Journal of Economic Behavior & Organization Vol. 39 (1999) 201–217

Efficiency wages and the quality of job matching Mohamed Jellal a , Yves Zenou∗,b,c a

c

Department of Economics, Université de Rabat, Rabat, Morocco b ERMES, Université Panthéon-Assas, Paris, France CERAS, Ecole Nationale des Ponts et Chausseès, 28 rue des Saints-Pères, 75007 Paris, France Received 16 June 1997; accepted 12 June 1998 Communicated by Dr. R. Day

Abstract We introduce the quality of job matching in the effort function in order to calculate the efficiency wage. We consider two cases. In the first one, the quality of the match is perfectly observable by the firm and we show that the equilibrium unemployment level is due to both high wages and mismatch. In the second case, we assume that job matching is a random variable and we show that there are some regions in which the (efficiency) wage raise generates an effort greater than the initial wage increase and others where the reverse prevails. ©1999 Elsevier Science B.V. All rights reserved. JEL classification: J41; D8 Keywords: Solow condition; Job complexity; Technology; Uncertain effort; Job matching; Wage dispersion; Unemployment

1. Introduction The efficiency wage literature (Akerlof and Yellen, 1986) stipulates that there is a direct and increasing relationship between the wage paid by firms and workers’ effort. What is generally assumed is that firms can evaluate the exact impact of their wage setting on workers’ effort level. In this context, maximizing profit firms set an efficiency wage such that the effort–wage elasticity is equal to one. This is referred to as the Solow condition (Solow, 1979). The employment level is then determined by equalizing the efficiency wage to the workers’ marginal productivity. The main properties of this efficiency wage are that it is independent of the firm’s technology and of the structure of the product market: it is only determined by productivity efficiency and it is not a result of the intersection between labor ∗

Corresponding author. E-mail: [email protected]

0167-2681/99/$ – see front matter ©1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 2 6 8 1 ( 9 9 ) 0 0 0 3 2 - 3

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supply and labor demand. If for example, there is a downward demand shock in the product market, this does not alter the efficiency wage but reduces the equilibrium employment level. However, several (empirical) studies have emphasized the fact that motivation and thus effort are strongly affected not only by wages, but also by non-pecuniary aspects of the job. Economists are often accused by sociologists and industrial psychologists of being too narrow in their focusing exclusively on monetary variables ignoring the perhaps more important psychological ones. This is partly true but there have been some recent papers on non-pecuniary attributes to the job. In particular, jobs being more and more complex (Lazear 1992,1995), the matching between jobs and workers is in general not perfect, even after vocational training. Moreover, sociological aspects such as social status (Frank, 1985; Blinder, 1988) and the feeling of being fairly treated (Akerlof, 1982; Akerlof and Yellen, 1990) are important factors in motivating workers. 1 Thus, even though firms set high wages, there may be a job matching problem because of the firm’s manpower strategy in terms of non-pecuniary aspects of jobs, which are not always under the control of the firm. This implies that one must introduce wages but also the quality of the job matching in the effort function in order to take into account all these factors. This drastically changes the analysis since the efficiency wage and the optimal level of effort will crucially depend on the quality of job matching. In this context, the standard result of the efficiency wage literature (i.e. the Solow condition) does not hold in general. Criticizing the Solow condition is nothing new. In their introduction, Akerlof and Yellen (1986) stipulate that the effort–wage elasticity is less than one. Different reasons have been given in the literature. Schmidt-Sørensen (1990) introduces fixed employment costs per worker (such as employer-provided health insurance) in the profit function. Pisauro (1991) takes into account specific taxes on labor. Rasmaswamy and Rowthorn (1991) drop the assumption of the labor-augmenting production function and use a general one. Lin and Lai (1994) propose a dynamic model with (external) turnover costs. Jellal and Zenou (1999) propose also a dynamic framework in which the effort increase is due to a learning by doing process. They have all shown that the Solow condition does not hold and that in general effort–wage elasticity is less than one. In this paper, we follow a different path by investigating the relationships between the non-pecuniary characteristics of the job, the effort–wage elasticity, unemployment and wage dispersion. If jobs are quite simple (e.g. assembly lines) so that job matching is rather good, firms can perfectly motivate their workers by using only pecuniary compensations. In this case, (efficiency) wages are such that the effort–wage elasticity is equal to one and unemployment is due to too high and downward rigid wages. If jobs are more complex so that the quality of job matching is less obvious, firms have to take into account non-pecuniary attributes of the job to motivate their workers. However, since a job is mostly defined by its technology which is in general not under the firms’ control (at least in the short run), firms must motivate their workers by using only monetary compensations. Two cases can be contemplated. In the first one, jobs are not so complex so that firms are able to observe 1 In sociology (in particular the theory of organization), the impact of the non-pecuniary aspects of the job on motivation within a firm has been studied for several years (see e.g. Roethlisberger and Dickson, 1939; Maslow, 1954; McGregor, 1960; Leavitt, 1969).

