Difference between revisions of "Firm Market Power and the Earnings Distribution"

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{{DES | des = [[Market Power|Market power]], a form of market failure, produces a  positive relationship between a firm's labor supply elasticity and the earnings of its workers.  This paper provides empirical evidence measuring market power and showing that employers with more power pay lower wages. | show=}}

{{Quotations|The Impact of Firm Market Power on the Earnings Distribution|quotes=true}}

The Impact of Firm Market Power on the Earnings Distribution

Douglas A. Webber ∗† 8-13-11

Using the Longitudinal Employer Household Dynamics (LEHD) data from the United States Census Bureau, I compute 􏰃rm-level measures of labor market (monop- sony) power. To generate these measures, I extend the semistructural model proposed by Manning (2003) and estimate the labor supply elasticity facing each private non-farm 􏰃rm in the US. While a link between monopsony power and earnings has traditionally been assumed, I provide the 􏰃rst direct evidence of the positive relationship between a 􏰃rm's labor supply elasticity and the earnings of its workers. I also contrast the semistructural method with the more traditional use of concentration ratios to measure a 􏰃rm's labor market power. In addition, I provide several alternative measures of labor market power which account for potential threats to identi􏰃cation such as endogenous mobility. Finally, I construct a counterfactual earnings distribution which allows the e􏰂ects of 􏰃rm market power to vary across the earnings distribution.

My 􏰃ndings suggest that there is signi􏰃cant variability in the distribution of 􏰃rm market power across US 􏰃rms, and that the semistructural method is superior to the use of concentration ratios in evaluating a 􏰃rm's labor market power. I 􏰃nd that a one-unit increase in the labor supply elasticity to the 􏰃rm is associated with wage gains of 3-5 percent. Furthermore, I 􏰃nd that the negative earnings impact is strongest in the lower half of the earnings distribution, and is a determinant of earnings inequality.

†I have greatly bene􏰃ted from the advice of John Abowd, Francine Blau, Ron Ehrenberg, Kevin Hallock, George Jakubson, and Alan Manning. I would also like to sincerely thank Henry Hyatt, J. Catherine Maclean, Matt Masten, Erika Mcentarfer, Ben Ost, and Michael Strain for their many helpful comments. All errors are mine.

There is good reason to believe that some 􏰃rms have non-trivial power in the labor market, that not all 􏰃rms act as price takers and pay their employees the prevailing market wage. Intuitively, most would not switch jobs following a wage cut of one cent, and we would not expect a 􏰃rm which raises wages by a small amount to suddenly have an in􏰃nite stream of workers. Empirically, a number of results point toward 􏰃rms having some degree of power in setting the wage.

While the industrial organization literature has theoretically and empirically modeled similar frictions in the product market, there has been comparatively less work done to ac- count for distortions of the labor market. This is primarily due to the comparative lack of rich labor market data (such as linked employer-employee data) versus product market data. Most of the theoretical work done on this topic resides in the search theory literature, with major contributions coming from Burdett and Mortensen (1998) and Shimer (2005) to

name a few1. This line of research has given rise to a "new monopsony" literature, popular- ized by Alan Manning's (Manning, 2003) careful analysis of labor-related topics absent the assumption of perfect competition. The new monopsony model of the labor market views a 􏰃rm's market power as derived from search frictions rather than solely geographic power as in a classic monopsony model. These search frictions originate from imperfections in the labor market such as imperfect information about available jobs, worker immobility, or heterogeneous preferences.

More recently, studies have attempted to directly estimate the average slope of the labor supply curve faced by the 􏰃rm, which is a distinct concept from the market labor supply elasticity2. Studying the market for nurses, Sullivan (1989) 􏰃nds evidence of monopsony using a structural approach to measure the di􏰂erence between nurses' marginal product of labor and their wages. Examining another market commonly thought to be monopsonistic, the market for schoolteachers, Ransom and Sims (2010) instrument wages with collectively bargained pay scales and estimate a labor supply elasticity between 3 and 4. In a novel

approach using German administrative data, Schmieder (2010) 􏰃nds evidence of a positive sloping labor supply curve through an analysis of new establishments.

Using a semistructural approach similar to this study, Ransom and Oaxaca (2010) and Hirsch et al. (2010) both separately estimate the labor supply elasticities to the 􏰃rm of men and women, each 􏰃nding strong evidence of monopsonistic competition. Ransom and Oaxaca (2010) use data from a chain of grocery stores, and 􏰃nd labor supply elasticities of about 2.5 for men and 1.6 for women. Hirsch et al. (2010) uses administrative data from Germany to estimate elasticities ranging from 2.5-3.6 and 1.9-2.5 for men and women respectively. Applying this approach to survey data, Manning (2003) 􏰃nds labor supply elasticities ranging from 0.68 in the NLSY to 1.38 in the PSID.

