The Role of Headhunters in Wage Inequality: It's All about Matching

Transcription

1 The Role of Headhunters in Wage Inequality: It's All about Matching Alexey Gorn February 11, 2016 Abstract Wage inequality increased dramatically in Anglo-Saxon countries during the last thirty years, being driven by the sharp increase of top wages. This paper relates the observed increase in the top wages to increased assortativeness of the matches between workers and rms, especially on the top. Matching between workers and rms is aected by labor market frictions and abilities of workers to search on-the-job. Matching technology for the top workers and rms changes over time, that is demonstrated by the increased importance of the headhunters in the labor market. Headhunters improve screening of workers and allow workers to search on-the-job easier, improving matches and increasing top wages. This eect is illustrated by a theoretical model that incorporates the main features of headhunter industry in a standard labor market framework a la Diamond-Mortensen-Pissarides. Change in the matching technology in the model alone accounts for 30-50% increase of the top 1% wage share in the US and for 50-95% of the increase in the 10% wage share. The paper also provides empirical evidence that the top wage shares were rising faster in the countries where the normalized fee revenues and the number of hires of headhunters were higher. Keywords: wage dispersion, top incomes, sorting, on-the-job search, headhunters JEL codes: E24, D83, C78, J24, J62, J63 Bocconi University, alexey.gorn@phd.unibocconi.it I gratefully acknowledge nancing by Fondazione CARIPLO Thesis Research Grant 1

2 1 Introduction Wage inequality was increasing steadily from the early 1970s in the United States, United Kingdom and Canada, while it increased only slightly in most countries in Continental Europe over the same period 1. The top 1% wage share rose from 5.1% in 1970s to 10.9% in 2010 in the US, while it was around 6-7% in France over the whole period (see Figure 1 2 ). And top 10% share increased from 25.7% to 34.5% in the US and stayed around 25-27% in France. Moreover, this increase in wage inequality has a substantial impact on the income inequality in the same countries. Top 10% income share in the US increased from less than 35% in 1970s to more than 45% in 2010 (by around 15%). So, the increase in the wage inequality accounts for around two thirds of the overall increase in income inequality. Despite the importance of wage inequality, existing explanations of the increase in the wage inequality fail to or explain only a part of the sharp increase in top wages and have diculties addressing the cross-country dierences (see for example the discussion in Piketty, 2014). This paper attempts to contribute to the existing explanations by adding a separate channel for hiring high-skilled workers into the standard model of labor market a la Diamond, Mortensen and Pissarides. The separate channel is motivated by the increasing role of headhunters in the labor markets of Anglo-Saxon countries, especially in the top wages segment (see Figure 2). Suppose that there are worker's skill and rm's productivity level complementarities (i.e. the production function is supermodular). In this case the wage of a high-skilled worker in a good rm is more than proportional to the wage of the same worker in a bad rm (comparing to the dierence of a less skilled worker in the same rms). Now, when high-skilled workers and high-productive rms have a separate channel to meet, the wages of highly skilled workers will increase with respect to the rest of the workers (because of complementarities) and the wage inequality will rise. So, the new channel improves sorting between workers and rms on the very top, increasing top wages. Calibrated version of the model is able to explain between 30 and 50% of the increase of top 1% wage share and between 50 and 95% of the increase in top 10% wage shares. The mechanism of the increase in top wages has two main components - screening of workers, and reaching workers not seeking for a job actively. Screening of workers helps more productive rms to match with high-skilled workers. Complementarities in the production technology make these matches extremely productive, especially relative to low-skilled workers in low-productivity rms, increasing the top wages and the share of the top wage earners in the total wage bill dramatically. With headhunters, high-productive rms are matched exclusively with high-skilled workers, and medium- and low-skilled workers are excluded from these rms. Assortative matching improves signicantly in the model with headhunters in comparison to the standard model with only one channel. In the standard model there are many low- and medium- skilled workers in the top rms and many high-skilled workers in low- and medium-productive rms. In the model with headhunters, not only the high-productive rms employ only high-skilled workers, but also the low-productive rms are almost never matched with high-skilled workers. So, assortativeness of the matching improves not only on the very top, where it is almost perfect with headhunters, but also in the bottom and the middle of the distribution. Reaching workers not actively searching for a (new) job is the second important feature of the mechanism. In the model without headhunters, even high-skilled workers stop looking for another job if they work in a medium-productive rm. On-the-job search through a standard channel is costly, so employed workers stop searching actively even if they are far from the best available job, because the probability of being matched with the best rm is very low, so expected gain is lower than the cost that they have to pay every period. 1 See, for example, Atkinson, Piketty, and Saez (2011). 2 source: Piketty (2014) 2

3 Headhunters solve this problem by helping high-skilled workers to climb the job ladder faster and freeing positions for medium- and low-skilled workers. With the headhunter channel, high-skilled workers do not have to pay the search cost every period, but only when a headhunter calls them and proposes to consider an oer. In this case, they pay the cost only if they receive a match, and they are ready to pay it because they know that only high-productive rm would hire through the headhunter. These two features of the channel change dramatically the worker-rm distribution, increasing assortativeness of the matching and subsequently the wage inequality. Moreover, the wage inequality is ecient in this case, i.e., it comes together with the increase of the aggregate output, that would be maximized under perfect assortative matching. The paper also studies the dierences in the intensity of headhunters use in dierent European countries and its consequences for the change in the income inequality over the last decades. It nds that the normalized revenues of headhunters are strongly correlated with the future growth of the top income shares. Figure 1: Top 10% and 1% shares of the total wage bill in the US There are several explanations of the observed increase in wage inequality, discussed in Lemieux (2008) and Atkinson, Piketty, and Saez (2011). Three main explanations are the decrease in the top marginal tax rate (Alvaredo et al, 2013, Piketty, 2003), institutional factors (for example, minimum wage and de-unionization, see Lemieux, 2008) and the skill biased technological change, or simply SBTC (see for example, Acemoglu, 2002). In the rst explanation it is assumed that a decrease in the marginal tax rates gives more incentives to top-earners to put higher eort or simply to work more, so their labor income increases. At the same time, with a lower marginal tax rate the worker's bargaining power increases because she gets higher net income with the same increase in wage. As Alvaredo et al (2013) show, there is a positive correlation between the reduction in marginal tax rates from 1960 to 2005 and the increase in the top 1% income share in the same period. Another possible explanation that they provide is that the reduction of top marginal income taxes reduces tax avoidance by the very rich, so increasing income inequality can be purely a statistical phenomenon. However, as they also note, it is more relevant for income inequality rather than wage inequality, because the tax avoidance came more from realized capital gains. Also, this explanation does not explain well the dynamics of changes in inequality. The 3

