1.1 Frictions and idiosyncracies

First, consider search models (for relatively recent reviews see Mortensen and Pissarides, 1999; Rogerson et al., 2005). In these models it is assumed that it takes time for employers to be matched with workers because workers’ information about the labor market is imperfect (an idea first put forward by Stigler, 1961, 1962)—in some versions, the job offer arrival rate can be influenced by the expenditure of time and/or money (see Section 2.2.1 below for such a model). These models have become the workhorse model in much of macroeconomics (see Rogerson and Shimer, 2011) because one cannot otherwise explain the dynamics of unemployment. But, taken literally, this model is not very plausible. It is not hard to find an employer—I can probably see 10 from my office window. But, what is hard is to find an employer who is currently recruiting² who is the same as my current one i.e. a perfect substitute for my current job. This is because there is a considerable idiosyncratic component to employers across a vast multitude of dimensions that workers care about. This idiosyncratic component might come from non-monetary aspects of the job (e.g. one employer has a nice boss, another a nasty one, one has convenient hours, another does not) or from differences in commuting distances or from many other sources. A good analogy is our view of the heavens: the stars appear close together but this is an illusion caused by projecting three dimensions onto two. Neglecting the multitude of dimensions along which employers differ that matter to workers will seriously overestimate our impression of the extent to which jobs are perfect substitutes for each other from the perspective of workers.

One other commonly given explanation for why there may be rents in the employment relationship is “specific human capital”. Although this is normally thought of as distinct from the reasons given above, it is better thought of as another way in which employers may not be perfect substitutes for each other—in this case in terms of the quality of the match or the marginal product of the worker. This comes out clearly in the discussion of specific human capital provided by Lazear (2003). He struggles with the problem of what exactly are specific skills, coming up with the answer that “it is difficult to generate convincing examples where the firm-specific component [of productivity] approaches the general component”. He goes on to argue that all skills are general skills but that different employers vary in how important those skills are in their particular situation. So, a worker with a particular package of general skills will not be faced with a large number of employers requiring exactly that package. As Lazear (2003, p. 2) makes clear, this relies on employers being thin on the ground otherwise a large supply of employers demanding exactly your mix of skills would be available and the market would be perfectly competitive. Again, it is the lack of availability of employers who are perfect substitutes that can be thought of as the source of the rents.

A key and eminently sensible idea in the specific human capital literature originating in Becker (1993) is that specific human capital accumulates over time. This means that rents in the employment relationship are likely to be higher for those workers who have been in their current job for a long time—very few labor economists would dissent from this position. The very fact that we turn up to the same employer day after day strongly suggests there are some rents from that relationship. More controversial is whether, on a worker’s first day in the job, there are already rents because the employer has paid something to hire them and the worker could not get another equivalent job immediately. This paper is predicated on the view that there are rents from the first day³ – that the worker would be disappointed if they turned up for work to be told there was no longer a need for them and that the employer would be irritated if the new hire does not turn up on the first morning.

One interesting question to think about is whether the rapid decline in the costs of supplying and acquiring information associated with the Internet is going to make labor markets more like the competitive ideal in the future than the past. There is no doubt that the Internet (and earlier communication technologies) have transformed job search. In late 19th century London an unemployed worker would have trudged from employer to employer, knocking on doors and enquiring whether there were any vacancies, often spending the whole day on it and walking many miles. In contrast, a worker today can, with access to the Internet, find out about job opportunities throughout the globe. Using the Internet as a method of job search has rapidly become near-universal. For example, in the UK Labour Force Survey the percentage of employed job-seekers using the Internet rose from 62% in 2005 to 82% in 2009 and the percentage of unemployed job-seekers using the Internet rose from 48% to 79% over the same period. These figures also indicate that the “digital divide”, the gap in access to the internet between the rich and the poor, may also be diminishing.

But, while there is little doubt that Internet use is becoming pervasive in job search, there is more doubt about whether it is transforming the outcomes of the labor market. Autor (2001) provides a good early discussion of the issues. While the Internet has increased the quantity of information available to both workers looking for a job and employers looking for a worker has gone up, it is much less clear that the quality has also risen. If the costs of applying for a job fall then applications become particularly more attractive for those who think they have little chance of getting the job—something they know but their prospective employer may only discover at some expense. One way of assessing whether the Internet has transformed labor markets is to look at outcomes. Kuhn and Skutterud (2004) do not find a higher job-finding rate for those who report using the Internet and the Beveridge curve does not appear to have shifted inwards.

So, the conclusion would seem to be that the Internet has transformed the labor market less than one might have thought from the most common ways in which frictions are modeled. If one thinks of frictions as being caused by a lack of awareness of where vacancies are, and the cost of hiring the cost of posting a vacancy until a suitable job application is received, then one might have expected a large effect of the Internet. But if, as argued here and later in this chapter, one thinks of frictions as coming from idiosyncracies in the attractiveness of different jobs, and the costs of hiring as being primarily the costs of selection and training new workers, then one would be less surprised that the effects of the Internet seem to be more modest.

1.2 Institutions and collusion

So far, the discussion has concentrated on rents that are inevitable. But rents may also arise from man-made institutions that artificially restrict competition. This implicit or explicit collusion may be by workers or employers. Traditionally it is collusion by workers in the form of trade unions that has received the most attention. However, this chapter does not discuss the role of unions at all because it is covered in another chapter (Farber, 2011).

Employer collusion has received much less attention. This is in spite of the fact that Adam Smith (1970, p. 84) wrote: “we rarely hear... of the combinations of masters; though frequently of those of workmen. But whoever imagines, upon this account, that masters rarely combine, is as ignorant of the world as of the subject”. Employer collusion where it exists is thought to be in very specific labor markets e.g. US professional sports or, more controversially, nurses (see, for example, Hirsch and Schumacher, 1995) and teachers who may have a limited number of potential employers in their areas (see Boal and Ransom, 1997, for a discussion).

There a number of more recent papers arguing that some institutions and laws in the labor market serve to aid collusion of employers to hold down wages. For example, Naidu (2010) explores the effect of legislation in the post-bellum South that punished (almost exclusively white) employers if they enticed (almost exclusively black) workers away from other employers. Although it might appear at first sight to be white employers who suffered from this legislation, Naidu (2010) presents evidence that, by reducing competition for workers, it was blacks who were made worse off by this. The legislation can be thought of as a way for employers to commit not to compete for workers, leading to a more collusive labor market outcome.

A more contemporary example would be the debate over the “National resident Matching Program” (NMRP) that matches medical residents and hospitals. In 2002 a class action suit was brought against hospitals alleging breach of anti-trust legislation, essentially that the NMRP enabled hospitals to collude to set medical resident wages at lower than competitive levels. This case was eventually resolved by Congress passing legislation that effectively exempted the NMRP from anti-trust legislation (details of this can be found at http://kuznets.fas.harvard.edu/~aroth/alroth.html#MarketDesign). There is some theoretical work (e.g. Bulow and Levin, 2006; Niederle, 2007) arguing whether, in theory, the NMRP might reduce wages. These papers look at the incentive for wage competition within the NMRP. More, recently Priest (2010) has argued that the “problems” of the labor markets for medical interns (which have led to the use of matching algorithms like the NMRP) are in fact the consequences of employer collusion on wages in a labor market with very heterogeneous labor and that a matching algorithm would not be needed if the market was allowed to be competitive. He also argues that the market for legal clerks is similar.

Another recent example is Kleiner and Won Park (2010), who examine how different state regulations on dentists and dental hygienists affect the labor market outcomes for these two occupations. They present evidence that states which allow hygienists to practice without supervision from dentists (something we would expect to strengthen the market position of hygienists and weaken that of dentists) have, on average, higher earnings for hygienists and lower earnings for dentists.