Utilizing data from the US Census Bureau's Longitudinal Employer Household Dynamics (LEHD) program, I estimate the market-level average labor supply elasticity faced by 􏰃rms in the US economy, similar to the Hirsch et al. (2010) study using German data. I then extend the approach to estimate 􏰃rm-level labor supply elasticities. This is accomplished through a semistructural estimation of the labor supply curve to the 􏰃rm following the search model proposed by Burdett and Mortensen (1998) and similar to the empirical strategy proposed by Manning (2003). This method allows me to examine the e􏰂ects of monopsonistic competition on the earnings distribution in great detail, and contributes to the existing literature in a number of ways. First, it is the 􏰃rst examination of monopsony power using comprehensive administrative data from the US. Second, my particular empirical strategy allows me to examine the distribution of monopsony power which exists in the US, and to provide direct evidence on the negative impact of a 􏰃rm's market power on earnings. I compare the performance of the market power measures derived in this study to that of the more traditional concentration ratio to illustrate the signi􏰃cant contribution of the new monopsony models. Finally, I construct a counterfactual earnings distribution in which 􏰃rms' market power is reduced in order to demonstrate the impact of imperfect competition on the shape of the earnings distribution.

I estimate the average labor supply elasticity to the 􏰃rm to be approximately 0.92. Esti- mates in this range are robust to various modeling assumptions and corrections for endoge- nous mobility. Furthermore, I 􏰃nd evidence of substantial heterogeneity in the market power possessed by 􏰃rms, ranging from negligible to highly monopsonistic. While a link between monopsony power and wages has traditionally been assumed (Pigou, 1924), I provide the 􏰃rst direct evidence of a positive relationship between a 􏰃rm's labor supply elasticity and the earnings of its workers, estimating that a one-unit increase is associated with a decrease of .05 in log earnings. I demonstrate that the e􏰂ect of monopsony power is not constant across workers: unconditional quantile regressions imply that impacts are largest among low paid and negligible among high paid workers. Finally, implications in the inequality literature are addressed through the construction of a counterfactual earnings distribution, which implies that a doubling of each 􏰃rm's labor supply elasticity would decrease the variance in earnings by 5 percent.

The concept of 􏰅monopsony􏰆 was 􏰃rst de􏰃ned and explored as a model by Robinson (1969). In her seminal work, Robinson formulated the analysis which is still taught in undergraduate labor economics courses. Monopsony literally means 􏰅one buyer􏰆, and although the term is most often used in a labor market context, it can also refer to a 􏰃rm which is the only buyer of an input.

􏰃nite labor supply elasticity, or upward sloping labor supply curve to the 􏰃rm. While the classic monopsony model is based on the idea of a single 􏰃rm as the only outlet for which workers can supply labor, the new framework de􏰃nes monopsony as any departure from the assumptions of perfect competition. Additionally, the degree of monopsonistic competition may vary signi􏰃cantly across labor markets, and even across 􏰃rms within a given labor market. Although it is tempting to include oligopsony in the new monopsony de􏰃nition, they are distinct concepts. Oligopsony implies collusion among the 􏰃rms, whereas the new monopsony framework emphasizes an equilibrium as the result of search frictions rather than collusion.

One of the most prominent reasons is that the typical worker does not have a continuous stream of job o􏰂ers (this point will be discussed further in the theoretical model section). This source of monopsony power has roots in the classic monopsony framework in that, all else held constant, workers in labor markets with more 􏰃rms are likely to have a greater number of o􏰂ers. However, this idea takes an overly simplistic view of the boundaries of a given labor market. Most employers are likely operating in many labor markets at any given time. A prestigious university may be competing in a national or international labor market for professors, a regional labor market for its high-level administrators and technical sta􏰂, and a local labor market for the low-level service workers. Even if the arrival rate of job o􏰂ers were the only source of monopsony power, it seems that geographic modeling alone would do a poor job of measuring that power. Another source of monopsony power is imperfect information about job openings (McCall, 1970; Stigler, 1962), which is not completely distinct from the arrival rate of job o􏰂ers since a decrease in information can

cause a reduction in job o􏰂ers. This is a particularly compelling example since studies such as Ho􏰉er and Murphy (1992) and Polachek and Robst (1998) estimate that imperfect information about job prospects depresses wages by approximately ten percent.

Firm speci􏰃c human capital also can be thought of as giving market power to the 􏰃rm, since there is in e􏰂ect a barrier to leaving a 􏰃rm when an individual's 􏰃rm speci􏰃c capital is large relative to their general human capital.

Possibly the biggest cost to changing jobs, however, is the cost to a worker's reputation. Potential employers would be very suspicious of hiring a worker who changes jobs the moment he is o􏰂ered any wage increase. For all of these reasons, and likely many more, workers must be selective with the wage o􏰂ers they choose to accept, thus leading to a labor market with substantial frictions.

Finally, while a worker's earnings represent an important market outcome, it is important to remember that wages make up only a part of the total 􏰅compensation􏰆 to the worker. The true quality of a job match has many dimensions, such as bene􏰃ts, working conditions, and countless other variables. The interaction of monopsony with these non-wage goods should be explored in future research.

of competing employers. Even assuming equal ability for all workers, wage dispersion is an equilibrium outcome as long as one assumes that the arrival rate of job o􏰂ers is positive but 􏰃nite (perfect competition characterizes the limiting case, as the arrival rate tends to in􏰃nity). The model for this study will primarily be derived from the Burdett and Mortensen model, with important contributions from Manning (2003). See Kuhn (2004) for a critique of the use of equilibrium search models in a monopsony context.