4 decreases of marginal taxes were introduced in the 1980s (1986 in the US) and stayed almost constant afterward, while inequality was increasing gradually starting before the reform and still keeps changing. Second explanation considering institutional factors such as minimum wage and labor unions aect mainly the wage setting process on the labor market. There is a vast empirical research evaluating the importance of these factors in changing wage inequality (see Lemieux, 2008, for the survey). Most of the studies conclude that changes in minimum wages and de-unionization are important for the wage inequality but they account not more than for one third of the overall change in wage inequality during the last 30 years. Moreover, these factors aect mainly the bottom part of the wage distribution and have very little eect on the top wages. Third explanation of the increased wage inequality is the skill-biased technological change. Because of increased returns on skill the wages of high-skilled workers rise. At the same time the medium-skilled workers are substituted with automated machines or computers, so the wages of medium-skilled workers fall (see for example Autor et al. 2006). Indeed, Acemoglu (2002) shows that between group wage inequality rose, for example the college degree premium rose by 25% from 1979 to But this explanation has diculties in explaining the sharp increase of the very top wages and cross-country dierences. It is hard to believe that technology changed dierently in dierent developed countries. Overall, the explanations discussed above denitely played a role in shaping the wage inequality during the last thirty years. If we talk in particular about the top wage shares (1% or 10%), the SBTC and the tax reductions played an important role. However, as emphasized in the recent book by Piketty (2014), we are far from the full understanding of the dierent patterns of wage inequality in dierent developed countries. Moreover, if we split the factors aecting the wage distribution into three categories - distribution of rms over productivity and workers over skills, wage setting mechanism, and matching process - existing explanations rely mainly on the rst two factors. The SBTC aects the distribution of rms with respect to demand for skill, and institutions and taxes aect the wage setting mechanism. At the same time the eect of the matching process on wage inequality is neglected in the literature with a few exception 3 - Uren and Virag (2011) and Bagger and Lentz (2014) - that will be discussed in more details below. The paper in hand attempts to contribute to the existing explanations of increased wage inequality by lling the gap of the third non-explored factor affecting wage inequality - the eect of the matching process. So, this paper provides an additional explanation of the increase of wage inequality. To do this the paper introduces a separate channel for high-skilled workers into a standard random matching model of the labor market. This channel is motivated by the increasing role of headhunters in the labor market. Headhunters provide an exclusive hiring channel for high-skilled workers that only high-productive rms can aord. This provides both, high-skilled workers and high-productive rms with mutually better matches, increasing the match surplus for such matches because of skill complementarities. A higher match surplus is associated with higher wages for the workers. Moreover, headhunters can provide contacts with not only unemployed workers but also already employed, so high-productive rms will be matched only with the most skilled workers. High-skilled workers do not have to do anything to receive a call by a headhunter, i.e. they do not need to search for a headhunter (as they need to search for a vacancy), so they do not pay a cost unless they receive a call and they agree to consider the oer. And high-skilled workers know that only good rms use headhunters, so they 3 The literature discussing positive assortative matching may possibly also be included in this category of explanations. 4

5 agree to consider an oer and to move to a better rm. With the appearance of the separate channel in 1960s and increasing access to this channel for rms during 1980s (for example due to the use of computers) the matching process in the top part of wage distribution is becoming more ecient. Then, because of the eect just described the wages of high-skilled workers increase. So, such change of the matching process has a dramatic eect on the wage distribution with the main eect on the very top. Supporting empirical evidence presented in the next section shows that the rise of wage inequality in the US, UK and Canada took place at the same time as the boom in the headhunter industry in these countries. Fee revenues 4 of major headhunter companies were increasing sharply during the period under consideration and they keep growing now. Also, there is a huge dierence in headhunters' fee revenues in North America and Continental Europe that suggests the fact that there is a role of headhunters in explaining wage inequality in a cross-country dimension. Moreover, the rise of headhunter coincided with the rise in wage inequality, hinting to a potential in explaining also the dynamics of inequality. The reason that headhunters started to gain popularity during 1980s might be the increased eciency due to technological developments. It is much easier to manage big databases of potential candidates and contact them with computers. Another important issue of using the data on the headhunter industry to explain the wage inequality is the problem of endogeneity. The headhunters may be more eective in countries where the top wage shares are already high, so they may get higher prots by hiring the same number of workers. However, preliminary evidence on the number of hires by headhunters in dierent countries suggests that the increase in wages is not the only driver of the headhunter revenues. Uren and Virag (2011) use a similar idea of random matching with skill requirements 5 to explain the increase in between-group inequality over the last thirty years together with the increase of within-group inequality for high-skilled workers and the decrease of within-group inequality for low-skilled workers. These empirical facts are also well documented in the literature (for example Lemieux, 2008). However, they need to impose skill-biased technological change to have these changes in wage inequality. So, from my point of view, the study by Uren and Virag does not cover the gap in potential explanations of wage inequality through the matching process but rather propose a mechanism of how SBTC aects the wage distribution given a specic matching technology. While, in this paper, the change in matching technology, motivated by the appearance and increasing use of headhunters by rms, alone is enough to have an increase in wage inequality. Also, Uren and Virag concentrate on explaining the patterns of changes in within-group inequality and between-group inequality rises with the technological and leave aside the increase in top wage shares over this period while it is the main focus of this paper. Another closely related study is the paper by Bagger and Lentz (2014). They consider similar baseline model of the labor market with heterogeneous workers and rms. They study the eect of the on-the-job search on the wage inequality. They show that sorting due to on-the-job search is an important factor in explaining wage inequality in Denmark. This result is in line with what we nd here, but we go one step ahead by adding an additional mechanism for increase in the top wages that is not present in Bagger and Lentz. Headhunters amplify the eects studied in Bagger and Lentz, particularly for the high-skilled workers, due to the two extra features of the channel discussed above. On the empirical part of the literature there is a number of studies documenting the increase in sorting among workers and rms over the last decades. Most importantly, Song et. al. (2015) 4 The fee revenues are not the perfect indicator of the importance of headhunters, like for example number of hires made by headhunters, but it is the only available information at this point of the development of the project. 5 In the model of Uren and Virag, a worker cannot work in a rm whose type is better than her own type. 5