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the non-pecuniary aspects of the job and thus the quality of job matching. As before, they set (efficiency) wages such that the effort–wage elasticity is equal to one. However, at this wage, some part of the motivation is not controlled since it depends on the non-pecuniary attributes of the job. We have here the same type of unemployment as before. In the second case, jobs are so complex that firms cannot even observe the quality of job matching and thus the workers’ effort level. In this context, we show that firms can either set wages such that the effort–wage elasticity is lower or greater than one, depending on the trade-off between effort and marginal productivity, and marginal effort and marginal productivity. This result is quite intuitive since the effort function is now a random variable and since firms are not able to evaluate the consequences of their wage policy on workers’ motivation. Therefore, there is no need to set high wages. According to these results and since unemployment is mainly due to high wages, its level can be either high or low depending on the complexity of the job. Finally, we are able to explain inter-industry as well as intra-industry wage differences for identical workers by assuming that industries are characterized by different types of jobs. The remainder of the paper is as follows. The Section 2 describes the model where the quality of job matching is perfectly observable by the firm. Section 3 investigates the case when the effort becomes uncertain because of the non-observability of the job matching. In Section 4, we explain inter-industry and intra-industry wage differences by using the results of the previous sections. Finally, Section 5 concludes the discussion.

2. Observable job matching In the standard literature (see e.g. Layard et al., 1991, Chap. 3), the effort of each worker is unobservable but the aggregate effort is observable. It is indeed difficult to estimate the quality of the work, the degree of initiative etc... In this case, the employer has to rely on his pecuniary compensation (the wage w) to motivate workers. The main result is that the effort–wage elasticity is equal to one. In this (canonical) model, the effort function depends only on pecuniary compensations and not on other factors that may affect productivity. We believe that this does not capture the entire story. As stated in the Introduction, recent studies (in particular in sociology) have shown the importance of the non-pecuniary aspects of the job. When a firm hires a worker, the latter does not know the different aspects of the job like its complexity, the relationships with his colleagues, his social status ... Lazear (1992,1995) has investigated (both theoretically and empirically) some of these aspects. For him, a job is a collection of tasks and tasks associated with a particular job are not determined in advance but are rather dependent on the particular worker that fills the vacant job. Empirically it is quite difficult to define a job, especially when one wants to take into account its non-pecuniary aspects and the quality of the job matching. Akerlof et al. (1988), Bowlus (1995), Lazear (1992,1995), Teulings (1995) have tried to define more precisely the characteristics of a job and its relation with job matching. Teulings (1995) shows that there is a strong correlation between job characteristics and job complexity. In order to define the non-pecuniary attributes of a job and the quality of job matching, Akerlof et al. (1988), Lazear (1992,1995), Bowlus (1995) introduce a dynamic aspect, namely, the path of a job. In their analysis, a good match is represented by a lengthy duration. Indeed, the quality of