Assume there are Mt equally productive workers (where productivity is given by p), each gaining utility b from leisure. Further assume there are Me constant returns to scale 􏰃rms which are in􏰃nitesimally small when compared to the entire economy. A 􏰃rm sets wage w to maximize steady-state pro􏰃ts π = (p-w)N(w,F) where N(w,F) represents the supply of labor to the 􏰃rm and F represents the distribution of wage o􏰂ers observed in the economy. All workers within a 􏰃rm must be paid the same wage. Employed workers will accept a wage o􏰂er w' if it is greater than their current wage w, and non-employed workers will accept w' if w'􏰋b where b is their reservation wage. Wage o􏰂ers are drawn randomly from the distribution F(w), and arrive to all workers at rate λ. Assume an exogenous job destruction rate δ, and that all workers leave the job market at rate δ to be replaced in nonemployment by an equivalent number of workers.

Burdett and Mortensen (1998), or alternatively Manning (2003), show that in this econ- omy, as long as λ is positive and 􏰃nite, there will be a nondegenerate distribution of wages even when all workers are equally productive. As λ tends to zero, the wage distribution will collapse to the monopsony wage, which in this particular economy would be the reservation wage b. As λ tends to in􏰃nity the wage distribution will collapse to the perfectly competitive wage, the marginal product of labor p.

where R(w,F) is the 􏰉ow of recruits to a 􏰃rm and s(w,F) is the separation rate. Nt+1(w, F ) = Nt(w, F )[1 − st(w, F )] + Rt(w, F ) (1)

This simply formalizes the de􏰃nitionally true statement that a 􏰃rm's employment next period is equal to the fraction of workers this period who stay with the 􏰃rm plus the number of new recruits. In steady state, we must have N(w,F)=R(w,F)/S(w,F). This steady-state assumption means that the quantities estimated in this paper represent the long-run labor supply elasticity to the 􏰃rm. Taking the natural log of each side and di􏰂erentiating we can write the elasticity of labor supply ε as a function of the elasticities of recruitment and separations.

ε = εR − εS (2) We can further decompose the recruitment and separation elasticities in the following

way

ε=θRεER +(1−θR)εNR −θSεES −(1−θS)εNS (3)

Where the elasticity of recruitment has been broken down into the elasticity of recruit- ment of workers from employment (εER) and the elasticity of recruitment of workers from nonemployment (εNR ). Similarly the elasticity of separation has been decomposed into the elasticity of separation to employment (εES ) and the elasticity of separation to nonemploy- ment (εNS ). θRand θS represent the share of recruits from employment and the share of separations to employment respectively.

assumption made in most of the previous literature that the total 􏰉ow of recruits is equal to the total 􏰉ow of separations. Next, Manning (2003, p. 100) notes that

εNR = εER − wθ‘R(w)/θR(w)(1 − θR(w)) (4)

Thisisderivedfromthesimplede􏰃nitionofθR,whichimpliesRN =RE(1−θR)/θR,where RN and RE are the recruits from nonemployment and employment respectively. Taking the log of each side of this relation and di􏰂erentiating yields the de􏰃nition of the elasticity of recruitment from nonemployment. The second term on the right-hand side of Equation (4) can be thought of as the bargaining premium that an employee receives from searching while currently employed. Thus, the labor supply elasticity to the 􏰃rm can be written as a function of both separation elasticities and the premium to searching while employed. This is important because there are established methods for estimating these quantities. By contrast, if we wanted to directly estimate the recruitment elasticities we would need data on all employment o􏰂ers received by each individual.

MaxΠ = pQ(L) − wL(w) (5) w

choice of wage w determines the labor supplied to the 􏰃rm L. Taking 􏰃rst order conditions,

substituting ε = w ∂L(w) , and solving for w yields: L(w) ∂w

w = pQ′(L) (6) 1+1

The numerator in Equation (6) is simply the marginal product of labor, and ε is the labor supply elasticity faced by the 􏰃rm. It is easy to see that in the case of perfect competition (ε = ∞) that the wage is equal to the marginal product of labor, but the wage is less than then marginal product for all 0 < ε < ∞.

The Longitudinal Employer Household Dynamics (LEHD) data are built primarily from Un- employment Insurance (UI) wage records, which cover approximately 98 percent of wage and salary payments in private sector non-farm jobs. Information about the 􏰃rms is constructed from the Quarterly Census of Employment and Wages (QCEW). The LEHD infrastructure allows users to follow both workers and 􏰃rms over time, as well as to identify workers who share a common employer. These data also include demographic characteristics of the worker and basic 􏰃rm characteristics, obtained through administrative record and statistical links. For a complete description of these data, see Abowd et al. (2009).

My sample consists of quarterly observations on earnings and employment for 46 states between 1985 and 20083. I make several sample restrictions in an attempt to obtain the

most economically meaningful results, analyses without these restrictions are presented as a robustness check later in the paper. These restrictions are necessary in large part because the earnings data are derived from tax records, and thus any payment made to an individual, no matter how small, will appear in the sample. As a consequence, there are many 􏰅job spells􏰆 which appear to last only one quarter, but are in fact one-time payments which do not conform with the general view of a job match between a 􏰃rm and worker.