6 show that sorting of workers and rms was one of the main factors in increasing wage inequality in the U.S. between 1980s and 2010s. The other important factor was the increase in the dispersion of workers' xed eects that might be attributed to the SBTC. In particular, they nd that variance of workers' xed eects and the covariance of workers' and rms' xed eects contributed by 40%, each, to the overall increase of the variance of wages over studied period. Important feature of their study is that they use the data from Social Security Administration covering more than 100 million workers, or 73% of all employed workers in the U.S.. In line with the result of Song et. al., Card et. al. (2013) nd that increased covariance between workers' and rms' xed eects contributed to 30% of the increase in wage dispersion in West Germany between 1985 and Moreover, they show that the correlation between the xed eects rose from 0.03 to 0.25 over the same period. Bagger et. al. (2013) document similar ndings using danish data. They nd that the correlation increased from in 1981 to 0.14 in Then they split the sample by the quartiles of worker xed eects and nd that the aggregate eect was driven by the top quartile of workers where the correlation increased from to 0.37, while the correlation stayed almost unchanged and around zero for the rest of the quartiles. Hakanson et. al. (2015) also document signicant increase in sorting in Sweden between 1986 and Another important stream of literature that this paper relates to discusses the formation and evolution of CEO compensations. Indeed, CEOs constitute a large share of the hires by the headhunters and therefore the evolution of CEO compensation for CEOs hired through headhunters is a good proxy for the evolution of other workers hired through headhunters. CEO compensation increased dramatically over the last 40 years and was one of the drivers of the top wage share increases. There are several explanations of the increasing CEO compensation. For example, Gabaix and Landier (2008) and Gabaix et al (2014) show that the CEO compensation rises with the size of the companies in the market, the increase of compensation in their framework is a result of increased productivity of CEOs in larger rms. Other explanations argue that CEOs may better extract the rent from the company (for example, Shivdasani and Yermack, 1999, Murphy and Sandino, 2010), or that the nature of required CEO skills changes and the competition for CEOs between rms rises, increasing the compensation (Murphy and Zabojnik, 2004). These studies, however, have a similar drawback because they assume that the workers and rms are perfectly matched, in the sense that the best worker works in the best rms, the second best worker in the second best rm, and so on. Even though this assumption gives analytical tractability of the models it is hardly justiable empirically, so frictions on the labor market must be also accounted for in order to properly study these mechanisms. There is another stream of literature related to the CEO compensation that focuses on the non-compete agreements between the CEO and the rm. Dierent states in the US have dierent legislations regarding the non-compete agreements. Some states, like California, forbit any type of non-compete agreements, while some states, like Florida, fully enforce these agreements in the court. Garmaise (2009) uses this variability across states in order to construct an enforceability index for each state and shows that in the states with high enforceability the CEOs have longer tenures and lower compensation. Enforceability of non-compete agreements should prevent headhunters to freely choose the candidates for a position, limiting their use, so the ndings of Garmaise (2009) are in line with the mechanism of this paper. This paper shows that the introduction and the increasing role of a separate channel for highskilled workers may generate an increase in wage inequality even when technology, distribution of workers' skills and wage setting stay the same. The increase in inequality comes together with increasing skill premium and assortativeness of matches, so the increase of inequality is ecient. Moreover, in a simulated model the presence of headhunters (or some other separate channel for 6

7 high-skilled workers) in the labor market may generate an increase in the top labor income share of a magnitude comparable to the data. Then, the paper analyzes the change of the CEO compensation in a rm after it changes CEO, it shows that rms pay signicantly higher compensation to new CEOs and this eect is larger during the periods when revenues of headhunters rise sharply. Finally, the paper shows preliminary evidence of correlation between the use of headhunters in European countries and future growth of top income shares. Countries where rms rely more on headhunters experience higher top income growth in following periods. The reminder of the paper is organized as follows. Section 2 discusses the available empirical evidence about headhunters and headhunter industry. Section 3 presents the theoretical model. Section 4 presents the calibration of the model and discusses the implications of the model on wage inequality. Section 5 discusses the implications of the model for assortiveness of the matching between workers and rms. Section 6 provides empirical evidence of cross-country dierences in the patterns of top income shares over the last thirty years and their relation to the headhunter industry. Section 7 presents empirical results of the eects of changing CEO on the compensation paid by the rm. Section 8 concludes. 2 Headhunter boom The rst headhunter companies were opened already in the 1950s, but in the rst decades of their activity they were not popular or very successful. The reason for this could be that it was dicult to manage big data bases of potential candidates and to reach a potential candidate at that time. In the 1980s with the increasing use of computers (Figure 21 in the Appendix) it became much easier for headhunters to create vast data bases with potential candidates and their abilities and contacts. Soon they started to nd and to screen candidates better than standard human resources departments and their popularity started to increase. The main advantage of headhunters as opposed to human resources departments is the fact that headhunters can contact candidates that do not look actively for a job and therefore can nd the best candidate for the position and not the best candidate on the market (who is searching actively for a job) 6. That was a start of the boom of the headhunter industry. For example, the world leader headhunter company Korn/Ferry's fee revenues increased from 501,461 in 1980 to 1,761,405 in 1985 only in UK, and then reached 13 million in 1990 in Europe (Faulconbridge, Hall, and Beaverstock, 2008). The industry still keeps growing, estimated total fee of the industry increased from $5 billion in 2004 to $10.6 billion in 2013 worldwide. 6 So, headhunters also solve the adverse selection problem. 7

8 Figure 2: Headhunter industry fee revenues It is important to distinguish between two types of headhunters - retained and contingency headhunters. Retained headhunters, that are under consideration in this paper, have an exclusive permanent contract with a company. When a company needs to hire a new worker the retained headhunter takes care of searching for potential candidates and evaluates them for the company. Retained headhunters mainly work with positions that are paid more than $150,000 per year (executives and other highly skilled workers). The average fee is around 30-40% of the workers annual salary and it is paid regardless of whether the search was successful or not. Contingency headhunters on the contrary do not have a permanent contract with the company and they are paid only if the rm hires the candidate provided by them. They work with medium- and high-skilled workers with the wage range from $15,000 to $150,000 a year that is a wide range of positions from nurses and clerks to accountants and top managers. It is not easy to estimate the exact share of hires made through headhunters because the information about headhunter's clients is private and rms often do not announce the opened position anywhere except to the headhunter. However, IACPR report (2003) states that headhunters ll 54% of positions with annual wage above $150,000 and most of the remaining positions are lled through internal promotion. So, headhunters are the primary source of outside hiring in the top part of the wage distribution. Headhunters work in the following way. A rm searching for a worker signs a contract with a headhunter. The headhunter searches for a suitable candidate in its databases or other sources. The headhunter calls the candidate (employed or unemployed) asking whether she wants to consider an oer without specifying any details (rm, wage, etc.) 7. If the candidate agrees to consider the oer she has an interview with the headhunter. If the interview is successful the oer is disclosed and the candidate is connected with the rm where she goes through the standard hiring procedure. The fact that headhunters may contact the employed workers who are not searching actively for another job is one of the main advantages of this hiring method. This solves the adverse selection 7 A decision to say yes or no is not straightforward. From one point of view, you may miss a big increase in your wage and a turning point of your career. But from another point, if the oer will be not worthy but your employer will know about you thinking to change the job, you may loose your current job or at least your credibility. See Capelli and Hamori (2013) for a detailed study of reasons to say yes or no. 8