All of these examples relate to very specific labor markets that might be thought to all be highly atypical. But there remains an open question as to whether employer collusion is important in more representative labor markets. It is clear that employers do not en masse collude to set wages, but there may be more subtle but nevertheless effective ways to do it. For example, as the physical location of employers is important to workers, it is likely that, for many workers, the employers who are closest substitutes from the perspective of workers are also geographically close, making communication and interaction between them easy. Manning (2009) gives an example of a model in which employers are on a circle (as in Bhaskar and To, 1999) and collude only with the two neighboring employers in setting wages. Although there is no collusion spread over the whole market, Manning (2009) shows that a little bit of collusion can go a long way leading to labor market outcomes a long way from perfect competition. One way of putting the question is “Do managers of neighboring fast food restaurants talk to each other or think about how the other might react if wages were to change?”. Ethnographic studies of labor markets may give us some clues. The classic study of the New Haven labor market in Reynolds (1951) did conclude there was a good deal of discussion among employers about economic conditions, and that there was an implicit agreement not to poach workers from each other. One might expect this to foster some degree of collusion though Reynolds (1951, p. 217) is clear that there is no explicit collusive wage-setting. In contrast, the more recent ethnographic study of the same labor market by Bewley (1999) finds that the employers source of information about their rivals comes not from direct communication but from workers or from market surveys provided by consultancies. Those institutions sound less collusive than those described by Reynolds. But, the honest answer is that we just don’t know much about tacit collusion by employers because no-one has thought it worthwhile to investigate in detail.

2.1 The costs of recruitment

2.2 The search activity of the non-employed

2.3 The costs of job loss

To estimate rents for the employed, the experiment one would like to run is to consider what happens when workers are randomly separated from jobs. There is a literature that considers exactly that question—studies of displaced workers (Jacobson et al., 1993; Von Wachter, Manchester and Song, 2009). One concern is the difficulty of finding good control groups, e.g. the reason for displacement is presumably employer surplus falling to less than zero. But, for some not totally explained reason, it seems that wages prior to displacement are not very different for treatment and control groups—it is only post-displacement that one sees the big differences. Under this assumption one can equate these estimates to loss of worker surplus.

For a sample of men with 5 years previous employment who lost their jobs in mass lay-offs in 1982, Von Wachter, Manchester and Song (2009) estimate initial earnings losses of 33% that then fall but remain close to 20% after 20 years. Similar estimates are reported in Von Wachter, Bender and Schmeider (2009) for Germany. These samples are workers who might plausibly be expected to have accumulated significant amounts of specific human capital, so one would not be surprised to find large estimated rents for this group. However, Von Wachter, Manchester and Song (2009) find sizeable though smaller earnings losses for men with less stable employment histories pre-displacement and for women. At the other extreme, Von Wachter and Bender (2006) examine the effects of displacement on young apprentices in Germany. For this group, where we would expect rents to be small, they find an initial earnings loss of 10%, but this is reduced to zero after 5 years.

We also have a number of other studies looking at how the nature of displacement affects the size of earnings losses. Neal (1995), and Poletaev and Robinson (2008) show that workers who do not change industry or occupation or whose post-displacement job uses a similar mix of skills have much smaller earnings losses. This is as one would expect given what was said earlier about the reason for rents being the lack of an alternative employer who is a perfect substitute for the present one. Those displaced workers fortunate enough to find another job which is a close substitute for the one lost would be expected to have little or no earnings loss. But, the sizeable group of workers whose post-displacement job is not a perfect substitute for the one lost will suffer larger earnings losses. For example, Poletaev and Robinson (2008) estimated an average cost of displacement for all workers of 7% but the 25% of workers who switch to a job with a very different skill portfolio suffer losses of 15%. The fact that 25% of workers cannot find a new job that is a close match to their previous one suggests there are not a large number of employers offering jobs that are perfect substitutes for each other.

2.4 Conclusions

The methods discussed in this section can be used to give us ballpark estimates of the extent of imperfect competition in labor markets. They perhaps suggest total rents in the 15–30% range with, perhaps, most of the rents being on the worker side. However, one should acknowledge there is a lot of variation in rents and enormous uncertainty in these calculations. Because we have discussed estimates of the rents accruing to employers and workers, one might also think about using these estimates to give us some idea of how the rents are split between worker and employer. However, because none of the estimates come from the same employment relationship, that would be an unwise thing to do. The next section discusses models of the balance of power between employers and workers and these are reviewed in the next section.

3.1 Bargaining and posting

The two main approaches that have been taken to modeling wage determination in recent years are what we will call ex post wage-bargaining and ex ante wage-posting (though we briefly discuss others at the end of the section). In ex post wage-bargaining the wage is split after the worker and employer have been matched, according to some sharing rule, most commonly an asymmetric Nash bargain. In ex ante wage-posting the wage is set unilaterally by the employer before the worker and employer meet.

These two traditions have been used in very different ways. The bargaining models are the preferred models in macroeconomic applications (see Rogerson and Shimer, 2011) while microeconomic applications tend to use wage-posting⁸. But, what is often not very clear to students entering this area is why these differences in tradition have emerged and what are the consequences. Are these differences based on good reasons, bad reasons or no reasons at all? Here we try to provide an overview which, while simplistic, captures the most important differences.

Although the models used are almost always dynamic, the ideas can be captured in a very simple static model and that is what we do here. The simple static model derives from Hall and Lazear (1984) who discuss a wider set of wage-setting mechanisms than we do here. Assume that there are firms, which differ in their marginal productivity of labor, p. A firm is assumed to be able to employ only one worker.

In ex post wage-bargaining models, the wage in a match between a worker with leisure value b and a firm with productivity p is chosen to maximize an asymmetric Nash bargain:

(9)

leading to a wage equation:

(10)

where α can be thought of as the bargaining power of the worker, which is typically thought of as exogenous to the model. The match will be consummated whenever there is some surplus to be shared, i.e. whenever p ≥ b so that there is ex post efficiency. There will not necessarily be ex ante efficiency if worker or employer or both have to make investments ahead of a match, investments either in the probability of getting a match or in the size of rents when a match is made. For example, if α = 0 workers get no surplus from the employment relationship so would not invest any time in trying to find a job.

Now consider a wage-posting model in which employers set the wage before being matched with a worker. To derive the optimal wage in this case we need to make some assumption about the process by which workers and employers are matched—for the moment, assume that is random though alternatives are discussed below. And assume that workers differ in their value of leisure, b—denote the distribution function of this across workers by G(b).

If the firm sets a wage w, a worker will accept the offer if w > b, something that happens with probability G(w). So expected profits will be given by:

(11)

This leads to the following first-order condition for wages:

(12)

where ε is the elasticity of the function G with respect to its argument and the notation used reflects the fact that this elasticity will typically be endogenous. Higher productivity firms offer higher wages. An important distinction from ex post wage-bargaining is that not all ex post surplus is exploited—some matches with positive surplus (i.e. with p > b) may not be consummated because b > w. In matches that are consummated the rents are split between employers and workers, so employers are unable to extract all surplus from workers even though employers can unilaterally set wages.

In this model G(w) can be thought of as the labor supply curve facing the firm, in which case can think of it as a standard model of monopsony in which the labor supply to a firm is not perfectly elastic and (12) as the standard formula for the optimal wage of a monopsonist. There is a simple and familiar graphical representation of the decision-making problem for the firm—see Fig. 1. In contrast, there is no such simple representation for the outcome of the ex post wage-bargaining model⁹.

