Choosing recruitment channels to fill high job positions

Choosing recruitment channels to fill high job positions Alexandra RUFINI∗

Dominique TORRE∗

December 22, 2010

Abstract This paper analyzes the recruitment strategies used by firms to fill high job positions. We consider different kinds of hiring channels: formal channels, employee referrals, promotion, and ‘top-notch’ universities. The model emphasizes three optimal recruitment policies according to firm and channel characteristics. When several firms are considered in a stationary equilibrium setting, the combination of channels generates multiple rational expectation equilibria. If they are heterogeneous in terms of size and technologies, conflicts of interest may emerge among firms, reflecting the recruitment difficulties of small and medium sized enterprises. We finally show how second best policies can be implemented. JEL Classification: D21; J23; M51 Keywords: heterogeneity of agents, recruitment channels, network economics.

∗ University of Nice Sophia-Antipolis - Gredeg - Cnrs, 250 rue Albert Einstein, 06560 Valbonne, France. E-mail: [email protected], [email protected]

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Introduction and Related Works

Lack of information in the labor market leads both workers and employers to invest in search strategies to find the best possible partners. The ways that workers find job positions, and firms fill vacancies, play an important role in the quality of this matching process. There is a strand of the economic literature that examines the strategies of job seekers and employers in terms of the recruitment channels they use. Since the seminal writings of Rees (1966) and Rees and Shultz (1970), most work that focuses on employers’ behavior distinguishes between formal and informal channels and points to a tradeoff between the quality and the size of the applicant pool (see, e.g., Roper 1988, Montgomery 1991, Simon and Warner 1992, Gorter and Van Ommeren 1999, De Varo 2005, 2008). On the one hand, formal channels, such as newspaper advertisements and placement agencies, provide extensive information, i.e. an important pool of applicants which reduces the time before the vacancy is filled. On the other hand, informal channels such as employee referrals, generate intensive information, i.e. better information about applicants’ characteristics which reduces the risk of adverse selection. The economics literature differs in its conclusions about what are the most relevant channels: while Gorter and Van Ommeren (1999) emphasize the importance of informal channels for senior positions, Pellizzari (2005, 2010) highlights that formal methods are the most relevant when firms are investing in serious recruitment processes. The number and type of channels varies depending on the labor market conditions, the firm’s size, the number of workers being sought, the sector or the types of positions being filled (Barron, Black and Loewenstein 1987, Bessy and Marchal 2007, Russo et al. 2000, Russo, Gorter and Shettkat 2001). Bessy and Marchal (2009) find that the number of recruitment channels used increases with firm size and employees’ skills. Using the French OFER survey (2005), which analyzes the recruitment practices of firms for a sample of over 4,050 companies, Bessy and Marchal show (i) that employer searches always result in a combination of a small number (on average 3.5) of channels, and (ii) that the nature of these channels varies from one firm to another. Their results confirm a the results of a survey on employer recruitment behavior conducted in the Netherlands and reported by Russo et al. (2000), that companies use an average number of 1.84 different channels. Before De Varo (2008), few theoretical studies have tried to capture the mechanisms used by firms to select recruitment channels. Montgomery (1991), Simon and Warner (1992) and Pellizzari (2005) propose theoretical models that focus essentially on the strategic choice between formal and informal channels, but ignore actual hiring channel strategies. None of these studies considers recruitment strategies in terms of the time involved, the complementarities among channels, or the ways that individual firms adjust the performance of the available channels to their own benefit. In all cases, social networks are seen as informal methods and are not rationalized, and, most of the time, no distinctions are made between the manager’s personal (family, friends) contacts and professional (former colleagues, or associates of executives in the company) contacts. While there may be few possibilities for companies to increase the performance of personal contacts, there are strategies that can be used to improve the efficiency of professional networks. A few papers analyze alumni network (Rebick 2000, Marmaros and Sacerdote 2002) but except for the paper by Simon and Warner (1992), not in terms of a general employer search analysis. Yet the empirical evidence confirms the crucial role of these 2

kinds of networks in the recruitment strategies of both jobseekers and employers. The economic and business press regularly promotes the advantages of “capitalizing on College ties”. HR magazine 1 reports managers’ views on the advantages of exploiting alumni networks to help with recruitment. Although the university sponsorship can be costly (around $25,000 a year), alumni networks are particularly useful for attracting people “who would not consider working for a utility company, such as accounting and business majors”. According to the magazine, the best employees are found through recommendations and university alumni provide these contacts, effectively extending the reach of human resource departments. BusinessWeek has also highlighted the significance of alumni networks for companies. Based on interviews with managers, two recent articles (3/13/20082 and 3/31/20093 ) conclude that an alumni network, as a trusted source, is particularly useful for finding investors, advisers, and employees. Alumni networks help both jobseeking graduates and recruiters - especially in the context of a financial crisis. The articles in BusinessWeek point to reliability as the most important benefit to recruiters of using alumni networks. Several managers testify to how searching alumni network helps to reduce the risk of a bad match. Therefore, introducing universities as a recruitment channel, within a framework devoted to employer search, seems to be relevant given the opportunities that alumni networks offer to firms. By hiring new graduates, firms obtain the immediate benefits of employees with a good level of skills and improved access to alumni networks as sources of subsequent external recruitment of high skilled workers. Achieving this access is complex but is enabled by firms building ties with universities. This can be achieved through collaborative research or response to fundraising appeals from universities. The “Council for Aid to Education” based on the Council’s annual “Voluntary Support of Education”4 survey reports that in 2007 fundraising by US colleges and universities yielded $29,75B. The top 20 universities, which represent just 2% of the survey respondents, raised more than a quarter of this total. For example, in 2007 Stanford and Harvard universities raised respectively $832M and $614M. Although firms may not be major contributors ($4.8B or around 16% of total gifts5 ), these donations ease future contacts with new graduates, endowing these generous firms with a good corporate image, making these “gifts” strategic investments to enable the universities to be used as a recruitment channel. This paper proposes a theoretical model for the strategic use and combination of different hiring channels. Focusing on the recruitment of high skilled workers, we argue that the choice of a hiring channel is a long term strategy. Hiring channels are chosen not just in a bid to acquire the best and most productive employees for the position in question, but also to enhance the propensity to recruit the best employees in the future. Such a long term strategy is relevant if firms have established promotion processes and 1

S. Taylor (2009), “Capitalizing on College ties”, www.stevens.edu/press J. Tozzi (2008), “Alumni Networks: Knotting the School Tie”, www.businessweek.com/smallbiz /content/mar2008 3 A. VanderMey (2009), “For Job-Seeking MBAs, Alumni May Be the Answer”, www.businessweek. com/bschools/content/mar2009 4 Council for Aid to Education (2008), “Voluntary Support of Education Survey”, www.cae.org 5 But note that this amount does not take account of the other ways that firms support universities, such as partnerships and sponsorships. 2

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if the new workers being hired are likely, after later promotion, to have an influence on future recruiting. We consider that three kinds of hiring channels are available to firms recruiting their top executive workforce: (i) external formal channels, (ii) external informal channel namely “employee referrals”, and (iii) the internal channel of promotion. Promotion leads to the recruitment of new “juniors” (highly skilled but less experienced workers), a process that we integrate in the framework. To recruit juniors, firms can use Top-Notch Universities (TNU hereafter) where new graduates are embedded within strong “old boy networks”6 but other hiring channels are also available. Based on the multiple possible combinations of these channels, we analyze how firms choose their hiring strategies and interact with other firms and TNU to build their top executive workforce. The paper is organized as follows. Section 2 describes the selection of an optimal recruitment strategy by an individual, isolated firm. We assume that five channels of recruitment are available: three to recruit executives and two to recruit juniors. We suppose exogenous exits from each kind of position and analyze, at the stationary state, the employer’s optimal recruitment strategies. We find three possible optimal strategies, each combining no more than three different recruitment channels. The best strategy for any company is defined by its production and search technology (net productivity of labor and the efficiency of its recruitment networks). One optimal strategy involves the recruitment of juniors using TNU channel to allow the firm to build sufficient resources / links for the future recruitment of executives. Section 3 presents and discusses the strategies adopted when the economy is constituted by homogeneous rather than heterogeneous firms. We test the effect of two assumptions: (i) that the efficiency of the alumni network depends positively on the size of this network, and (ii) that the wages of young new graduates depend positively on the number of alumni employed. In relation to assumption (i), we find that the positive effect of network size generates different stationary equilibria and possible cases of multiplicity. We analyze these cases as cases of coordination failure between the firms and the universities. We also consider the case of heterogeneous firms and find that this case extends the possible number of equilibria and also may generate coordination failures. If we add in assumption (ii), we find that possible conflicts of interest can emerge on the part of the firms and universities on the one side, and other firms. We conclude this section with an analysis of possible second-best policies. Section 4 provides some comments and conclusions.

