dynamic matching and evolving reputations this paper introduces a general model of matching that includes evolving public bayesian reputations and stochastic production despite productive complementarity assortative matching robustly fails for high discount factors unlike in becker 1973 this failure holds around the highest lowest reputation agents for high skill low skill technologies we find that matches of likes eventually dissolve in another life cycle finding young workers are paid less than their marginal product and old workers more also wages rise with tenure but need not reflect marginal products information rents produce non monotone and discontinuous wage profiles

the empirical content of the roy model this paper clarifies and extends the classical roy model of self selection and earnings inequality the original roy model based on the assumption that log skills are normally distributed is shown to imply that pursuit of comparative advantage in a free market reduces earnings inequality compared to the earnings distribution that would result if workers were randomly assigned to sectors aggregate log earnings are right skewed even if one sectoral distribution is left skewed most major implications of the log normal roy model survive if differences in skills are log concave however few implications of the model survive if skills are generated from more general distributions we consider the identifiability of the roy model from data on earnings distributions the normal theory version is identifiable without regressors or exclusion restrictions sectoral distributions can be identified knowing only the aggregate earnings distribution for general skill distributions the model is not identified and has no empirical content with sufficient price variation the model can be identified from multimarket data cross sectional variation in regressors can substitute for price variation in restoring empirical content to the roy model

supplier relations and the market context a theory of handshakes abstract this paper analyzes the degree of formality in industrial procurement contracts impose cost discipline on suppliers but stifle cooperative innovation noncontractual procurement provides cooperation but poor cost discipline however cost discipline comes naturally when there is not much vertical integration because the promise of finding an alternative buyer to use as a bargaining threat enhances the supplier s incentive to make efficiency enhancing investments thus highly integrated industries use contracts while less integrated industries do business on handshakes in the latter cooperative innovations flourish this may help explain some international comparisons and changes in business practices observed over time

efficient non contractible investments in large economies abstract do investors making complementary investments face the correct incentives especially when they cannot contract with each other prior to their decisions we present a two sided matching model in which buyers and sellers make investments prior to matching once matched buyer and seller bargain over the price taking into account outside options efficient decisions can always be sustained in equilibrium we characterize the inefficiencies that can arise in equilibrium and show that equilibria will be constrained efficient we also show that the degree of diversity in a large market has implications for the extent of any inefficiency journal of economic literature classification numbers c78 d41 d51

decentralized college admissions we study decentralized college admissions with uncertain student preferences colleges strategically admit students likely to be overlooked by competitors highly ranked students may receive fewer admissions or have a higher chance of receiving no admissions than those ranked below when students attributes are multidimensional colleges avoid head on competition by placing excessive weight on school specific attributes such as essays restricting the number of applications or wait listing alleviates enrollment uncertainty but the outcomes are inefficient and unfair a centralized matching via gale and shapley s deferred acceptance algorithm attains efficiency and fairness but may make some colleges worse off than under decentralized matching

agents ability to manage information in centralized markets comparing two wholesale fish markets abstract in this paper we perform an empirical investigation to detect if and how agents behavior changes with the amount of available information they have to this aim we use data from two wholesale fish markets of different thicknesses we tackle the issue by investigating features such as the dynamics of the structure of attendance in auctions the varieties of fish presentations during the seller s turn and the presence of long term relationships between buyers and sellers we perform the investigation in this way instead of focusing on the dispersion and dynamics of prices to prevent unobserved quality differences of the traded fish varieties from biasing the results of the analysis the results of our investigation are consistent with a situation in which the magnitude of phenomena like buyers loyalty to sellers and agents following rules of thumb increases with the market thickness

two sided search marriages and matchmakers this article analyzes the provision of matching services in a model of two sided search agents belong to two heterogeneous populations and are distributed on 0 1 their utility is equal to the index of their mate in a search equilibrium agents form subintervals and are only matched to agents inside their class marriage brokers match agents according to a centralized procedure if the matchmaker charges a uniform participation fee only agents of higher quality participate in the centralized procedure if the matchmaker charges a commission on the matching surplus only agents of lower quality go to the intermediary

the role of individual financial contributions in the formation of entrepreneurial teams abstract this paper studies how entrepreneurs limited in how much they are able to contribute to a joint business organize in partnerships and how this process is impacted by the frictions common for team production it demonstrates that moral hazard and reliance on simple equity sharing contracts create incentives for the entrepreneurs making large contributions to team up together even if the production technology exhibits decreasing returns to scale to total investment the paper formalizes this novel mechanism in a matching model and illustrates that the model s predictions regarding co owners financial contributions and ownership shares are consistent with the empirical evidence from the kauffman firm survey data

investments holdup and the form of market contracts the authors analyze incomplete contracts to induce efficient investment with exogenous switching costs fixed price contracts are efficient generate some rigidity in prices are renegotiated intermittently by possibly small amounts and when inflation is positive generate asymmetric responses to shocks all consistent with evidence on prices and wages with two sided specific investments efficiency requires prices to have sufficient escalator clauses to avoid renegotiation as observed in many long term contracts a third case with one sided specific investments can generate take or pay contracts and explain why firms sometimes pay for specific investments that appear to benefit employees directly

competitive search equilibrium in this paper i construct an equilibrium for markets with frictions which is competitive in the sense that all agents are price takers and maximize utility subject to a set of market parameters i show that the equilibrium allocation is socially optimal i also show how the competitive search equilibrium can be achieved if employers with vacancies can advertise publicly the wages they pay