One might think that the two wage Eqs (10) and (12) are very different. But they can easily be made to look more similar. Suppose that the supply of labor can be written as:

(13)

where b₀ is now to be interpreted, not as a specific worker’s reservation wage, but as the lowest wage any worker will work for. Then the wage equation in (11) can be written as:

(14)

which is isomorphic to (9) with . In some sense, the bargaining power of workers in the wage-posting model is measured by the elasticity of the labor supply curve to the firm. However, note that the interpretation of the reservation wage in (10) and (14) is different—in (10) it is the individual worker’s reservation wage while in (14) it is the general level of reservation wages measured by the lowest in the market.

The assumption of random matching plays an important role in the nature of the wage-posting equilibrium so it is instructive to consider other models of the matching process. The main alternative to random matching is “directed search” (see, for example, Moen, 1997). Models of directed search typically assume that there is wage-posting but that all wage offers can be observed before workers decide on their applications.

Although models of directed search make the same assumption about the availability of information on wage offers as models of perfect competition (i.e. complete information), they do not assume that an application necessarily leads to a job, so there is typically some frictional unemployment in equilibrium caused by a coordination problem. So the expected utility of a worker applying to a particular firm is not just the wage, but needs to take account of the probability of getting a job. In the simplest model this expected utility must be equalized across jobs, giving the model a quasi-competitive feel, and it is perhaps then no surprise that the outcomes are efficient. The literature has evolved with different assumptions being made about the number of applications that can be made, what happens if workers get more than one job offer, what happens if the first worker offered a job does not want it (e.g. Albrecht et al., 2006; Galenianos and Kircher, 2009; Kircher, 2009). It would be helpful to have some general principles which help us understand the exact feature of these models that do and do not deliver efficiency.

3.2 The right model?

Rogerson et al. (2005, p. 984) conclude their survey of search models by writing that one of the unanswered questions is “what is the right model of wages?”, with the two models described above being the main contenders. If we wanted to choose between these two descriptions of the wage determination process, how would we do so? We might think about using theoretical or empirical arguments. As economists abhor unexploited surpluses, theory would seem to favor the ex post wage-bargaining models in which no match with positive surplus ever fails to be consummated¹⁰. One might expect that there would be renegotiation of the wage in a wage-posting model if p > b > w.

However, over a very long period of time, many economists have felt that this account is over-simplistic, that wages, for reasons that are not entirely understood, have some form of rigidity in them that prevents all surplus being extracted from the employment relationship. There are a number of possible reasons suggested for this. Hall and Lazear (1984) argue this is caused by informational imperfections while Ellingsen and Rosen (2003) argue that wage-posting represents a credible commitment not to negotiate wages with workers something that would cost resources and raise wages. There is also the feeling that workers care greatly about notions of fairness (e.g. see Mas, 2006) so that this makes it costly to vary wages for workers who see themselves as equals. There is also the point that if jobs were only ever destroyed when there was no surplus left to either side, there would be no useful distinction between quits and lay-offs, though most labor economists do think that distinction meaningful and workers losing their jobs are generally unhappy about it. The bottom line is that theory alone does not seem to resolve the argument about the “best” model of wage determination.

What about empirical evidence? In a recent paper Hall and Krueger (2008) use a survey to investigate the extent to which newly-hired workers felt the wage was a “take-it-or-leave-it” offer, as ex ante wage-posting models would suggest. All those who felt there was some scope for negotiation are regarded as being ex post wage-bargaining. They show that both institutions are common in the labor market, with negotiation being more prevalent. In low-skill labor markets wage-posting is more common than in high-skill labor markets, as perhaps intuition would suggest.

This direct attempt to get to the heart of the issue is interesting, informative and novel, but the classification is not without its problems. For example, some of those who report a non-negotiable wage may never have discovered that they had more ability to negotiate over the wage than the employer (successfully) gave them the impression there was. For example, Babcock and Laschever (2003) argue that women are less likely to negotiate wages than men and more likely to simply accept the first wage they are offered.

Similarly, there are potential problems with assuming that all those without stated ex ante wages represent cases of bargaining. For example, employers with all the bargaining power would like to act as a discriminating monopsonist tailoring their wage offer to the circumstances of the individual worker, not the simple monopsonist the wage-posting model assumes. Hall and Krueger (2008) are aware of this line of argument but argue it is not relevant because wage discrimination would result in all workers in the US being held to their reservation wage, a patently ridiculous claim. But, there is a big leap from saying some monopsonistic discrimination is practiced to saying it is done perfectly, so this argument is not completely compelling.

There is also the problem that the methodology used, while undoubtedly fascinating and insightful, primarily counts types of contract without looking at the economic consequences. For example, Lewis (1989, p. 149) describes how Salomon Brothers lost their most profitable bond-trader because of their refusal to break a company policy capping the salary they would pay. Undoubtedly, this contract should be described as individualistic wage-bargaining, but there were limits placed on that which resulted in some ex post surplus being lost as suggested by the wage-posting models.

One possible way of resolving these issues would be to look at outcomes. For example, ex post individualistic wage-bargaining would suggest, as from (10), that there would be considerable variation in wages within firms between workers with different reservation wages—see (10). On the other hand, ex ante wage-posting would suggest no wage variation within firms between workers with different reservation wages. Machin and Manning (2004) examine the structure of wages in a low-skill labor market, that of care workers in retirement homes. They find that, compared to all other characteristics of the workers, a much greater share of the total wage variation is between as opposed to within firms. Reservation wages are not observed directly, but we might expect to be correlated with those characteristics, so ex post wage-bargaining would predict correlations of wages with those variables¹¹.

One could spend an enormous amount of time debating the “right” model of wage determination. But we will probably never be able to resolve it because the labor market is very heterogeneous, so that no one single model fits all, so the question of “what is the right model?” is ill-posed. In fact, it is the very existence of rents that gives the breathing-space in the determination of wages in which the observed multiplicity of institutions can survive. In a perfectly competitive market an employer would have no choice but to pay the market wage and to deviate from that, even slightly, leads to disaster.

It is also worth reflecting that, in many regards, wage-bargaining and wage-posting models are quite similar (e.g. they both imply that rents are split between worker and employer) so that it may not make very much difference which model one uses as a modeling device. The main substantive issue in which they differ is in whether one thinks that all ex post surplus is extracted. But, because even ex post efficiency does not mean ex ante efficiency, this may not be such a big difference in practice. However, this is not to say that the choice of model has had no consequences for labor economics because too many economists see the labor market only through the prism of the labor market model with which they are most familiar.

For example, as illustrated above, a wage-posting model naturally leads one to think in terms of the elasticity of the labor supply curve to an individual firm and that one can represent the wage decision using the familiar diagram of Fig. 1. It is easy to forge links with other parts of labor economics, so it is perhaps not surprising that this has often been the model of choice for microeconomic models of imperfect competition in the labor market. It is much more difficult to forge such links with an ex post bargaining model and the literature that uses such models sometimes seems to have developed in a parallel universe to more conventional labor economics and has concentrated on macroeconomic applications.

3.3 Other perspectives on wage determination

I have described the two most commonly found models of wage determination. But just as I have emphasized that one should not be thought as obviously “better” than the other, so one should not assume that these are the only possibles. Here we simply review some of the others that can be found in the literature. We make no attempt to be exhaustive (e.g. see Hall and Lazear, 1984, for a discussion of a range of possibilities we do not discuss here).

The simple model sketched above only has workers moving into jobs from non-employment because it is a one-period model. In reality, over half of new recruits are from other jobs (Manning, 2003a; Nagypal, 2005) so that one has to think about how wages are determined when a worker has a choice between two employers.

In models with ex-post wage-bargaining, on-the-job search is a bit tricky to incorporate into standard models because it is not clear how to model the outcome of bargaining when workers have a choice of more than one employer, and different papers have taken different approaches, e.g. Pissarides (1994) assumes that the fall-back position for workers with two potential employers is unemployment while Cahuc et al. (2006) propose that the marginal product at the lower productivity firm be the outside option. Shimer (2006) points out that the value function for employed workers is typically convex in the wage when there is the possibility of moving to a higher-wage job in the future, and derives another bargaining solution, albeit one with many equilibria.