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the match is not known ex ante, but must be experienced (Jovanovic, 1979). They show that non-pecuniary match characteristics play an important role in labor mobility. Another important feature that defines non-pecuniary attributes of a job is to consider its sociological aspects. Akerlof (1982) and Akerlof and Yellen (1990) show that each worker considers himself as belonging to a group where he can evaluate its mean characteristic. Therefore, the feeling of being fairly treated according to the group reference is an important element of workers’ motivation (see also Fehr et al., 1993 who show through experiments the influence of sociological aspects on work effort). Moreover, Frank (1985) and Blinder (1988) have pointed out the fact that workers care deeply about their relative status in society: their utility and thus their effort function depends not only on the level of income, but also on their social status. All these elements can be summarized by stating that there is a matching problem between the worker and the job and that the worker discovers the complexity and the sociological aspects of the job once he is employed. Obviously, his effort level will depend strongly on these aspects and thus on the quality of the job matching. All of these non-pecuniary aspects of the job can be summarized by the technology which dictates certain aspects of the job, such as whether it can be part-time or full time, or how hard you need to work. In other words, technology indicates the characteristics of the job and thus the degree of its complexity (Teulings, 1995) and firms have no control over it. We are aware that there are other non-pecuniary aspects of the job over which firms have some control like how pleasant the work environment is, whether the place is adequately heated etc... but we believe that the technology component is the most important one and we therefore intend to focus on it. However, in this section we consider only non-complex jobs so that, even if the firm does not have any control over it, it can easily observe the matching between the worker and the job. There is a one-to-one relationship between job complexity and the observation of the quality of the job matching. In other words, when the job is not complex, the quality of the job matching is perfectly observable by the firm, even though it has no control over it. In order to capture this idea, we assume that the worker’s indirect utility function is a function of the wage, w, the effort, e, and the quality of the job matching, θ so that it writes: V (w, e, θ). It is assumed that: 2 Vw (.) > 0,

Vww (.) < 0,

Vθ (.) > 0,

Veθ (.) > 0,

Ve (.) ≷ 0,

Vee (.) < 0,

Veθ θ (.) < 0,

Veeθ (.) < 0

Vew (.) > 0,

The employer knows that, given w and θ (taken as given), each worker chooses e that maximizes his utility function. We have therefore: maxV (w, e, θ) e

(1)

First-order condition of Eq. (1) yields: 3 Ve (w, e, θ) = 0 2 3

All functions with subscripts indicate partial derivatives. It is easily checked that the second-order condition is always satisfied.

(2)

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Since all workers are assumed to be identical, Eq. (2) characterizes the following aggregate effort function: 4 e = e(w, θ)

(3)

which by totally differentiating (3), has the following properties: Vew >0 Vee Veθ > 0, eθ (w, θ ) = − Vee

ew (w, θ ) = −

Veww Vee − Vew Veew < 0, (Vee )2 Veθθ Vee − Veθ Veeθ eθθ (w, θ) = − 0 and f 00 (.) ≤ 0. In this context, given the effort function (3) and given the assumption on the production function, the maximization of the profit function with respect to w and l yields: 5w (w, θ ) = f 0 (e(w, θ)l)ew l − l = 0 0

5l (w, θ ) = f (e(w, θ)l)e(w, θ) − w = 0

(4) (5)

By combining Eqs. (4) and (5), we obtain the following efficiency wage w∗ (θ ): 8e/w =

ew (w ∗ , θ)w∗ =1 e(w∗ , θ)

(6)

This is the generalization of the so-called Solow condition (in which θ = 1) stating that effort–wage elasticity 8e/w is equal to 1. Observe that Eq. (6) is an equilibrium condition that follows from the effort function and the production function. Observe also that the efficiency wage depends only on the parameters of the effort function and not on the production technology. This efficiency wage w∗ does not in general clear the market and unemployment will prevail in equilibrium. The firm chooses the employment level that maximizes its profit. 4 Observe that the effort function is different from the one introduced by Layard et al. (1991) and others in which e = e(w, w) where w is the average wage of the sector. The main difference is that in equilibrium all firms set the same (efficiency wage) w = w whereas here w is always different to the quality of the job matching θ, even in equilibrium.

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By using Eq. (5), we obtain the following condition stating that the labor cost is equal to marginal productivity: w∗ (θ ) = f 0 (e(w∗ (θ), θ)l ∗ ) e(w∗ (θ ), θ)

(7)

If we suppose that there are M identical firms in the economy, they all set the same efficiency wage w ∗ (θ). Since all firms are identical, the aggregate employment level L is such that L = Ml. Hence, if we now introduce the aggregate production function, F (.), defined for all L by F (e(.)L) = Mf (e(.)L/M), and observe that by definition F 0 (e(.)L) = Mf 0 (e(.)L/M)(1/M) = f 0 (e(.)l), it follows that in equilibrium, the profit maximization condition must have the equivalent aggregate form: w ∗ (θ ) = F 0 (e(w∗ (θ), θ)l ∗ ) e(w∗ (θ ), θ)