First, I only include an employment spell in the sample if at some point it could be considered the dominant job, de􏰃ned as paying the highest wage of an individual's jobs in a given quarter4. I also remove all spells which span fewer than three quarters. This sample restriction is related to the construction of the earnings variable. Since the data do not contain information on when in the quarter an individual was hired/left, the entries for the 􏰃rst and last quarters of any employment spell will almost certainly underestimate the quarterly earnings rate (unless the individual was hired on the 􏰃rst day or left employment on the last day of a quarter). Thus, in order to get an accurate measurement of the earnings rate I must observe an individual in at least one quarter other than the 􏰃rst or last of an employment spell. Additionally, I limit the analysis to 􏰃rms with 100 total employment spells of any length over the lifespan of the 􏰃rm. For the full-economy monopsony model, these sample restrictions yield a 􏰃nal sample of 130,937,872 unique individuals who had 295,131,926 total employment spells at 572,740 di􏰂erent 􏰃rms. Additionally, for analyses using the 􏰃rm-level measure of the labor supply elasticity, only 􏰃rms which have greater than 25 separations to employment, 25 separations to unemployment, and 25 recruits from employment over the lifespan of the 􏰃rm are considered. This reduces the analysis sample to 104,381,863 unique individuals having 234,163,233 employment spells at 279,251 unique 􏰃rms.

4This formulation allows an individual to have more than one dominant job in a given quarter. The rationale behind this de􏰃nition is that I wish to include all job spells where the wage is important to the worker. Restricting the dominant job de􏰃nition to only allow one dominant job at a given time does not alter the reported results.

I construct an overall measure of the percent of the industry-speci􏰃c labor market that each 􏰃rm employs (Number of workers at 􏰃rm i/number of workers in 􏰃rm i's county and in 􏰃rm i's industry) using North American Industry Classi􏰃cation System (NAICS) industry de􏰃nitions. While this variable is far from a perfect measure of an employer's power to set wages, it has several advantages over the semistructural measures to be used later in the paper. Both the construction of these measures and the regression estimates using them are transparent. Endogeneity, misspeci􏰃ed equations, etc. are of less concern in the construction of these labor concentration measures, and the interpretation of the regression coe􏰄cients on these variables is straightforward. This analysis corresponds to the traditional concentration ratio approach of analyzing labor market power.

every 􏰃rm in the sample (as well as on the whole sample for comparison purposes), where the unit of observation is an employment spell, thus one individual can appear in multiple 􏰃rm's models. Looking 􏰃rst at the separation elasticities, I model separations to nonemployment as a Cox proportional hazard model given by

where λ() is the hazard function, λ0 is the baseline hazard, t is the length of employment, log(earnings) is the natural log of individual i's quarterly earnings, and X is a vector of explanatory variables including gender, race, age, education, and year control variables (in- dustry controls are also included in the full-economy model). While the entire sample will be used, workers who transition to a new employer or who are with the same employer at the end of the data series are considered to have a censored employment spell. In this model, the parameter β represents an estimate of the separation elasticity to nonemployment. In an analogous setting, I model separations to employment as

λE(t|βE,seplog(earnings)i +XiγE,sep)=λ0(t)exp(βE,seplog(earnings)i +XiγE,sep) (8)

with the only di􏰂erence being that the sample is restricted to those workers who do not have a job transition to nonemployment. As before, β represents an estimate of the sep- aration elasticity to employment. To estimate the third quantity needed for equation (3), wθ‘R(w)/θR(w)(1 − θR(w)), Manning (2003) shows that this is equivalent to the coe􏰄cient on log earnings when estimating the following logistic regression

Prec = exp(βE,reclog(earnings)i + XiγE,rec) (9) 1 + exp(βE,reclog(earnings)i + XiγE,rec)

where the dependent variable takes a value of 1 if a worker was recruited from employment and 0 if they were recruited from nonemployment. The same explanatory variables used in the separation equations are used in this logistic regression. At this point the results listed in the theoretical section can be used (along with calculating the share of recruits and separations to employment) in conjunction with equation (3) to produce an estimate of the labor supply elasticity facing each 􏰃rm.

One concern with this methodology is that I am only able to estimate a time-invariant long-run labor supply elasticity to the 􏰃rm. Since 􏰃rms, particularly young ones, certainly see changes in their market power, the interpretation of the labor supply elasticities derived in this paper is not straightforward. These values may not represent the true elasticities at any point in time, but can rather be thought of as an average of many short-run elasticities. If you assume that a 􏰃rm's market power grows with the 􏰃rm, then the estimated elasticities will be conservative (less monopsonistic) estimates of the current level of market power which 􏰃rms possess. Additionally, this could be seen as measurement error in the earnings equations presented in Tables 7 and 8, which would likely bias the coe􏰄cients toward zero.

To provide some intuition on the models being estimated, consider the analysis of sepa- rations to employment. A large (in absolute value) coe􏰄cient on the log earnings variable implies that a small decrease in an individual's earnings will greatly increase the probability of separating in any given period. In a perfectly competitive economy, we would expect this coe􏰄cient to be in􏰃nitely high. Similarly, a very small coe􏰄cient implies that the em- ployer can lower the wage rate without seeing a substantial decline in employment. One concern with this procedure is that this measure of monopsony power is actually proxying for high-wage 􏰃rms, re􏰉ecting an e􏰄ciency wage view of the economy where 􏰃rms pay a wage considerably above the market wage in exchange for lower turnover. This is much more of a concern in the full economy estimate of the labor supply elasticity to the 􏰃rm found elsewhere in the literature than in my 􏰃rm-level estimation since the models in this paper are run separately by 􏰃rm. The logic behind this di􏰂erence is that in the full economy

model cross-sectional variation in the level of earnings is used to identify the labor supply elasticity. In a 􏰃rm-speci􏰃c model, however, the labor supply elasticity of 􏰃rm A does not mechanically depend on the level of earnings at 􏰃rm B. This e􏰄ciency wage hypothesis will be directly tested.