unravelling of dynamic sorting we consider a two sided finite horizon search and matching model with heterogeneous types and complementarity between types the quality of the pool of potential partners deteriorates as agents who have found mutually agreeable matches exit the market when search is costless and all agents participate in each matching round the market performs a sorting function in that high types of agents have multiple chances to match with their peers however this sorting function is lost if agents incur an arbitrarily small cost in order to participate in each round with a sufficiently rich type space the market unravels as almost all agents rush to participate in the first round and match and exit with anyone they meet copyright 2005 wiley blackwell

search theoretic models of the labor market a survey we survey the literature on search theoretic models of the labor market we show how this approach addresses many issues including the following why do workers sometimes choose to remain unemployed what determines the lengths of employment and unemployment spells how can there simultaneously exist unemployed workers and unfilled vacancies what determines aggregate unemployment and vacancies how can homogeneous workers earn different wages what are the tradeoffs firms face from different wages how do wages and turnover interact what determines efficient turnover we discuss various modeling choices concerning wage determination and the meeting process including recent models of directed search

ability and power over production in the distribution of earnings t he aggregate distribution of earnings in all western countries is approximately lognormal over most of its range but the earnings of the top 10 or 20 of individuals follow the pareto form which generates a great excess of very high earnings compared with the tail of a lognormal distribution individuals at the top appear to be paid according to the job they perform rather than their ability this paper explains these features in terms of profit maximising behaviour from time to time a single new manager or management team improves a company s profit by millions of dollars per year this shows that a senior manager can influence the company s total output far more than a junior employee his greater influence over output derives from having much more control over the company s resources profit maximising companies offer high salaries for senior management jobs because even a small improvement in their performance leads to a worthwhile increase in output and competitive bidding for the best managers then drives their salaries up to high levels this in outline is the explanation for high earnings developed formally in the rest of this paper

a new theory of corporatism and wage setting abstract the standard view on corporatist institutions for wage setting in many european economies is based of the insider outsider model corporatism is associated with lack of wage flexibility this paper discusses a new approach starting from the importance of nominal contracts the rationale for these contracts is to avoid future bargaining adjusting these contracts ex post to aggregate shocks would raise their efficiency however avoiding the bargaining required for this adjustment was the main reason for negotiating these contracts in the first place this is the fundamental contradiction under corporatism outside institutions can play this role these institutions provide therefore a type of flexibility not available in decentralized economies empirical evidence supports the basic ideas of this model

how the market solves an assignment problem the matching of lawyers with legal claims in the market for lawyers observable data on promotion and turnover can be explained by reference to the idea that there is positive assortative mating of lawyers and legal claims there is a scale of resources effect under which it is optimal to assign larger claims to lawyers of higher quality in a law firm the institution of tenure performs a sorting function lawyers found to be of high quality are given tenured positions and the rest leave the value of legal claims handled by a firm determines its sorting problem which in turn determines its promotion ladder and turnover

intra firm bargaining under non binding contracts we present a new methodology for studying the problem of intra firm bargaining based on the notion that contracts cannot commit the firm and its agents to wages and employment we develop and analyse a general non cooperative multilateral bargaining framework between the firm and its employees and consider outcomes which are immune to renegotiations by any party equilibrium firm profits are characterizable as both a weighted average of a neo classical non bargaining firm s profits and a generalization of shapley value for a corresponding cooperative game furthermore the resulting payoffs induce economically significant distortions in the firm s input and organizational design decisions

optimal search learning and implementation we characterize the incentive compatible constrained efficient policy second best in a dynamic matching environment where impatient privately informed agents arrive over time and where the designer gradually learns about the distribution of agents values we also derive conditions on the learning process ensuring that the complete information dynamically efficient allocation of resources first best is incentive compatible our analysis reveals and exploits close formal relations between the problem of ensuring implementable allocation rules in our dynamic allocation problems with incomplete information and learning and between the classical problem posed by rothschild 1974 20 of finding optimal stopping policies for search that are characterized by a reservation price property

the macrodynamics of sorting between workers and firms we develop an equilibrium model of on the job search with ex ante heterogeneous workers and firms aggregate uncertainty and vacancy creation the model produces rich dynamics in which the distributions of unemployed workers vacancies and worker firm matches evolve stochastically over time we prove that the surplus function which fully characterises the match value and the mobility decision of workers does not depend on these distributions we estimate the model on us labour market data from 1951 2007 and predict the fit for 2008 12 we use the model to measure the cyclicality of mismatch between workers and jobs

the right man for the job this paper describes a search model with a continuum of worker and job types free entry and transferable utility we apply a second order taylor expansion to characterize the equilibrium derive the cost of search and show that it is decreasing in the substitutability of worker types this cost of search is then decomposed into three components unemployment vacancy costs and mismatch our contact technology rules out congestion effects between different worker types and therefore exhibits increasing returns to scale one third of those increasing returns in contacts are shown to be absorbed by firms and workers being more choosy the resulting equilibrium is not efficient unemployment benefits can reduce the loss by serving as a search subsidy numerical simulations of the model show that our taylor expansions are quite accurate 2004 the review of economics studies limited

