1 Search, Applications and Vacancies

Transcription

1 1 Search, Applications and Vacancies Steven Stern 1 INTRODUCTION Over the last few years the efficiency of search equilibria has been examined by a number of authors. In a series of papers, Diamond (1981; 1982a; 1982b; 1984) has studied this issue in depth. Diamond (1981) shows that in a market with a distribution of match specific mobility costs, an unemployment insurance programme can improve the ex ante welfare of all workers by inducing each of them to forego opportunities with high mobility costs. Diamond (1982b) shows that in a market with no competition among agents, there are multiple equilibria, all of which are Pareto inefficient. The inefficiency occurs because no agent internalizes the value of his increased search activity to other searchers. Diamond and Maskin (1979; 1981), and Mortensen (1981; 1982a; 1982b) show in matching models that the characteristics of the inefficiencies in equilibrium depend upon the search technology. With the exception of Mortensen (1981), (1982a) none of these models allows for contemporaneous competition among searchers. Wilde (1977) has developed a model where the equilibrium price distribution is determined by the level of search intensity of consumers. When each consumer increases his intensity, all sellers lower their prices. This implies that the equilibrium search intensity is Pareto inefficient if only the welfare of consumers is considered; each consumer's welfare would increase if all consumers searched a little harder. Wilde's results depend crucially upon a lack of competition among consumers for the goods being sold. Most labour markets are characterized by some degree of competition for a small number of job openings. This is especially true when the unemployment rate is high or there is a particularly attractive job opening. Firms may limit the number of job openings because of diminishing returns to scale in production and lags in the hiring process. If the number of job openings is small relative to the number of workers searching for those openings, then the competition among 5

2 ..., 6 Search Unemployment: Theory and Measurement the workers will be a crucial aspect of the economic environment of the workers. 1 The rivalry literature 2 has shown that when there is a common goal that a number of agents are striving to achieve, and when all of the benefits of achieving that goal go only to the first agent who is successful, then there is excessive rivalry among the agents. Each agent must choose an intensity with which to strive for the goal given the intensity of other agents. Marginal units of intensity are costly. An externality results because each agent ignores the effect his intensity has on the other agents' probability of achieving the goal first. The rivalry problem has been used mostly to examine the market for research and development. This paper examines a generalized rivalry problem in the labour market. It employs a simple labour supply model as a framework to analyse labour markets characterized by search with competition among searchers. First, the labour market process for new hires is described. The searching worker's opportunities are determined by the market parameter which is the probability that an application will not generate a job offer. The model is closed by determining the value of the market parameter given the search strategy that each worker individually follows. There exists a non-trivial equilibrium in steady state. At this equilibrium a social planner can improve each worker's welfare by inducing each worker to search less intensively. 2 THE MARKET MECHANISM There are B firms, each of which costlessly advertises n vacancies in the local want ads every period. All firms advertise the same wage although this can be generalized as in Stern (1986). A period is the length of time it takes for a firm to list an ad, receive applications, make offers, receive replies and hire those who accept. No deceptive advertising is allowed. There are also N identical unemployed workers every period who costlessly look through the want ads and determine the number of firms, m, to which they should apply. The cost of applying to m firms is C(m). This represents transportation costs, time costs, and any direct costs of informing firms of one's interest in a job. It is assumed that marginal cost is positive and non-decreasing (C'(m) > 0, C'(m) ~ 0), that leaving the market is costless (C(O) = 0) and that the cost of applying to every firm C(B) is very large relative to the benefits of getting a job.