In contrast, models based on wage-posting do not find it hard to incorporate on-the-job search, as they typically simply assume that the worker accepts the higher of the two wage offers. But, they do find it difficult to explain why the employer about to lose a worker does not seek to retain them by raising wages. A number of papers look at the institution of offer-matching (Postel-Vinay and Robin, 2002) in which the two employers engage in Bertrand competition for the worker. However, many have felt that offer-matching is not very pervasive in labor markets and have offered reasons for why this might be the case (see, for example, the discussion in Hall and Lazear, 1984).

4.1 Estimates of rent-sharing

In a bargaining framework, we are interested in how wages respond to changes in the surplus in the employment relationship, i.e. to measure something like (10). There is a small empirical literature that seeks to estimate the responsiveness of wages to measures of rents. These studies differ in the theoretical foundation for the estimated equation, the way in which the rent-sharing equation is measured and the empirical methodology used.

The Eq. (10) was derived from a model of bargaining between a worker and employer where the bargaining relationship covers only one worker. But, there are alternative ways of deriving a similar equation from other models. For example, Abowd and Lemieux (1993) assume that the firm consists of a potentially variable number of workers with a revenue function F(N), and that the firm bargains with a union with preferences N(w – b) over both wages and employment, i.e. we have an efficient bargaining model (McDonald and Solow, 1981). That is, wages and employment are chosen to maximize:

(15)

One way of writing the first-order condition for wages in this maximization problem is:

(16)

i.e. wages are a weighted average of revenue per worker and reservation wages with the weight on revenue per worker being α. The similarities between (16) and (10) should be apparent as F(N)/N is the average productivity of labor. In this model employment will be set so that:

(17)

There are other models from which one can derive a similar-looking equation to (16), though we will not go into details here. For example, if one assumes that employment is chosen by the employer given the negotiated wage (what is sometimes called the right-to-manage or labor demand curve model—see, for example, Booth, 1995) or a more general set of ”union” preferences.

In all the specifications derived so far, it is a measure of revenue per worker or quasirents per worker put on the right-hand side. But, many studies write the wage equation in terms of profits per worker, i.e. take −αw from both sides of (16) and write it as:

(18)

In all these cases it should be apparent that the outcome of rent per worker or profit per worker is potentially endogenous to wages, so that OLS estimation of these equations is likely to lead to biased estimates. Hence, some instrument is used, and the obvious instrument is something that affects the revenue function for the individual firm but does not affect the wider labor market (here measured by b). Although revenue function shifters sound very plausible, it is not clear that they are good instruments. For example if the revenue function is Cobb-Douglas (so the elasticity of revenue with respect to employment is a constant) then the marginal revenue product of labor is proportional to the average revenue product and the employment equation in (17) makes clear the marginal revenue product will not be affected by variables that affect the revenue function. In this case shifts in the revenue function result in rises in employment such that rents per worker and wages are unchanged¹². The discussion in Abowd and Lemieux (1993, p. 987) is very good on this point. In cases close to this, instruments based on revenue function shifters will be weak. Many of the rent-sharing studies are from before the period when researchers were aware of the weak instrument problem (see Angrist and Pischke, 2008, for a discussion) and the instruments in some studies (e.g. Abowd and Lemieux, 1993) do not appear to be strong.

Some estimates of the rent-sharing parameter are shown in Table 4. In this table we have restricted attention to those that estimate an equation that is either in the form of (16) or (18) or can be readily transformed to it¹³. Table 4 briefly summarizes the data used in each study, the measure of rents or profits used, and the method (if any) used to deal with the endogeneity problem. In some studies the instruments are lags of various variables while others use exogenous shifts to demand, e.g. as caused by exchange rate movements. There are a couple of “case studies” of the impact of de-regulation in various industries.

What one would ideally like to measure is the effect of a change in rents in a single firm on wages in that firm. It is not clear whether that is what is being estimated. For example, several studies in Table 4 use industry profits as a measure of rents. If labor has any industry-specific aspect to it then a positive shock to industry profits would be expected to raise the demand for labor in a competitive market and, hence, raise the general level of wages (represented by b in the model above)¹⁴. If this is important one would expect that the estimates reported in Table 4 are biased upwards. And the studies that use firm-level profits or rents but instrument by industry demand shifters are potentially vulnerable to the same criticism.

The final column in Table 4 presents estimates of the α implied by the estimates. Most of these studies do not report an estimate of α directly (e.g. the dependent variable is normally in logs whereas the theoretical idea is in levels) so a conversion has taken place based on other information provided or approximations. For example if the equation is specified with the log of wages on the left-hand side and the log of profits on the right-hand side so that the reported coefficient is an elasticity then one needs to multiply by the ratio of wages to profits per head to get the implied estimate of α. If, for example the share of labor in value-added is 75% then one needs to multiply the coefficient by 3, while if it is 66% one needs to multiply by 2. In addition there is a wide variation in the reported ratio of wages to profit per head in the data sets used in the studies summarized in Table 4 from a minimum of 1.1 to a maximum of 5.3. Unsurprisingly this can make a very large difference to the estimates of α and this is reflected in Table 4. In addition, the difficulty in computing the “true” measure of profits or rents may also lead to considerable variation in estimates.

There are a number of studies (Christofides and Oswald, 1992; one of the samples in Hildreth and Oswald, 1997) where α is estimate to be close to zero, but a number of other estimates are in the region 0.2-0.25. Studies from Continental European countries—the Italian and Swedish studies of Arai (2003), Guiso et al. (2005) and Card et al. (2010)— are markedly lower—this might be explained by the wage-setting institutions in those countries where one might expect the influence of firm-level factors to be less important than in the US (see the neglected Teulings and Hartog, 1998, for further elaboration of this point) though there are also some methodological differences from the other studies. And the study of Rose (1987) also looks an outlier with an estimate of α around 0.7. However, this estimate is derived using some back-of-the-envelope calculations and is for a very specific industry so may not be representative. It is worth remarking that all of these studies suggest that most rents accrue to employers, not workers while the direct estimates of the size of rents accruing to employer and workers in previous sections perhaps suggested the opposite. That is an issue that needs to be resolved.

The estimates of α discussed so far have all been derived from microeconomic studies. But the rent-splitting parameter also plays an important role in macroeconomic models of the labor market, and such studies often use a particular value. It has been common to assume the rent-splitting parameter is set to satisfy the Hosios condition for efficiency (often around 0.4), though no convincing reason for that is given, sometimes calibrated or estimated to help to explain some aspects of labor market data (and Hagedorn and Manovskii, 2008 suggest a value of 0.05 based on some of the studies reported in Table 4). A recent development (e.g. Pissarides, 2009; Elsby and Michaels, 2008) has been to argue that there is an important difference between the sensitivity of the wages of new hires and continuing workers to labor market conditions. The micro studies reviewed in Table 4 have not pursued this dimension.

Many of the studies summarized in Table 4 are of unionized firms, motivated by the idea that non-union firms are much less likely to have rent-sharing. Although a perspective that there are pervasive rents in the labor market would lead one to expect that even non-union workers get a share of the rents, one might expect unions to be institutions better-able to extract rents for workers, so that one would estimate a higher α in the union sector. But the few studies that distinguish between union and non-union sectors (e.g. Blanchflower et al., 1996, 1990¹⁵) often find that, if anything, the estimate of α is larger in the non-union sector. However, this is what one might expect from a wageposting perspective, because a union setting a take-it-or-leave-it wage makes the labor supply to a firm more wage elastic (like the minimum wage) than that faced by a nonunion firm. Hence, one then predicts one would find a higher rent-sharing parameter in the non-union sector. This leads on to estimates of rent-sharing based on the elasticity of the labor supply curve to employers.