assortative matching with explicit search costs in this paper i analyze a decentralized search and matching economy with transferable utility composed of heterogeneous agents i explore whether becker s assortative matching result generalizes to an economy where agents engage in costly search in an economy with explicit additive search costs complementarities in joint production supermodularity of the joint production function lead to assortative matching this is in contrast to previous literature which had shown that in a search economy with discounting assortative matching may fail even when the joint production function is supermodular

why there are organized futures markets i shall present an explanation of the existence of organized futures markets with more predictive power than the two prevailing rival views my explanation briefly is this an organized futures market facilitates trade among strangers one of the rival prevailing views is a defense of futures trading it asserts that an organized futures market furnishes legitimate businessmen with a means of hedging so that they can obtain insurance against price risk the other prevailing view is an attack on organized futures markets it asserts that such markets enable speculators to manipulate prices to the detriment of outsiders who are less well informed and to the detriment of legitimate businessmen such as farmers the attack on organized futures markets likens them to gambling casinos the defense sees them as a form of insurance neither the attack nor the defense is valid the correct explanation is closely related to why we conduct trade using money instead of by barter

the excess sensitivity of layoffs and quits to demand excessive layoffs in bad times and excessive quits in good times both stem from the same weakness in practical employment arrangements the specific nature of worker firm relations creates a situat

sorting and decentralized price competition we investigate the role of search frictions in markets with price competition and how it leads to sorting of heterogeneous agents there are two aspects of value creation the match value when two agents actually trade and the probability of trading governed by the search technology we show that positive assortative matching obtains when complementarities in the former outweigh complementarities in the latter this happens if and only if the match value function is root supermodular that is its nth root is supermodular where n reflects the elasticity of substitution of the search technology this condition is weaker than the condition required for positive assortative matching in markets with random search

directed search with multiple job applications we develop an equilibrium directed search model of the labor market where workers can simultaneously apply for multiple jobs the main result is that all equilibria exhibit wage dispersion despite the fact that workers and firms are homogeneous wage dispersion is driven by the simultaneity of application choice risk neutral workers apply for both safe and risky jobs the former yield a high probability of a job oer but for low pay and act as a fallback option the latter provide with higher potential payo but are harder to get furthermore the density of posted wages is decreasing consistent with stylized facts unlike most directed search models the equilibria are not constrained ecient

contractual form and market thickness in trucking a central proposition of the transaction costs literature is that firms will substitute more complicated contractual arrangements for simple spot arrangements when transactions involve relationship specific investments i investigate this proposition by testing whether simple spot arrangements are less common when local trucking markets are thin i find that doubling the thickness of the market increases the likelihood that simple spot arrangements govern transactions by about 30 for long hauls i find weaker evidence of relationships between local market thickness and contractual form for short hauls hauls for which quasi rents are particularly small contracts protect quasi rents over a surprisingly large range but they play a less important role as quasi rents decrease

matching with contracts comment the theory of two sided matching markets has interested researchers for its theoretical appeal and its relevance to the design of real world institutions the medical residency matching mecha nism in the united states the national resident matching program nrmp and student assign ment systems in new york city and boston are important mechanisms designed by economists using the theory 1 hatfield and paul r milgrom 2005 present a unified framework of matching with contracts which includes the two sided matching and package auction models as well as a simplified version of a labor market model of alexander kelso and vincent p crawford 1982 as special cases they introduce the substitutes condition of contracts which is an adaptation of the substitutability condition in the matching literature roth and marilda a oliveira sotomayor 1990 to matching with contracts they show that there exists a stable allocation if contracts are substitutes for hospitals and that a number of other results in matching generalize to problems with contracts they further claim that the substitutes condition on individual hospitals prefer ences is necessary to guarantee the existence of a stable allocation for all possible singleton preferences of others that is if contracts are not substitutes for a hospital then there exists a preference profile of other hospitals with single job openings and doctors such that there exists no stable allocation we show that this last claim of hatfield and milgrom 2005 does not hold in general the counterexample we present involves a hospital which has two different kinds of positions and the preferences of the hospital are a combination of preferences of these two positions while the substitutes condition does not hold for that hospital we adopt a technique developed by bettina klaus and flip klijn 2005 and show that there exists a stable allocation we then present the weak substitutes condition which we show is necessary to guarantee existence of stable allocations the modified result we present as well as the original contribu tion of hatfield and milgrom 2005 suggest a connection between the substitutes condition and stability 2

appropriation and efficiency a revision of the first theorem of welfare economics the first theorem of welfare economics rests on the assumption that individuals have neither price making nor market making capacities we offer a revision in which individuals have such capacities the revision emphasizes two keys for market efficiency i the need to align private rewards with social contributions called full appropriation and ii the need for an assumption to counter the possibility of coordination failures in the choice of produced commodities called noncomplementarity we also emphasize that information about prices of unmarketed commodities involves decentralized knowledge available only to product innovators and that pecuniary extemalities are important potential sources of market failure jel d51 d60 d62

endogenous matching and the empirical determinants of contract form empirical work on contracts typically regresses contract choice on observed principal and agent characteristics if i some of these characteristics are unobserved or partially observed and ii there are incentives whereby particular types of agents end up contracting with particular types of principals estimated coefficients on the observed characteristics may be misleading we address this endogenous matching problem using a data set on agricultural contracts between landlords and tenants in early renaissance tuscany controlling for endogenous matching has an impact on parameters of interest and tenants risk aversion appears to have influenced contract choice