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A single firm model

We first consider a firm where the positions requiring to be filled correspond to junior and top executive roles. Juniors are hired through the external market; top executive positions are filled through promotions or external recruitment. By juniors, we mean well-educated but inexperienced workers, i.e. individuals who have just graduated from higher education with a Masters or doctoral degree. For the most senior positions, firms 6

An “old boy network” is an association of former students who maintain links throughout their professional careers.

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require workers with experience. The recruitment of juniors is done either through TNU (denoted U ) or “other” channels7 (denoted O). Other channels include informal and formal channels, such as employee/personal referrals, newspaper advertisements, “temp” agencies and Internet job agencies. None of these channels require previous investment in social or professional links. In filling their senior positions, firms are unable to use TNU since new graduates do not have (enough) professional experience immediately following their graduation from higher education. External recruitment channels are divided into Formal (denoted F ) and employee Referrals (denoted R). Formal channels include advertisements in newspapers, private recruitment agencies and Internet recruitment methods (job sites and advertisements on company websites). The employee Referrals channel is based on the “address books” and other contacts of current employees. Its effectiveness depends greatly on the proportion of TNU graduates among the firm’s top executive, and on size of the TNU network. Promotion (denoted P ) has the advantage of involving an accurate selection process and increasing the performance of the employee Referrals channel, given the proportion of juniors recruited originally via the TNU channel.

2.1

Juniors and top executives

The size of the firm i is defined by the pair (J¯i , E¯i ), representing respectively the number of junior and top executive positions. We assume that this size is given. It depends on various circumstances (sector of activity, age and notoriety of the firm, location. . .) not related directly to the recruitment strategy. The turnover generated by the end of the activity or decisions of the employees and employers determines the given annual exit rates, k¯ and k¯0 respectively for juniors and top executives (with k¯ > 0 and k¯0 > 0). The firm must determine the number of juniors JiU and JiO originally recruited through TNU and other channels, and the number of executives, EiF , EiR and EiP respectively, recruited using Formal channels, employee Referrals and Promotion. If we limit the analysis to stationary values of JiU , JiO , EiF , EiR and EiP , such that the size of each subpopulation of employees in the firm remains constant over time, determination of these P five populations inside the firm will be equivalent to entry flows jiU , jiO , eFi , eR i and ei for each category. Here, we need to make two more assumptions: (i) promotions are effective at the beginning of the year and exit decisions are effective at the end of the year; (ii) promotions are uniformly distributed among juniors and are independent of their origins and tenure in the firm. If k 00 represents the endogenous annual promotion rate of juniors (with k 00 > 0), the dynamics of populations are as depicted in Figure 1.

7 Since the goal of this paper is to analyze the recruitment of top executives, we do not describe these other hiring channels.

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Juniors J¯i

Executives E¯i k¯0 EiR

¯ U kJ i

jiU Top-Notch Universities

Employee Referrals EiR ¯ J¯i jiP = k 00 (1 − k)

JiU

eR i

Promotion

EiP

Formal channel

EiF

k¯0 EiF

eFi

k¯0 EiP

Other channels JiO ¯ O kJ i

jiO

Figure 1: Dynamics of populations

When applied to the components of high job positions, the stationary conditions then become: jiU jiO eFi eR i P ei ePi

= = = = = =

¯ U + k 00 (1 − k)J ¯ U kJ i i O 00 ¯ ¯ kJi + k (1 − k)JiO k¯0 EiF k¯0 EiR k¯0 EiP ¯ J¯i k 00 (1 − k)

(1) (2) (3) (4) (5) (6)

These conditions are completed by the identities (7) and (8): JiO = J¯i − JiU EiR = E¯i − EiF − EiP

2.2

(7) (8)

Heterogeneity of recruitment channels

The five recruitment channels analyzed in this paper are differentiated by three main characteristics: productivity of workers; workers’ wages; and the hiring costs supported by the employer (integrating the penalties associated with the time required to fill a vacancy). For simplicity, we identify these three characteristics in relation to the net productivity of the employees in the firm. Net productivity is the productivity of the worker minus his/her wage and recruitment costs. 2.2.1

Net productivity of juniors

¯ O according to the hiring channel The net productivity of juniors is given by QU and Q O ¯ is assumed to be a given positive parameter (Q ¯ O ≥ 0), (TNU or Other). While Q 6

the net productivity of TNU graduates is endogenous. Indeed, a TNU graduate’s wage is linked to the size of the TNU network N U . This relation between wages and N U renders the net productivity of TNU graduates QU (N U ) endogenous. To gain access to the TNU new graduate job market8 , firms have to invest regularly in “social links” incurring donations and also opportunity costs (e.g. for time spent delivering courses in universities or supervising students in firms). We assume that these donations represent an annual fixed cost c¯U which is assumed to be the average cost to firms of entering this job market. As we are not interested by analyzing the intrinsic effect of training on graduates’ productivity, we do not exclude any ranking between the relative net productivity of TNU graduates and juniors recruited using Other channels: ¯ O , juniors ˆ Case I: For the prevalent level N U of the TNU network, QU (N U ) ≤ Q hired through the TNU channel have lower “net productivity” than those hired through other channels. In this case, if firms choose TNU to recruit new graduates, it is not to increase the direct profit they could expect from their productivity but a way of accessing the TNU network, which may improve the efficiency of future executive recruitment. ¯ O , juniors ˆ Case II: For the current level N U of the TNU network, QU (N U ) > Q hired through the TNU channel have higher “net productivity” than those hired through other channels. If the fixed cost c¯U could be amortized, firms recruit juniors from TNU due to their high net productivity and may (depending on the model’s other parameters) promote these juniors to fill future executive positions. 2.2.2

Net productivity of executives

The net productivity of executives recruited through Formal channel or Promotion is ¯F , Q ¯ P . The net productivity of represented respectively by the positive parameters Q U U executives recruited through employee Referrals is expressed by the function QR i (N , Ji , R P Ei , Ei , φ) where φ is an indicator variable taking the discrete values φ = 1 when the form invests in the TNU and φ = 0 when it does not. Among the three elements which compose this net productivity (gross productivity of the executive recruited through employee Referral, wage, and hiring costs supported by the employer), only the related wage is considered exogenous, while gross productivity and hiring costs are related to the performance of the TNU network. We suppose that the efficiency of the alumni network and consequently the efficiency of employee Referrals channel depend on the size of the alumni network. It is easier to recruit a productive worker from the TNU if the TNU network is large. Hence, the size of the TNU network improves the gross productivity of executives and decreases the time required to fill the vacancy (hiring costs decrease). The net productivity of executives recruited through employee Referrals depends ultimately on (i) the size of this network N U and (ii) the capacity of the firm i to access the TNU channel via JiU , EiP , EiR and φ. (i) Size of the network: expressed as the total number N U of juniors on the job originally recruited from TNU employed in firms (and not the pool of graduates from 8

Since being a TNU graduate is a personal characteristic, these juniors can be reached by the TNU channel but also by Other channels. But we suppose that only juniors who have been recruited through the TNU channel are embedded in an alumni network.

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TNU). It is these junior employees who are assumed to endow the firm with professional networks because they have been hired based on the partnerships between firms and TNU. We assume then that the higher the total number N U of juniors on the job originally from TNU, the higher will be the productivity of agents hired through employee Referrals. Obviously, if no firms recruit graduates from the TNU channel, there is no TNU network and the productivity of executives recruited through employee Referrals depends only on U ¯R its exogenous component such that QR i (N = 0) = Q . (ii) Idiosyncratic capacity of the firm i to access the TNU network: which depends on the decision to invest in the TNU channel φ, the amount JiU of the juniors originally from TNU and the number EiP of promoted executives in the firm i. If the firm i does not recruit juniors from TNU or does not promote juniors, the firm does not benefit from the positive TNU network effect and the productivity of executives recruited through employee Referrals depends only on its exogenous component such that: QR i (φ = 0) = ¯ R , QR (J U = 0) = Q ¯ R and QR (E P = 0) = Q ¯ R . The number E R of executives hired Q i i i i i through employee Referrals also impacts positively on the firm’s capacity to access the TNU network since they have been referred by promoted executives originally recruited via the TNU. Here, we are capturing a self reinforcing effect: if the firm recruits juniors through TNU and promotes them, then the more the employee Referrals channel is used, the greater will be the firm’s capacity to access the TNU network and the higher will be the net productivity of the executives hired through this channel.

2.3

Profit maximization

The objective of the firm is to maximize its intertemporal profit given by: lim

T X

T →+∞

πit (1 + r)−t

t=0

where πit is the annual profit of firm i at time t and r is the rate of actualization that we assume independent of time. At stationary equilibrium, all the undiscounted terms of the periodic profits are identical and the stationary solutions to intertemporal profit are also the solutions to periodic profit maximization. This profit incorporates several argu00 F R P O P U ments represented by 11 variables {jiU , jiO , eFi , eR i , ei , Ji , Ji , Ei , Ei , Ei , k } connected by 8 independent linear conditions (1) to (8). The employer then has only three free controls at stationary equilibrium: once these have been determined, the values of the eight remaining variables can be deduced from conditions (1) to (8). Note that some pairs of variables cannot be controlled for simultaneously by the employer: e.g., eFi and R EiF , or eR i and Ei . However, among the possible compatible controls, the employer has many available possibilities: for instance, he/she can choose {JiU , EiR , EiP } as profit function arguments9 . Under the assumption of stationarity, the optimal periodic profit is represented in this case by: πi∗ =

max

JiU ,EiR ,EiP ,φ

πi (JiU , JiO , EiF , EiR , EiP , φ)

(9)

where 9

We chose these three variables control {JiU , EiR , EiP } but there are other possibilities with one control variable for juniors and two for executives, e.g., {JiU , EiF , EiP }, or {JiO , EiR , EiP } or {JiO , EiR , EiF }.