4.2 The elasticity of the labor supply curve to an individual employer

As the formula in (12) makes clear, a wage-posting model would suggest that it is the elasticity of the labor supply curve facing the employer that determines how rents are split between worker and employer. This section reviews estimates of that elasticity. An ideal experiment that one would like to run to estimate the elasticity of the labor supply curve to a single firm would be to randomly vary the wage paid by the single firm and observe what happens to employment. As yet, the literature does not have a study of such an experiment.

What we do have are a number of quasi-experiments where there have been wage rises in some firms—these are summarized in Table 5. Typically those experiments have been of public sector firms where there have been perceived to be labor shortages because wages have been set below prevailing market levels. So, they sound like the type of situation where one would expect to be tracing out the elasticity of a labor supply curve.

Staiger et al. (2010) examine the impact of a legislated rise in the wages paid at Veteran Affairs hospitals. They estimate the short-run elasticity in the labor supply to the firm to be very low (around 0.1), implying an enormous amount of monopsony power possessed by hospitals over their nurses. Falch (2010a) investigates the impact on the supply of teachers to individual schools in northern Norway in response to a policy experiment that selectively raised wages in some schools with past recruitment difficulties. He reports an elasticity in the supply of labor to individual firms in the region 1.0-1.9—higher than the Staiger et al study, but still very low.

Looking at these studies, one clearly comes away with the impression not that it is hard to find evidence of monopsony power but that the estimates are so enormous to be an embarrassment even for those who believe this is the right approach to labor markets. The wage elasticities are too large to be credible.

This means it makes sense to reflect on possible biases. There are a number of possibilities that come to mind. First, some of these studies only look at the response of employment to wage changes over a relatively small time horizon. As one would expect supply elasticities to be smaller in the short-run, these estimates are not reliable as estimates of the long-run elasticity. There is a simple back-of-the-envelope rule that can be used to link short-run and long-run elasticities. Boal and Ransom (1997) and Manning (2003a, chapter 2) show that if the following simple model is used for the supply of labor to a firm:

(19)

where s(w) is the separation rate and R(w) is the recruitment rate, then there is the following relationship between the short-run and long-run elasticities:

(20)

So one needs to divide the short-run elasticity by the quit rate to get an estimate of the long-run elasticity. If, for example, labor turnover rates are about 20% then one needs to multiply the estimates of short-run elasticities by 5 to get a better estimate of the long-run elasticity.

A second issue is whether the wage premia are expected to be temporary or permanent. If they are only temporary then one would not expect to see such a large supply response. In this regard, it is reasonable to think of the wage increases studied by Staiger et al. (2010) as permanent, those studied by Falch (2010a) as temporary. It is not clear whether an argument that the wage premia were viewed as only temporary are plausible as explanations of the low labor supply elasticities found.

Here, I suggest that there is another, as yet unrecognized, problem with these estimates of labor supply elasticities. The reason for believing this comes from thinking about estimates of the labor supply elasticities from an alternative experiment—force an employer to raise its employment level and watch what happens to the wages that they pay. This is what is analyzed by Matsudaira (2009) who analyzes the effect of a 1999 California law that required all licensed nursing homes to maintain a minimum number of hours of nurses per patient. This can be thought of as a mandated increase in the level of employment.

According the simplest models of monopsony in which there is a one-to-one relationship between wages and labor supply to the firm, the wage response to the mandated employment increase should give us an estimate of the inverse of the wage elasticity. If the studies of mandated wage increases cited above are correct and the labor supply elasticity is very small, we should see very large wage increases in response to mandated employment changes. This is especially true if the short-run elasticity is very low. In fact, Matsudaira finds that firms that were particularly affected by the mandated increased in employment did not raise their wages relative to other firms who were not affected. As a result, the labor supply to the employer appears very elastic, seemingly inconsistent with studies of mandated wage increases. It is possible that, as these are studies of different labor markets there is no apparent inconsistency but I would suggest that is not the most likely explanation and that the real explanation is a problem with the simple model of monopsony.

How can we reconcile these apparently conflicting findings? The problem with the simple-minded model of monopsony is that it assumes that the only way an employer can raise employment is by raising its wage. A moment’s reflection should persuade us that this is not very plausible. There are a number of possible reasons for this—I will concentrate on one in some detail and then mention others.

We have already seen that hiring costs money and used estimates of these hiring costs to shed light on the size of employer rents from the employment relationship. If employers want to hire more workers, they can spend more resources on trying to recruit workers, e.g. advertising vacancies more frequently or extensively. Hence, the supply of workers to the firm will then be a function not just of the wage but also of the expenditure on recruitment. This model is examined in Manning (2006), who terms it the “generalized model of monopsony” and it can easily explain the paradox described above.

To see how it can do this assume there are constant marginal hiring costs, h(w), which might depend on the wage. If the separation rate is s(w) a flow of s(w)N recruits is necessary for the employer to maintain employment at N which will cost s(w)h(w)N. This represents the per period expenditure on recruitment necessary to keep employment at N if the wage paid is w. Note that, unlike the simple monopsony model, any level of employment is compatible with any level of the wage but that there are associated recruitment costs. If, in the interests of simplicity, we ignore discounting (the recruitment costs of a worker must be paid up-front but profits accrue in the future), the profits of the firm can be written as:

(21)

First, consider the choices of wage and employment by an unconstrained profit-maximizing firm. The wage will be chosen to satisfy the first-order condition:

(22)

Denote this choice by w*. The first-order condition for employment will then be:

(23)

Now, consider what happens in this model when we mandate wages or mandate employment. Consider, mandated employment first, as in the Matsudaira paper. If the government requires an increase in employment, the optimal thing for the firm to do is to increase recruitment activity—the optimal wage (22) remains completely unchanged. This is, to a first approximation, what Matsudaira finds. However, it tells us nothing about the degree of imperfect competition in the labor market which is related to the elasticity of separation rates and recruitment with respect to the wage.

Now consider a mandated increase in the wage. This reduces separations and may reduce the marginal cost of recruitment. But, if it is a small increase from the optimal wage the first-order effect will be to leave employment unchanged—the employer responds by reducing recruitment expenditure. One might explain the small positive effects on employment found in the literature as being the result of mandated wage increases in public sector firms where wages had been held artificially low.

In the generalized model of monopsony, the two experiments of mandated wage or employment increases are no longer mirror images of each other. A rise in mandated wages which, ceteris paribus, leads to a rise in labor supply to the firm could be met with an off-setting fall in recruitment activity, leaving overall employment unchanged. On the other hand, a rise in mandated employment may be met with a rise in recruitment activity to generate the extra supply with no increase in wages. This can be understood with Fig. 2. Starting from an initial position the line labelled “mandated wage” rise tells us how employment will change if the firm is forced to raise wages. This suggests a low elasticity of supply. The line labelled “mandated employment” rise tells us how wages will change when the firm is forced to raise employment—this suggests a high elasticity of labor supply.

We have used a very simple model to break the one-to-one link between wages and employment found in the standard model of monopsony. The change is plausible but does substantially affect how one interprets the empirical results of estimates of the effects of raising wages on employment (or vice versa). This is not the only way in which one might seek to reconcile these conflicting empirical findings. Another alternative is to assume that workers are heterogeneous in terms of quality so that employers also face an intensive margin in deciding the cut-off quality level for workers. Employers do not simply accept all workers who apply—they reject those they deem of poor quality, and how poor one has to be to be rejected is clearly endogenous. An example in Appendix B shows how, if the distribution of worker ability in the applicant pool is exponential then firms respond to mandated wage increases by increasing worker quality and not employment, and to mandated employment increases by reducing worker quality and not increasing wages. It also shows how a model with non-wage aspects of work can deliver the same conclusion.