worker allocation hierarchies and the wage distribution economists have traditionally viewed the allocation of workers among jobs through the concept of comparative advantage this paper investigates hierarchical production models which display an absence of comparative advantage in order to demonstrate that for hierarchical production there is a second allocating factor which plays an important role two results are found first the allocation of workers among jobs tends to match high ability workers with positions which value ability highly second despite the fact that the models display an absence of comparative advantage i e the standard theoretical explanation for why wage distributions might be skewed the models wage distributions are skewed to the right relative to the underlying ability distributions

risk sharing vs incentives contract design under two sided heterogeneity we study the matching patterns between heterogeneous principals and agents in a principal agent model the resulting equilibrium relationship between risk and incentives could be negative positive or u shaped these results may provide an explanation for the absence of systematic empirical support for the standard risk model d 2005 elsevier b v all rights reserved

bertrand equilibrium with capacity constraints and restricted mobility this paper considers price competition among firms when there are capacity constraints and buyers have limited ability to visit firms a natural method of allocating buyers among firms arises in the equilibrium of the buyers search game sufficient conditions are given under which the buyers equilibrium varies continuously with the prices charged by firms capacity constraints are used to guarantee that this ensures existence of mixed strategy equilibria for the pricing game played by sellers we show that natural pure strategy equilibria arise when the game is made large in appropriate ways since bertrand s criticism of cournot it has been known that models where sellers compete with prices may have undesirable properties when the commodities traded are homogenous in the simplest models with constant marginal costs price may be driven down to the competitive level even when there are only two firms more problematic if sellers are subject to capacity constraints nash in prices equilibrium may not exist at all these problems all arise because of a discontinuity in firms profit functions that arises when the prices of two or more firms are equal there have been many attempts to resolve this problem the simplest is to constrain sellers prices to be equal and to force them to compete in quantities this is the basis of most of the literature on monopolistic competi

mechanism design by competing sellers a dynamic model with many sellers and buyers is constructed agents failing to trade may trade in the next period an equilibrium is found where sellers hold identical auctions and buyers randomize over the sellers they visit the distribution of buyer valuations is endogenous an auction with efficient reserve is an optimal mechanism from each seller s point of view in spite of the ability of any seller to alter the distribution of buyer types participating in the seller s mechanism by altering the mechanism copyright 1993 by the econometric society

the importance of bundling in a gorman lancaster model of earnings the idea that the labor market of individuals can be decomposed into payments to separate productive attributes has an enduring appeal in economics assuming that demographic groups differ only in their endowments of productive characteristics it is possible to rationalize observed demographic earnings differentials without invoking the arguments that characteristics specific to a particular demographic group are direct objects of employer demand by aggregating skills over all demographic groups it is possible to produce a theory of the market determination of the prices of skills held in different amounts by different demographic groups this paper considers conditions under which characteristics are uniformly priced across sectors of a multisector economy the paper presents empirical evidence that rejects uniform pricing of characteristics as a description of the us labor market bundling may account for this evudence but other hypotheses do as well authors

negative assortative matching of risk averse agents with transferable expected utility abstract i give necessary and sufficient conditions for expected utility to be transferable among agents with different state independent risk preferences who share a risk they cannot influence in an assignment game where participants choose partners based on risk aversion the conditions permit a simple proof that matching is negative assortative

sorting through search and matching models in economics toward understanding assortative matching this is a self contained introduction to research on search and matching we first explore the nontransferable and perfectly transferable utility matching paradigms and then a unifying imperfectly transferable utility matching model motivated by some unrealistic predictions of frictionless matching we flesh out the foundational economics of search theory we then revisit the original matching paradigms with search frictions we finally allow informational frictions that often arise such as in college student sorting

perfect competition in the continuous assignment model abstract this paper provides a rigorous formalization in the context of the transferable utility assignment model of perfect competition as the inability of individuals to favorably influence prices the central tool for the analysis is the social gains function the central issue is differentiability of the gains function with respect to the population seven conditions are shown to be equivalent to perfect competition perfect competition and imperfect competition are possible for both finite and continuum assignment economies but most finite economies are imperfectly competitive while most continuum economies are perfectly competitive however most large finite assignment economies are approximately perfectly competitive journal of economic literature classification numbers c61 c62 c78

frictional assignment i efficiency abstract this paper examines the two sided matching problem where the agents on each side of the market are heterogeneous and the matching process is time consuming this is cast in a labor market setting where workers of different skills match with different machine qualities i characterize the efficient allocation and then show that it can be decentralized by a market mechanism the efficient assignment is not always positively assortative despite the fact that machine qualities and skills are complementary in production to decentralize the efficient allocation the market mechanism requires the firms to post wages and commit each machine quality to a particular skill implications on wage inequality are briefly examined journal of economic literature classification numbers j31 e24 j64

sorting multidimensional types theory and application this article studies multidimensional matching between workers and jobs workers differ in manual and cognitive skills and sort into jobs that demand different combinations of these two skills to study this multidimensional sorting problem i develop a theoretical framework that generalizes the unidimensional notion of assortative matching and sufficient conditions on the technology under which sorting obtains i derive the equilibrium in closed form and use this explicit solution to study biased technological change the main finding is that an increase in worker job complementarities in cognitive relative to manual inputs leads to more pronounced sorting and wage inequality across cognitive relative to manual skills this can trigger wage polarization and boost aggregate wage inequality i then estimate the model for the u s and identify sizable technology shifts during the last two decades worker job complementarities in cognitive inputs strongly increased whereas complementarities in manual inputs decreased in addition to this bias in complementarities there has been a cognitive skill bias in production counterfactual exercises suggest that these technology shifts as opposed to changes in skill supply and demand can account for observed changes in worker job sorting wage polarization and a significant part of the increase in u s wage dispersion