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ˆ πi is the periodic profit of firm i with,

¯F + EP Q ¯ P + E R QR (φ, J U , E R , E P , N U ) πi = EiF Q i i i i i i   ¯O +φ JiU QU (N U ) − c¯U + JiO Q

(10)

ˆ φ = {0, 1} expresses that, at stationary equilibrium, the employer must invest in the TNU (and pay c¯U ) only if he recruits juniors from TNU; ˆ QR (·) and QU (·) are functions continuous on the arguments.

The structure of the objective function (10)10 , the form of the equality and inequality constraints, and the properties of the functions satisfy the continuity and compactness conditions required to obtain for each admissible values of the parameters and N U , a set ∗ ∗ ∗ ∗ ∗ of solution variables JiU , JiO , EiF , EiR , EiP , k 00 ∗ and φ∗ associated with πi∗ . In the rest of this paper we exclude the singular cases of vanishing measures where this set is not unique. We deduce from this set and from conditions (1) to (8) the optimal annual levels ∗ ∗ ∗ ∗ ∗ of recruitment or promotion jiU , jiO , eFi , eR and ePi of firm i. i Proposition 1 Assumptions about QR i (·) generate three possible optimal recruitment policies: ˆ not investing in the TNU channel for juniors and recruiting executives through only one channel (the most efficient among the three); ˆ recruiting juniors only from the TNU channel and recruiting executives through Formal channel only; ˆ recruiting juniors partly or fully from the TNU channel and using mainly employee Referrals and Promotion to recruit executives.

Proof : see Appendix 1. ¯F , Q ¯ O and c¯U are The first and third of the above policies are polar cases. When Q R large and the recruitment technology Qi (·) not efficient, the employer has no advantage in recruiting juniors through the TNU, or executives through the employee Referrals channel: Other channels are used according to their performance. On the contrary with the third policy, the employee Referrals channel is prioritized, and complemented by the recruitment of TNU young graduates, who will subsequently be promoted to executive positions. This policy is explained by the role of the alumni associations. Note that it this could be the best policy even if the net productivity of TNU new graduates is less than the productivity of juniors recruited through Other channels. In the case of the second, more classical policy, the employer is attracted to TNU based on the higher productivity of young graduates. Below, we develop a specification of the functions QR (·) and QU (·) illustrating these three possible policies. 10

In preliminary versions we tested more elaborated expressions of the profit, including, e.g., possible synergy among executives recruited by different channels: these refinements decrease the technical tractability of the model without changing the results, or the rest of the paper.

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2.4

A specification of the model

U We specify the productivities QR i (·) and Q (·) in the following way:   R P E E ( 13 ) U i i U R U P R U P R ¯ + φbN Qi (Ji , Ei , Ei , N ) = Q Ji Ei + ¯ Ei and

¯U − d N U QU (N U ) = Q


2

(11)

(12)

where b, (b > 0), is the index of quality of the TNU network and d, (d > 0), the strength of the endogenous part of the wage for the TNU channel. The efficiency of the employee Referrals channel QR i (·) is related to the quality of 1 U(3) the TNU network bN . It is related also to recruitment of Juniors in the firm JiU , to the number of promoted workers in firm EiP and to the number of executives from TNU hired through employee Referrals based on executives promoted from juniors from TNU, EiP EiR /E¯i . The expression of QU (·) is simple: the decreasing form of QU (N U ) in this case captures an upward pressure of increased demand of TNU workers on the wages of the new graduates. The policies exhibited by Proposition (1) are summarized in Table 1. Table 1: Analytical solutions of the model φ∗

{J

U∗

;J

O∗

∗

∗

∗

{E F ; E R ; E P }

}

¯ 0; 0} if Q ¯ F > sup[Q ¯ R, Q ¯P ] {E; φ=0

¯ {0; J}

¯ 0} if Q ¯ R > sup[Q ¯P , Q ¯F ] {0; E; ¯ if Q ¯ P > sup[Q ¯ R, Q ¯F ] {0; 0; E} ¯ 0; 0} {E;

φ=1

¯ 0} {J;

or

√ {0;

¯ J( ¯Q ¯ R −Q¯P +bE ¯ JN ¯ U 1/3 )N U 1/3 bE √ ; E¯ 1/3 U ¯ 3bJN

√ −

¯ J( ¯Q ¯ R −Q¯P +bE ¯ JN ¯ U 1/3 )N U 1/3 bE √ } 1/3 U ¯ 3bJN

Table 1 distinguishes the three kinds of solutions emphasized in the previous section. ˆ When the cost of investment in TNU is large, the wage of the young graduated not so low (or their gross productivity not so high) and the efficiency of the employee Referrals not so strong, the employer does not “invest” in TNU (φ = 0). Since the firm is not able to recruit juniors through TNU, the employer uses only the other channels. For executive recruiting, the firm will choose those with the highest net productivity and use only one of the three available channels. ˆ When the cost of investment in TNU is small and the wage of the young graduate quite low (or gross productivity is quite high), the firm will support the fixed cost c¯U (φ = 1). We can obtain corner solutions for the case of juniors where the firm decides to recruit only through TNU. For executives, the linearity of the profit function in E F induces two kinds of solutions:

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– In the first sub-case, the size of the TNU network is quite small and the efficiency of employee Referrals is fairly weak. Then the firm will recruit executives only from the Formal channel: investment in the TNU network is not aimed at using the employee Referrals channel to recruit executives but rather to benefit from low recruitment wage (or the high gross productivity) of the TNU new graduates. This is probably of less relevance since we can assume that the recruitment wage for TNU will not be so low relative to their productivity (this solution corresponds to Case II); – In the second sub-case, the firm uses a combination of Promotion and employee ∗ Referrals to recruit executives (E F = 0). In this case, the size of the TNU network and the efficiency of the employee Referrals are quite high. Then, the employer chooses to invest in TNU and to recruit, and then promote, young graduates since they provide the internal resources that allow the employer search to be reduced thus decreasing hiring costs through the use of the employee Referrals channel. This recruitment policy is of more interest for the remainder of this paper. We selected numerical examples to illustrate the possible outcomes generated by Proposition 1 Example 1. ¯ F = 2.5, Q ¯ P = 2, Q ¯ R = 1, Q ¯ U = 1, Q ¯ O = 1.05 Agents’ net productivity: Q Size: J¯i = 10, E¯i = 40 TNU fixed cost: c¯U = 2 Index of quality of TNU network: b = 0.0015 Number of juniors from TNU on the job: N U = 50 Table 2 shows the optimal values for level of recruitment or promotion maximizing firm i’s profits, within these parameters. Table 2: Optimal values of the level of recruitment and promotion with the associated profit ∗ ∗ ∗ ∗ ∗ J U ; J O ; EF ; ER ; EP Associated Profit U∗ O∗ J = 0 ; J = 10 φ=0 π ∗ = 110.5 ∗ ∗ F∗ E = 40 ; E R = 0 ; E P = 0 ∗ ∗ φ=1 J U = 10 ; J O = 0 π ∗ = 107.5 ∗ ∗ ∗ corner solutions only E F = 40 ; E R = 0 ; E P = 0 ∗ ∗ φ=1 J U = 10 ; J O = 0 π ∗ = 101.29 ∗ ∗ ∗ corner & interior solutions E F = 0 ; E R = 17 ; E P = 23 We see that firm i does not invest in TNU since the associated firm profit is lower than the profit without this investment, i.e. πi∗ (φ = 0) > πi∗ (φ = 1). This choice has an obvious impact on recruitment of juniors as well as on recruitment of executives. Since there is no agent originating from TNU among the juniors, those who are promoted do not have access to the TNU network. Then firm i hires executives only via the Formal ¯F > Q ¯ R and Q ¯F > Q ¯ P ). channel which is the most efficient in this case (Q 11

This result is explained by the small number of juniors from TNU that are in post (N ). Since juniors recruited via the TNU channel are costlier than those recruited via ¯ O ),the firm i will choose to invest in this channel other channels (here we have QU < Q only if the improvements in relation to the recruitment of executives are fairly significant. On the other hand, it might be that the size of the firm (J¯i and E¯i ) is too small relative to the fixed cost of TNU channel of recruitment c¯U . To prove these intuitions, let us consider the same parameter values, associated first with a higher value for the number of juniors from TNU on the job (Example 2), and then with a larger firm size (Example 3). U