log(quarterly earningsij) = βmarketpowerj + γXij + δYj + θZi + εij (10)

The dependent variable is the natural log of individual i's quarterly earnings in employ- ment spell j. The market power variable represents 􏰃rm j's estimated labor supply elasticity or the share of the local working population employed at the 􏰃rm. X is a vector of person characteristics, which may vary by the employment spell, including age, age-squared, tenure (quarters employed at 􏰃rm), tenure-squared, education6, gender, race, ethnicity, and year ef- fects. Y is a vector of 􏰃rm characteristics which includes indicator variables for the two-digit NAICS sector and the size (employment) of the 􏰃rm. Z is a vector of person 􏰃xed-e􏰂ects and ε is the error term. Time-invariant characteristics in X are excluded in models with person 􏰃xed-e􏰂ects.

6Reported educational attainment is only available for about 10 percent of the sample, although sophis- ticated imputations of education are available for the entire sample. The results presented in this paper correspond the the full sample of workers (reported education and imputed education). All models were also run on the sample with no imputed data, and no substantive di􏰂erences were observed. In particular, since the preferred speci􏰃cation includes person 􏰃xed-e􏰂ects, and thus educational attainment drops out of the model, this is of little concern.

Under this approach, unconditional quantile regressions are performed on every 5th quan- tile of the earnings distribution using the same model as Equation (10). The estimated coe􏰄cients on the labor supply elasticity variable from each regression will then be used to simulate the impact of a one unit increase in the labor supply elasticity to the 􏰃rm on earnings in the associated quantile.

Table 1 reports summary statistics from my analysis sample. Since the unit of observation is the employment spell, and only dominant jobs are included, some statistics deviate slightly from typical observational studies of the labor market (such as a nearly even split of job spells between men and women). The average employment spell lasts about two and a half years, with a little over eighty percent of spells resulting from a move from another job. The quarterly nature of the LEHD data make it di􏰄cult to precisely identify7 whether

an individual separated to employment or nonemployment, and therefore the proportion of separations to employment is slightly higher than comparable statistics reported in Manning (2003).

Also of note are the employment concentration ratios, with the average 􏰃rm employing roughly 9 percent of their county's industry speci􏰃c labor force.

Table 2 presents the estimated impact of a ten percentage point increase in the concentra- tion ratio in various speci􏰃cations of Equation (10). These results suggest that, in general, a 􏰃rm's geographic dominance does not appear to signi􏰃cantly alter the wage bill it pays. Note that when the models are run separately by North American Industry Classi􏰃cation System (NAICS) sector, as depicted in Table 3, there is evidence that 􏰃rms with high concentration ratios in certain industries (such as the utilities sector) pay slightly lower wage bills. How- ever, the e􏰂ect sizes are small relative to the observed distribution of concentration ratios. Given the small results, and the fact that the industry-speci􏰃c e􏰂ects seem to be centered around zero, it seems plausible to conclude that geographic constraints in the labor market play at most a small role in wage determination for the average worker.

I 􏰃rst compute the average labor supply elasticity to the 􏰃rm prevailing in the economy by estimating Equations (7)-(9) on a pooled sample of all (dominant) employment spells, and

combining the results according to Equation (3). Table 4 presents the output of a several speci􏰃cations of the full-economy monopsony model. The estimated elasticities range from 0.55 to 0.61 depending on the speci􏰃cation (inclusion of 􏰃xed e􏰂ects, etc.). These elasticities are certainly on the small side, implying that at the average 􏰃rm a wage cut of one percent would only reduce employment by .6 percent. However, this magnitude is still within the range observed by Manning (2003) in the NLSY79. Additionally, even the inclusion of 􏰃xed- e􏰂ects still puts many more restrictions on the parameter estimates than separate estimations for each 􏰃rm. Based on a comparison of the full-economy model and the 􏰃rm-level model presented in the next section, the failure to fully saturate the full economy model likely produces downward biased estimates. A detailed discussion of factors which may attenuate these estimates, as well as structural reasons we should expect these results from US data, is given in the 􏰅Discussion and Extensions􏰆 section.

Table 5 displays information about the distribution of 􏰃rms' labor supply elasticities, and Figure 1 presents a kernel density plot of the market power measure8. This distribution is constructed by separately estimating Equations (7)-(9) for each 􏰃rm. While the median supply elasticity (0.74) is close to the estimate from the full-economy model, there appears to be signi􏰃cant variation in the market power possessed by 􏰃rms. I estimate a mean labor supply elasticity of 0.92, however, there are many 􏰃rms (about 3 percent of the sample) with labor supply elasticities greater than 5. It appears that while there is a nontrivial fraction of 􏰃rms whose behavior approximates a highly competitive labor market, the majority of the distribution is characterized by signi􏰃cant frictions.While not surprising, to my knowledge this is the 􏰃rst documentation of the large discrepancy in 􏰃rms' ability to set the wage.

Table 6 reports average labor supply elasticities broken down by NAICS sector. The manufacturing sector appears to enjoy the least wage-setting power, with a labor supply

The central focus of this paper is presented in Tables 7, which estimates various speci- 􏰃cations of Equation (10) in order to measure the impact of market power on the earnings distribution. Unconditionally, a one unit increase in the labor supply elasticity increases earnings by .16 log points. With the addition of detailed 􏰃rm characteristics and person 􏰃xed e􏰂ects, the e􏰂ect declines to .05 log points. This is an important result for the new monopsony literature, since it rules out the possibility that their identi􏰃cation strategy is actually identifying high-wage 􏰃rms whose employees do not often switch jobs due to the high wages.