9 problem - good workers working in good rms will not search actively for even better jobs, while if a headhunter calls them they may want to consider a new oer. The study by Capelli and Hamori (2013) show that more than half of executives want to consider an oer when a headhunter calls them. It is also important to notice the correlation between the growth of the fee revenues and the top 1% wage share, cumulative changes of the two series are presented in Figure 3. The headhunter revenues increased by more than 10 times over the period while top 1% share of wages doubled. What is evident from the gure is that the two series had experienced periods of sharp increases over the same time. Similar business cycle behavior is also striking, but it is of no interest for this paper. This correlation doesn't imply causality by itself, it might be that higher top wages automatically translate to higher revenues because the fees are paid as a fraction of wages. So, the increase in fees just reect the growth of wages. Or, alternatively, headhunters become more active because of higher wages, because it becomes more protable for them. Anyway, headhunter revenues would rise because of the rise in top wages and not the opposite. However, this paper presents the mechanism how the opposite occures - exogenous change in technology (mainly IT) makes headhunters more ecient. Which direction of the causality is the true one is impossible to determine just from the aggregate behavior. More detailed analysis addressing the causality will be presented in Section 7. Figure 3: Cumulative change in headhunters fee revenues and top 1% wage share The popularity of retained headhunters was increasing dramatically during the 1980s and is still growing rapidly. The overall share of this type of headhunters in 2010s can be estimated to be at least 5% in the overall labor market and 90% in the top part of the wage distribution. 9

10 3 The model Environment The economy is populated by a continuum of heterogeneous workers diering in their skill level, e, who supply inelastically one unit of labor if employed. When a worker is unemployed she benets from home production activity, unemployment subsidies, leisure and other possible sources she cannot enjoy during employment, collectively represented by b. Also, there is a continuum of heterogeneous rms that dier in their productivity level, p. Each rm can hire one worker. To do this a rm needs to post a vacancy or to contact a headhunter company. Both workers and rms discount their future utility with discounting rate β. All workers, unemployed and employed, can search for a job. Each period workers decide whether to search for a job checking vacancies (search actively) and/or to be available for a headhunter company (search passively) if her skill is higher than a threshold ê. Workers searching for a job and rms posting a vacancy are matched randomly by a standard CRS matching technology. Firms using headhunters are randomly matched with workers with a skill level above ê with a possibly dierent matching technology. In the baseline model the wage in a match is determined period by period as a fraction of resulting production. The production of a match depends on the rm's productivity level and the worker's skill level. Firms can choose only one channel while workers can search both actively and passively (if they are eligible). Separation of matches depends on two factors: 1) idiosyncratic exogenous separation shock, s; 2) worker quitting to another job, s Q (.). There is no aggregate uncertainty in the model. So, the paper considers only stationary equilibria. Timing Assume that time is discrete. Inside every period, rst, existing matches produce and wages and unemployment benets are paid. Then exogenous separations happen. Workers decide in which markets to participate, new rms decide to enter the market and choose the market to search. After that workers searching for a job and rms searching for a worker are matched. Matching There are two channels in the labor market: the vacancy and the headhunter channels. In channel i = {V, H} workers and rms meet by a standard matching technology: m i = m i (u i + a i, i), where m i is the number of matches, u i and a i are numbers of unemployed and employed workers participating in this channel, respectively, and i is the number of rms participating in the channel. So, the job nding rate for a worker using channel i is f i (u i, a i, i) = m i(u i +a i,i) u i +a i and the rm's worker nding rate is q i (u i, a i, i) = m i(u i +a i,i). i Wages and production technology For simplicity, in the baseline model, the wage is proportional to the match productivity: w (e, p) = ψ y (e, p) with ψ < 1. Where y (e, p) is increasing and concave in both components, that is y p > 0, y e > 0, y pp 0 and y ee 0. Moreover, y (e, p) has a property of complementarity between the worker's skill and rm's productivity, having positive cross-derivatives: y ep > 0, y pe > 0. 10

11 The production function must be supermodular, so that it generates the incentives for positive assortative matching. Worker problem Consider rst the problem of a low-skilled unemployed worker. The low-skilled unemployed worker is excluded from the headhunter channel, so the only choice that she does is between searching through vacancies and not searching. Low-skilled worker's value of search can be written as: where: S U (e) = max {S UV (e), 0}, if e < ê (1) S UV (e) f V (.) E p V [max {W (e, p), U (e)} U (e)] c wv If she decides to search through vacancies, with probability f V (.) she will receive an oer that will be drawn from a distribution of rms posting vacancies. She also has to pay the search cost, c wv, every period of active searching. When the worker receives an oer she will choose between working in a rm with productivity p and getting the dierence between the value of employment, W (e, p), and unemployment, U (e), or staying unemployed and having no gain. For the high-skilled unemployed worker the problem is the same but she chooses between four options: to search through vacancies, to wait for a headhunter call, to do both, or be inactive. The value of searching through vacancies is the same as for the low-skilled unemployed worker. The value of waiting for a headhunter call, or searching passively, diers in four respects: it has dierent probability of an oer arrival, f H (.); it has dierent search cost, c wh ; the search cost is payed only if the oer arrives; and, the oer is drawn from a dierent distribution - distribution of rms using headhunters. The value of searching through both channels is just a combination of the two, with an implicit assumption that better rms are using the headhunter channel 8. So, the value of the search of a high-skilled unemployed worker can be written as: where S U (e) = max {S UV (e), S UH (e), S UV H (e), 0}, if e ê (2) S UH (e) f H (.) ( E p H [max {W (e, p), U (e)} U (e)] c wh ) S UV H (e) f H (.) ( E p H [max {W (e, p), U (e)} U (e)] c wh ) + +f V (.) (1 f H (.)) E p V [max {W (e, p), U (e)} U (e)] c wv The unemployed worker who did not receive or reject an oer this period consumes the unemployment benets and continues the search in the next period. So, the value of unemployment for a worker can be written as: U (e) = b + β (U (e) + S U (e)) (3) Now consider an employed worker. She also decides whether to participate in the markets, but with a dierent outside option. Similarly to the unemployed workers, the employed low-skilled 8 This assumption is used already here for convenience of notation. 11