Example 2. In this example, we increase the number of juniors from TNU on the job from 50 to 250. The impact of this change on the optimal values for levels of recruitment and promotion is presented in Table 3. Table 3: Optimal values of the level of recruitment and promotion with the associated profit with a larger network size

φ=0 φ=1 corner solutions only

φ=1 corner & interior solutions

∗

∗

∗

∗

∗

J U ; J O ; EF ; ER ; EP Associated Profit U∗ O∗ J = 0 ; J = 10 π ∗ = 110.5 ∗ ∗ F∗ E = 40 ; E R = 0 ; E P = 0 ∗ ∗ J U = 10 ; J O = 0 π ∗ = 95.5 ∗ ∗ ∗ E F = 40 ; E R = 0 ; E P = 0 ∗ ∗ J U = 10 ; J O = 0 π ∗ = 112.2 ∗ ∗ ∗ E F = 0 ; E R = 20 ; E P = 20

Table 3 highlights the relevance of the TNU channel (here πi∗ (φ = 1) > πi∗ (φ = 0)). With a higher number of juniors from TNU on the job, the efficiency of the TNU network increases and results in a higher than expected profit if the firm i invests in this channel. As a result, firm i will recruit all juniors through TNU and use the Promotion and employee Referrals channels for executive recruitment. Note that even if a higher number encourages firms to invest in TNU (via the increased productivity of the executives hired through employee Referrals), too great success of recruitment via TNU will discourage the firm from investing because of the upward pressure it creates on wages. Without any changes in the other parameter values in Example 2, we can confirm that if N U = 500, firms do not invest, and the optimal values of the control variables return to the values in Example 1.

Example 3. The number of juniors in post, recruited via TNU, is the same as in Example 1 ,N U = 50 but here we consider a larger firm such that J¯i = 20 and E¯i = 80 (the proportion of juniors to executives remaining the same). Optimal values for levels of recruitment and promotion in a larger firm are presented in Table 4. The size of the firm has an effect on the composition of the juniors and executives teams: the larger the firm, the smaller proportionally is the weight of the fixed recruit12

Table 4: Optimal values of the level of recruitment and promotion with the associated profit with a larger firm

∗

φ=0 φ=1 corner solutions only

φ=1 corner & interior solutions

∗

∗

∗

∗

J U ; J O ; EF ; ER ; EP Associated Profit U∗ O∗ J = 0 ; J = 20 π ∗ = 221 ∗ ∗ F∗ E = 80 ; E R = 0 ; E P = 0 ∗ ∗ J U = 20 ; J O = 0 π ∗ = 217 ∗ ∗ ∗ E F = 80 ; E R = 0 ; E P = 0 ∗ ∗ J U = 20 ; J O = 0 π ∗ = 404.4 ∗ ∗ ∗ E F = 0 ; E R = 43 ; E P = 37

ment costs of access to the TNU job market. All things being equal, large firms have a greater potential to optimize the use of employee Referrals. The results of comparative statics analysis are presented in Table 5. Table 5: Comparative Statics

F∗

E ∗ ER ∗ EP

¯P > Q ¯R if Q N U b J¯ − − − + + + − − −

¯P < Q ¯R if Q N U b J¯ − − − − − − + + +

E¯ + + +

¯P , Q ¯R ∀Q ¯F Q ¯R Q ¯P Q + − − − + − − − +

We have illustrated the importance of the size and performance of the TNU network for determining the recruitment paths of a given firm and its investment in the higher education system. The size of the TNU network, which we have consider as given, is however the result of the interactions among the decisions made by the firm.

3

Equilibrium and coordination with several firms

When the labor market as a whole is considered, the number of employed juniors N U recruited via TNU becomes endogenous. This number depends on the individual decisions of firms about recruitment JiU (with i = 1, 2, . . . n), which conversely depend on ˜ U (since N ˜ U appears in the expectations of individual firms about TNU network size N ∗ U ˜U ˜U the determination of JiU through functions QR i (N ) and Q (N )). Then the stationary “rational expectation” equilibria are determined by the coincidence between the expec˜ U used by firms concerning the extent and efficiency of the network, and the tations N actual size N U of this network, determined by the optimal choices of the firms. To analyze these equilibria, we first consider firms’ expectations, choices and profits in the case of homogeneous firms, then we extend the analysis to some heterogeneous firm cases. Finally, the possible occurrence of multiple equilibria motivates a welfare analysis.

13

3.1

Homogeneous firms

If there are n homogeneous firms, the size of the network N U is obtained by a multiple of the optimal level of juniors from TNU employed by a single firm: N

U∗

=

n X

∗

∗

˜U) ˜ U ) = nJiU (N JiU (N

(13)

i=1

The general form of equation (10) is compatible with many specifications of the function JiU ∗ . This last depends in turn on the nature of the recruitment policy, and then on ˜ U when the efficiency of the employee Referrals channel. This efficiency increases with N ˜U QR i (·) increases with N , i.e. when the size of the alumni network has a negative effect on the hiring costs of the employer (and a positive effect on the productivity of executives hired by the employee Referrals channel). This network effect creates an increase in the ˜ U on JiU ∗ , for a constant demand for young graduates, i.e. generates a positive effect of N net productivity of young graduates from TNU. At the same time, the wage paid to a young graduate can increase (resulting from the combination of increased demand and increased reputation of TNU), remain stable or even decrease (as an indirect result of the increase in the supply of young graduates, as a consequence of the variation in the size ˜ U ). According to the variation in this wage, the effect of an increase of N ˜ U can be of N an increase or a decrease in N U ∗ . Note however that, if the parameters are such that Case II occurs, the function ˜ U ) cannot be strictly increasing since all firms decide to recruit all their juniors N (N ˜ U = 0. through TNU when N ˜U) If the parameters are such that Case I occurs, the properties of the functions QU (N U∗ ˜U ˜U and QR (N ). A small expected i (N ) give information on the shape of the curve N ˜ U means that firms expect a small TNU network size. Then, the productivity of the N ˜U executives recruited through employee Referrals QR i (N ) remains low. Therefore, if recruiting graduates through TNU, in order to benefit from their “small” network is not ∗ an efficient strategy, the effective TNU network size N U is still equal to 0. For higher ˜ U , the expected size of the network becomes sufficient to generate a posvalues of N ˜U itive effect on QR i (N ) counterbalancing the alumni association fees and the negative ˜ U ) and Q ¯ O . For this value of N ˜ U , firms will begin to recruit difference between QU (N juniors through TNU in order to use the networks for the recruitment subsequently of ∗ executives. Then, the effective TNU network size N U rises sharply to a strictly positive U ¯ U , (0 < N ¯ U ≤ nJ). ¯ When N ˜ continues to increase, many possibilities emerge value N associated with different forms of the net productivity of young graduates. If, from a ˆ U of N ˜ U , the negative effect of an increase in wages (reputation and demand new value N effects dominate the possible supply effect) and/or a decrease in gross productivity (to increase their supply, TNU accept a greater number of students with a lower average ˜ U on level) of young TNU recruited graduates begin to dominate the positive effect of N the efficiency of the employee Referrals channel, then a “reswitching” can occur and the firms may reduce or discontinue their use of this channel. This choice automatically decreases, more or less sharply, the level N U of the TNU young graduates recruited annually. U∗

14

˜U According to the parameter values and to the form of the functions QR i (N ) and ˜ U ), several cases of stationary equilibria associated with different recruitment chanQU (N ∗ ˜U nel choices are possible. Figures 2 and 3 depict the shape of the curve N U (N ) and the U ˜ ) for different values of the parameters asassociated profit curve for the firm i πi∗ (N sociated with the specification in subsection 2.4. They represent respectively what might happen in Cases I and II. The function specification and the values of the parameters chosen are the same as those used in the above numerical examples with the exception ¯ P = 1.5. Note that the parameters b, d, Q ¯ U differ from of two parameters: c¯U = 10 and Q case to case. b 0.002 NU

d 0.000035

¯U Q 1

¯O Q 1.05

b 0.002 NU

∗

d 0.00001

¯U Q 1

¯O Q 1.05

∗

• z

∗

∗

EiF ∗ EiR ∗ EiP |

EiF ∗ EiR ∗ EiP

= 40 =0 =0

•

{z

}

|

˜U N

}| { ∗ JiU = 10 O∗ =0 Ji ∗ EiF = 0 R∗ = 22 Ei ∗ EiP = 18

= 40 =0 =0

•

{z

}

˜U N

πi∗

πi∗

˜U N

˜U N Figure 2b

Figure 2a

Figure 2: Examples of stationary equilibria with homogeneous firms when recruiting TNU graduates is not profitable for juniors

