example, Nevo (2001) uses prices in other geographic markets to instrument for city-level prices of various products in the ready-to-eat cereal industry.

The main threat to identification for the instrumental variable strategy is that productivity shocks could be correlated across areas. For example, a national level decline in the productivity of customer service representatives would likely increase concentration and decrease wages in most labor markets. Therefore, the instrument protects us against a spurious correlation between concentration and outcomes that is due to local changes in productivity, but not against national-level changes in productivity (for an occupation relative to other occupations) that influence both concentration and other labor market outcomes.

The instrument may not be not fully exogenous in the sense that it may have a direct effect on wages that does not go through local concentration. However, it is plausibly more exogenous that the local market HHI, in particular because it is less likely to be correlated with uncontrolled-for variations in local productivity. We exploit this idea by deriving bounds for the causal effect of HHI on wages using the method developed by Conley, Hansen, and Rossi (2010). Suppose that the instrument is not fully exogenous in the sense that it has a direct effect on posted wages, with a coefficient of γ≠0. If we assume a range of values for γ between zero (perfectly exogenous) and the reduced form effect, we can derive an interval for the causal effect of the HHI on wages that takes into account deviations from exogeneity (γ≠0). This procedure allows us to determine how big the direct effect of the instrument on wages could be for the interval of the causal effect of HHI on wages to exclude zero.

B. Regression Results

We find that higher labor market concentration is associated with significantly lower real wages. Table 4 Panel A shows the results from the baseline wage regressions. In the first regression, using vacancy-share HHIs and only year–quarter fixed effects, we find that a one log point increase in the HHI is associated with a decline in wages of about 0.103 log points. Further controlling for market fixed effects (CZ by six-digit SOC) reduces the coefficient to -0.0347, showing that some of the negative relationship between posted wages and HHI is driven by cross-sectional variation in posted wages. Specification 3 shows that controlling for log tightness does not substantially change the result from Specification 2. We consider Specification 3 to be the baseline for OLS results. Figure 7 shows a binned scatterplot corresponding to Specification 3; the relationship between the residualized wages and the residualized HHI is negative and linear, similar to the raw relationship between wages and HHI (Figure 5).

Figure 7

Binned Scatter of Residualized Log HHI Based on Vacancies and Residualized Log Real Wage

Notes: This figure shows a binned scatter plot of the residuals of a regression of log HHI (based on vacancy shares) on log tightness, CZ-by-SOC fixed effects, and CZ-by-year–quarter fixed effects and the residuals of a regression of log real wage in the same market, also on log tightness, CZ-by-SOC fixed effects, and CZ-by-year–quarter fixed effects.

Specifications 4 and 5 allow for commuting zone and occupation effects to change over time. Adding year–quarter-by-CZ fixed effects does not affect the impact of HHI on wages (compare Columns 3 and 4 in Table 4), showing that the effects are not driven by time-varying effects at the CZ level. When we further add year–quarter-by-six-digit SOC fixed effects (Column 5), the impact of HHI on wages remains negative and of a similar size. This shows that the negative impact of HHI on wages is not explained away by changes in occupational wages over time, due to, for example, technological change.

Specifications 6–8 show analogous results but based on the IV estimation strategy (see Table 3 for the first stage). The estimated effect is still negative but much larger in absolute value. The IV estimate may be higher because it corrects the endogeneity bias from market-level labor supply and demand effects, and possibly also corrects for measurement error. A one log point increase in the HHI is associated with a decline in wages of about 0.14 log points. This implies that an increase in HHI of 200 in a market with an HHI of 2000 (moderately concentrated), which is an increase of ten log points, is associated with a decline in wages of about 1.4 percent. Going from the 25th percentile of market concentration to the 75th percentile of market concentration is associated with a decline in wages of 5 percent according to Specification 3 and of 17 percent according to Specification 7, our baseline specification for the IV.⁵

The main threat to identification for the instrumental variable strategy is that productivity shocks to occupations could be correlated across areas. We cannot control for occupation-by-time fixed effects in the IV specifications due to the fact that the instrument is essentially defined at that level. Nevertheless, it is reassuring to see that controlling for occupation-by-time effects does not substantively change the OLS results (Column 4).

We recognize that the instrument may not be not fully exogenous, and we provide bounds on the second-stage effect of HHI on wages, assuming a degree of endogeneity in the instrument. Using market-level data, we regress wages on the instrument and controls (Table 5), which gives us the reduced form effect of the instrument. We then calculate the bounds for the second-stage effect of HHI on wages, assuming that the direct effect of the instrument on wages (γ) ranges from zero (perfectly exogenous) to the reduced form effect. We use Stata’s plausexog and start with a simple specification in Column 1, and control for tightness in Column 2. When controlling for tightness, the second-stage effect of HHI on wages ranges between -0.177 and 0.036 (Table 5, Column 2, β bounds). The bounds for the second-stage estimate exclude zero as long as the direct effect of the instrument is smaller than -0.112 (γ_max in Table 5 , Column 2), or 75 percent of the reduced form effect. Specification 3 adds year–quarter-by-CZ fixed effects, and the results are very similar to Specification 2. We conclude that the negative impact of concentration on wages is robust to a large degree of instrument endogeneity. The instrument would have to be very endogenous for the impact of concentration on wages to plausibly take positive values.