3 Stern: Search, Applications and Vacancies 7 To be more precise, m should be either an integer or a representation of a mixed strategy, and the first-order analysis should be adjusted accordingly. However, as long as m > 1, the continuous approximation to the problem provides much insight with little loss of accuracy. Each worker applies to firms without knowing exactly what other workers are doing. However, he knows or can derive the distribution function of the number of applicants at each firm. Once a firm has received applications for a period, if it receives at least n applications, it randomly offers n applicants jobs at a wage of w. 3 If it receives fewer than n applications, it offers all applicants jobs at the same wage. Firms are not allowed to have waiting lists. A worker will accept any offer made to him unless he receives more than one offer in the same period. Then, since all offers have the same value, the worker randomly selects one of the offers. Once he has accepted an offer from a firm, he works for that firm forever receiving a wage of w once a period. He receives an unemployment compensation payment, U < w, once a period until he finds a job. It is assumed that the equilibrium is a symmetric Nash equilibrium 4 (which is sometimes called a 'supply-side equilibrium' since all choices in the model are made by the suppliers of labour, i.e. the workers). This means that each unemployed worker treats the application strategies of other workers, and thus the probabilities of receiving job offers, as given, and that at equilibrium all workers adopt the same strategy. A worker prefers to apply to jobs with high probabilities of receiving offers over firms with low probabilities of receiving offers and randomly chooses among firms with the same probability of receiving an offer. Each worker forms expectations either through past experience in the labour market, through contact with other workers, or by computing where the Nash equilibrium will occur.5 The probability of being offered a job at a particular firm depends upon how many vacancies the firm advertises and the distribution function of the number of applicants it will receive. The explicit formula for this probability is derived later in the paper. For now, it is important only to recognize that in equilibrium, the probability of any worker receiving an offer from any firm must be the same for all firms. If, for anyone worker, there were two firms with different probabilities of making offers, then the two firms would have different probabilities for everyone. Everyone applying to the low probability firm would have incentive to apply to the high probability firm

4 8 Search Unemployment: Theory and Measurement instead. But then the probability of receiving an offer at the low probability firm would be unity; it actually would be a high probability firm. Therefore, the application strategies could not be a Nash equilibrium. Thus, it must be true that in equilibrium, all firms have the same ex ante probability of offering a worker a job, and so a worker's decision is characterized by the number of firms to which he applies. 3 THE WORKER'S PROBLEM The first step in solving the supply-side equilibrium is deriving the unemployed worker's objective function. As in most of the search literature, it is assumed that a worker maximizes the expected value of search which equals the values of having a job and of continued search, each weighted by the probability of being in that state, minus search costs. Let: y = probability of not being offered a job at a firm to which a worker applies. If a worker applies to m firms, the probability of being offered at least one job is (1-ym). Let ~ be each worker's discount factor. Let V(m) equal the value of applying to m firms. Then V(m) = u - C(m) + ~(1 - ym)w/(1-~) + ~ymv* (3.1) = u - C(m) + ~w/(1-~) - ym[~w/(1-~) - ~V*] where V* is the value of the optimal strategy that will be followed next period. Since the market is in a steady state, the optimal strategy will be the same every period. The behaviour of each worker can be derived by looking at the first order condition for equation (3.1): ijv(m)/ijm = -C'(m) - ym[~w/(1-~) - ~V*] In y = O. (3.2) The second order condition is -C"(m) - ym[~w/(1-~) - ~V*](ln y)2 < O. (3.3)