Figures 2a and 2b depict Case I where recruiting TNU graduates for junior positions is not profitable. In Figure 2a there is one single stable equilibrium and in Figure 2b there are two equilibria. In these two representative cases (Figures 2a and 2b), the equilibrium ˜ U = N U ∗ = 0 is obtained: if firms expect that no juniors will be recruited through the N TNU channel, they do not use it. Firms recruit juniors through TNU only if they believe it will be beneficial for future recruitment of high quality executives, which is not the case if firms expect a small TNU network size. This decision not to use TNU induces low levels of profit for these firms. At this equilibrium, firms recruit juniors only through Other channels, and use Formal channel to recruit executives. ˜ U and N U ∗ leads to a second stable In Figure 2b, the increasing relation between N 15

equilibrium with different optimal recruitment choices. If firms expect a high value of ˜ U , they will decide to hire all their juniors through the TNU channel. This creates N higher levels of profit due to the positive impact of the workers from TNU on future recruitments. At this second equilibrium, firms activate the TNU channel while the recruitment of senior executives is done through Promotion and employee Referrals. b 0.001 NU

d 0.00001

¯U Q 2

¯O Q 1.05

∗

• z

}| { ∗ EiF = 40 ∗ EiP = 0 ∗ EiR = 0 ∗ JiU = 10 ∗ JiO = 0

˜U N πi∗

˜U N Figure 3

Figure 3: Examples of stationary equilibria with homogeneous firms when recruiting TNU graduates is profitable for juniors U

¯ and Q ¯ O such that Case II occurs In Figure 3, we have chosen the values of Q ∗ ˜U meaning that recruiting TNU graduates is profitable for junior staff and that N U (N ) U ˜ = 0 but the is never an increasing function. Here, firms invest when they expect N recruitment channel choices are different. Firms hire all their juniors through the TNU ˜ U . Here, the convexity of QU (N ˜ U ) does not play an channel whatever the value of N important role since the pressure on wages is not strong (d is low) enough to reduce the ˜ U . Had the function QU (N U ) number of juniors hired through TNU for high values of N been increasing, we would have the same equilibrium but different values for firm profit. Here the profit function is decreasing due to the negative effect of network size on the net productivity of TNU. A positive effect would have made it increasing. Returning to the general case11 , we can prove the following proposition: 11

∗

With the specification that we chose, the effective size of the TNU network N U can jump from 0 to

16

Proposition 2 When firms are homogeneous, there are multiple rational expectation stationary equilibria if (i) the net productivity of juniors recruited from TNU is lower than those recruited through other channels and if (ii) the optimal recruitment policy of firms consists in recruiting mainly their juniors from TNU when they expect a large network size. This multiplicity generates possible coordination failures but no conflicts of interest among firms. Proof. see Appendix 1. The coordination failures correspond to cases where multiple equilibria are Pareto rankable. In our setting, multiple equilibria can exist when Case I occurs. Specifically, there can be two stable equilibria: a “low” equilibrium where no firms use TNU to recruit graduates, and a “high” equilibrium where all firms recruit one part of their juniors through the TNU channel. Proposition (2) establishes that the profit is systematically higher at equilibrium, when firms choose to use the TNU channel in preference to other channels to recruit juniors. This multiplicity can cause coordination problems (individual firms can expect different stationary equilibria). They also may coordinate over a “low equilibrium”. However, whichever equilibrium causes them to coordinate, all firms rank the two possible equilibria similarly. There are no conflicts of interest among firms. At high equilibrium, firms recruit juniors using the TNU channel and pay the expenses incurred: in this case, the interests of the firms converge with the interests of the universities. The multiplicity of stable stationary equilibria generates only coordination failures between firms and the TNU. If some action can be initiated by the TNU and/or the state to lead employers to ˜ U , this would benefit both firms and TNU. expect a high level of N

3.2

Heterogeneous firms

Different forms of heterogeneity among firms can be considered. Technological differentiation creates a source of heterogeneity with consequences for the productivity parameters. ¯ k¯0 ). Other sources of heterogeneity are firm size (J¯i , E¯i ) and rate of employee turnover (k, In this paper, we focus on two sources of heterogeneity: firm size, and productivity of ¯ U . We tested the TNU recruited graduates captured by the level of the parameter Q other and more complete sources of heterogeneity but the results neither contradicted nor radically enriched the results in this subsection. 3.2.1

Firms heterogeneous by their size

Consider first the case where firms differ only in terms of size, and not the internal distribution of employees between juniors and executives. Suppose that there are nS small firms and nL large firms. The size of small firms is given by (J¯i , E¯i ) = (J¯S , E¯S ), ∀i(i = 1, 2, . . . , nS ), and the size of large firms is given by (J¯l , E¯l ) = (J¯L , E¯L ), ∀l(l = 1, 2, . . . , nL ) with J¯L /J¯S = E¯L /E¯S = m where m > 1. The definition of N U is now given by (14): max max ˜ U . This is due to the linearity of the productivity function QR (·) in NU or from N U to 0 with N i U R J . If the function Qi (·) increased at a decreasing level in J U , a smoother relation would be observed ˜ U and N U , with the possibility of high level stable equilibrium at a value of N U smaller than between N U max N .

17

∗

∗

˜ U ) + nL J U (N ˜U) N U = nS JiU (N l

(14)

As in the case of homogeneous firms, there can be more than one equilibrium. If Case I occurs, hiring junior staff through the TNU channel is not profitable and the equilibrium is unique or not (as in Figure 2a and 2b); if Case II occurs, hiring through the TNU channel is profitable in the case of juniors and the equilibrium is always unique (as in Figure 3). In this second case, both small and large firms invest in the TNU channel ˜ U , i.e. N ˜ U = 0 if the costs incurred and hire graduates for the same particular level of N by using the TNU channel c¯U are quite low, otherwise only large or no firms at all use the TNU channel. ˜ U on the Let us consider Case I where multiple equilibria can occur. The values of N basis of which firms decide to hire through TNU, differs according to firm size. Small ˜ U since they get lower returns on firms never use the TNU channel for lower values of N the fixed costs incurred by this channel. Similarly, small firms never invest for higher ˜ U if there is negative effect of N ˜ U on profit (due to the negative effect of the values of N upward pressure from wages) since their small size exerts a negative effect on these firms’ net productivity. In other words, the heterogeneity of firm size impacts on the range of ˜ U for which recruiting graduates is profitable. The range of the values of the values of N ˜ U where small firms will invest in the TNU channel is never broader than the range of N investment of large firms. If we consider the ranking of equilibria in the case of multiplicity, the analysis is the same as for homogeneous firms. Whatever their size, firms always decide to hire through ˜ U . This decision then is a consequence the TNU channel when their profits increase with N ˜U of the positive effect associated with QR i (N ) on the recruitment of executives. If profit ˜ U )), firms will no longer activate the TNU network. In decreases, (it could be via QU (N this context, small and large firms rank equilibria similarly. Figures 4, 5 and 6 depict the ∗ ˜U shape of the curve N U (N ) when there are multiple stationary equilibria, along with ˜ U ) and large firms π ∗ (N ˜ U ). the associated profit curves for small firms πi∗ (N l It is straightforward to verify that there can be two or three stable equilibria at most, according to the values of the parameters. Let us describe these two situations: ˆ When the values of the parameters involve two stable equilibria, the first is always ˜ U = 0 and neither small nor large firms recruit a “low” equilibrium such that N ˜U > 0 through the TNU channel. The other is a “high” equilibrium such thatN where either small and large firms recruit new graduates or only large firms do so. If both small and large firms recruit through the TNU channel (see Figure 4), the high equilibrium is associated with a larger profit compared to the low equilibrium for all firms. If only large firms recruit through TNU channel (see Figure 4), the equilibrium then gives the same profit for small firms at the low equilibrium, but gives the highest profits to large firms. ˆ When the values of the parameters involve three stable equilibria, the first is always a “low” equilibrium where neither small nor large firms recruit through the TNU channel. The second is a “medium” equilibrium where only large firms invest in the TNU channel and the third is a “high” equilibrium where either both small and large firms or only large firms recruit new graduates using TNU. Suppose that

18

the medium equilibrium is associated with the highest profits for large firms. This ˜ U corresponding occurs only if small firms invest in the TNU channel for values of N to decreasing profits for large firms (this negative effect of N U on profit in this case is ˜ U )). the result of the consequence of the locally decreasing form of the function QU (N ˜ U ) decreases the profit for large firms, it obviously decreases Yet, if the level of QU (N the profit for small ones, which contradicts our assumption: it is not advantageous for small firms to invest in TNU for the third stable equilibrium if it already is not profitable for the second one. We can conclude then that the “high” equilibrium also is greater than the second equilibrium for large firms. For small firms, the “high” equilibrium always gives a greater profit (see Figure 6). Once again, there will be no conflicts of interest among firms. 3.2.2