C. Controlling for Job Titles

Marinescu and Wolthoff (2020) showed that job titles are an important predictor of wages and are informative about the type of job and required skills beyond a pure wage-signaling effect. We are thus interested in studying to what extent market concentration affects wages through job titles and to what extent it has a direct effect beyond the effect that can be explained by job titles. For this purpose, we conducted regressions at the individual vacancy level, controlling for job title fixed effects (based on strings capturing the first three words in the vacancy’s job title).

The results are shown in Table 4, Panel B. The first three specifications show results using the same controls as in the market-level baseline regressions, and we find similar results. The fourth specification controls for commuting zone-by-job title fixed effects. The effect has a negative sign and is statistically significant, but the magnitude is about one-half of the effect without job title fixed effects. This mitigation of the effect is present in both the OLS and the IV specifications.

This indicates that the effect of an increase in market concentration on wages is expressed both directly through lower wages conditional on a job title, as well as by increasing the likelihood of posting lower-wage job titles.

A. Interaction with City Size

We tested whether the negative effect of market concentration on wages is driven by small or large cities, or whether it holds across the whole range of city sizes in our sample. For this purpose, we ran a specification interacting the vacancy HHI in a market with a fifth-order polynomial in the percentile of the population of that market’s commuting zone, which we instrument using a fifth-order polynomial in the mean of log(1/N) for the same occupation in other CZs.

The estimated effect of market concentration as a function of commuting zone population percentile is shown in Figure 8, together with 95 percent confidence bands. The effect is negative and significant over the range of population going from the 10th to the 90th percentile, and it is higher (in absolute value) for smaller markets than larger markets.

Figure 8

Effect of Log HHI (Vacancies) on Log Real Wage by Commuting Zone Population Percentile

Notes: Estimated effect from a panel IV regression of log real wage on a fifth-order polynomial in log HHI (in terms of vacancies), instrumented with a fifth-order polynomial in average log 1/N in other commuting zones for the same occupation, controlling for log tightness, CZ-by-six-digit SOC fixed effects and time fixed effects. Data are for the period 2010Q1–2013Q4. We cluster standard errors at the market level.

Therefore, less populated commuting zones are not only more concentrated on average, but an increase in concentration has a more negative effect on wages.

B. Controlling for the Number of Vacancies

A key threat to identification is that wages are affected by local demand. We can use the number of posted vacancies as a proxy for local demand. The negative effect of HHI on posted wages remains of the same magnitude in both OLS and IV when controlling for the log of the number of vacancies posted (Table 6, Columns 1 and 2).

C. Excluding Monopsony (HHI=1) Markets

The histogram in Figure 3 shows that many markets in the sample only have one firm hiring. We checked that our estimates are not sensitive to excluding these markets by running additional regressions that do exactly that. The results from the panel IV specification are reported in Table 6, Specifications 3 and 4, which show that the magnitude and significance of the estimated effect is similar to the analogous specification in the baseline in both OLS and IV.

D. Alternative Market Definitions

We chose SOC-6 as the definition of a market in terms of occupation. Broadening the definition of the labor market to SOC-2 by CZ instead of SOC-6 by CZ makes the effect of HHI on wages larger in both OLS and IV (Table 6, Columns 5 and 6). On the other hand, narrowing the definition of the labor market to a job title by commuting zone makes the estimated effect of HHI on posted wages smaller (Table 6, Columns 7), and the effect becomes insignificant in IV (Table 6, Columns 8). One possible explanation for this pattern of results is measurement error: a broader market definition entails more vacancies that the HHI can be calculated from, thereby reducing measurement error.

In terms of geography, we chose to use commuting zones as a market definition because they were designed to capture meaningful geographic labor markets based on commuting patterns across counties. However, the correct geographic definition for labor market competition for hiring is still an open question. We decided to test the sensitivity of our results by using an alternative definition based on counties and running panel IV specifications analogous to our baseline.

The results are shown in Table 7, Specification 3. The estimated coefficient is similar to those in the baseline, indicating that our results are robust to other plausible geographic labor market definitions.

E. Alternative Concentration Measures

As a robustness check, we estimated panel IV regressions similar to our baseline specification from Table 4, Column 6, but using log 1/N as the measure of market concentration. The results are similar to the baseline, as shown in Table 7, Specification 1.

We also estimated regressions using log HHI based on share of applications as the measure of concentration, again with similar results; see Table 7, Specification 2. This shows that our results are robust to using a range of standard measures of market concentration and therefore not driven by a particular choice of measure.