(8)

We are interested in the relation between w and θ which is made explicit by the following proposition. Proposition 1. The relation between w and θ is as follows: dw ≷ 0 dθ

⇔

4ew /θ ≷ ϒF 0 /e 4e/θ

(9)

where 4ew /θ = ewθ θ/ew , 4e/θ = eθ θ/e and ϒF 0 /e = F 00 e/F 0 are respectively the marginal effort-job matching elasticity, the effort-job matching elasticity and the marginal productivity-effort elasticity. Proof. By totally differentiating Eq. (4), we obtain: 5wθ dw =− dθ 5ww The concavity of the profit function implies that 5ww < 0. So   dw = sgn (5wθ ) sgn dθ where 5wθ = F 0 ewθ + F 00 eθ ew . Therefore, we have:  
dw = sgn F 0 ewθ − F 00 eθ ew sgn dθ Thus: dw ≷ 0 dθ

⇔

F 0 ewθ ≷ eθ ew F 00

which by rearranging this condition leads to Eq. (9). The following comments are in order. First, the impact of θ on w depends on the two production technologies, F (.) and e(.), and thus on the curvature of these functions. If ϒF 0 /e

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is small, i.e., the marginal productivity of effective labor (eL) is not very sensitive to effort, then dw/dθ is more likely to be positive. Therefore, if the production is very concave, that is, there are very important decreasing returns to scale in effective labor, then the better the job match the lower the wage. Second, when the quality of job matching gets better, the resulting increase in the marginal effort can be greater or lower than the resulting increase in the effort level. If, for example, it is lower, then dw/dθ < 0. This means that the increase in θ has a larger influence on e than on ew and therefore maximizing profit firms can reduce the efficiency wage. Third, θ can be different among workers. For example, when ex ante identical workers apply to the firm, it may be that ex post they are heterogeneous in terms of job matching. Imagine that all applicants have a bachelor degree in economics but once employed have a different match with their jobs. If they are all hired at the same wage (which is natural since they all have the same diploma), then there will be a distribution of efforts according to the quality of the job match. Since θ is perfectly observable, the firm can discriminate between workers according to Eq. (9). This can be a testable prediction to explain inter-industry wage differences. 5 It is because θ varies across industries that wages are different. Last, if we denote by N the total labor force, the (equilibrium) unemployment level is equal to: U ∗ = N − L∗ (w ∗ , θ)

(10)

which depends crucially on θ. We have therefore: ∂L∗ ∂w∗ ∂L∗ dU ∗ =− − dθ ∂w ∂θ ∂θ

(11)

where the first term of the RHS of Eq. (11) is the indirect effect via the wage and the second term is the direct effect. Since ∂L∗ /∂w < 0 and since sgn (∂w∗ /∂θ ) = −sgn (∂L∗ /∂θ ), we have: if

∂w ∗ ≷ 0, ∂θ

then

∂U ∗ ≷ 0 ∂θ

(12)

The intuition runs as follows. If ∂w∗ /∂θ < 0 (this is what we should generally expect, i.e. the better the quality of the job match, the lower is the wage needed to motivate workers), then when job matching worsens, unemployment level increases. This is typically a mismatch type of unemployment as pointed out by Pissarides (1990) and Layard et al. (1991). We have shown in another context (where workers and firms are heterogeneous and when there is imperfect competition in the labor market) that mismatch is an important feature of the labor market which helps understanding the microfoundations of unemployment (see Jellal et al. (1997)). Let us illustrate this case by an example. The utility function is given by: i e2 h V (w, e, θ) = e −a + (wθ)b − 2 5

We will extensively discuss this issue in Section 4.

