Personal Contacts and Earnings: It is who you know! Mortensen and Vishwanath (1994)

Transcription

1 Personal Contacts and Earnings: It is who you know! Mortensen and Vishwanath (1994) Group Hicks Dena, Marjorie, Sabina, Shehryar It s not what you know, it s who you know! A postdoctoral student in biology received a letter from an institution to which he applied for a job directly, saying that there were no openings for an individual with your qualifications. But when his thesis adviser took a position at the same institution, the younger man went along as a research assistant; he subsequently received an effusive letter expressing the college s delight at his appointment. Granovetter (1995) 1

2 This paper discusses information sources used by workers searching for jobs. They are: (i) (ii) direct applications to employers and contact through friends, colleagues and relatives etc. Wishing to derive the equilibrium effects of different mixes of the two information sources that workers most commonly use, the authors find differences in equilibrium wages and attribute them to the differential access to information sources. They conclude that under certain assumptions, those workers who are more likely to obtain wage information through contacts will earn more in equilibrium. Section 1: Introduction The paper aims to derive the equilibrium effects of the two sources of information as mentioned above. The model includes both unemployed and employed workers in the analysis. Unemployed workers accept the first wage offer they get that is above the reservation wage b, whereas, employed workers move from lower to higher paying jobs. A market clearing equilibrium, given the assumptions below, is the wage that gives the same maximal profit to all employers offering different wage rates that the equilibrium can support. The equilibrium solution is unique, as is proven in section 4. Assumptions Workers try and maximize the returns from various information sources and these returns depend on the market composition of the sources Equally productive, homogenous, and immortal workers! Distribution of wages earned depends on workers information mix Wage information is a random draw from wages offered by employers and the wages earned through contacts In equilibrium, all employers offer the competitive market wage and make the same maximal profit Steady state conditions hold 2

3 Section 2: Model and market equilibrium Before describing how the use of contacts affect earnings, the authors state necessary properties for an equilibrium given the assumptions above. The immortality assumption implies that total quantity of labor force is constant in model. Wage determination by a firm is a one shot game and is given by the distribution F(w); this means that after offers are made there is no possibility for negotiations and employees either accept or reject. Each worker continuously searches for job opportunities through contacts and direct offers by firms, whether employed or unemployed. Notation λ = frequency of wage offers b = unemployment benefit α = fraction of offers through contacts w = wage offered/earned δ = rate of separation γ = fraction of workers earning highest wage φ = fraction of employers offering highest wage TR (L) = total revenue from employing L workers F(w) = offer distb. function (direct quotes) G(w) = wage distb. function (contacts) M = Total workforce E = # of employed workers in the steady state π = firm profits L (w) = Labor supply for wage w Given an F(w), the behavior of workers along with the assumption that job-worker relationships dissolve exogenously will yield a unique steady state G(w). This induces a steady state in the labor market. Wage quotes and indirect offers in the steady state come from F(w) or G(w) respectively. The equal profit condition is given by π = R [L(w)] [w*l(w)] in the steady state. This implies that all firms, irrespective of what wages they pay their employees, make equal profits. 3

4 Properties of equilibrium (a) If ŵ is the highest wage offered and the employment corresponding to it is L, then the marginal revenue product will equal the highest wage, i.e. R (L ) = ŵ (b) From (a), it automatically implies that firms offering a wage less than ŵ will have a marginal product that exceeds the wage rate they offer An implication of (a) and (b) is that no employer offers a wage that exceeds the marginal revenue product as such a case would violate the profit maximization condition. Labor supply jumps at mass points and workers only move to higher wages so any employer offering a slightly higher wage will have more workers available to them. When R (L ) > ŵ it would be profitable to increase employment when L <(L ( ŵ) or increase both employment and wages when L =L ( ŵ). (c) If any two wages (say w 1 and w 2 ) come from the distribution F(w) and both are less than ŵ, then w 1 <w i <w 2 also comes from F(w) for any i (d) In case of wage dispersion, the lowest wage offered is the unemployment benefit irrespective of other wage offers. The available labor supply for any individual firm depends only on the fraction of firms offering a higher wage. A wage range that is not continuous would mean the two lowest wage firms have the same level of labor available to them in spite different wage rates. This in turn would mean these two firms earn different profits violating the equal profit condition. Property (d) just means that the labor supply for the lowest wage firm is the same regardless of the wage offered so they will offer b. 4