All of these quasi-experimental studies described above are studies of mandated changes to wages or employment which might be thought to force employers to move along their labor supply curves. But, another empirical strategy is to consider changes in variables which induce moves along the labor supply curve. To identify the labor supply curve (which is all we want here) a variable that shifts the MRPL curve without shifting the supply curve is needed. One can then use this as an instrument for the wage or employment (depending on which way round we are estimating the supply curve) in estimating the supply curve. But, of course, it requires us to be able to provide such an instrument.

If one is interested in estimating the elasticity of labor supply to an individual firm then the instrument needs to be something that affects the demand curve for that firm but has negligible impact on the labor market as a whole. The reason is that a pervasive labor market demand shock will raise the general level of wages, so is likely to affect the labor supply to an individual firm. So, for example, the approach of using demand shocks caused by exchange rate fluctuations (as in Abowd and Lemieux, 1993) does not seem viable here. Sullivan (1989) uses the population in the area surrounding the hospital as an instrument affecting the demand for nurses This is a serious attempt to deal with a difficult problem, but their instruments are not beyond criticism. If the main variation in the number of children or the number of patients comes from variation in population it is also likely that the supply of nurses in an area is proportional to population as well.

The studies reviewed in this section do provide us with the best estimates we have of how employers respond to mandated wage and employment changes. But, as has been made clear, they probably do not tell us about the wage elasticity of the labor supply to an individual firm, which was the original motivation. How we might estimate that elasticity is the subject of the next section.

4.3 The sensitivity of separations to wages

This section reviews estimates of the sensitivity of separations to wages. Although this might be thought a topic of interest in its own right, we include it here because such studies might shed some light on the elasticity of the labor supply curve to individual employers. Why this might be thought useful can be explained very simply. Suppose that the flow of recruits to a firm is R(w), that this dependent only on the wage (an assumption we relax below where we allow for recruits to also be affected by recruitment expenditure) and the separation rate is s(w) also dependent on the wage. In a steady-state, recruits must equal separations, which leads to:

(24)

As pointed out by Card and Krueger (1995), this implies that:

(25)

so that knowledge of the elasticities of recruitment and quits with respect to the wage can be used to estimate the elasticity of labor supply facing the firm. The elasticity of separations with respect to the wage is important here but so is the elasticity of recruits with respect to the wage. However, as discussed below there are arguments for linking the two. But, before discussing that argument, let us discuss estimates of the sensitivity of separations with respect to the wage.

There is a long tradition of being interested in the sensitivity of labor turnover to the wage, quite apart from any insight these studies might have for the extent of imperfect competition in the labor market. These studies are not confined to economics, e.g. see Griffeth et al. (2000) for a meta-analysis from the management literature. The bottom line is that, as predicted by models of imperfect competition, a robust negative correlation between the wages paid and labor turnover is generally found, so that the vast majority (though not all) of the studies reported below do find a significant link between separations and wages.

4.4 Measuring labor market frictions

We conclude this section with a discussion of a very different approach to measuring the degree of rent-splitting. A simple yet plausible idea is that the higher the degree of competition among employers for workers, the greater will be workers’ share of the surplus. In the important and influential strand of work that sees rents in the labor market as deriving primarily from labor market frictions, the fact that it takes time for workers and employers to find each other, a natural way to capture this idea is to seek some measure of transition rates between employment and non-employment and from one employer to another.

One particular measure that has been used in the literature is the ratio of the arrival rate of job offers for an employed worker (denote this by λ_e) to the rate at which workers leave employment for non-employment (denote this by δ). We will denote this ratio by k. A higher value of k is more competition among employers for workers, which would be expected to raise wages. In many canonical search models e.g. Burdett and Mortensen (1998), the share of rents going to the workers can be shown to be some function of k. It can be interpreted as the expected number of job offers a worker will receive in a spell of employment (Ridder and van den Berg, 2003).

There are a lot of measures of k in the literature, with a large degree of variation. Often these estimates come from the estimation of structural models in which it is not entirely clear which features of the data play the most important role in influencing the estimates. Here, we will simply describe ways in which k can be estimated directly using data on labor market transition rates.

δ can be estimated very simply using data on the rate at which the employed leave for non-employment. λ_e is more complicated, as the theoretical concept is the rate at which job opportunities arrive to the employed. One might think about simply using the job-to-job transition rate, but as the employed only move jobs when the new offer is better than the current one, this is an under-estimate of the rate at which new job opportunities arise. However, in simple search models there is a mapping between the two. The reason is that if all workers always prefer high-wage to low-wage jobs and always move whenever they get a higher wage offer (however small the wage gain), then there is a simple expression for the fraction of workers G(f) who are in jobs at or below position f in the wage offer distribution. Equating inflows and outflows we have that:

(48)

where u is the unemployment rate. As, in steady-state we must have that:

(49)

(48) can be written as:

(50)

Now the transition rate to unemployment rate is δ and the transition rate to other jobs is:

(51)

which means that the ratio of transition rates to employment relative to transition rates to non-employment is given by:

(52)

This is monotonically increasing in k. In a steady-state this can be shown to be equal to the fraction of recruits who come from unemployment, a measure proposed by Manning (2003a).

One might wonder about the relationship between k and estimates of the labor supply elasticity discussed earlier in this section. In many search models there is a simple connection between the two because one can always write the profit-maximizing choice of the wage as being related to the elasticity of the labor supply curve to the firm so that k must be related to this. However, if, for example, one relaxed the assumption that it is only current or future wages that motivate job changes, then k would not seem to be a good measure of the market power of employers while an estimate of the wage elasticity still gets to the heart of the issue.

How do estimates of the balance of power between workers and employers based on this methodology compare to those based on the wage elasticity of the labor supply curve (or separations)? The advantage is perhaps that they are relatively easy to compute with nothing more than data on labor market transitions, but the disadvantage is that they are indirect (not requiring any data on actual wages) and may rely for their validity on assumptions that do not hold. For example, in these models perfect competition is the case where there is massive churning of workers, where the employer you work for one day (or hour?) has no bearing on who you work for the next. In some sense, that is a correct characterization of a perfectly competitive equilibrium, as that determines the market wage but not who of the large number of identical employers a worker works for, which is indeterminate. But, the inclusion of even a small fixed cost of changing jobs would change the prediction to one of very little turnover in an equilibrium close to perfect competition. Secondly, there is good reason to believe that not all turnover is for wage gains, which is what is relevant for employers deciding on the wage to pay. The one empirical application (Hirsch and Schumacher, 2005) does not find this measure works well in explaining variation in nurse pay across US cities.

4.5 Conclusions

This section has reviewed estimates we have of the distribution of rents in the typical employment relationship. These estimates do suggest the existence of non-trivial rents in the employment relationship. However, it is not completely clear that they are internally consistent. For example, the estimates of the rent-splitting parameter would suggest that most of the rents go to the employer. However the estimates from the actual size of rents probably suggest the workers getting most of the rents. Clearly, there is more work to be done here. While the importance of imperfect competition in labor markets might be regarded as intrinsically interesting, one still has to deal with the “so what?” question, what difference does this make to how one thinks about labor markets.

6.1 The law of one wage

In a perfectly competitive market, the elasticity of labor supply to a single firm is perfectly elastic at the market wage for that type of worker²³. Any attempt to pay a lower wage will result in a complete inability to recruit any workers at all, while any higher wage simply serves to reduce profits. As a result, all employers who employ this type of worker will pay them the same wage—the law of one wage holds. And all workers of that quality will be paid the same wage, irrespective of their reservation wage.