5 Stern: Search, Applications and Vacancies 9 Since [~w/(1-~) - ~V*] is the difference in value between getting a job and not having a job, it must be positive; otherwise there would be no search. Thus, the assumption that C'(m) ~ 0 implies that the second order condition holds globally. Therefore, the first order condition is necessary and sufficient for an interior global maximum. Equation (3.2) provides an implicit equation for m*, the optimal level of applications. The necessary conditions for positive search can be derived by evaluating ijv/ijm at m = 0: ijv(o)/ijm = -C(O) - [~w/(1-~) - ~V*(O)] lny (3.4) = -C(O) - ~(w - u) Iny/(1-~) > 0 (3.5) since if m = 0 is the optimal strategy today, it will also be the optimal strategy tomorrow. Thus, if the difference between wand u is high enough, y is low enough, and C(O) is low enough, there will be a positive search. 6 It can be shown by looking at the derivative of ijv/ijm with respect to exogenous variables what the comparative statics for the workers are i)m*/ij~>o, ijm*/i)w>o, ijm*/iju<0,7 ijm*/ijc< 0,8 (3.6) and ijm*/ijy has the opposite sign of (m* lny + 1). If w rises, then the difference in value between working and searching increases. This causes the worker to search more. If ~ rises, then the worker discounts the future less heavily, causing the value of the wage stream to rise more than the application costs. Thus, the number of applications rises. Similarly, higher marginal search costs cause the worker to apply less. Finally, if y rises, then the incremental probability of getting a job by searching a little harder is -y"'-l(m lny + 1) whose sign is ambiguous. At very low values of y, there is no need to apply to many firms since anyone is likely to generate an offer, and at very high values of y, the applications are worth very little because they are unlikely to result in an offer. 4 PROBABILITY OF REJECTION The only open parameter left to determine is y, the probability of the worker not receiving an offer at a firm to which he applied. With little

6 10 Search Unemployment: Theory and Measurement loss of generality, n can be set equal to unity and N and B can be allowed to approach infinity at the same rate so that Nt B approaches "". The rejection probability can be computed easily by thinking of it as.l [Pr(not offered job I a + 1 applicants apply) x a=o Pr(a other applicants apply)]. (4.1) The first term is the probability of rejection conditional on the number of applicants: 1 - [li(a + 1)]. The second term is the discrete probability function for the number of applicants. Since Nand B approach infinity, this distribution is a Poisson distribution with parameter m",,: Pr(a other applicants) = e-mf!m""ala! (4.2) which can be simplified to y = 1 -~ (1 - e-mf!). m"" (4.3) This is equivalent to the rejection probability in Pissarides (1985). The search technology in this paper is quite different than that presented in the continuous time models of Diamond (1981), (1982a), (1982b) and Mortensen (1982b). In contrast to this model, neither of their technologies (linear or quadratic) allows for a worker's search intensity to negatively affect the probability of another worker finding a job contemporaneously. All of the competition among workers in their models is intertemporal. 5 EQUILIBRIUM It can be shown that there exists a steady state Nash equilibrium to the supply side. An equilibrium is characterized by the triple (",,*, m*, y*) such that when the ratio of workers to vacancies is "" *, each worker chooses the number of applications to send m* conditional on the rejection probability such that (1) the rejection probability is y* and the ratio of workers to vacancies next period is "" *. The proof begins by showing there is a fixed point for (",,*, m*, y*). Let n l = NIl Bo be the number of workers per original vacancy, and let

7 Stern: Search, Applications and Vacancies 11 bt = BtlB o be the number of vacancies per original vacancy. Assume that the number of workers per original vacancy next period equals the number of workers per original vacancy this period who found no job plus the number of new entrants per original vacancy: (5.1) where Znt is the number of new entrants per original vacancy. There is a similar equation for vacancies: (5.2) where A is the probability of a vacancy not being filled. A vacancy is filled only when a worker finds a job. Thus (5.3) Finally, the rejection probability is determined by equation (4.6): (5.4) Steady state is characterized by m,!l, y, n, and b not changing over time: n = zn/(l - ym), b = zb/(l - A), 1 - A =!l(1 - ym), and (5.5) (5.6) (5.7) y = 1 - [(1 - e-m")/m!ll (5.8) Equations (5.5), (5.6) and (5.7) imply that Zn = Zb = z. The steadystate equations can be maniputaled to find an equation to determine!l in terms of the initial difference n - b = a:!l = z/[z - a(l - ym)]. (5.9) Note that Z > a(l - ym); otherwise z/(l - ym) = n > a = n - b which implies that b < o. This places a restriction on ym since Z and a are