12 worker may choose between searching through vacancy or not to search at all. Now, the outside option for the worker is her previous employment rather than unemployment. For a low-skilled worker the value of search can be written as: where S E (e, p) = max {S EV (e, p), 0}, if e < ê (4) S EV (e, p) f V (.) E p V [max {W (e, p ), W (e, p)} W (e, p)] c wv The employed high-skilled worker may choose again between four options: searching through vacancy, headhunter, or both channels, or not to search at all. So, for a high-skilled worker the value of search can be written as: S E (e, p) = max {S EV (ep), S EH (e, p), S EV H (e, p), 0}, if e ê (5) where the value of search through the vacancies is exactly the same as for a low-skilled worker and S EH (e, p) f H (.) ( E p H [max {W (e, p ), W (e, p)} W (e, p)] c wh ) S EV H (e, p) f H (.) ( E p H [max {W (e, p ), W (e, p)} W (e, p)] c wh ) + +f V (.) (1 f H (.)) E p V [max {W (e, p ), W (e, p)} W (e, p)] c wv If a worker decides to stay in a rm or does not receive an oer, she consumes the current wage this period, and next period the match can be exogenously separated with probability s, in which case the worker becomes unemployed, or with probability (1 s) the match survives and the worker can continue to search on-the-job. So, the value of work for any worker is: Firm problem W (e, p) = w (e, p) + β (su (e) + (1 s) (W (e, p) + S E (e, p))) (6) Firms also choose channels in the same manner as the workers, but they all solve the same problem (regardless of their productivity level) and they may choose only one channel, having the value of a vacanct job dened as: V (p) = max {V V (p) ; V H (p) ; 0} (7) If the rm decides to post a vacancy, it pays the per-period cost c fv p and is matched with a worker with probability q V (.) and hires her if she accepts the oer. It happens when the worker doesn't have a better oer at the same period and if she worked in a worse rm (if searching on-the-job). The value of posting a vacancy for a rm is: V V (p) = c fv p + β ( V (p) + q V (.) E e V [P (A) (J (p, e) V (p))] ) (8) where P (A) is the probability of a acceptance of the oer by the worker. In general, this probability might depend on many factors: the skill of the worker, the productivity of this rm, the productivity of the current employer of the workers, other oer to the worker, etc. But in the structure of an equilibrium that will be considered here, the exact form of this probability is relatively simple. 12

13 Similarly, if a rm decides to hire through a headhunter, it pays a per-period cost c fh p and is matched with a worker with probability q H (.). The value of hiring through a headhunter is: V H (p) = c fh p + β ( V (p) + q H (.) E e H [P (A) (J (p, e) V (p))] ) (9) where E e i is the expectation over a worker's skill level conditional on the use of channel i. If the rm hires a worker or a match stays for this period, the rm receives the product of the match, pays the wage and in the next period the match is separated for exogenous reasons with probability s or because the worker quits to another rm with probability s Q (.) 9, and the rm has to substitute the worker, or survives otherwise. So the value of a rm can be written as: J (p, e) = y (e, p) w (e, p) + +β ((s + s Q (.) (1 s)) V (p) + (1 s Q (.)) (1 s) J (p, e)) The free entry condition for the rms is the following: (10) E p [V (p)] = F (11) where F is a xed cost of creating a rm that is paid once to enter the market. It is assumed that before entering the market, rms do not know their level of productivity. Another interpretation of this assumption can be that a rm is created with not just single vacancy but with a distribution of positions that it needs to ll. Steady-state separating equilibrium In this section a particular structure of the equilibrium will be considered. The most reasonable scenario, given supermodularity of the production function, is that high-productive rms would hire through the headhunter channel while low-productive rms would use the standard channel. Distributions First, we need to specify distributions that will be used in expectations. Let F (p) be an initial distribution of rm productivity levels and G (p) the measure of rms with an open vacancy (both CDFs have support [ p, p ] ). Also denote as ˆp the cuto level of rm productivity, such that rms with productivity above ˆp hire a headhunter and rms below post a vacancy, so the fraction of rms posting a vacancy is G(ˆp). G(p) Let H (e) be the initial distribution of all workers over skill levels, L V (e) be the measure of employed workers searching for a job through the vacancy channel, L H (e) the measure of employed workers searching for a job through the headhunter channel, L H (e) the measure of employed workers searching for a job through both channels, and U (e) the measure of unemployed workers over the skill level (all with support[e, e]). Finally, let Φ (e, p) be the joint measure of active matches. And Λ i (e, p) be the measure of active matches in which a worker is searching for a new job through channel i {V, H, V H}. Workers Given the structure of the equilibrium under consideration and the distributions we can now specify the expectations. Under our assumptions, low-skilled workers are excluded from the headhunter channel so they can search only through vacancies. So, their value of search will be: 9 The arguments of the function are dropped for convenience of notation, but in general it depends on the rm productivity level, worker's skill level, and characteristics of the labor market in both channels. 13