5 Section 3: Equilibrium Relationships This section lays out the necessary relationships between L(w), F(w), and G(w) in order to later construct an equilibrium. The authors treat the set of workers and the set of employers as continua and assume that there is only one employer in the economy. The purpose of this assumption is to simplify calculations and reach their results less tediously. In the steady state, the movement into a group of workers earning an arbitrary wage w or less, must equal the movement out of that group, as shown below. λ [α*g(w) + (1-α)*F(w)] (M-E) = δ*e*g(w) + λ*e*g(w) {α*1-g(w)] + (1-α)*1-F(w)]} λ*α*g(w)*(m-e) + λ*(1-α)*f(w)*(m-e) Unemployed people entering employment at wage w or below Employed workers leaving their jobs either to move from w to a higher wage or due to exogenous reasons In the steady state, employers offering the highest wage must replace employees that leave and this relationship is described in equation (2): The left hand side describes the number of workers who are not currently employed at the highest paying firms and will apply to work at these firms. The right hand side describes the number of workers at the highest paying firms who will leave for exogenous reasons. 5

6 By definition it must be true that: Note that in this section, L^ is being used as the number of workers demanded rather than the definition used in property (a). Equation (3) tells us that that the number of employees demanded by the highest paying firms will equal the number of workers employed at the highest wage. In the steady state, because the flows of labor into and out of the workforce must be equal, the number of employed workers is given by: E = M * λ λ+δ (4) Substituting (4) into (1), and solving for F(w), we get (See appendix for derivation) F (w) = δ +λ G(w) δ + λ G(w) + α (1 α) * λ 1 G w G(w ) δ + λg (w ) for all w < ŵ (5) The authors also make use of an identity This indicates that the steady state number of workers earning w or below will be equal to the workers demanded by firms for a wage w or below. This can be thought of as a steady state market clearing requirement. Using equation (5) with this identity and differentiating allows us to get equation (6). This expression enables us to express available labor supply in terms of the contact probability and the wages earned distribution (assuming fixed δ and λ). 6

7 Substituting (6) into the equal profit condition, and considering the fact that under wage dispersion b will be the lowest wage offered, implying that G(w) = 0, we get equation (7). L(b) in equation (7) is the labor a firm employs corresponding at the lowest wage, b. Because of the equal profit condition, the profit of the firm paying the lowest wage will be equal to that of the firm paying the highest wage. This enables us to find an expression involving the largest firm size at a given contact rate. Equation (8) is the profit function for the largest firm at contact rate, α: Where L α is the largest firm size associated with a given contact rate. By properties (c) and (d), there will be a range of dispersed wages from [b, w], which will possibly be united with w. Note that w now refers to the highest wage offered by employers who are not among the possible mass offering w. Because w is less than the potential highest wage w=r L α, properties (a) and (b) imply: 7

8 Section 4: Constructing the Equilibrium: The authors offer the following steps for constructing the equilibrium: 1. Determine the equilibrium π through equation (7) for a specific value of α and the given values of δ and λ. 2. Solve π = R*L(w)+ *w*l(w)+ for L(w) using the π as in 1 above. There will be two solutions as R(L) is strictly concave but only the smaller one satisfies equilibrium conditions. We can see that this will be true by looking at Figure 1: Imagine a wage on the isoprofit line π that is less than w. There are two firm sizes that will give us profit π at this wage. But, to move to R (L)=w, we would have to increase w while increasing L. If we started from the higher L to move to this point we would have to increase w while decreasing L. So, only the lower L is non-decreasing in w. 3. For the value of L(w) obtained as per 2 above, solve equation (6) to get the distribution G(w) 4. The G(w) we obtained is only one possible distribution given specific values of the parameters in equation (6). We can repeat the process and get a different G(w) if any of α, δ or λ change. Employers offer the competitive market clearing wage in two cases: 8