8 12 Search Unemployment: Theory and Measurement exogenous. Thus Il is determined by equation (5.9), y by equation (5.8) and m by equation (3.2). Since (j2v/om 2 < 0 for all m, there exists a unique solution to equation (3.2) for any values of y > 0 and V*. Since V* is the maximum value of V(m) conditional on y, it is straightforward to show that V* is a continuous, differentiable function of y. Thus, there exists a unique solution to equation (3.2) for any value of y. Denote this solution as m = M(y). The function M(y) satisfies In C'(M(y)) - M(y)ln y = g(y) (5.10) if M(y) ;:::: 0 where g(y) = In( -In y) + In[~w/(1 - ~) - ~V*(y)]. Otherwise M(y) = O. The function g(y) is continuous and differentiable at all values of yon the interval (0,1) except for one point. 9 The derivative, M'(y), exists for all values of M(y) where M(y) is positive. Thus, in equation (3.2), m can be written as a continuous function of y on the half-open interval (0,1] that is differentiable at all points except for one. It can be shown that lim M(y) = 0 as y ~ O. If M(O) is defined to be zero, then M is defined and continuous on the closed interval [0.1]' Also, from equation (5.8), y can be written as Let y = f(m, Il). (5.11) F(y, Il) = f(m(y), Il) (5.12) F(y, Il) is the probability of being rejected by a firm conditional on Il if everyone thought that the probability of being rejected by a firm was y. If each worker thought that the probability of not being offered a job was y, each would apply to m* = M(y) firms, and then the actual probability of not being offered a job would be f(m*, Il). F(y, Il) is continuous. From equation (5.9), Il can be written as Il = <I>(y, m) where <I> is continuous and differentiable in both arguments over feasible values of y and m. Let G(y) = f(m(y), <I>(y, M(y))). (5.13) The solution to G(y) = y is the fixed point. G(y) is continuous and both its range and domain are the unit interval. Thus, by Brouwer's fixed point theorem, there exists a point y* where

9 Stern: Search, Applications and Vacancies 13 Figure 2.1 Equilibrium points G(y*) = y*. (5.13) This point, y*, corresponds to a supply-side equilibrium where m* = M(y*) is the symmetric Nash equilibrium strategy for each worker and Il* = <l>(y*, m*) is the steady-state ratio of workers to vacancies. Thus, there is at least one Nash equilibrium. The argument above demonstrates only the existence of an equilibrium. In fact the equilibrium may be at y = O. It can be shown that there is also at least one non-trivial equilibrium (0 < y < 1). This is shown for the case where C"(m) = 0 although the result holds for the more general case, C'(m) ;:?; O. First, note that if y = 1, then workers have no incentive to apply to any firm. But if no one applies at all, then equation (5.8) implies that F(l, Il) = 0 for any Il > O. It can be shown that lim fjflfjy = 00 as y ~ o for any Il > 0 and that lim F(y, Il) ;:?; 0 as y ~ O. Since F(y) is below y at unity, there must be a 0 < y < 1 where F(y, Il) = y.lo This is seen most easily by studying Figure 2.1.

10 14 Search Unemployment: Theory and Measurement 6 WELFARE RESULTS It already has been noted that y increases as m* increases. But for any particular worker, y is a function of all other workers' m*s, and any particular worker's m* affects all other workers' ys. Because the cost that a worker incurs in applying for a job includes only his search cost and no charge for the worker's effect on other workers' chances of getting a job when he submits extra applications, worker search at equilibrium is inefficiently large. The most efficient equilibrium would occur when a social planner placed each worker at a firm with a vacancy. This would prevent frictions caused by each worker's inability to observe the choices of other workers, and it would minimize search costs. We assume such an equilibrium cannot occur because it requires a social planner with more power and knowledge than is realistic. 11 The first order condition for each worker is described in equation (3.2). But this equation does not include a term for the effect of m* on y. On the other hand, if the workers were to form a coalition for one period, they would consider the effect of m* on y. Thus, the coalition's first order condition for the maximization problem described in equation (3.1) would be -C'(m)-y'" -~w -~V* ] lny-myn-l- dy [~W - -~V*] = o. [ 1-~ dm 1-~ (6.1) At the competitive equilibrium, the first two terms of equation (6.1) are the first order conditions for each worker. Thus, the marginal value of another application on the competitive equilibrium is -my p AV*] dm 1-~ m-l dy [~W (6.2) which has the opposite sign as dy/dm. When m increases it affects y directly and also indirectly through"" since y'" affects"" and"" affects y. It can be shown that (6.3) Both ijy/ijm and ijy/ij"" are positive. Only ij!.tiijym needs to be signed.