14 S U (e) = S UV (e) f V (u V, a V, v) ˆ ˆp p (W (e, p) U (e)) dg (p) c wv (12) For high-skilled unemployed workers it is optimal to search through both channels, so their value of search is the following: ( ) p S U (e) = S UV H (e) f H (u H, a H, h) (W (e, p) U (e)) dg (p) c ˆp wh +f V (u V, a V, v) (1 f H (u H, a H, h)) ˆp (W (e, p) U (e)) dg (p) c (13) p wv Under our assumption, better rms use the headhunter channel, so if unemployed high-skilled worker receives an oer from a headhunter she will accept it regardless of receiving an oer through vacancy channel or not. Instead, this worker will accept an oer from vacancy channel only if she doesn't receive an oer from the headhunter channel at that period. Again, for employed workers the value of search is the same as the value of search for unemployed except from the outside option. So, we can dene the value of search of low-skilled employed worker as: S EV (e, p) f V (u V, a V, v) Or, opening the max inside the integral: ˆ ˆp S EV (e, p) f V (u V, a V, v) p max {W (e, p ) W (e, p) ; 0} dg (p ) c wv (14) ˆ ˆp p (W (e, p ) W (e, p)) dg (p ) c wv So, employed worker accepts a new match only if she is matched with a better rm. To search from employment, the value of search for a worker with skill e working in a rm with productivity p must be positive: S EV (e, p) 0 This equation (when satised with equality) implicitly determines the level of the rm productivity such that a worker with a skill level e does not search for a new job: p V (e) (for e < e). So that, if a worker with skill e works in a rm with productivity below p V (e), she searches for another job, and doesn't search otherwise. Her value function of searching will be as before: S E (e, p) = max {S EV (e, p) ; 0} For a high-skilled employed worker the value of search is now consists of four options, but in this structure of equilibrium, one of them (searching only through vacancies) will never be optimal. So that the value of search can be dened as: S E (e, p) = max {S EV (e, p) ; S EH (e, p) ; S EV H (e, p) ; 0} = max {S EH (e, p) ; S EV H (e, p) ; 0} For a high-skilled worker with skill level e, there are now two cuto productivity levels p V H (e) and p H (e), with p H (e) > p V H (e). If the worker is employed in a rm with productivity below p V H (e) she will search for another job through both channels. If she works in a rm with productivity level between p V H (e) and p H (e), she will search only through headhunter channel. While if she works in a rm with productivity above p H (e), she will not search for another job at all. Before dening the conditions that determine these cutos we need to dene the value functions. 14

15 Value of search through headhunter channel for a high-skilled worker can be dened as: (ˆ p ) S EH (e, p) f H (u H, a H, h) (W (e, p ) W (e, p)) dg (p ) c wh max{ˆp;p} And the value of search through both channel can now be dened as: ( ) p S EV H (e, p) f H (u H, a H, h) (W (e, ˆp p ) W (e, p)) dg (p ) c wv + +f V (u V, a V, v) (1 f H (u H, a H, h)) ˆp (W (e, (16) p p ) W (e, p)) dg (p ) c wv note that in this case the rst integral starts always in ˆp because it will never be optimal to search through both channels if a worker is already working in a rm that hires through headhunter channel. This is the feature of the structure of equilibrium. In other structure of equilibrium, that will be discussed in extensions, not all rms above the cuto ˆp will be using the headhunter channel, so the limits of the integral will be dierent. It is easy to see that, given e, S EV H (e, p)is higher than S EH (e, p) for small p, but S EV H (e, p) decreases faster, so they will always have just one intercept. And the equality: S EV H (e, p) = S EH (e, p) denes the cuto productivity level of searching through both channels for each worker type, p V H (e), while the equality S EH (e, p) = 0 denes the cuto productivity level for searching only through headhunters, p H (e). The value functions of working and unemployment are dened as before. Firms We can also rewrite the values of posting a vacancy and hiring through headhunter channel given distributions dened above. The value function of rms posting a vacancy in this case is: V V (p) = c fv p + β +q V (u V, a V, v) +q V (u V, a V, v) ( +q V (u V, a V, v) a V u V +a V V (p) + q V (u V, a V, v) u V u V +a V a V u V +a V u V u V +a V ê (J (p, e) V (p)) du (e) + e (1 f H (u H, a H, h)) e (J (p, e) V (p)) du (e) + ê e p p λ V (e,p )dp p (1 f H (u H, a H, h)) e ê ê p λ V (e,p )dp (J (p, e) V (p)) dl V (e) + p p λ V H(e,p )dp p p λ V H(e,p )dp (J (p, e) V (p)) dl V H (e) where the rst part in the summation is the expected value of a match after meeting an unemployed low-skilled worker, the second - unemployed high-skilled worker, the third - employed low-skilled worker, and the forth - employed high-skilled worker. Similarly, the value function of rms using headhunters is: V H (p) = c fh p + β ( +q H (u H, a H, h) +q H (u H, a H, h) V (p) + q H (u H, a H, h) a H p e p λ H(e,p )dp u H +a H ê p a H e u H +a H ê u H e u H +a H ê (J (p, e) V (p)) du (e) + (J (p, e) V (p)) dl p λ H(e,p )dp H (e) ) p p λ V H(e,p )dp (J (p, e) V (p)) dl p p λ V H(e,p )dp V H (e) 15 ) (15)

16 where again the rst part in the summation is the expected value of a match after meeting an unemployed worker, the second - employed worker searching only through the headhunter channel, and the third - employed worker searching through both channels. One can show that under reasonable conditions on the value of the search costs and production function, the value of hiring through a headhunter, V H (p), is lower than the value of posting a vacancy, V V (p), for small p. But, V H (p) is increasing faster with p. So, there will be only one intercept between V H (p) and V V (p), ˆp, such that for p < ˆp and max {V V (p) ; V H (p)} = V V (p) max {V V (p) ; V H (p)} = V H (p) for p > ˆp. And the cuto productivity is determined by V V (ˆp) = V H (ˆp) Now, given the distributions, we can specify also the quit rate of a worker with skill e from a rm with productivity p: 0 ( ) if p max { p V (e) ; p H (e) ; p V H (e)} G(ˆp) G(p) f V (u V, a V, v) if p < p G(ˆp) G(p) V (e) and e < e ( ) s Q (e, p, ω) = f H (u H, a H, h) G(p) G(p) if p G(p) G(ˆp) V H (e) < p < p H (e) and e e ( ) f H (u H, a H, h) G(p) G(p) + if p < p G(p) G(ˆp) V H (e) and e e ( ) + (1 f H (u H, a H, h)) f V (u V, a V, v) G(ˆp) G(p) G(ˆp) G(p) where ω = (u V, a V, v, u H, a H, h) is a vector of labor market characteristics. Finally, the value of an active match for a rm is dened as before, substituting the value functions dened above and the function for quit rates. Equilibrium The steady state equilibrium, given the initial distributions of workers over skills and rms over productivity, the skill threshold, matching function, and production function, is dened by the value functions, the endogenous distributions, and decision rules. Decision rules, together with the endogenous distributions, must satisfy the balances such that the endogenous distributions are stationary. [add the balances] Solution method The steady state equilibrium of the model is solved for using Matlab. To nd an equilibrium the following algorithm is used: 1. Guess the search decision rules for workers and rms (the cuto levels of productivity) 16