(13)

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where a > 0 and 0 < b < 1. It is easily checked that: Vw = ebwb−1 > 0, Vθ = eb(wθ)b−1 > 0,

Vww = eb(b − 1)wb−1 < 0,

Vew = Vwe = bwb−1 > 0,

Veθ = Uθe = b(wθ )b−1 > 0,

Vθ θ = eb(b−1)(wθ )b−1 0,eww < 0, ewθ > 0, eθ > 0 and eθ θ < 0. The efficiency wage is equal to: 7  1/b a 1 ∗ w = (15) θ 1−b where dw ∗ 0 Vee

From the firm’s viewpoint there is a similar problem. Indeed, because of the complexity of the job, the employer does not observe perfectly the effort level and does not know if the effort stems from the wage or the quality of job matching. Taking that into account, the firm solves the following program: Z ˜ ˜ − wL (θ) max F (e(w, θ)L)dH w,L 

which is equivalent to: h i ˜ − wL maxE F (e(w, θ)L) w,L

where E[.] is the mathematical expectation operator. The first-order conditions yield: i h ˜ ˜ 0 (e(w, θ)L) =w (18) E e(w, θ)F 8 We keep the same hypotheses as in Section 2 with θ = θ. ˜ The randomness of θ does not affect the effort decision of the worker since it takes it as given. 9 We assume that V ew θ˜ > 0 and Veeθ˜ < 0.

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h i ˜ 0 (e(w, θ)L) ˜ E ew (w, θ)F =1

(19)

Since F (.) and e(.) ˜ are clearly dependent (they both depend on θ˜ ), we can rewrite Eqs. 10 (18) and (19) as: h i h i h i ˜ E F 0 (e(w, θ)L) ˜ E e(w, θ) + cov e(w, θ˜ ), F 0 (e(w, θ˜ )L) = w (20) i h i h i h ˜ E F 0 (e(w, θ)L) ˜ + cov ew (w, θ˜ ), F 0 (e(w, θ˜ )L) = 1 E ew (w, θ)

(21)

where cov [.] is the covariance operator. The crucial point here is first the negative link between effort and marginal productivity in efficient units of labor, and second, the negative link between marginal effort and marginal productivity in efficient units of labor. Indeed, we have: i h ˜ ˜ F 0 (e(w, θ)L) 0, because if θ increases (dθ > 0), then e(w, θ) wθ 0 00 ˜ but F (e(w, θ )L) decreases since F (.) ≤ 0. The following comments are in order. First, there is a negative relation between effort or marginal effort and marginal productivity. In other words, when effort (or marginal effort) increases (the firm does not know if it is because of high wages or better job matching), workers become more efficient (e(w, θ˜ )L increases) but marginal productivity decreases (decreasing returns to scale in production). ˜ has a high value, the value of F 0 (e(w, θ˜ )L is low. Second, it ˜ or ew (w, θ) So when e(w, θ) is well known that cov[X, Y ] = E [(X − E[X])(Y − E[Y ])]. This means that the covariance is a close concept to the variance since it measures how two random variables vary simultaneously and how they deviate from their mean values. In our context, Eq. (22) (resp. Eq. (23)) indicates how both effort (resp. marginal effort) and marginal productivity depart from their mean values: the greater this deviation, the larger the covariance. We are now able to state the following result: Proposition 2. When the quality of the job matching is not observable by the firm, the efficiency wage w˜ ∗ is equal to: h i h i ˜ w˜ ∗ − w˜ ∗ cov ew (w, θ˜ ), F 0 (e(w, θ˜ )L) E ew (w˜ ∗ , θ) i = h i (24) w˜ ∗ h ˜ E e(w˜ ∗ , θ) w˜ ∗ − cov e(w, θ˜ ), F 0 (e(w, θ˜ )L) Proof. By combining Eqs. (20) and (21), and by rearranging some terms, we easily obtain Eq. (24).  10 If two random variables X(θ) ˜ and Y (θ) ˜ are dependent, then cov[X, Y ] = E[X.Y ] − E[X].E[Y ]. This implies that E[X.Y ] = E[X].E[Y ] + cov[X, Y ].