Those who have studied actual labor markets have often observed that the law of one wage seems to be violated, that there is, to use the jargon, equilibrium wage dispersion. Such a conclusion can be found from studies dating back to the late 1940s (e.g. Reynolds, 1946; Lester, 1946; Slichter, 1950) but more recent empirical studies all come to much the same conclusion. The existence of equilibrium wage dispersion requires some degree of imperfect competition in labor markets.

In models of imperfect competition that are based on ex post wage-bargaining, it is simple to explain the existence of equilibrium wage dispersion. Refer back to the wage Eq. (10)—this has wages depending on the specific productivity of that employer and the specific reservation wage of the worker, something that should not happen in a perfectly competitive labor market²⁴.

In wage-posting models the most celebrated paper is Burdett and Mortensen (1998). They present a model with homogeneous workers and employers in which the only possible equilibrium is a wage distribution with no mass points. While that is an elegant and striking result, there is a very good reason for thinking it is deficient as an account of the origin of equilibrium wage dispersion. The reason is that one can track the result to an assumption of the model, which is very unappealing as an assumption about the real world and, if this assumption is made more realistic, the result collapses. That assumption is that all workers will move for the smallest gain in wages. How this delivers equilibrium wage dispersion as the only possible equilibrium can be explained with a simple diagram. Think about the labor supply curve facing an individual employer in which there is a mass of firms paying some wage w₀. The labor supply curve will be discontinuous at this point so looks something like that drawn in Fig. 3. No profit-maximizing employer would then want to pay the wage w₀—they would rather pay something infinitesimally higher and get a lot more workers. The mass point will unravel.

But the assumption that all workers move for the smallest gain in wages is totally implausible, so this is not a credible account of the origin of equilibrium wage dispersion. Furthermore, we do observe mass points of wages at, for example, the minimum wage and round numbers. Does this mean this type of model has no credible explanation of equilibrium wage dispersion? Far from it—the simplest and most plausible explanation is that, faced with the same labor supply curve that is always continuous in the wage, heterogeneous employers will choose to locate at different points on that supply curve. As put succinctly by Mortensen (2003, p. 6) “wage dispersion is largely the consequence of search friction and cross-firm differences in factor productivity”.

The failure of the law of one wage in labor markets has important consequences, some of which we will discuss below. It means that achieving a higher level of earnings is, in part, the result of working oneselfinto the best jobs, but that the outcome of this process will contain a considerable element of luck.

6.2 Labor market regulation

If labor markets are perfectly competitive then we know that the equilibrium will be Pareto efficient and that regulation can only be justified on distributive and not efficiency grounds. If labor markets are imperfectly competitive there is no such presumption that the market is efficient and there is at least the potential for some regulation to improve efficiency.

The labor market regulation that has received the most attention is the minimum wage. If the labor market is perfectly competitive then a minimum wage must reduce employment, as it raises the cost of labor. However, this is not necessarily the case if the labor market is imperfectly competitive. To illustrate this, we will consider the case of monopsony, though one could do the same with a matching-style model.

In the simplest model of monopsony, in which there is a single employer and the wage is the only available instrument for influencing its labor supply, there is a very simple formula relating the minimum wage to the elasticity of the labor supply to an individual employer. As we have emphasized that the labor supply to individual firms is not very sensitive to the wage, this would suggest very large potential rises in employment could be obtained from an artfully chosen minimum wage.

However, there are at least two important reasons for why such a conclusion is likely to be misleading. First, we have emphasized how the simple model of monopsony is not the best way to think about the labor market. Secondly, the model of market power we have used is a model of a single employer that ignores interactions between employers, so is only a partial equilibrium analysis.

Let’s consider the first point first. Take the model of the previous section in which the labor supply curve is given by (35) and can be influenced not just by the wage paid but also by the level of recruitment activity. To keep things simple assume the marginal revenue product of labor is constant and equal to p. First, consider the optimal employment level given the wage paid. This satisfies the first-order condition:

(53)

Re-arranging leads to the following “labor demand curve”:

(54)

Assume, again, that n(w) is iso-elastic with elasticity ε. If the employer has a free choice of the wage we know they will choose a wage like (38). First, consider the minimum wage that will maximize employment, i.e. the wage that maximizes (54). It is easy to show that this is given by:

(55)

The important point is that this is bigger than the wage that the employer will choose for itself, which will be given by:

(56)

where the “m” superscript denotes the choice of a monopsonist. The log difference between the free market wage and the employment-maximizing wage is hence given by:

(57)

Now consider the gain in employment from an artfully chosen minimum wage. Using (54) and the wage Eqs (55) and (56), one can show that this is given by:

(58)

The standard monopsony case corresponds to the case where β = 0. This leads to the prediction of very large potential employment gains from an artfully-chosen minimum wage, e.g. even a high wage elasticity of 5 leads to a predicted employment gain of 91 log points from a wage rise of 18 log points. But if β = 0.8 this is much lower—a predicted employment gain of 9 log points from a wage rise of 3.3 log points.

The important point to note is that, unlike the simple model of monopsony, the potential gains from the minimum wage are not just influenced by the wage elasticity ε but also the parameter β, which is the relationship between average and marginal costs of hiring.

This is a partial equilibrium conclusion and not a reliable guide for policy. There are two important distinctions between partial equilibrium models of monopsony and general equilibrium models of oligopsony. First, in general equilibrium there is an important distinction between the elasticity of labor supply to the market as a whole and to individual employers. While the gap between marginal product and the wage is determined by the elasticity of the labor supply curve facing an individual employer, any employment effect will be determined by the elasticity of the labor supply curve to the labor market as a whole. There is no reason why these should be the same but it is exactly that assumption that is made by the model of a single monopsonist.

Secondly, it is important to take account of heterogeneity. There is no doubt that the minimum wage is a blunt instrument, applied across whole labor markets on employers who would otherwise choose very different wages. This means that it is almost certainly the case that the minimum wage will have different effects on employment in different employers and any measure of the impact on aggregate employment must take account of this heterogeneity. Manning (2003a, chapter 12) takes account of both these effects, showing that even in a labor market in which all employers have some market power, a minimum wage, however low, may always reduce employment.

However, models of imperfect competition are different from models of perfect competition in not making a clear-cut prediction about the employment consequences of raising the minimum wage. It is empirical studies that are important and, though this is a long debate which will not be surveyed here (see Brown, 1999, for an earlier survey), recent studies with good research designs typically fail to find any negative effects on employment for the moderate levels of minimum wages set in the US (Dube, Lester and Reich, forthcoming; Giuliano, 2009).

Although the employment effect of minimum wages has become the canonical issue in wider debates about the pros and cons of regulating labor markets, one should also recognize that models of imperfect competition in the labor market often have different predictions from competitive models about many interventions. For example, one can show that regulation to restrict aspects of labor contracts like hours or holidays can improve employment (Manning, 2003a, chapter 8). However, although imperfect competition can be used as a justification for some regulation on efficiency grounds, it always predicts some limits to regulation, with quite what those limits are left to empirical research to decide.

6.3 The gender pay gap

When Joan Robinson (1933) invented the term monopsony she used it as a potential explanation of the gender pay gap. If the labor supply of women to a firm is less elastic than that of men, then a profit-maximizing employer will choose to pay lower wages to women than men even if they have the same productivity.

A recent literature essentially builds on that observation to explain at least part of the gender pay gap. The main approach has been to see whether the separation elasticity of women is lower than that of men and then apply the logic outlined in Sections 4.3.1 and 4.3.2 to argue that this can explain some of the gender pay gap. A priori this sounds a plausible idea, as women do report that non-wage attributes are more important in their choice of a job and that they are more restricted by domestic commitments in the employment they can accept. However, this conclusion does not pop out of all the estimates. Some studies that estimate distinct separation elasticities for men and women (e.g. Barth and Dale-Olsen, 2009; Hirsch et al., 2010; Ransom and Oaxaca, 2010) do report estimates suggesting that female separation elasticities are lower than the male but this is not true of all studies (e.g. it is not true for any of the four data sets examined in Manning, 2003a, chapter 6). Perhaps worryingly, Barth and Dale-Olsen (2009) report that the estimates are sensitive to the specification used, arguing that, in their data, better specifications do deliver the conclusion that the female elasticity is below the male.