There are two main reasons why these results may be underestimated and instead inter- preted as lower bounds. First, each labor supply elasticity is a weighted average of many more precisely de􏰃ned elasticities which would more accurately measure a 􏰃rm's market power over a particular individual. For example, 􏰃rms likely face di􏰂erent supply elasticities for every occupation, and potentially di􏰂erent elasticities across race and gender groups. From a measurement error perspective, regressing the log of earnings on the average labor supply elasticity to the 􏰃rm would attenuate the estimates relative to the ideal scenario where I could separately identify every occupation speci􏰃c elasticity.

Secondly, the inclusion of tenure and its squared term in the model is likely overcontrol- ling, and introduces downward-biasing endogeneity into my results. To see why, consider a study which attempts to estimate the gender wage gap. The inclusion of occupational 􏰃xed- e􏰂ects is often seen as overcontrolling, and providing an underestimate of the gap, because in many cases occupation is at least partially 􏰅caused􏰆 by gender (particularly in the historical case). In the case of this study, the underlying model of monopsony and even de􏰃nition of a labor supply elasticity implies that a 􏰃rm's market power is a partial 􏰅cause􏰆 of tenure.

Table 8 details the disproportionate e􏰂ect which 􏰃rms' market power has on workers at the low end of the earnings distribution. Assuming a doubling of each 􏰃rm's labor supply elasticity (the median 􏰃rm moves from 0.74 to a still modest 1.48), the 10th percentile of the earnings distribution increases by 0.071 log points under the counterfactual assumption, while the median worker sees an increase of 0.035 log points and the 90th percentile remains unchanged. The nonlinear impacts are also clearly seen in the unconditional quantile regres- sion coe􏰄cients, which are 4-5 times greater than the OLS coe􏰄cient at lower quantiles and essentially zero at the upper end of the distribution.

Standard measures of inequality are also reported in Table 8 for both the empirical and counterfactual distributions. A 100 percent increase in 􏰃rms' labor supply elasticity is associated with a 5 percent reduction in the variance of the earnings distribution (0.93 to 0.48 log points). Similarly, we see considerable decreases in the 90-10 ratio (1.32 to 1.3), 50-10 ratio (1.18 to 1.16), and 90-50 ratio (1.12 to 1.11).

These results could arise from a number of di􏰂erent scenarios, the examination of which is beyond the scope of the current paper. It may re􏰉ect low-ability workers having few outside options for employment. This could be due to strict mobility constraints, a less e􏰂ective job referral network (Ioannides and Loury, 2004), lower job search 􏰅ability􏰆 (Black, 1981), or simply being quali􏰃ed for fewer jobs. Another mechanism through which a 􏰃rm's market power might di􏰂erentially a􏰂ect low wage workers is gender discrimination, as suggested by Hirsch et al. (2010) or racial discrimination. These questions deserve a much deeper treatment, and should be explored in future research.

Figure 2 plots both the empirical earnings distribution and the counterfactual distribution under a more drastic assumption which more closely approximates perfect competition, that each 􏰃rm's labor supply elasticity is increased by a factor of 10 (median elasticity goes from .74 to 7.4). The variance of the counterfactual distribution is considerably lower, with nearly all of the movement occurring in the lower half of the distribution. The striking fact about

Figure 2 is that the Burdett and Mortensen model predicts the exact same behavior of the earnings distribution as the arrival rate of job o􏰂ers increases.

First, it should be noted that the only other studies to estimate the labor supply elasticity to the 􏰃rm with comprehensive administrative data used European data. Given the very restrictive (from the point of view of the employer) employment laws in place in many European countries, this result is not surprising. Assuming that job security accrues over time within 􏰃rm but drops following a transition to a new 􏰃rm, any law which makes it more di􏰄cult to 􏰃re a worker e􏰂ectively lowers the cost to the employee of switching jobs because job security is less of a factor.

One potential criticism of the labor supply elasticities derived in this paper is that the data do not contain detailed occupation characteristics. This problem is mitigated by the fact that the measures are constructed at the 􏰃rm level in that I am only comparing workers in the same 􏰃rm in the construction of a 􏰃rm's monopsony power. Additionally, previous studies such as Hirsch et al. (2010) and Manning (2003) 􏰃nd that the addition of individual- level variables had little impact on the estimated labor supply elasticities and that it was the addition of 􏰃rm characteristics which altered the results. As a further check of this problem, I compute the aggregate monopsony measures in the NLSY, as done in Manning (2003), both with and without detailed occupation characteristics. As shown in Table 9, I 􏰃nd that the di􏰂erence between these labor supply elasticities is about 0.2 and is not statistically signi􏰃cant. Keep in mind that even if this di􏰂erence were statistically signi􏰃cant, the estimates in this paper are still a long way from implying perfect competition. Thus, I

conclude that the absence of occupation controls in the LEHD data will not seriously bias the results of this study.