micro foundations for wage flexibility wage insurance at the firm level to what extent do firms insulate their workers wages from fluctuations in product markets which firm and worker attributes are associated with wage flexibility at the micro level we first rely on guiso pistaferri and schivardi 2005 to estimate dynamic models of sales and wages finding that in portugal workers wages respond to permanent shocks on firm performance as opposed to transitory shocks we then explore the factors associated with wage flexibility finding that collective bargaining and minimum wages are associated with higher wage insurance by the firm while the threat of firm bankruptcy reduces it managers receive less protection against permanent shocks than other workers

on the segmentation of markets this paper endogenizes the market structure of an economy with heterogeneous agents who want to form bilateral matches in the presence of search frictions and when utility is nontransferable there exist infinitely many marketplaces and each agent chooses which marketplace to be in agents get to choose not only whom to match with but also whom they meet with perfect segmentation is obtained in equilibrium where agents match with the first person they meet all equilibria have the same matching pattern although perfect assortative matching is not obtained in equilibrium the degree of assortativeness is greater than in standard models

marriage and class here we consider a matching model where agents are heterogeneous and utilities nontransferable we utilize this framework to study how equilibrium sorting takes place in marriage markets we impose conditions that guarantee the existence of a steady state equilibrium and then characterize it several examples are developed to illustrate the richness of equilibria the model reveals an interesting sorting externality that can support multiple steady state equilibria even with constant returns to matching excerpt

sorting versus screening search frictions and competing mechanisms in a market where sellers compete by posting trading mechanisms we allow for a general search technology and show that its features crucially affect the equilibrium mechanism price posting prevails when meetings are rival i e when a meeting by one buyer reduces another buyer s meeting probability under price posting buyers reveal their type by sorting ex ante only if the meeting technology is sufficiently non rival price posting is not an equilibrium multiple buyer types then visit the same sellers who screen ex post through auctions

matching with noise and the acceptance curse abstract this paper explores matching with both search and information frictions specifically everyone observes only a noisy signal of the true type of any potential mate in this context matching decisions must incorporate not only information about a partner s attribute conveyed by the noisy signal but also as in the winner s curse in auction theory information about a partner s type contained in his or her acceptance decision we show that there exists an equilibrium exhibiting a stochastic positive assorting of types generalizing becker j polit economy 81 1973 813 846 in equilibrium selection is adverse being accepted reduces an agent s estimate of a potential partner s type a phenomenon that we call the acceptance curse effect

steady states in matching and bargaining abstract we establish the existence of steady states in two classic matching and bargaining models with general trader asymmetries search processes and production functions

efficiency of simultaneous search this paper presents an equilibrium labor search model in which workers can simultaneously apply to multiple firms to increase their search intensity they observe firms wage postings before choosing where to apply owing to coordination frictions a firm may not receive any applications otherwise it is able to hire unless all its applicants have better offers it is shown that the equilibrium converges to the efficient walrasian outcome as application costs vanish even for nonnegligible application costs the entry of firms the search intensity and the number of filled vacancies are constrained efficient wage dispersion is essential for constrained efficiency

competition among sellers who offer auctions instead of prices abstract in this paper we study a large market in which sellers compete by offering auctions to buyers instead of simple fixed price contracts two variants of the model are studied one extends a model first analyzed by wolinsky rev econ stud 55 1988 71 84 in which buyers learn their valuations only after meeting sellers the other variant extends the model of mcafee econometrica61 1993 1281 1312 in which buyers know their valuations before they choose among available auctions the equilibrium array of auctions is characterized for each case and the efficiency properties of the equilibria are analyzed journal of economic literatureclassification numbers d41 d44 d82

student portfolios and the college admissions problem we develop a decentralized bayesian model of college admissions with two ranked colleges heterogeneous students and two realistic match frictions students find it costly to apply to college and college evaluations of their applications are uncertain students thus face a portfolio choice problem in their application decision while colleges choose admissions standards that act like market clearing prices enrollment at each college is affected by the standards at the other college through student portfolio reallocation in equilibrium student college sorting may fail weaker students sometimes apply more aggressively and the weaker college might impose higher standards applying our framework we analyse affirmative action showing how it induces minority applicants to construct their application portfolios as if they were majority students of higher caliber

trade and market thickness effects on organizations globalization by raising the number of buyers available to each seller and the number of sellers available to each buyer raises the thickness or the effective number of participants of every market market thickness can have subtle effects on incentives and organizations alleviating hold up problems resulting in less vertical integration more informal contracting and more cooperative and innovative relationships with subcontractors however it can also weaken long run relationships distorting relationship specific investments and risk sharing this paper surveys the theory and empirical evidence indicating when market thickness helps and when it hurts jel f15 l14 l22