9 If R (E) = b and here everyone pays the same (minimum) wage b If R (E) > b, it is profitable for the firm to pay a worker more than b The profit earned in a competitive equilibrium in the second case is given by π* = R(E) R (E)*E All firms offer the competitive wage if π(α) < π*. This is because the largest firm size would be less than the average labor force per firm E in violation of the market clearing requirement. Therefore, if π(α) π*, we have φ = γ = 1 and ŵ = R (E) Because L α is decreasing in α and approaches 0 as α approaches 1, the single price equilibrium will prevail for all α greater than the unique solution to π(α )= π*. On the other hand, any equilibrium involving a contact rate less than this unique solution must involve wage dispersion. Otherwise, there is an opportunity to make greater profits by offering a lower wage. Wage dispersion occurs with or without a mass of firms offering the highest wage (ŵ) and this in turn depends on α. To find a cut off point between the cases, the authors solve for an α that satisfies: Where L α is the largest firm size associated with α and L 1, α is L w. Because of the properties of these functions as outlines earlier in the paper, they will be equal be at some unique point less than δ δ + λ. Also if α > α, then there will be a mass of employers who offer ŵ. If not, we will run into a contradiction because F w = 1 along with equation (12) implies L w = L 1, α > L α. But this would contradict equation (9). What remains is to calculate what fraction of employers (workers) offer (earn) the highest wage using equations (2)-(4). First, we must indicate that there will be a unique, positive solution for these variables if and only if α lies between α and α*. 9

10 Proof: Using equations (8) and (11), and the fact that R(L) is strictly concave, we can see that saying that Figure 2 We can find another relationship, equation (13), between and through using equations (3) and (4) to eliminate ˆL. Taking the derivative the with respect to we get: Taking into consideration all of our results in this and the previous section, we have This is significant because we know that (13) is satisfied at ==1 and = =0. The slope of (13) initially starts less than that of the ray expressed by equation (3), and (13) is convex in. Therefore, (13) will increase until it cross the ray (3) once within this interval. This unique solution will always be for [γ, φ+ < *1,

11 Section 5 : Personal Contacts and Wage Outcomes First 2 propositions given below, are similar in meaning, but proposition 2 is much stronger, as it implies that wage earnings increase with probability of referrals being from contact disregarding whether wage offers disperse or not. Proposition 1 Given an F(w) with dispersed offers, the corresponding G(w) is stochastically increasing in α. Intuition: Given a distribution of offers that is dispersed, workers receiving an offer through contacts are more likely to get a higher offer as employers understand applicants are aware of the level of wages earned. Keeping in mind that employed workers only move to higher wage firms, an increasing contact rate in the economy increases the number of high wage offers. So in next time period we will end up with higher wages paid in economy, in comparison with the initial stage. Proposition 2 The equilibrium earning distribution is stochastically increasing in α. Proof: Under assumption of profit equality on any wage level, we can propose that profit at b level of wage will be equal to any profit with different salary. So given π = R(L(w)) wl(w) and equation (6), we get equation (15): Differentiating both sides based on we have. As R (L(b))- b > R (L(w)) w > 0 for all w < ŵ, fraction part of the equation is greater than 1, and We have dg (w) dα < 0 what implies that as α increases the distribution of wages G(w) will come more compact near to w* (competitive wages) 11

12 Section (6): Different contacts, Different Information Access In reality, it is reasonable to assume that there might not be homogenous access to information to all workers. Differences in race, sex, age, academic background and various other factors may well lead to the case for different contact probabilities for workers. For comparison, the authors assume equally productive homogenous workers facing the same b, λ and δ. However, α i and M i represent the probability of an offer being from a contact and the number of workers per employer respectively for any worker type i. If profit in this case, as shown below, is greater than the competitive equilibrium profit, there is a dispersed equilibrium. The exact same analysis that was used to prove Proposition 2 also applies here in the asymmetric information case. This leads the authors to conclude their paper with Proposition 3 for the multiple type case. This proposition means that Proposition 3 Given a dispersed equilibrium with two or more types denoted as i and j, α i > α j implies G i (w) < G j (w) for all w between the lowest and the highest offer. Summary/Findings 1. For the unemployed who enter the labor force, the distribution of wages received is higher for those who obtained information through contacts compared to those who applied directly to the employer. 2. For the already employed workers who wish to move to another job, the wage will be higher if the new job is obtained via a contact. 3. Those who found their jobs through contacts are less likely to quit a particular job because they re earning more than the direct applicants. So essentially, all this excessively mathematical manipulation leads to a conclusion that: Those who have lower contacts can expect to earn less even without any intentional discrimination by the firm! 12

13 APPENDIX Source: Granovetter, Mark (1995) Getting a Job: A study of contacts and careers, The University of Chicago Press 13

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