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Observe that Eq. (24) is a generalization of the Solow condition. Indeed, if θ could have been certain (thus not varying), then cov[.] = 0 and we would have obtained exactly Eq. (6). Another case where we would have exactly Eq. (6), even though θ is a random variable, i h ˜ ˜ is when F (e(w, θ)L) = e(w, θ)L. Indeed, in this case, cov e(w, θ˜ ), F 0 (e(w, θ˜ )L) = i h i h i h ˜ F 0 (e(w, θ˜ )L) = cov ew (w, θ˜ ), 1 = 0. Obcov e(w, θ˜ ), 1 = 0 and cov ew (w, θ), serve also that contrarily to the certainty case, the efficiency wage w˜ ∗ depends now on the firm technology described by the production function F (.). It will be interesting to see if the Solow condition is less, equal or greater than one. Proposition 3. We have the following equivalence: ˜ e/ 8 ˜ w˜ T 1

⇔

wˆ T 1

(25)

where ˜ e/ 8 ˜ w˜

h i ˜ E ew (w˜ ∗ , θ) i = w˜ ∗ h ˜ E e(w˜ ∗ , θ)

is the elasticity of expected effort with respect to wage and i h ˜ −F 0 (e(w, θ)L) ˜ cov ew (w, θ), h i wˆ = ˜ −F 0 (e(w, θ)L) ˜ cov e(w, θ), Proof. By using Eqs. (22) and (23), we have: i h i h ˜ = cov e(w, θ˜ ), −F 0 (e(w, θ˜ )L) > 0 and: – cov e(w, θ˜ ), F 0 (e(w, θ)L) i h i h ˜ F 0 (e(w, θ)L) ˜ =cov ew (w, θ˜ ), −F 0 (e(w, θ˜ )L) > 0. – cov ew (w, θ), Moreover, by using Eq. (24) we obtain: h i h i ˜ w˜ ∗ + w˜ ∗ cov ew (w, E ew (w˜ ∗ , θ) ˜ θ˜ ), −F 0 (e(w, ˜ θ˜ )L) i = h i T 1 w˜ ∗ h ˜ E e(w˜ ∗ , θ) w˜ ∗ + cov e(w, ˜ θ˜ ), −F 0 (e(w, ˜ θ˜ )L) which is equivalent to: i h i h ˜ −F 0 (e(w, θ)L) ˜ ˜ θ), T cov e(w, ˜ θ˜ ), −F 0 (e(w, ˜ θ˜ )L) w˜ cov ew (w, This leads to Eq. (25).



Let us comment this proposition. First, we have obtained a general result that formalizes in the context of uncertainty the statement of Stiglitz (1987). He argues that many of the results of the efficiency wage theory depend crucially on the existence of some region(s) where an increase in wage leads to more than proportionate increases in work effort. We show here that there are also some regions where a wage raise generates an effort lower or equal to

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the initial wage increase. Indeed, when w˜ ∗ ∈]w, ˆ +∞[, the (expected) elasticity of effort  in ˜ e/ respect to the wage is greater than 1 (8 ˆ is small (w˜ ∗ ∈ 0, wˆ ), it is ˜ w˜ > 1) while when w ˜ e/ ˆ (a wage for less than 1 (8 ˜ w˜ < 1). This means that efficiency wages are higher, the lower w which the elasticity of effort with respect to wage is greater than 1 is obviously lower than a wage characterized by an elasticity less or equal to 1). Second, wages depend strongly on the complexity of the job and thus on job matching. As a matter of fact, according to ˜ e/ ˆ is greater (lower) than 1. In particular, we have: Proposition 3, 8 ˜ w˜ > 1 (< 1) when w ˜ e/ 8 ˜ w˜ ≷ 1 when

i h ˜ F 0 (e(w, θ)L) ˜ cov ew (w, θ), i h ˜ ˜ F 0 (e(w, θ)L) ≶ cov e(w, θ),

(26)

However, it is more convenient to rewrite this relation by using the linear correlation coefficient since, contrary to the covariance, it does not depend on the units chosen. By using the definition of the linear correlation coefficient, Eq. (26) can be rewritten as: ˜ e/ 8 ˜ w˜ ≷ 1 when

i h ˜ F 0 (e(w, θ)L) ˜ σew cor ew (w, θ), h i ˜ F 0 (e(w, θ)L) ˜ ≶ cor e(w, θ), σe