17 2. State the system of equations corresponding to the balances of endogenous distribution of matched rms and workers 3. Solve the system using non-linear solution methods (trust-region algorithm or Broydn algorithm) for the invariant distribution 4. Compute the value functions given the distributions 5. Compute the decision rules given the value functions 6. Compare the decision rules, if dierent - update the decision rules and go to 2. 4 Inequality Calibration The calibration strategy is the following. First, the version of the model without headhunter channel is calibrated to match the labor market in the US in Then the parameters related to the headhunter channel are calibrated to match the properties of the headhunter industry in the US in 2010s. This way we isolate the eect of the headhunter channel on the distribution of wages from other potential causes of changes in the distribution, for example, the change of wage setting process, or changes of initial distributions. So, this experiment answers the question - how much of the increase in top wages we can explain only by the change in the matching technology? Implementation of other potential causes of the increase in inequality will be discussed in the robustness section. To calibrate the model we need to specify the initial distributions of workers, H (e), and rms, F (p), the productivity function, y (e, p), the matching function, m (u, v), skill threshold, ê, and the search costs, c fh, c fv, c wh, and c wv. The functional form for the initial distributions of rms and workers is chosen to be beta with the same parameters λ 1 and λ 2, and truncated on p = e. The matching has standard Cobb-Douglas form: and the production function has a form: m (u, v) = Mu σ v 1 σ y (e, p) = e p it is easy to see that this production function is supermodular with 2 y(e,p) = 2 y(e,p) = 1 > 0. e p p e All parameters, except for the search costs in the headhunter channel and the skill threshold are calibrated to match the wage distribution and other labor market variables in 1970s, where available, or as early as possible. There are seven parameters to calibrate for the steady state without headhunters: parameters of the distribution, λ 1 and λ 2, the maximum type, p or e, separation rate, s, matching function eciency, M, search cost through vacancy channel for workers, c wv, and for rms, c fv. To set these seven parameters, seven targets are chosen: top 1% and 10% wage shares, median to average wage ratio, unemployment rate, job nding rate, quit rate, and estimate of vacancy cost relative to annual worker's wage. Seven parameters are jointly calibrated to match the targets. For the headhunter channel there are just three parameters to calibrate - search costs for workers, c wh, and rms, c fh, and the skill threshold, ê. Three targets are chosen - estimate of the 17

18 positive response rate by managers to a call by a headhunter 10, average fee of headhunters, and the share of rms that use the headhunters for hiring. This way, the targets do not directly aect the wage distribution, so the calibration strategy does not drive the results. Robustness checks for the choice of parameters for the headhunter channel will be presented in the subsequent sections. The results of the calibration are presented in Table 1. The model matches well the main characteristics of the wage distribution and the labor market in 1970s. Results Parameter Value Target Data In the model 1970 Beta parameter, λ Top 1% wage share 5.1% 4.76% Beta parameter, λ 2 9 Top 10% wage share 25.7% 25.8% Maximum types, p, e 13 median/average (1990) 72% 76% Separation rate, s Unemployment rate 5% 5.17% Matching function, M 1 Job nding rate 50% 48.59% Search cost - vacancies, c wv 2.5 Quit rate 2% 1.97% Vacancy cost, c fv 0.13 Vacancy cost estimates 8% 8% 2010 Headhunter search cost, c wh 1.5 Positive response rate 50% 52.67% Headhunter rm cost, c fh 2.65 Headhunter average fee 30% 30% Skill threshold, ê 2.64 Headhunter usage top 5% 5.61% Table 1: Calibrated parameters The headhunter channel allows to separate high-skilled workers reducing frictions for them and providing them with exclusive opportunity to work in high-productive rms. The presence of this channel changes the distribution of the workers over the wages. Without headhunter channel the distribution has a peak close to minimal possible wage and then decreases, having a form close to Pareto (Figure 4). When the headhunter channel is present in the model, the distribution still has similar form but has a fatter right tail (Figure 5), similar to what is observed in the data. So, the headhunter channel generates the fat tail of the wage distribution in this model. The reason for this is the following, without headhunter channel the probability of matching a high-skilled worker with a high-productive rm is lower than matching a high-skilled worker with a low-productive rm (due to the fact that there are relatively few high-productive rms), so there will be big shares of high-skilled workers working in low-productive rms and low-skilled workers in highproductive rms. Because of skill complementarities, wages of low-skilled workers are lower than wages of high-skilled workers in the same type of rm. And because only some high-productive rms will be matched with high-skilled workers there will be a small mass of workers getting very high wages. When, instead, there is a possibility to hire only high-skilled workers through the headhunter channel, high-productive rms will be matched only with high-skilled workers and all of them will receive relatively high wages; this corresponds to the fat tail of the distribution. 10 Estimated by Cappelli and Hamori (2013) 18

19 Figure 4: Distribution of wages without headhunter channel Figure 5: Distribution of wages with headhunter channel As it was stated before, the increase in wage inequality was mainly driven by the sharp increase of top wages. Figure 1 shows the top 10% and the top 1% wage shares in the US from 1970 to The top 1% share increased from 5.1% in 1970 to 10.9% in 2011, and the top 10% share increased from 25.7% to 34.5%. The shares in the 1970 were targeted in the calibration, but the 19

20 shares in 2011 were not. So, the results of this experiment show how much of the overall increase in top wages can be explained only by the additional channel in the labor market. The results are presented in Table 2. In the model the top 1% share increases by 2.7%, from 4.76% to 7.49%, while in the data in increases by 5.8%, so the model is able to explain 47% of the actual increase in the top 1% wage share. For the top 10% wage share, the model predicts 8.52% increase, while the actual increase is 8.8%. So, the model accounts for 96% of the actual increase in the top 10% wage share. The reason for so high increase in top 10% wage share in the model, relative to top 1%, is that in the model all the rms above a certain threshold hire through headhunters, while in the data it is not entirely true, because many rms use internal promotion to ll in major positions. To account for this, an extension where not all rms are allowed to use the headhunter channel will be considered in the robustness section. Model Top 1% Top 10% Data Top 1% Top 10 % Without HH 4.76% 25.8% % 25.7% With HH 7.49% 34.32% % 34.5% Table 2: Top wage shares in the model and data Another important feature of the data that the model predicts, apart from the increase in top wages, is the increase of the average wage relative to the median wage. It comes naturally with the increasing top wages. The change in the median and average wage in the US and the ratio of the two is depicted in Figure 6. The ratio of median to average wage decreased from around 72% to 65% from 1990 to The model was calibrated to match the median average ratio for the version without headhunter channel to match the 72% target, and it was not targeted in the version with headhunters. In the version of the model with headhunters the medium to average ratio decreases from 76% to 71.5%. So, the calibrated model may account for the 4.5% decrease in the ratio, or for 64% of the actual decrease. The levels of the average to median ratios are a bit higher in the model than in the data, but the magnitude of the decrease is comparable to the observed decrease. Figure 6: Average and median wages 20