consumption smoothing in island economies can public insurance reduce welfare abstract in this paper we study the effects of certain types of public compulsory insurance arrangements for aggregate shocks on private allocations in environments with limited commitment we show that this type of insurance can improve the wellbeing of private situations but it can also deteriorate it we also describe how different characteristics of the environment affect the role of public insurance using data on the mexican progresa program we document the impact that some government programs have in crowding out private transfers

competitive equilibrium with search frictions a general equilibrium approach abstract when the trading process is characterized by search frictions traders may be rationed so markets need not clear we build a general equilibrium model with transferable utility where the uncertainty arising from rationing is incorporated in the definition of a commodity in the spirit of the arrow debreu theory prices of commodities then depend not only on their physical characteristics but also on the probability that their trade is rationed the standard definition of competitive equilibrium is extended by replacing the market clearing condition with an exogenous matching function which describes a trading technology that is not frictionless as is typical in search models the matching function relates the rationing probabilities of buyers and sellers to the ratio of buyers to sellers in the market when search frictions vanish our model is equivalent to the continuous assignment model of gretsky et al 20 we adapt their approach which uses linear programming techniques and duality theory to show that a competitive equilibrium exists and is constrained efficient in our environment our competitive equilibrium notion is equivalent to that of directed or competitive search the strength of our formulation and the linear programming approach is that they allow us to generalize the constrained efficiency and existence results in the directed search literature to a much broader class of economies our framework also opens the door to the use of existing algorithms for computing equilibria and taking these models to the data

holdups and efficiency with search frictions a natural holdup problem arises in a market with search frictions firms have to make a range of investments before finding their employees and larger investments translate into higher wages in particular when wages are determined by ex post bargaining the equilibrium is always inefficient recognizing that capital intensive production relations have to pay higher wages firms reduce their investments this can only be prevented by removing all the bargaining power from the workers but this in turn depresses wages below their social product and creates excessive entry of firms in contrast to this benchmark we show that efficiency is achieved when firms post wages and workers can direct their search toward more attractive offers this efficiency result generalizes to an environment with imperfect information where workers only observe a few of the equilibrium wage offers we show that the underlying reason for efficiency is not wage posting per se but the ability of workers to direct their search toward more capital intensive jobs

competitive pricing and efficiency in search equilibrium we consolidate and generalize some results on price determination and efficiency in search equilibrium extending models by rubinstein and wolinsky and by gale heterogeneous buyers and sellers meet according to a general matching technology and prices are determined by a general bargaining condition when the discount rate r and search costs converge to 0 we show that prices in all exchanges are the same and equal the competitive market clearing price given positive search costs efficiency obtains iff bargaining satisfies hosios condition and r 0 when prices are set by third party market makers however we show that search equilibrium is necessarily efficient

wage vacancy contracts and multiplicity of equilibria in a directed search model of the labour market this paper studies a directed search model of the labour market which is standard in all aspects except two first we allow firms to post wage vacancy contracts advertising the number of workers they would pay as well as the payment all will receive second we consider two cases one where workers are risk neutral and one where workers are risk averse both in finite and large economies our paper shows that when firms post wage vacancy contracts whether workers are modelled as risk neutral or risk averse matters the types of symmetric equilibria and the nature of multiplicity of equilibria are different somewhat surprisingly when there are finite numbers of risk neutral workers and firms we obtain a finite number of symmetric equilibria but when workers are risk averse we obtain a continuum of equilibria furthermore our paper sounds a cautionary note on using large economies as an approximation of finite economies when workers are risk neutral the nature of equilibrium is preserved going from a finite to a large economy but the nature of equilibrium is different when workers are risk averse les contrats salaire emploi et la multiplicite des equilibres au sein d un modele de recherche dirigee applique au marche du travail cet article etudie un modele de recherche dirigee applique au marche du travail qui differe du modele standard en deux points premierement les entreprises peuvent proposer des contrats dits salaire emploi qui en plus du salaire indiquent le nombre de travailleurs qu un employeur est dispose a recruter deuxiemement nous considerons deux cas un ou les travailleurs ne presentent pas d aversion au risque et l autre ou ils sont averses au risque a chaque fois pour des economies avec une nombre fini puis infini d agents l article demontre que la presence ou non d aversion au risque a de l importance quand les entreprises peuvent proposer des contrats salaire emploi car les types d equilibres symetriques et la nature des multiplicites different dans les deux cas par exemple si l on considere une economie avec un nombre fini de travailleurs il existe un nombre fini d equilibres symetriques lorsque les travailleurs ne presentent pas d aversion au risque alors qu il en existe un continuum lorsque les travailleurs sont averses au risque qui plus est l article invite a la prudence en utilisant une economie a nombre infini d agents comme approximation d une economie peuplee d un nombre fini d agents car en allant de l une a l autre la nature des equilibres est preservee dans le cas de travailleurs ne presentant pas d aversion au risque alors qu elle change lorsque les travailleurs sont averses au risque

investment and competitive matching we study markets in which agents first make investments and are then matched into potentially productive partnerships equilibrium investments and the equilibrium matching will be efficient if agents can simultaneously negotiate investments and matches but we focus on markets in which agents must first sink their investments before matching additional equilibria may arise in this sunk investment setting even though our matching market is competitive these equilibria exhibit inefficiencies that we can interpret as coordination failures all allocations satisfying a constrained efficiency property are equilibria and the converse holds if preferences satisfy a separability condition we identify sufficient conditions most notably quasiconcave utilities for the investments of matched agents to satisfy an exchange efficiency property as well as sufficient conditions most notably a single crossing property for agents to be matched positive assortatively with these conditions then forming the core of sufficient conditions for the efficiency of equilibrium allocations