(27)

where cor[.] is the correlation coefficient whose value is between 0 and 1, and σew and σe are the standard deviations of ew and e, respectively. Furthermore, if we assume that σew = σe , then Eq. (27) reduces to a comparison of correlation coefficients between the negative relation of marginal effort and marginal productivity and the negative one of effort ˜ e/ and marginal productivity. More precisely, 8 ˜ w˜ > 1 (< 1) when the (negative) impact of marginal effort on marginal productivity is greater (lower) than the one of effort on marginal productivity. This result is quite intuitive since if the negative impact on F 0 (.) of ew (e) is greater than the one of e (ew ), then the firm increases its wage up to the point ˜ ˜ w˜ < 1), that is, when the marginal effort is greater (lower) than the ˜ e/ where 8 ˜ w˜ > 1 (8e/ ˜ e/ average effort. This implies that firms set higher wages when 8 ˜ w˜ < 1. Third, since F (.) or F 0 (.) reflects the technology or equivalently the job complexity, the result of Proposition 3 and if the job is such that i depend h on the type of job. Indeed, i h thus firms’ wage policy 0 0 ˜ ˜ ˜ ˜ cor ew (w, θ ), F (e(w, θ)L) < cor e(w, θ), F (e(w, θ )L) , then firms pay a low wage since the impact of wage on effort is not very important. In other words, when the job is very complex and the quality of job matching difficult to evaluate, it is not efficient to pay high wages to workers. As a consequence, when the quality of job matching is unobservable, wages in very complex jobs are lower than wages in less complex jobs. Last, according to Eq. (27), the quality of the job match θ˜ affects w˜ ∗ in two different ways: it can imply either a high value or a low one. Since here the unemployment formation is only due to very high wages, depending on job complexity, there can either be a high or a low level of unemployment (compared e.g. with the case of the previous section in which θ is

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observable). If we denote by U˜ ∗ the equilibrium level of unemployment in the context of uncertainty, we have therefore: i h i h ˜ F 0 (e(w, θ)L) ˜ < (resp. >) cor e(w, θ˜ ), F 0 (e(w, θ˜ )L) , if cor ew (w, θ), then U˜ ∗ is low (resp. high).

4. Job complexity, job matching, wage dispersion and unemployment In this section, we want to explain inter-industry wage differences and unemployment formation. Several empirical studies (Dickens and Katz, 1987a,b; Krueger and Summers, 1987,1988; Murphy and Topel, 1987) have shown systematic and persistent industry wage differentials even when standard individual characteristics are controlled. This sheds some doubt on the standard competitive model in explaining these facts and the efficiency wage models have been proposed as an alternative explanation for the wage differentials 11 (Bulow and Summers, 1986; Klundert, 1989; Albrecht and Vroman, 1992; Saint-Paul, 1996; Smith and Zenou, 1997, among others). In general, the difference among sectors is due to job complexity which reflects the difficulty of monitoring workers. In this context, firms must set efficiency wages to deter shirking in the sector characterized by complex jobs (the primary sector) and a competitive or minimum wage in the other sector where job complexity is absent (the secondary sector). This implies a hierarchy between sectors since in the primary sector wages and utilities are greater than in the secondary one. Therefore, these theories explain why identical workers earn different wages and how unemployment is formed. Another type of theoretical explanation has been based on search theory (Lang, 1991; Montgomery, 1991). There are some frictions in the labor market which lead to a job mismatch: firms do not fill instantaneously their vacancies and workers do not instantaneously find jobs. In this context, it is shown that offering high wages increases the probability of filling a vacancy. Thus, firms for which unfilled vacancies are relatively more expensive (i.e. highly profitable firms and firms with high capital–labor ratios in which expensive machinery would sit idle if a vacancy persisted) will pay higher wages. As a result, inter-industry wage differences are obtained for identical workers. In our model, we consider an alternative approach to explain inter-industry wage differences. To start with, let us consider just two sectors, each of them being characterized by M identical firms (so that we can analyze the behavior of one representative firm) and by the type of jobs they provide. The first sector is characterized by very complex jobs so that the quality of the job matching is not observable by firms (θ is a random variable denoted by θ˜ ) whereas in the second sector jobs are less complex so that θ is perfectly observable by the firm. It is therefore the complexity of jobs and thus the observability of job matching that differentiates the two sectors. It is obvious that our assumptions bear some resemblance with the above theories of inter-industry wage differences and dual labor markets. However, job complexity and job matching are defined in a different way since for us these two concepts 11

It is the inter-industry wage differences literature as well as the dual labor market literature.