Heterogeneity of firms based on size and technology

When we add a second level of heterogeneity, the range of possible outcomes increases. We still have 2 or 3 stable equilibria and there is also the possibility to observe coordination ¯U failures. But other outcomes can now emerge. Suppose that a heterogeneity for Q ¯U > Q ¯ U , i.e. is added to the heterogeneity for firm size. For instance, suppose that Q i l that the net productivity of TNU graduates is higher for small firms than for large ones. This case (see Figure 7) could correspond to the coexistence of large “industrial” firms with quite low levels of productivity of high skilled labor, and rather small firms in the services sector, with much higher levels of productivity from the same skilled labor. Another interpretation of heterogeneity in technology could be that the education implied by TNU is more aligned to small than large firms. In such a setting we can prove the following proposition: Proposition 3 In the case of multiplicity, when small firms’ technology is more aligned to the initial training gained at TNU than is large firms’ technology, then conflicts of interest between small and large firms may exist. Proof. see Appendix 3. Figure 7 illustrates one possible case with three stationary (and two stable) equilibria. ˜ U . From N ˜ U = 0 to This figure can be examined in three parts according to the level of N ˜ U = 167, small firms recruit all graduates from TNU to fill junior positions due to their N ˜ U = 167 to N ˜ U = 212, small firms still hire only graduates high productivity. From N through TNU and large firms hire a significant proportion of university graduates given ˜ U = 212 to N ˜ U = 300 their expected positive impact on future executive hirings. From N (this latter proportion being the total number of vacant junior positions), only large firms will recruit through the TNU channel. The first stable equilibrium occurs in the first part of the figure, i.e. when only small ˜ U , small firms have higher firms invest in the TNU channel. For these small values of N profits than in the reservation case, whereas large firms receive the reservation profit. The second stable equilibrium, which is shown in the third part of the figure, gives the reverse results for profits. While small firms do not hire through the TNU channel and achieve the reservation profit, large firms that recruit graduates from TNU, receive greater profit. This illustrates how and why there can be conflicts of interest between small and large 19

firms. Further, these conflicts of interest reflect a stylized fact of the labor market relating to recruitment difficulties experienced by small and medium sized enterprises (SME). A UK report12 shows that 20% of SME feel effective recruitment inhibits their growth, largely due to the higher pay and “perks” larger firms are able to offer. In particular, small business employers find it difficult to recruit TNU graduates although they need their highly specific competences in some sectors (e.g. the case of start-ups in France specialized in open source software13 ). The setting of our model, which emphasizes these inefficiencies, allows us to study whether public policy can help reduce them.

3.3

Welfare analysis

The possibility of a conflict of interest among firms suggests the value of a welfare comparison of equilibria and exploration of the adapted second best solutions. In this setting, the relevant welfare index is the sum of the profits of the firms increased by a term relative to TNU. The index of utility u of TNU has two components. The first is a positive multiple of the total annual fixed cost c¯U supported by the access of n firms to these universities14 . The second component is related to the firms’ payrolls. It might be supposed that tuition fees depend on employment rates and the starting wages of graduates after completion of their education. Then, the utility of TNU could be written as: u = λ(nS + nL )¯ cU + g(N U , QU )

(15)

where g is a continuous function such that δg/δN U > 0 and δg/δQU > 0 since the interest of TNU will be to achieve the highest possible level of recruitment at the higher wage. Then, we can describe the economic welfare of the recruitment system as: W = n S πi + n L πl + u

(16)

When firms are heterogeneous in terms of size and technologies, there can be a maximum of only two stable equilibria (see Appendix 2) which we call equilibrium 1 and equilibrium 2 (denoted E1 and E2 ). We compare the profits of small firms at E1 and E2 and do the same for large firms and the universities. For small firms, E1 (associated with a small TNU network size) always involves a high level of profit since the new graduates hired are more productive and are paid a relatively low starting wage. At the second stable equilibrium E2 (associated with a higher TNU network size), the profit of small firms is smaller, due to the negative effects of the upward pressure of wages. We express the losses from E2 to E1 by ∆πi = (πi )2 − (πi )1 < 0. For large firms, the ranking of E1 and E2 is reversed, i.e. E2 is always more profitable than E1 since an increased network size makes the recruitment of executives more efficient. The extra-profit from E2 to E1 then is such that ltaπl = (πl )2 − (πl )1 > 0. On the TNU side, the ranking of these equilibria is less straightforward because from one equilibrium to the other, the two components of the utility function can move in 12

Tenon Forum Report (2005), Report on Entrepreneurial Britain Wave 1, www.tenongroup.com Le Monde Informatique (2008), “Logiciels libres : les start-up et les PME en mal de recrutement”, www.lemondeinformatique.fr 14 The TNU does not receive the whole of the annual fixed costs since these costs include donations and also opportunity costs. 13

20

opposite directions. The first component λ(nS + nL ) c¯U is related to the number of firms making donations. All things being equal, if there are more small firms than large firms, this first component is greater with E1 than with E2 . Conversely, if there are more large firms than small ones this first component is greater with E2 than with E1 . The second component g(N U , QU ) depends positively on the size of the TNU network and on the level of wages (which also depends positively on the size of the TNU network). E2 then is always associated with the highest value of the second component of the TNU network. In summary, TNU do not always rank equilibria in the same way. According to the relative number and weight of small and large firms, TNU may have conflicts of interest with either small firms or large firms. A sensible case emerges if small firms use the TNU channel only at E1 . Proposition 4 In the case of conflicts of interest, and if small firms use TNU channel only at E1 , if there are more small than large firms nS > nL and if the spread of income from firm donations is higher than the income from tuition fees λ c¯U (nS − nL ) > g2 (N U , QU ) − g1 (N U , QU ), there will be conflicts of interest between large firms and topnotch universities. If these two conditions are not fulfilled, conflicts of interest will emerge between small firms and top-notch Universities. Proof. see Appendix 4. Figure 8 depicts conflicts of interest between firms and TNU. To describe the utility of TNU, we choose the following specification: u = λ(nS + nL )¯ cU + µN U QU . On the one hand, we use the same parameters15 as in Figure 7. Adding the TNU utility function to Figure 7, gives Figure 8a. For these parameter values, we have nS > nL and λ¯ cU (nS − nL ) < g2 (N U , QU ) − g1 (N U , QU ). Figure 8a emphasizes the conflicts of interest between small firms and TNU. On the other hand, in Figure 8b we have chosen parameter values16 such that conflicts of interest emerge between large firms and TNU, i.e. nS > nL and λ¯ cU (nS − nL ) > U U U U g2 (N , Q ) − g1 (N , Q ). The difference in utility from E2 to E1 is such that ∆u = (u)2 − (u)1 expresses extrautility when ∆u > 0 and utility losses when ∆u < 0. Finally, four scenarios can arise: When ∆u > 0 – scenario i: ∆πl + ∆u < ∆πi =⇒ W1 is the “high equilibrium” – scenario ii: ∆πl + ∆u > ∆πi =⇒ W2 is the “high equilibrium” When ∆u < 0 – scenario iii: ∆πl < ∆πi + ∆u =⇒ W1 is the “high equilibrium” 15 ¯ U = 1; Q ¯ U = 2; Q ¯ O = 1.05; J¯S = 10; b = 0.00042; d = 0.00001; c¯U = 5; Q i l ¯ EL = 80; nS = 14; nL = 12; λ = 0.9; µ = 0.5 16 ¯U ¯ O = 1.05; J¯S = 7; b = 0.00042; d = 0.00001; c¯U = 5; QU l = 1; Qi = 2; Q ¯ EL = 200; nS = 20; nL = 10; λ = 0.9; µ = 0.2

21

¯S = 40; J¯L = 20; E ¯S = 28; J¯L = 50; E

– scenario iv: ∆πl > ∆πi + ∆u =⇒ W2 is the “high equilibrium” The government could subsidize the recruitment of TNU graduates in such a way as to achieve the “high” equilibrium state. Consider scenario i. E1 is the “high equilibrium” since the extra-profit for small firms is higher than the losses of the large firms and TNU. To move the recruitment system towards this equilibrium, government must compensate large firms unable to recruit through TNU due to the small size of the network, and compensate TNU that do not receive sufficiently high tuition fees. To achieve this, a part of the small firms’ extra-profit δS could be redistributed to large firms and TNU such that: δS = ∆πl + ∆u. Now consider scenario ii. E2 is the “high equilibrium”. Here, small firms need to be compensated since they are no longer able to recruit TNU graduates (despite their being very productive for these firms) due to the high levels of wages. A part of the large firms extra-profit and TNU extra-utility δL and δT N U could then be redistributed to small firms such that δL + δT N U = ∆πi . Similar logic can be applied to the second set of scenarios. For scenario iii, part of the small firms’ extra-profit and TNU extra-utility should be redistributed to large ones, while for scenario iv, a part of the large firms’ extra-profit could be redistributed to small firms and TNU.