matching turnover and unemployment this paper develops the view that workers move into and out of the labor market because of changes in the perceived value of their market opportunities a search model is combined with a matching model to yield movement of workers from job to job and into and out of employment

hard to get the scarcity of women and the competition for high income men in urban china reports of the difficulties of elite women in finding suitable mates have been increasing despite the growing availability and value of men in china we rationalize this leftover women phenomenon within the directed competitive search framework which uniquely allows for equilibrium crowding out within this framework we show that the leftover women phenomenon can be the result of women s aversion to men who have a lower income than themselves hereafter alm and the long predicted complementarity between women s non market traits in particular beauty and male earnings for high income h women even when high income h men are more plentiful and richer the direct effect of the greater number of desirable men can be overwhelmed by the indirect effect of competitive entry by low income l women particularly the beautiful we test for these competitive search effects using online dating field experimental census and household survey data consistent with the competitive entry of l women when sex ratio and h men s income increase the search intensity of beautiful l women for h men increases in response to this competitive entry plain h women who are constrained by their alm to search predominantly for h men also increase the search intensity however only their marriage probability decreases our evidence is consistent with intra female competitive search for spouses who can cover the labor market opportunity cost of marriage and childbirth which increases with a woman s income

matching with contracts we develop a model of matching with contracts which incorporates as special cases the college admissions problem the kelso crawford labor market matching model and ascending package auctions we introduce a new law of aggregate demand for the case of discrete heterogeneous workers and show that when workers are substitutes this law is satisfied by profit maximizing firms when workers are substitutes and the law is satisfied truthful reporting is a dominant strategy for workers in a worker offering auction matching algorithm we also parameterize a large class of preferences satisfying the two conditions

the assignment of workers to jobs in an economy with coordination frictions this paper studies the assignment of heterogeneous workers to heterogeneous jobs owing to the anonymity of a large labor market workers use mixed strategies when applying for jobs this randomness generates coordination frictions two workers may apply for a particular job whereas an identical job gets no applications the model generates assortative matching with a positive but imperfect correlation between matched workers and firms types it predicts that a worker s wage is increasing in her job s productivity and a firm s profit is increasing in its employees productivity the model also yields a version of the welfare theorems

self selection and the distribution of hourly wages this article formulates and estimates alternative equilibrium models of industrial wage determination and self selection in explaining industrial wage differentials we find that it is important to account for heterogeneous sector specific skills and self selection decisions by agents concerning their sector of employment the classical roy model is rejected so is an efficiency units model of the labor market a revised roy model that accounts for comparative advantage in the choice of industrial sectors and choice between market and nonmarket work is much more successful in explaining cross section wage distributions and their evolution over time

pricing and matching with frictions suppose that n buyers each want one unit and m sellers each have one or more units of a good sellers post prices and then buyers choose sellers in symmetric equilibrium similar sellers all post one price and buyers randomize hence more or fewer buyers may arrive than a seller can accommodate we call this frictions we solve for prices and the endogenous matching function for finite n and m and consider the limit as n and m grow the matching function displays decreasing returns but converges to constant returns we argue that the standard matching function in the literature is misspecified and discuss implications for the beveridge curve

marriage markets and assortative mating with household public goods theoretical results and empirical implications this paper analyzes marriage market equilibria when the gains from marriage result from joint consumption of household public goods assuming transferable utility within marriage the paper proves that marriage markets will be characterized by positive assortative mating on wealth when spouses differ only in endowments and the gains to marriage result only from public goods when spouses differ in wages and household public goods are produced at home the results imply offsetting effects with public good economies creating an incentive for positive assortative mating on wages and gains from specialization creating an incentive for negative assortative mating on wages the results help explain the persistent lack of empirical support for becker s prediction of negative assortative mating on wages and have implications for empirical analysis of all joint living arrangement decisions

a dynamic generalization of becker s assortative matching result abstract this paper considers a dynamic matching model in which each agent s future productivity depends in part on their current match as in labor markets schooling intergenerational marriage markets and other environments the planner s endogenous rankings of human distributions are characterized these planner rankings are then used to develop sufficient conditions for positive assortative matching to be dynamically efficient one lesson that emerges is that complementarity assumptions alone are insufficient for a robust sorting theory the curvature of the static production function is also critical to determine optimal sorting patterns in addition the planner s ranking of distributions over human capital yield characterizations of individual attitudes toward human capital gambles in an associated market equilibrium finally the implied dynamics for 1 individual wages and 2 wage distributions across age cohorts are characterized

insider effects in wage determination abstract the paper attempts to shed new light on the determinants of industry wages by a cross country comparison of wage setting relationships making use of comprehensive and consistent panel data on industries from the early 1960s to the mid 1980s the empirical analysis involves estimations of identically specified industry wage equations for each of five countries sweden norway finland germany and the united states a key finding is that industry wages in the u s are the most responsive to sectoral price and productivity changes by contrast industry wages in the nordic countries are largely unaffected by sectoral conditions the results cast doubt on the competitive model as an accurate characterization of wage setting under decentralization