11 Stern: Search, Applications and Vacancies 15 There are three cases to consider. If I..t = 1, then as ym increases Nand B increase at the same rate so that I..t does not change. If I..t > 1, then as ym increases Nand B increase but I..t = N/ B decreases. If I..t < 1 then I..t increases. These results are apparent from equation (5.9). Thus if I..t = 1, dy/dm = ijy/ijm > O. If I..t > 1, dy/dm > ijy/ijm > O. It is only if I..t < 1 that the sign of dy/dm is ambiguous. As long as I..t ~ 1, equation (6.2) is negative. For this case, the marginal net value of an application to the coalition is negative at the competitive equilibrium. A social planner could improve each worker's ex ante welfare by inducing each worker to search less intensively. There are two externalities in this market. The externality caused by contemporaneous competition is ijy/ijm. This always makes the coalition's optimal m less than the competitive m. The externality caused by intertemporal competition is the second term of equation (6.3). This term has an ambiguous sign when I..t < 1 but strengthens the effect of the contemporaneous externality when I..t > 1. The intertemporal externality is the kind discussed by previous authors. The contemporaneous externality is discussed only by Mortensen (1981; 1982a) and then only in a model with no intertemporal externalities. A social planner could maximize a representative worker's value of search by implementing an unemployment compensation programme supported by a tax on the wages of workers once they were employed. The programme could be built so that expected discounted compensation payments to each worker would be paid for by expected discounted wage tax revenues from that worker. Even though each worker's net balance would not equal zero, on average the programme would be in discounted budget balance and the deviation from budget balance would be insignificant relative to the size of the programme. 12 The social planner would have to be aware of how each worker would react to both a compensation programme and a tax on wages. He would have to maximize a representative worker's value of search subject to the reaction function of workers to his programme. A social planner's problem would be to solve max't w. u L = u - C(m) + ~w(1-'tw)l(1-~) - ym[~w(1-'tw)l(1-~) - ~V*] (6.4) s.t. - C'(m) - ym[~w(1-'tw)/(1-~) - ~V*] lny = 0 u = [~W'tw(1_ym)]/(1-~) where 'tw is a tax on wages and u is a compensation payment per

12 16 Search Unemployment: Theory and Measurement period. The first constraint states that each individual maximizes his value of search taking as given government policy and the rejection probability, and the second constraint states that expected discounted compensation payments equal expected discounted tax revenues. The tax, 't w, should be thought of as a steady state tax rate that started in the infinite past. The optimal positive wage tax, 't w, and unemployment compensation, u, will be at a point where the derivatives of the Lagrangian for equation (6.4) with respect to 'tw and u are equal to zero and the constraints are satisfied. The solution to this problem is intractable. But it can be shown that both the optimal 'tw and u are positive. In equation (6.4), substitute the government budget constraint into the Lagrangian for u: L = -C(m) + ~w/(l-~) - ym[~w/(l-~) - ~V*]. (6.5) Note that since there is a balanced budget, equation (6.5) contains no tax terms. Government intervention affects welfare only through its incentive effect on m. Now differentiate equation (6.5) with respect to 'tw at 'tw = 0: dl(o)/d'tw = [-C'(m*)_ym*(~w/(l-~)-~V*) In y]dm*id'tw - m*'tm*-l[~w/(l-~) - ~V*] «ijy/ijm*)/ (1 - (ijy/ijm*)(ijm*/ijy»(dm*id'tw) (6.6) where which is the total change in m* at 'tw = 0 when 'tw is changed, and m* equals individuals' choice of m at 'tw = O. The first term of equation (6.6) is an individual's first order condition, and the second term is the effect of increases in m* on ym*. Since the first term equals zero, dl(o)/d'tw = -m*ym'-l[~w/(l-~) - ~V*] «ijy/ijm*)/ (1 - (ijy/ijm*)(ijm*/ijy»)(dm*id'tw) (6.7) which is positive for stable equilibria (see note 10). The increase in L at 'tw = 0 is the incremental reduction in not being offered a job by y falling a little because m falls by Dm*/D'tw. Thus the welfare of a representative worker can be improved at 'tw = 0 by increasing 'two