A potentially more serious problem in the estimation of the labor supply elasticity to the 􏰃rm is endogenous mobility. Consider the standard search theory model with on the job search: A worker will leave their current job if they receive a higher wage o􏰂er from another 􏰃rm. Their wage at the new 􏰃rm is then endogenously determined since in e􏰂ect it was drawn from a distribution truncated at the wage of the their previous job. In this sense, the earnings data for those individuals who were hired away from another job is biased upward, which will bias estimates of the labor supply elasticity to the 􏰃rm downward. I deal with the endogenous mobility bias in several di􏰂erent ways. First, I estimate the average earnings premium an individual gets from moving to their nth job (where n is the job number in a string of consecutive employment spells). For instance, workers' earnings increase on average .19 log points when they move from their 􏰃rst to their second jobs. I then reduce the earnings of all job movers by the average premium associated with a move from job n-1 to n. For example, all workers in their second jobs of a string of employment spells would have their earnings reduced by .19 log points.9 The rationale behind this adjustment is that I only observe workers moving from one job to another if they receive a higher wage o􏰂er (This is a typical assumption of on-the-job search models, and is overwhelmingly true in the data). Thus, the earnings I observe in the second job are endogenously determined, since they were in a sense drawn from a strictly positive o􏰂er distribution.

Second, I recalculate the labor supply elasticities with a Heckman selection correction. In this model I de􏰃ne the selected group as those who separate from one job to another, and use the number of new jobs in an individual's state and industry as the excluded variable. The logic behind this restriction is that the state-industry speci􏰃c labor market should be highly correlated with the likelihood that an individual moves to a new job, but should

be uncorrelated with that individual's unobserved 􏰅ability􏰆 to move. The inverse Mills ratio from the Heckman selection model is included as a regressor in each of the Equations (7)-(9). As noted in Table 9, each of these corrections leads to a trivial change in the labor supply elasticity distribution.

One 􏰃nal concern regarding endogenous mobility is that we do not observe the complete history of workers, only that within the time-frame of the LEHD infrastructure. Thus, any employment spells in progress at the beginning of our window which are the result of a hire from another 􏰃rm may introduce bias into the results. To assess the degree to which this is a problem, I again employ the NLSY79. I use a Monte Carlo approach to compare the estimated labor supply elasticities using the complete worker histories and using only employment spells which occurred in the 􏰃nal third of the sample window. This is the ideal comparison, where the 􏰃rst calculation takes into account the entire work histories of each individual and the second calculation uses only those spells observed after an arbitrary date. The Monte Carlo analysis 􏰃nds that using the complete worker histories leads to a statistically insigni􏰃cant decrease of the estimated labor supply elasticity. This implies that the use of some partial histories in this study is not likely a problem, and at worst yields an underestimate of monopsony power.

For the reasons mentioned in this section and probably many others, critics may claim that this paper does not accurately estimate the labor supply elasticity to the 􏰃rm, and they could be right. As with any identi􏰃cation strategy, this study relies on assumptions, not all of which are testable. But while the average 􏰃rm's labor supply elasticity may not be exactly .92, the variable which I call a supply elasticity is certainly some kind of weighted average highly correlated with mobility and individuals' responsiveness to changes in earnings. The fact that this measure is highly correlated with earnings, especially for those at the bottom of the distribution, tells us that our economy is far less competitive than we commonly assume.

This study 􏰃nds evidence of signi􏰃cant frictions in the US labor market, although the severity of these frictions varies greatly between labor markets. I estimate the average 􏰃rm's labor supply elasticity to be quite monopsonistic at 0.92, however there is a nontrivial fraction of 􏰃rms who do appear to be operating in an approximately competitive labor market. While identifying the precise frictions which contribute to 􏰃rms' labor market power is beyond the scope of this study, I can conclude that a 􏰃rm's geographical dominance alone does not account for all or even most of their ability to a􏰂ect the wage o􏰂er distribution.

I extend the semistructural empirical strategy proposed by Manning (2003) to identify 􏰃rm level labor supply elasticities. The use of these measures of 􏰃rm market power in earnings regressions provides the 􏰃rst direct test of the validity of the new monopsony model. I 􏰃nd that a one unit increase in a 􏰃rm's labor supply elasticity is associated with a 5 percent increase in earnings on average. Further exploring the earnings distribution, I 􏰃nd highly nonlinear e􏰂ects implying that the negative e􏰂ects of monopsony power are concentrated at the lower end of the distribution.

J. Abowd, B. Stephens, L. Vilhuber, F. Andersson, K. McKinney, M. Roemer, and S. Wood- cock, 􏰅The lehd infrastructure 􏰃les and the creation of the quarterly workforce indicators,􏰆 in Producer Dynamcs: New Evidence from Micro Data, J. B. J. T. Dunne and M. J. Roberts, Eds. The University of Chicago Press, 2009, pp. 149􏰇234.

J. Robinson, The economics of imperfect competition. Macmillan, 1969.

Figure 1

Figure 2

Age Female White Hispanic High School Some College College Degree+ Tenure (Quarters) Log(Quarterly Earnings) Firm Concentration Firm Industry-Concentration Recruited from Employment

0.78 0.41 0.11 0.31 0.3 0.46 0.32 0.47 0.24 0.42 10.1 10.7

8.5 1 0.01 0.02 0.09 0.16 0.83 0.4

Impact of a ten percentage point increase in concentration ratio on log(earnings) Demographic and human capital controls Employer controls Tenure Controls State 􏰃xed-e􏰂ects R-Squared

0.0213 0.0053

No Yes

No No No No No No 0.0013 0.2369

0.0109 0.0066

*A pooled national sample of all dominant employment spells is used in this set of regressions. The dependent variable is the natural log of quarterly earnings. Demographic and human capital controls include: age, age-squared, and indicator variables for gender, ethnicity, racial status, and education level. Employer controls include indicator variables for each of the 20 NAICS sectors and number of employees working at the 􏰃rm. Tenure controls include the length (in quarters) of the employment spell, as well as its squared term. Year e􏰂ects are included in all models. The results are not reported for the models with 􏰃rm and person 􏰃xed e􏰂ects because the coe􏰄cient was deemed to be biased due to severe multicollinearity. Standard errors are not reported because all t-statistics are greater than 50.