4

Conclusion

The model proposed in this paper analyzes the choice of recruitment channels for high job positions, in a microeconomic setting. We study three recruitment channels used to hire high skilled workers: formal channel, employee Referrals, and internal Promotion. This last channel is used for the recruitment of “juniors” (high skilled but less experienced workers) which can be facilitated by the use of traditional channels or use of top-notch Universities (TNU). In the higher education system, TNU are defined as prestigious institutions providing both high levels of education and strong professional networks among graduates. In the model, this involves connections between juniors hired through the TNU channel and executives hired through the employee Referrals channel. The efficiency of the former channel is dependent on the size of the TNU network in the labor market. If we consider the recruitment choices of individual firms, determination of the optimal hiring decision depends essentially on the firm’s technology, the size of the firm and the size of the TNU network. The model highlights three optimal recruitment policies. If juniors recruited through TNU have lower net productivity than those recruited by Other channels and if both firm and network are small, firms tend to use only one recruitment channel to hire top executives and do not invest in the TNU channel for junior positions. If network and firm are large, then the choice will be to use the TNU channel and to recruit top executives mainly through employee Referrals and Promotion. Finally, if TNU graduates have the highest net productivity, a third recruitment policy can emerge where the firm invests in the TNU channel but uses the Formal channel to recruit top executives when both network and firm are small.

22

When several firms are considered in a stationary equilibrium setting, the same recruitment trends are observed, but the combination of channels generates multiple rational expectation equilibria. We show the existence of potential coordination failures when firms are homogeneous or when heterogeneity is limited. When the heterogeneity of firms is more pronounced, and if the size of the TNU network to some extent exerts a negative effect on firm profit, conflicts of interest can emerge. These can be between small and large firms and also may involve TNU. In particular, this occurs if small firms’ technology is more aligned than large firms’ technology to the initial training received in the top-notch Universities, and if the TNU network size involves an upward pressure on wages. In this case, small firms make higher profits with a smaller TNU network size since the upward pressure on wages is limited, whereas large firms need a large TNU network size to improve their recruitment through employee referrals. These conflicts of interest can lead to a situation where large firms massively recruit TNU graduates thereby preventing small firms from hiring these workers due to their high salary costs. In this case, the model emphasizes the well known recruitment problems faced by SMEs. However, we show that second best policies can be implemented to improve the welfare properties of the market equilibria. Among the five recruitment channels studied, the characteristics of the TNU channel used to recruit juniors, are significant for determining firms’ hiring policies. Strategic connections between this channel and the employee referrals channel, used to recruit top executives, can lead firms to consider the recruitment process as part of a long term ¯ U ) and the TNU network quality (b) are especially strategy. Graduates productivity (Q important in the model. TNU network quality is the intensity of interactions between graduates. For instance, a high quality TNU network is one where graduates stay in touch throughout their professional careers which helps their employers to recruit more efficiently in the future. Hence, if the quality of the TNU network quality is high, firms will recruit graduates and promote them thus benefitting from their efficient networks via the employee Referral channel. At the same time, the net productivity of graduates matters and may be a barrier to such a recruitment policy if TNU graduates are too expensive in terms of wages, compared to juniors recruited via other channels. At this stage, it could be argued that the two critical parameters (graduates’ productivity and TNU network quality) could become endogenous through the actions of the top-notch Universities. In this paper, we described the utility of TNU but without introducing strategic behavior or possible control variables. However, even though the endogeneity of these parameters will increase the complexity of the model, it will not change the main results. The strategic choices made by these high performing TNU might determine whether one recruitment policy is preferred over another but will not change the type of the recruitment policy. For instance, the TNU network may work on strengthening the ties among members, which may lead some firms to invest more in this channel and to exploit employee Referrals and Promotion. However, if the TNU network quality is not very good (weaker ties among members) firms will be more likely to concentrate their recruitment policies on the Formal channel and recruit fewer TNU graduates. Moreover, some of the top-notch Universities’ strategies will generate coordination failures as well as conflicts of interest among firms. In the context of this paper, integrating the strategic choices made by TNU does not provide any supplementary results. Yet, the role of TNU necessarily changes the way 23

informal recruitment is used by employers. More particularly, when employers choose to recruit using informal channels, different kinds of networks may be mobilized such as friends, relatives, former colleagues but also former students. As a result, the role of TNU matters since such institutions could be seen as “providers of networks” through the actions of their alumni associations. Thus, looking inside the “black box” of informal recruitment and considering TNU as a strategic actor would appear to be important, and should be the subject of future research.

Appendix Appendix 1: Proof of Proposition 1 Given the expression of the periodic profit (10) and the assumptions in subsection 2.2 on the form of function QR (·) in which EiF and JiO are deduced by equations (1) to (8) from the control variables (JiU , EiR , EiP ), the optimized profit (9) can be written as: πi∗ =

max

JiU ,EiR ,EiP ,φ

¯F + EP Q ¯P + ERQ ¯ R + Q0R (J U , E R , E P , φ) [(Ei − EiR − EiP )Q i i i i i i U ¯O] +φ(JiU QU ¯U ) + (Ji − JiU )Q i (N ) − c

Given that φ = {0, 1}, this expression can be rewritten as:    ¯i − E R − E P )Q ¯F + EP Q ¯P + ERQ ¯ R + (Ji − J U )Q ¯O max (E  i i i i i  J U ,E R ,E P i  i i  sup ¯i − E R − E P )Q ¯F + EP Q ¯P + ERQ ¯ R + Q0R (J U , E R , E P , 1) + J U QU (N U ) − c¯U + (Ji − J U )Q ¯O (E  i i i i i i i i i i i  U max P R Ji ,Ei ,Ei

If the first term of this expression is the greatest, the optimal solution is a corner solution with φ∗ = 0, JiU ∗ = 0 and JiO∗ = J¯i . In this case, we also obtain corners solutions ¯ P > sup[Q ¯F , Q ¯ R ], the optimal solution has the components in EiR , EiP and EiF . If Q P F ∗ R∗ P∗ ¯ > sup[Q ¯F , Q ¯ R ], the optimal solutions become (Ei = E¯i , Ei = 0, Ei = 0), if Q ¯ R > sup[Q ¯F , Q ¯ P ], the optimal solutions are (EiP ∗ = 0, EiR∗ = 0, EiF ∗ = E¯i ) and when Q (EiP ∗ = 0, EiR∗ = E¯i , EiF ∗ = 0). If the second term is the greatest, we have φ∗ = 1. Two sub-cases then become possible: ¯ O ≤ QU (N U ), we have J U ∗ = J¯i and J O∗ = 0. According to the specification of (i) if Q i i i P P∗ Q0R = 0, EiR∗ = 0, EiF ∗ = i (·) and the magnitude of Q , the remaining solutions are (Ei P ∗ R∗ F ∗ P ∗ R∗ F ∗ E¯i ), (Ei = E¯i , Ei = 0, Ei = 0) or (Ei > 0, Ei > 0, Ei ≥ 0) which can be interior in two or three arguments. When (EiP ∗ = 0, EiR∗ = 0, EiF ∗ = E¯i ), the employer pays the TNU in order to benefit from the high net productivity of the young graduates. The employee Referral channel is not used because the Formal channel is more efficient to recruit executives. When (EiP ∗ ≥ 0, EiR∗ > 0, EiF ∗ ≥ 0)) are components of the optimal solution, the fees are paid to recruit young graduates and to use, to a greater or lesser extent, the employee Referral channel for the appointment of executives. ¯ O ≥ QUi (N U ), we have JiU ∗ > 0 and JiO∗ = J¯i − JiU ∗ . In all cases, we have (ii) if Q then (EiP ∗ > 0, EiR∗ > 0, EiF ∗ ≥ 0). The employer pays the TNU because the employee Referral channel is efficient: since it is necessary to recruit new graduates to activate this 24

channel, the firm accepts the high wages demanded by less productive juniors as payment for “buying their networks”. Finally, we can obtain three possible optimal policies: - (φ∗ = 0, JiU ∗ = 0, JiO∗ = J¯i , EiP ∗ = {0, E¯i }, EiR∗ = {0, E¯i − EiP ∗ }, EiF ∗ = {0, E¯i − EiP ∗ − EiR∗ }) - (φ∗ = 1, JiU ∗ = J¯i , JiO∗ = 0, EiP ∗ > 0, EiR∗ > 0, EiF ∗ ≥ 0) - (φ∗ = 1, JiU ∗ > 0, JiO∗ = J¯i − JiU ∗ , EiP ∗ > 0, EiR∗ > 0, EiF ∗ ≥ 0) which correspond to the three possibilities presented in Proposition 1.

Appendix 2: Proof of Proposition 2 ˜ U = 0. If Case I occurs N U = Consider first the optimal choices of firms when N P Pn ∗ ∗ n U U U ¯ i=1 Ji (0) = nJi > 0. i=1 Ji (0) = 0 and if Case II N = ∗

In Case I, N U ∗ = 0 is a stationary equilibrium with ∀i, JiU = 0 and c¯U = 0. Since ˜ U increases, they all choose to invest or not in TNU chanfirms are homogeneous, when N ¯ U (as in the examples in Figures 2a and 2b). If N U (N ¯U) ≥ N ¯U, nel for the same value of N ¯ U . In this case, there is always there is a stationary but unstable equilibrium at N U = N ¯ U , and nJ¯i . If this a third stationary equilibrium which may be stable or not, between N second stable equilibrium exists, at this equilibrium, the profit of the firm is still greater than the profit associated with the equilibrium N U ∗ . If not, the firms that expect the level N U ∗∗ for the alumni network would have chosen not to recruit juniors through the TNU channel: since this choice contradicts the stationary nature of N U ∗∗ , we conclude that the profit corresponding to N U ∗∗ is greater than the profit corresponding to N U ∗ = 0. In Case II, given that firms are identical and since they can expect no special gain from the promotion of juniors that were recruited through the TNU, when N U = 0, EiR (N U ) = 0 but since all firms are the same, ∀i, JiU (N U ) = J¯i . If recruitment is via TNU, this is justified only by the net productivity of these employees as juniors. The only stationary equilibrium then is N U ∗ = n J¯i (see Figure 3) where all firms choose to recruit juniors through the TNU channel. We conclude that Case II is a case of uniqueness. We conclude also that as there is more than one stable stationary equilibrium, the equilibrium corresponding to the larger size of the alumni network is preferred by all firms.