13 8 CONCLUSIONS Stern: Search, Applications and Vacancies 17 A supply-side equilibrium search model with no distribution of wage offers is presented in this paper. Workers search for job openings rather than high offers. Stern (1989) has empirically shown that this type of search is more prevalent than search for high offers. The existence of competition among workers for a limited number of job openings leads to an inefficiently high amount of search. Nevertheless, an unemployment compensation programme set up in the proper way can induce each worker to choose the socially optimal search intensity. Many authors have discussed the effects of unemployment insurance on the behaviour of workers looking for a job. Theoretical papers include Mortensen (1977) and Lippman and McCall (1979). Empirical papers include Barron and Gilley (1979) and Clark and Summers (1982). The overwhelming consensus is that unemployment insurance decreases search intensity and increases the average spell of unemployment. The same result occurs in this paper. However, contrary to most other papers, this is found to have some positive value. ACKNOWLEDGEMENTS I have gained much insight from discussions with Paul Schultz, Kenneth Wolpin, T. N. Srinivasan, Chris Pissarides, Reuben Gronau, N. Kiefer, Russell Cooper, Jonathan Eaton, Brian Wright, Maxim Engers, and two anonymous referees. Participants of workshops at Yale, Cornell, Chicago, Penn, Virginia, Cal Tech, Tel Aviv and Johns Hopkins have provided useful comments. Special thanks are due to my dissertation adviser, Paul Milgrom. All remaining errors are mine. Financial assistance was provided by the Social Science Research Council under Grant No. Ss Notes 1. Lucas and Prescott (1974) present an equilibrium search model with competition. However, the competition affects only the equilibrium wage because markets clear each period. 2. See, for example, Loury (1979) and Mortensen (1981; 1982a; 1982b). 3. The model can be generalized to allow for a distribution of advertised wage offers as is done in Stern (1986). However, the advertised wage

14 18 Search Unemployment: Theory and Measurement offer must be paid, even if some workers would be willing to accept a lower wage. A firm uses its wage offer as a signal of how anxious it is to hire workers. If it can lower the offer once it observes how many' applicants it has, the signal provides no information. 4. Even though asymmetric equilibria may exist, they are not considered here. Since workers are homogeneous with respect to all relevant characteristics, symmetric equilibria are the natural ones to consider. 5. Computation poses some problems when there is more than one Nash equilibrium. 6. This assumes that unemployed workers receive u whether or not they search. If u is paid to all unemployed workers, then workers only consider the difference between wand u in their search decision. If u is paid only to unemployed workers who search, then the sizes of wand u enter the search decision in a nonlinear way. 7. u is really the unemployment compensation to be received the next period which increases V*. The unemployment compensation received this period has no effect on m since it is only a negative sunk cost of search. 8. This is for a case where the marginal cost of applying rises by a constant amount for all ms. For example, if CCm) = cm, then C'(m) = c. More precisely, if Ca(m) = c(m) + um, then Co(m) = CCm) and C'a(m) = C'(m) + u. The assertion is that dm*/du < O. 9. The one point is y' where M(y') = 0 and M(y) > 0 for any y < y'. To the left of this point dv*/dy < 0, and to the right of this point dv*/dy = O. This occurs because negative applications are not allowed. So if the solution to equation (5.1) is negative, then M(y) must be defined as equal to zero. The point where the non-negativity constraint becomes binding is not differentiable, but it is stili continuous. 10. It is very difficult to determine how many equilibria there are since it is difficult to determine Fy(y, I-t) at points other than y = O. If there is only one equilibrium, then it will be stable. If there are more than one, then generically every other one will be stable. Assume that expectations about yare adaptive, i.e.: (5.13a) for some positive constant u. Then equilibria are stable if F(y, I-t) intersects y from above. This occurs when (ijflijm*)(ijm/ijy) < Waiting lists partially play the role of such a social planner in that they reduce the coordination problem. They do not prevent it, however. It can be shown that there is excessive search even with waiting lists directly for small economies such as one with three workers and two firms. 12. Since the maximum and minimum net balance conditional on a search history are both finite, the variance of any worker's net balance is finite. Each worker's net balance is insignificantly negatively correlated with each other worker's net balance. If net balances were independent, the law of large numbers would imply that the mean net balance approaches zero as the number of workers approaches infinity. The negative correlation reduces the variance of the mean for any given sample size.