It is important to realize that a difference in separation elasticity is not necessary for models of imperfect competition to be able to explain the gender pay gap. Nor is actual wage discrimination by employers. It could simply be that women are more likely to interrupt their careers with spells of non-employment, primarily to look after young children. In a labor market where the law of one wage does not hold, this will reduce the ability of women to work themselves into and remain in the best-paying jobs. Several recent studies of the gender pay gap find that career interruptions can explain a sizeable proportion (Bertrand et al., 2009). While the most common explanation for this is that those with career interruptions accumulate less human capital, the size of the pay penalty for even small interruptions seem very large. It is not surprising that career interruptions reduce wages, but is the penalty proportionate? Research in this area needs to answer this question.

Finally, mention should be made of the effects of equal pay legislation. In the US, equal pay legislation did not seem to have an immediate effect on the gender pay gap. But, in some other countries (e.g. the UK and Australia) there was a very clear fall in the gender pay gap associated with the passing of the legislation. This change in relative wages was far more dramatic than the wage changes induced by rises in the minimum wage. If the labor market was perfectly competitive, we would expect this legislated rise in the relative wage of women to result in a fall in their relative employment. Yet, this is not what seemed to happen and Manning (1996) argues this is because the labor market has monopsonistic elements.

6.4 Economic geography

Much of economic geography is about explaining the distribution of economic activity over space—in particular, why it is so uneven, the phenomenon of agglomeration. There are many theories of agglomeration which are not reviewed here. The current literature on agglomeration tends to focus on the product market more than the labor market—but there is considerable useful research that could be done on labor market explanations.

In his classic discussion of agglomeration, Alfred Marshall (1920) speculated about possible labor market explanations, e.g. “a localized industry gains a great advantage from the fact that it offers a constant market for skill. Employers are apt to resort to any place where they are likely to find a good choice of workers with the special skill which they require; while men seeking employment naturally go to places where there are many employers who need such a skill as theirs and where therefore it is likely to find a good market. The owner of an isolated factory, even if he has access to a plentiful supply of general labor, is often put to great shifts for want of some special skilled labor; and a skilled workman, when thrown out of employment in it, has no easy refuge”.

The important point is these arguments make little sense if the labor market is perfectly competitive. In such a market the prevailing wage conveys all the information a firm or worker needs to know about the labor market²⁵. In a perfectly competitive labor market, an employer who is small in relation to the whole market will not care about the total supply of labor to the market except insofar as it affects the prevailing level of wages. Hence, to make any sense of Marshall’s arguments, one would seem to require some degree of imperfect competition in labor markets. The formalization of Marshall’s “labor pools” theory in Krugman (1991) rests explicitly on there being a small number of employers in the labor market.

Once the labor market is monopsonistic, one can begin to make sense of some of Marshall’s arguments for agglomeration. If the labor supply curve to an individual employer is upward-sloping it makes sense to talk about a labor supply curve being “further out” because of a generally high supply of labor. One might think that monopsony models would struggle to explain agglomeration because it might be thought that an employer would like to be the only employer in an area because they would then have enormous monopsony power over the workers in that area. But that is based on a misunderstanding. Although the degree of monopsony power over the workers in an area will be high, there will be few of them and this is not to the advantage of an employer. Fig. 4 conveys this very simply. It draws two labor markets, one (the “village”) in which there are very few workers but over whom the employer has a lot of monopsony power so the labor supply curve is very inelastic. In the other (the “city’), there are more workers but less monopsony power. In which labor market will the employer choose to locate? They will choose the market where the level of employment they desire can be obtained most cheaply. So, if the desired level of employment is low, they will choose the village, while if it is high they will choose the city. Manning (forthcoming) uses this idea to explain the existence of agglomeration with employers who desire to be small locating in rural areas where they have more monopsony power and large employers locating in urban areas. And Overman and Puga (2009) investigate the implication that firms with more volatile employment will want to locate where the labor supply curve is more elastic.

Another aspect of spatial economics that has received some attention is the estimation of commuting costs. From the perspective of a perfectly competitive labor market, one would expect workers to be fully compensated for a longer commute so that the costs of commuting can be estimated using an earnings function with the commute as an explanatory variable. But, in a labor market with frictions, we would not expect full compensation for a long commute (see Hwang et al., 1998; Manning, 2003b) so that this approach will under-estimate the cost of recruiting. An alternative approach is to use a method based on job search that worker separation rates will be based on the utility in the job and that one can get some idea of the costs of commuting by examining how wages and commute affect separations (Manning, 2003b; Van Ommeren et al., 2000). These studies often suggest a higher commuting cost, with potentially important implications for transport planning and regional development policies.

6.5 Human capital accumulation and training

Imperfection in labor markets has important implications for the incentives to acquire human capital and make investments to raise productivity. As shown by Acemoglu (1998), part of the returns to investments by workers in general human capital can be expected to accrue to future employers of the worker as the wage will be below the marginal product—this is very different from the prediction of Becker (1993) that all of the returns to general human capital will accrue to workers. The argument that workers do not fully capture the returns to investment in human capital could be used to provide a justification for the massive level of public subsidy to education that is a marked feature of all the richest economies.

Imperfect labor markets can also offer an explanation for why firms often seem to pay for the acquisition of general training by their workers—explaining this is a major problem for those who believe the labor market to be perfectly competitive. A series of papers by Acemoglu and Pischke (1998, 1999a,b) outline the theory, emphasizing the role of ”wage compression” and provide some evidence in support of that theory. They conclude that “labour market imperfections have to be an ingredient of any model attempting to understand why firms pay for general training (Acemoglu and Pischke, 1999a, p. F139).

Some other papers have found evidence supportive of their ideas. For example, Booth et al. (2004) examine the effect of the UK National Minimum Wage on training, concluding that there is no evidence it reduced the training of the affected workers (as a perfectly competitive model would predict) and some evidence that training increased. Benson (2009) investigates the reason why many hospitals sponsor students to train as nurses in local nursing schools. In a perfectly competitive labor market, this behavior would not make sense, as it is a subsidy to general training. But, in a monopsonistic labor market one can explain it as a desire of a local employer to increase its supply of labor if, as seems plausible and can be verified from the data, nurses are likely to remain in the area in which they trained. But the incentives for hospitals to subsidize nurse-training are higher where the hospital represents a higher share of nurse employment. In labor markets where there are several hospitals one might expect them to subsidize joint programs, as they have a collective interest in increasing nurse supply. Benson (2009) claims to find evidence for these predictions.

6.6 Conclusion

The list of issues, where the perspective of imperfect competition might be thought to make a difference, given above is far from exhaustive. Another chapter in this Handbook (Rogerson and Shimer, 2011) discusses potential insights of interest to macroeconomists. But there are many other labor market phenomena where imperfect competition might be thought to offer plausible explanations. Examples include the growth in wages over the life-cycle as workers try to exploit the wage dispersion in the labor market, the earnings assimilation of immigrants. Brown et al. (2008) and Hotchkiss and Quispe-Agnoli (2009) argue that monopsony can be used to explain why undocumented workers earn lower wages while the firms that employ them seem to make more profits.

What this section should have made clear is that the perspective that labor markets are pervasively imperfectly competitive has important implications for “big” questions, about the desirability and impact of labor market regulation, about the gender pay gap and about decisions about human capital accumulation. It is simply not true to claim that the perspective of perfect competition tells us all we need to know.