.55 .6

Only 􏰃rms with an individually estimated elasticity .61

*These labor supply elasticities were obtained by estimating equations (7)-(9), on a pooled sample of all (dominant) employment spells. Each model contained age, age-squared, along with indicator variables for female, nonwhite, Hispanic, high school diploma, some college, college degree or greater, year, and each of 20 NAICS sectors.

Table 5: Distribution of Estimated Firm-Level Labor Supply Elasticities

0.92 0.21 0.42 0.74 1.17 1.74

*Three separate regressions, corresponding to equations (7)-(9), were estimated separately for each 􏰃rm in the data which met the conditions described in the data section. The coe􏰄cients on log earnings in each regression were combined, weighted by the share of recruits and separations to employment, according to equation (3) to obtain the estimate of the labor supply elasticity to the 􏰃rm. Demographic and human capital controls include: age, age-squared, and indicator variables for gender, ethnicity, racial status, and education level. Employer controls include number of employees working at the 􏰃rm and industry indicator variables. Year e􏰂ects are included in all models.

Table 6: Mean Labor Supply Elasticity by Sector

1.11 1.06 1.03 1.14 1.36 1.13 0.84 1.11 0.86 0.98 0.84 0.86

0.72 0.69 0.79 0.67 0.68 0.79 0.97 0.97

*The numbers in this table represent averages by NAICS sector of the estimated labor supply elasticity to the 􏰃rm. Three separate regressions, corresponding to equations (7)-(9), were estimated separately for each 􏰃rm in the data which met the conditions described in the data section. The coe􏰄cients on log earnings in each regression were combined, weighted by the share of recruits and separations to employment, according to equation (3) to obtain the estimate of the labor supply elasticity to the 􏰃rm. Demographic and human capital controls include: age, age-squared, and indicator variables for gender, ethnicity, racial status, and education level. Employer controls include number of employees working at the 􏰃rm. Year e􏰂ects are included in all models.

Coe􏰄cient on labor supply elasticity Demographic and human capital controls Employer controls Tenure controls State 􏰃xed-e􏰂ects Person 􏰃xed-e􏰂ects R-Squared

0.16 0.12 0.05 0.03 0.03 0.05 No Yes Yes Yes Yes Yes

No No Yes Yes Yes Yes No No No Yes Yes Yes No No No No Yes Yes No No No No No Yes

0.009 0.238 0.317 0.335 0.341

0.783

*A pooled national sample of all dominant employment spells subject to the sample restriction described in the data section is used in this set of regressions. The dependent variable is the natural log of quarterly earnings. Demographic and human capital controls include: age, age-squared, and indicator variables for gender, ethnicity, racial status, and education level. Employer controls include the number of employees working at the 􏰃rm and industry indicator variables. Tenure controls include the length (in quarters) of the employment spell, as well as its squared term. Year e􏰂ects are included in all models. Standard errors are not reported because the t-statistics range from 500-1000, but are available upon request along with all other estimated coe􏰄cients.

Table 8: Counterfactual Distribution Analysis

Change in 0.071 0.055 log(earnings)

Earnings .93 1.32 distribution

Counterfactual .88 1.30 distribution

0.035 0.016 0.00

*The counterfactual distribution was constructed by estimating unconditional quantile regressions at every 􏰃fth quantile of the earnings distribution, and using the supply elasticity coe􏰄cient from each regression to simulate the e􏰂ect at each quantile of a doubling of the labor supply elasticity. Demographic and human capital controls include: age, age-squared, and indicator variables for gender, ethnicity, racial status, and education level. Employer controls include the number of employees working at the 􏰃rm and industry indicator variables. Tenure controls include the length (in quarters) of the employment spell, as well as its squared term. Year e􏰂ects are included in all models.

.74

.73

.75

Table 9: Robustness Checks

*Panel A: Equations (7)-(9) were estimated on a sample of employment spells from the NLSY79 from 1979-1996 (the last year for which detailed information on recruitment and separation dates are available). The speci􏰃cations include the same variables available through the LEHD data: age, age-squared, year e􏰂ects, along with gender, ethnicity, race, industry, and education indicators. The 􏰃rst column compares the labor supply elasticities with and without the inclusion of occupational 􏰃xed e􏰂ects. The second column compares the labor supply elasticities with and without the assumption that only the last third of every individual's work history is known.

**Panel B: The second column represents a recalculation of the labor supply elasticity in which workers who are recruited away from another job have their earnings adjusted downward by the average premium of moving from job n to job n+1. The third column represents a recalculation of the labor supply elasticity in which the inverse mills ratio of a Heckman selection model for mobility is controlled for in each of Equations (7)-(9). The omitted category in the Heckman model is the number of new local jobs in each workers current industry.