F. Cross-Sectional Specification

Our baseline specification identifies the effect of market concentration on wages purely from variation within a market over time. One may also be interested in identification from cross-sectional variation. We implemented a specification based on the entire 2010–2013 period. We included CZ fixed effects and six-digit SOC fixed effects, so that our estimates are not driven by variation in average wages across cities or in average wages across occupations. Similar to the baseline, we instrument the log HHI using the log 1/N, except that we use the number of firms for the entire period. The impact of concentration on posted wages is still negative and significant in this cross-sectional data (Table 7, Specification 4). Furthermore, we find that the impact of concentration on prevailing wages measured from the BLS occupational employment statistics is also negative and significant (Specification 5). Figure 9 plots the negative relationship between residualized HHI and wages in these IV regressions (Panels C and D). For comparison, in Panels A and B, the figure also shows the relationship between residualized HHI and wages in OLS, which is less steep than in IV.

Figure 9

Binned Scatter of Residualized Log HHI Based on Vacancies and Residualized Log Real Wage, Cross-Sectional Variation

Notes: Panels A and B show binned scatter plots of the residuals of a regression of log HHI (based on vacancy shares) on log tightness, CZ fixed effects and SOC fixed effects, and the residuals of a regression of log real wage in the same market, also on log tightness, CZ fixed effects, and SOC fixed effects. The wages in Panel A are from CareerBuilder and in Panel B from the BLS Occupational Employment Statistics. Panels C and D show binned scatter plots of the residuals of a regression of the predicted first-stage log HHI (based on vacancy shares) on log tightness, CZ fixed effects, and SOC fixed effects, and the residuals of a regression of log real wage in the same market, also on log tightness, CZ fixed effects, and SOC fixed effects. The predicted first-stage log HHI refers to the predicted values from a first-stage IV regression of log HHI on the average log(1/N) for the same occupation in other markets, controlling for log tightness, CZ fixed effects, and SOC fixed effects. The wages in Panel C are from CareerBuilder and in Panel D from the BLS Occupational Employment Statistics.

The estimated impact of HHI on occupational wages is smaller than on posted wages, presumably because the market concentration among vacancies has a more direct effect on posted wages than on the wages of incumbent workers. Indeed, the wages of stayers, which are included in the BLS occupational wage, are less sensitive to economic conditions than the wages of new hires (Carneiro, Guimarães, and Portugal 2012; Haefke, Sonntag, and van Rens 2013). Overall, these results alleviate the concern that our results are driven by the less than fully representative nature of our data.

G. Controlling for Fraction of Vacancies Posting Wages

An important limitation of the data set is that only a fraction of the vacancies on CareerBuilder post wages. At the market level, it may be that wage posting is correlated with an omitted variable that determines both wages and concentration. This could bias the estimated coefficient on concentration in the wage regression. To assess the potential for such a bias, we run a panel IV specification controlling for the fraction of vacancies in each market that post wages. Table 7, Specification 6 shows the results. We find that this variable has a positive effect on wages, but does not meaningfully affect the coefficient on log HHI.

H. Controlling for Tightness Based on Searches Instead of Applications

Another concern is that the tightness measure could be endogenous with respect to wages—high-wage vacancies get more applications, so this lowers the tightness measure. As an alternative measure of tightness, we use the log of the ratio of total vacancies in the market to total searches in the market. Searches should not be affected by posted wages because workers do not search by wage but typically by job title and location, so this can address the endogeneity concern. Table 7, Specification 7 shows the results from the corresponding panel IV specification, which are similar to those in the baseline specification.

I. Remaining Limitations

Our analysis accounts for a number of biases in the estimation of the relationship between labor market concentration and posted wages. However, a number of limitations remain.

Only 20 percent of vacancies post wages, and we are therefore not measuring all wages in a given occupation by commuting zone market. However, Marinescu and Wolthoff (2020) show that the distribution of posted wages on CareerBuilder is very similar to the distribution of wages for employed workers in the Current Population Survey. Therefore, posted wages are typical of wages overall in the labor market.

Our data come from a single website, CareerBuilder.com. While this is the largest U.S. job-search website, and it contains about one-third of U.S. vacancies, it does not contain all vacancies in the occupations that are in our sample. This could lead us to overestimate labor market concentration for the selected occupations. At the same time, smaller occupations that were not included in our sample will typically be even more concentrated, which results in a higher average concentration when a broader sample of occupations is used (Azar et al. 2020). Furthermore, the fact that we only capture some of the vacancies should not affect our estimate of the relationship between posted wages and labor market concentration.

Our data contain the most frequent occupations by number of vacancies on CareerBuilder.com and a number of manufacturing occupations. Therefore, our results, while fairly general, do not necessarily apply to the whole U.S. labor market. It is noteworthy that Benmelech, Bergman, and Kim (2022) and Rinz (2022) find a negative and significant relationship between wages and employment concentration at the county and industry level. Therefore, studying employment rather than vacancies and changing the labor market definition does not affect the basic fact that wages are negatively associated with labor market concentration.