21 Robustness/Extensions To check how much the magnitude of the increase is dependent on the choice of the skill threshold for the headhunter channel, we do similar experiments for top 2% or 3% of workers being eligible to the headhunter channel. The results are presented in Table 3. In the right side of the table for 3% and 2% thresholds are the dierences between the top wage share with headhunters and without headhunters, and their shares relative to the increase in the data. Not surprisingly, higher thresholds (more ecient screening by headhunters) increase the wage share of top 1% of the workers but decrease the share of top 10%. This happens because with a higher threshold, the most ecient workers are more concentrated in the top rms, for example they all work in top 2% of the rms instead of top 5%. Their wages increase even more due to complementarities, so the top 1% wage share increases more. Instead, for the workers in the 10-1% bracket the probability of working in the best rms decreases with a higher threshold. Workers in 5-3% are excluded from the headhunter channel and many of them and up in bad or average rms, so the top 10% wage share drops despite the top 1% wage share increase. The overall eect of the sorting mechanism is still striking - it explains between 47% and 59% of the actual increase in the top 1% share of wages and between 73% and 96% of the top 10% wage share. Model Top 1% Top 10% Data Top 1% Top 10 % Without HH 4.76% 25.8% % 25.7% With HH on top 5% 7.49% 34.32% % 34.5% With HH on top 3% 7.9% 32.53% Di/% 3.14/ /76 With HH on top 2% 8.18% 32.25% Di/% 3.42/ /73 Table 3: Top wage shares in the model and data for other skill thresholds In the data rms do not hire workers through headhunters for all positions above a certain wage, for some positions they use other channels or just internally promote candidates 11. Screening might be worse (or better, but it would result in even stronger sorting eect) in the case of using other channel. To account for this we run another set of experiments by forbidding some rms in the top to use headhunter channel, so they have to use the standard channel (with no screening). We set the intensity of the headhunter channel, the share of the rms allowed to use it, to be 20%, 40%, 60%, or 80%. The results are presented in Table 4. Of course, the increase of the top wage shares is decreasing with lower share of rms (among the top rms) using headhunters. But the major part of the eect is still there even if every 5th rm in the top part is allowed to use the headhunter channel every period. In this case the model is still able to explain 39% of the increase in top 1% wage share and 59% of the increase in the top 10% wage share. So, the assumption that all rms above a certain threshold use the headhunter channel does not drive the result. 11 See Cappelli and Hamori (2013) 21

22 Model Top 1% Top 10% Data Top 1% Top 10 % Without HH 4.76% 25.8% % 25.7% With HH, 100% 7.49% 34.32% % 34.5% With HH, 80% 7.37% 32.91% Di/% 2.61/ /81 With HH, 60% 7.25% 32.41% Di/% 2.49/ /75 With HH, 40% 7.10% 31.96% Di/% 2.34/ /70 With HH, 20% 7.03% 30.98% Di/% 2.27/ /59 Table 4: Top wage shares in the model and data for dierent intensity of the use of headhunter channel Another issue arising from the results of the simulations is the shape of the distribution. In the model with the headhunter channel the wage distribution has two peaks, one next to the minimal wage in the left part of the distribution similar to the model without headhunters and one in the right part of the distribution right after the threshold for workers being eligible for the headhunter channel. The real wage distribution doesn't have second peak and decreases monotonously, as it can be seen in the Figure 7. The small spikes in the right tail of the distribution are merely accounting phenomena because the size of the segments in the gure increases with the wage growth. To solve the issue with double-peaked distribution, one can think about some errors or constraints in the headhunter channel. The constraints were considered above when not all good rms are allowed to use the headhunter channel. Indeed, it helps to smooth the wage distribution, but not completely. Simulated wage distribution for the case when only 20% of good rms can use the headhunter channel is presented in Figure 8. The second peak is still there but it is not as apparent as before. Second extension that would help to smooth the wage distribution is related to the worker side. Suppose that the headhunters can do errors while they screen workers, so sometimes they call workers that are below the skill threshold. In this case, there will be some low-skilled workers working in the best rms (there are no such workers in the baseline). This will also smooth the wage distribution. [add results of simulations] 22

23 Figure 7: Wage distribution in the US, 2013 Figure 8: Distribution of wages with only 20% of good rms using the headhunter channel Final, but the most important extension is the change in the initial distributions of workers over skills and/or rms over productivity together with the appearance of headhunters. This change in the distributions can be interpreted as the skill biased technological change. On the extreme, we x the model only with the standard channel and check how much should the initial distributions change to explain the observed increase in wage inequality. Is this change in the distributions plausible? [add results of simulations] 23

24 Discussion As it was discussed before, the main eect of the headhunter channel on the wage distribution comes from the separation of the labor markets for high-paying and low-paying jobs. With the headhunter channel in place only high-skilled workers get to high-paying jobs and their wages increase dramatically due to skill and rm productivity complementarities. Moreover, headhunter channel allows high-skilled workers to search on-the-job less costly because they don't have to pay the search cost every period but only when they receive a call from the headhunter. Because of this, high-skilled workers agree to consider an oer even when they work in medium and highproductive rms, while they would stop searching for a job actively working in such rms without the headhunter channel. Low-skilled workers, in contrast, lose their possibility to work in highpaying jobs, therefore their wages are compressed to lower levels after the introduction of the headhunters. Simulations presented in this section show that the change of the matching technology can explain a major part of the increase in wage inequality. The results are quite robust to dierent extensions that bring the model closer to the real world. 5 Assortative matching The main mechanism behind the increase in wage inequality in the model is the increase in sorting between workers and rms. To see have it changes from adding headhutners in the model we split the workers and rms over ten cathegories by their skill or productivity level and plot the joint distribution before and after introducing headhunters in the model. Figure 9 shows the distribution without headhunters, Figure 10 show the distribution with headhunters, and Figure 11 shows the change of the distribution. Figure 9: Joint worker and rm type distribution without headhunters 24