Appendix 3: Proof of Proposition 3 Suppose that conditions c1, c2 and c3 hold. c1: the profit of small firms is a decreasing ¯ O ). c2: when large firms are not considered, function of N U (i.e. we are in Case I, QU ≥ Q there is one single stationary equilibrium N U ∗ such that 0 < N U ∗ < nS J¯i +nS J¯l and this equilibrium is stable. c3: when large firms are included, N U ∗ is still equilibrium and corresponds to the case where only small firms invest in the TNU channel. These assumptions are perfectly compatible with the dual form of heterogeneity assumed in ˜ U = 0. This this section. If c2 holds, small firms invest in the TNU channel when N U ¯ of the juniors recruited through this investment is motivated by the productivity Q i 25

channel. Given c1 to c3, N U ∗ is the first equilibrium when all firms are considered. The second equilibrium N U ∗∗ is then located on an increasing portion of N U ∗∗ . This second equilibrium is unstable and corresponds to a situation where large firms recruit some or all of their juniors through TNU. If there is a third (and stable) stationary equilibrium ˜ U , this equilibrium corresponds to a N U ∗∗∗ , since the small firms profit decreases with N ˜ U = N U ∗∗∗ , case where the profits of large firms are locally decreasing. However, when N the large firms choose to maintain a positive level of recruitment of juniors from TNU: this implies that their profit is greater when N U = N U ∗∗∗ than when N U = N U ∗ . Between N U ∗ and N U ∗∗∗ , then, there is a conflict of interest between the small and the large firms.

Appendix 4: Proof of Proposition 4 Consider the case where firms are heterogeneous in terms of size and technologies. Appendix 2 shows that conflicts of interest arise between firms when there are two stable equilibria. More precisely, recall that this situation involves the following properties of equilibria. At equilibrium 1, only small firms recruit through the TNU channel. At equilibrium 2, there are two possible cases: either that both small and large firms recruit through TNU, or only large firms do so. Figure 9 depicts these two cases which we analyze from the TNU viewpoint. If at equilibrium 2, both small and large firms invest in the TNU channel (see Figure 9a), the utility associated with each equilibrium is such that u1 = λ(nS ) c¯U +g1 (N U , QU ) and u2 = λ(nS + nL ) c¯U +g2 (N U , QU ) whereu2 > u1 since g(N U , QU ) is an increasing function of N U and QU (involving g2 (N U , QU ) > g1 (N U , QU )). Then, in this case there will always be conflicts of interest between small firms and TNU. If at equilibrium 2, only large firms invest in the TNU channel (see Figure 9b), the levels of utility become u1 = λ(nS ) c¯U +g1 (N U , QU ) and u2 = λ(nL ) c¯U +g2 (N U , QU ). At this stage, it is clear that if nL > nS , then u2 > u1 and, again, conflicts of interest between small firms and TNU emerge. Conversely, if nL < nS , the equilibrium associated with the highest utility depends on the comparison between the spread of income from firms’ donations and the spread of income from tuition fees. Thus, if λ c¯U (nS − nL ) < g2 (N U , QU ) − g1 (N U , QU ), then there will be conflicts of interest between small firms and TNU. Finally, it becomes obvious that conflicts of interest between large firms and TNU emerge only if nL < nS and λ c¯U (nS − nL ) < g2 (N U , QU ) − g1 (N U , QU ).

References Barron, M.J., Black, D.A. and Loewenstein, M.A. (1987). “Employer size: the implications for search, training, capital investment and wage growth”, Journal of Labor Economics, 5, pp. 76-89. Bessy, C. and Marchal, E. (2009). “Le rˆole des r´eseaux et du march´e dans les recrute´ ments. Enquˆete aupr`es des entreprises”, Revue Fran¸caise de Socio-Economie, 3, pp. 121-146. Bessy, C. and Marchal, E. (2007). “L’usage des canaux de recrutement par les entreprises”, Document de travail du Centre d’´etudes de l’emploi 89. 26

DeVaro, J. (2008). “The labor market effects of employer recruitment choice”,European Economic Review, 52, pp. 283-314. DeVaro, J. (2005). “Employer recruitment strategies and the labor market Outcomes of New Hires”, Economic Inquiry, 43, pp. 263-282. Gorter, C. and Van Ommeren, J.N. (1999). “Sequencing, timing and filling rates of recruitment methods”, Applied Economics, 31, pp. 1149-1161. Marmaros D. and Sacerdote B. (2002). “Peer and Social Networks in Job Search”, European Economic Review, 46, pp. 870-879. Montgomery, J.D. (1991). “Social networks and labor-market-outcomes: toward an economic analysis”, American Economic Review, 81, pp. 1408-1417. Pellizzari, M. (2010). “Do friends and relatives really help in getting a good job?”, Industrial and Labor Relations Review, 63, pp. 494-510. Pellizzari, M. (2005). “Employers’ search and the efficiency of matching”, IZA Discussion Paper 1862. Rebick, M. (2000). “The Importance of Networks in the Market for University Graduates in Japan: A Longitudinal Analysis of Hiring Patterns”, Oxford Economic Papers, 52, pp. 471-496. Rees, A. (1966). “Information networks in labor markets”, American Economic Review, 56, pp. 559-566. Rees, A. and Schultz, G.P. (1970). Workers and wages in an urban labor market, Chicago, University of Chicago Press. Roper, S. (1988). “Recruitment methods and vacancy Duration”, Scottish Journal of Political Economy, 35, pp. 51-64. Russo, G., Gorter, C. and Shettkat, R. (2001). “Searching, hiring and labour market conditions”, Labour Economics, 8, pp. 553-571. Russo, G., Rietveld, P., Nijkamp, P. and Gorter, C. (2000). “Search channel use and firms’ recruitment behaviour’, De Economist, 148, pp. 373-393. Simon, J.C. and Warner, T. (1992). “Matchmaker, matchmaker: the effect of old boy networks on job match quality, earnings and tenure’, Journal of Labor Economics, 10, pp. 306-330.

27

b

d

J¯S

¯S E

J¯L

¯L E

nS

nL

0.002

0.00001

10

40

20

80

15

10

NU

∗

˜U N Equilibrium correspondence

πi∗

˜U N πl∗

Small firms profit

˜U N Large firms profit

Figure 4: Example of two stationary equilibria where both small and large firms recruit through TNU channel

28

b

d

J¯S

¯S E

J¯L

¯L E

nS

nL

0.001

0.00001

10

40

20

80

15

10

NU

∗

˜U N πi∗

Equilibrium correspondence

˜U N πl∗

Small firms profit

˜U N Large firms profit

Figure 5: Example of two stationary equilibria where only large firms recruit through TNU channel

29

b

d

J¯S

¯S E

J¯L

¯L E

nS

nL

0.002

0.00001

10

40

30

120

25

5

NU

∗

˜U N πi∗

Equilibrium correspondence

˜U N πl∗

Small firms profit

˜U N Large firms profit

Figure 6: Example of three equilibria where both small and large firms recruit through TNU channel

30

b

d

¯O Q

¯U Q l

¯U Q i

J¯S

¯S E

J¯L

¯L E

nS

nL

0.00042

0.00001

1.05

1

2

5

10

20

80

14

12

NU

∗

˜U N πi∗

Equilibrium correspondence

˜U N πl∗

Small firms profit

˜U N Large firms profit

Figure 7: Conflicts of interest with firms heterogeneous by their size and technology

31

Figure 8a: Conflicts of interest between small firms and top-notch Universities

NU

Figure 8b: Conflicts of interest between large firms and top-notch Universities

∗

NU

∗

˜U N πi∗

˜U N

Equilibrium correspondence

πi∗

Equilibrium correspondence

˜U N πl∗

˜U N

Small firms profit

πl∗

Small firms profit

˜U N u∗

˜U N

Large firms profit

u∗

Large firms profit

˜U N

˜U N

TNU utility

TNU utility

Figure 8: Conflicts of interest between firms and top-notch Universities

32

NU

∗

NU

∗

˜U N

˜U N

Figure 9a: Both small and large firms recruit through TNU at equilibrium 2

Figure 9b: Only large firms recruit through TNU at equilibrium 2

Figure 9: Properties of equilibria when there are conflicts of interest between firms

33