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are linked together. Indeed, in our approach, job complexity refers to the characteristics of the job and in particular to the technology associated with each job. We do not focus on its consequence on monitoring but on the quality of job matching: the latter is more and more difficult to evaluate for the firm when jobs become more complex. Observe that our concept of job matching is different from the one introduced in the job search literature since it means the adequation between a specific skill and job technology. It is actually close to the one introduced by Sattinger (1993) and Thisse and Zenou (1998), even though we assume the workers to be homogeneous. We want to explain inter-industry wage differences but, as we will see, the sector with more complex jobs will not always offer higher wages than the other sector. In order to capture this idea, we split the first sector (characterized by complex jobs) into two so that two types of jobs are available. The first type of complex i h jobs is the one characterized by a wˆ > 1 (see Proposition 3) or equivalently by cor ew (w, θ˜ ), F 0 (e(w, θ˜ )L) < i h ˜ . The second type is defined by wˆ < 1. Therefore in this econcor e(w, θ˜ ), F 0 (e(w, θ)L) omy, we can consider three sectors so that three types of jobs are provided; identical workers can be allocated randomly between them (the probability of finding a job in each sector is the same). Sectors 1 and 2 are characterized by complex jobs with wˆ > 1 and wˆ < 1, respectively, while in Sector 3 non-complex jobs are present. Let us denote by wi the wage in sector i (i = 1, 2, 3). Proposition 4. There are inter-industry wage differences because of differences in job complexity and thus in the quality of the job matching. We have: w2 > w3 > w1

(28)

Proof. By using the results of the previous sections, Sectors 1, 2 and 3 are characterized by an efficiency wage such that the elasticity of effort with respect to the wage is greater, lower and equal to unity respectively. This implies Eq. (28).  Since there is a hierarchy in wages and thus in utilities, everybody wants to work in the second sector, then in the third sector (if a second sector job is not available) and lastly in the first sector (we assume that w2 is greater than the unemployment benefit so that workers always prefer to work than to be unemployed). In this context, we have an explanation of why identical workers do not get the same wage and the same level of utility. We also have an explanation of unemployment which is due to high wages, job rationing and mismatch. Thus differences in salary among jobs reflect non-pecuniary attributes of the job which are captured by the quality of job matching. This has some testable predictions. Indeed, the aim of the empirical literature on inter-industry wage differences is to explain why workers with identical skills can earn different wages. In particular, Krueger and Summers (1987,1988) have shown that workers’ industry affiliation exerts a substantial impact on their wage, even after controlling for human capital variables and other variables such as unionism, discrimination and a variety of job characteristics. Other studies have found that other variables can explain inter-industry wage differences like, for example, unobserved heterogeneity in workers’ abilities (Dickens and Katz, 1987; Murphy and

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Topel, 1987; Gibbons and Katz, 1989). However, there is not a clear consensus and the actually observed wage differentials are no doubt explained by a variety of different factors. In our model, we explain wage dispersion for identical workers by differences in non-attributes of the job or equivalently by the quality of job matching. The interesting feature of our model is that we have a close link between job complexity, job matching and wage setting. These three elements explain wage dispersion and unemployment formation. Finally, observe that we are also able to explain intra-industry and even intra-firm wage differences. Indeed, if one assumes that jobs are different within a sector or within a firm (which is certainly the case), then we easily obtain these results. Jobs differ indeed in complexity even within a firm due to difference in technologies.

5. Conclusion In this paper, we have introduced the non-pecuniary aspects of the job in the effort function. This is motivated by the fact that jobs are more complex and that sociological aspects matter in motivating workers. If firms take this into account, then its optimal wage setting (efficiency wage) depends strongly on the quality of job matching. If firms can observe the job match perfectly, then they set an efficiency wage such that the effort–wage elasticity is equal to one. However, it is not clear that an increase in the quality of job matching decreases with the efficiency wage. Therefore, even if the global effect on unemployment is ambiguous, we can show (for some specific forms) that the better the job matching the lower the unemployment level, putting forward the importance of mismatch in the microfoundation of unemployment. On the other hand, if firms cannot observe the quality of job matching, then effort–wage elasticity is not in general equal to one. Rather, there are some regions in which it is greater and others where it is lower. In this case, the efficiency wage becomes dependent of the firm’s technology and the equilibrium unemployment level is affected by the quality of the job matching.

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