15 REFERENCES Stern: Search, Applications and Vacancies 19 Barron, J. M. and O. W. Gilley (1979) 'The Effect of Unemployment Insurance on the Search Process', Industrial and Labor Relations Review, Vol. 32, pp Clark, K. B. and L. H. Summers (1982) 'Unemployment Insurance and Labor Force Transitions', National Bureau of Economic Research, Working Paper No. 920, June. Diamond, P. A. (1981) 'Mobility Costs, Frictional Unemployment, and Efficiency', Journal of Political Economy, Vol. 89, pp Diamond, P. A. (1982a) 'Wage Determination and Efficiency in Search Equilibrium', Review of Economic Studies, Vol. 49, pp Diamond, P. A. (1982b) 'Aggregate Demand Management in Search Equilibrium', Journal of Political Economy, Vol. 90, pp Diamond, P. A. (1984) 'Money in Search Equilibrium', Econometrica, Vol. 52, pp Diamond, P. A. and E. Maskin (1979) 'An Equilibrium Analysis of Search and Breach of Contract, I: Steady States', Bell Journal of Economics, Vol. 10, pp Diamond, P. A. and E. Maskin (1981) 'An Equilibrium Analysis of Search and Breach of Contract, II: A Non-Steady State Example', Journal of Economic Theory, Vol. 25, pp Lippman, S. and J. J. McCall (1979) 'Search Unemployment: Mismatches, Layoffs, and Unemployment Insurance', Working Paper No. 297, Western Management Science Institute, University of California, Los Angeles, September. Loury, G. (1979) 'Market Structure and Innovation', Quarterly Journal of Economics, Vol. 94, pp Lucas, R. and E. C. Prescott (1974) 'Equilibrium Search and Unemployment', Journal of Economic Theory, Vol. 7, pp Mortensen, D. T. (1977) 'Unemployment Insurance and Job Search Decisions', Industrial and Labor Relations Review, Vol. 30, pp Mortensen, D. T. (1981) 'The Economics of Mating, Racing and Related Games', Northwestern Discussion Paper No. 482S, March. Mortensen, D. T. (1982a) 'Property Rights and Efficiency in Mating, Racing and Related Games', American Economic Review, Vol. 72, pp Mortensen, D. T. (1982b) 'The Matching Process as a Noncooperative Bargaining Game', in The Economics of Information and Uncertainty, ed., J. J. McCall, University of Chicago Press, Chicago. Pissarides, C. (1985) 'Taxes, Subsidies and Equilibrium Unemployment', Review of Economic Studies, Vol. 52, pp Stem, S. (1986) 'Nonsequential Search Among Heterogeneous Firms', University of Virginia Working Paper, November. Stem, S. (1989) 'Estimating a Simultaneous Search Model', Journal of Labor Economics, Forthcoming. Wilde, L. (1977) 'Labor Market Equilibrium Under Nonsequential Search', Journal of Economic Theory, Vol. 16, pp