aggregation and linearity in the provision of intertemporal incentives we consider the problem of providing incentives over time for an agent with constant absolute risk aversion the optimal compensation scheme is found to be a linear function of a vector of n accounts which count the number of times that each of the n kinds of observable events occurs the number n is independent of the number of time periods so the accounts may entail substantial aggregation in a continuous time version of the problem the agent controls the drift rate of a vector of accounts that is subject to frequent small random fluctuations the solution is as if the problem were the static one in which the agent controls only the mean of a multivariate normal distribution and the principal is constrained to use a linear compensation rule if the principal can observe only coarser linear aggregates such as revenues costs or profits the optimal compensation scheme is then a linear function of those aggregates the combination of exponential utility normal distributions and linear compensation schemes makes computations and comparative statics easy to do as we illustrate we interpret our linearity results as deriving in part from the richness of the agent s strategy space which makes it possible for the agent to undermine and exploit complicated nonlinear functions of the accounting aggregates

identifying sorting in theory assortative matching between workers and rms provides evidence of the complementarities or substitutes in production the presence of complementarities is important for policies that aim to achieve the optimal allocation of resources for example unemployment insurance we argue that using wage data alone it is virtually impossible to identify whether assortative matching is positive or negative even though we cannot identify the sign of the sorting we can identify the strength i e the magnitude of the cross partial and the associated welfare loss we show rst that the wage for a given worker is non monotonic in the type of his employer this is due to the fact that in a sorting model wages reect the opportunity cost of mismatch we show analytically that this non monotonicity prevents standard rm xed eects to correlate with the true type of the rm we then propose an alternative procedure that measures the strength of sorting in the presence of search frictions knowing the strength of sorting facilitates the measurement of the output loss due to mismatch

a note on aggregation of skills and labor quality we use a unique new data set that combines data on individual workers and their employers to estimate marginal productivity differentials among different types of workers we then compare these to estimated relative wages leading to new evidence on

marriage as a rat race noisy premarital investments with assortative matching we study the efficiency of premarital investments when parents care about their child s marriage prospects in a large frictionless marriage market with nontransferable utility stochastic returns to investment ensure that equilibrium is unique we find that generically investments exceed the pareto efficient level unless the sexes are symmetric in all respects girls will invest more than boys if their quality shocks are less variable than shocks for boys or if they are the abundant sex the unique equilibrium in our continuum agent model is the limit of the equilibria of finite models as the number of agents tends to infinity

does competition solve the hold up problem in an environment in which heterogeneous buyers and sellers undertake ex ante investments the presence of market competition for matches provides incentives for investment but may leave inefficiencies namely hold up and coordination problems this paper shows using an explicitly non cooperative model that when matching is assortative and investments precede market competition buyers investments are constrained efficient while sellers marginally underinvest with respect to what would be constrained efficient however the overall extent of this inefficiency may be large multiple equilibria may arise one equilibrium is characterized by efficient matches but there can be additional equilibria with coordination failures

stable marriages and search frictions stable matchings are the primary solution concept for two sided matching markets with nontransferable utility we investigate the strategic foundations of stability in a decentralized matching market towards this end we embed the standard marriage markets in a search model with random meetings we study the limit of steady state equilibria as exogenous frictions vanish the main result is that convergence of equilibrium matchings to stable matchings is guaranteed if and only if there is a unique stable matching in the underlying marriage market whenever there are multiple stable matchings sequences of equilibrium matchings converging to unstable inefficient matchings can be constructed thus vanishing frictions do not guarantee the stability and efficiency of decentralized marriage markets

heterogeneous firms and the organization of production firms in the same industry exhibit systematic differences in the organization of production and the structure of employment entrepreneurial ability is the specific scarce input that limits the size of a firm this input must be allocated to two activities coordinating production and monitoring workers able entrepreneurs can convert calendar time into larger supplies of coordinating effort that enable them to assemble large firms greater ability implies a higher shadow price of time which increases the implicit costs of monitoring a dispersion of entrepreneurial abilities generates an equilibrium size distribution of firms differences in monitoring costs affect the choice of worker productivities the design of products and the organization of production the monitoring cost hypothesis advanced in this paper goes a long way in explaining the equilibrium of an industry containing heterogeneous firms that differ in size and behavior

hedonic prices and implicit markets estimating demand and supply functions for differentiated products in choosing the level of quality to purchase the buyer of a differentiated product also chooses a point on the marginal price schedule for that product hence in general the demand functions for product characteristics cannot be consistently estimated by ordinary least squares market equilibrium results in a matching of characteristics of demanders and suppliers this matching restricts the use of buyer and seller characteristics as instruments when estimating demand and supply functions for product characteristics the paper develops these issues a stochastic structure for hedonic equilibrium models is then proposed identification results are presented and estimation procedures are outlined

a competitive distribution of auctions in this paper a competitive distribution of auctions is described for an economy consisting of an infinite number of buyers and sellers all of whom differ according to their valuation for the single indivisible object being traded a competitive distribution of auctions is such that no seller can improve his profits by deviating to any alternative direct mechanism it is shown that the competitive distribution of auctions will have the property that each buyer and seller s best reply is independent of his beliefs about the tastes of other buyers and sellers on the market the purpose of this paper is to provide an equilibrium for an economy in which sellers compete by offering different direct mechanisms to buyers no attempt is made to give a complete characterization of all possible equilibria rather we focus on one equilibrium in which the contracts that are offered by sellers in equilibrium and buyer s behaviour under these contracts are both independent of traders beliefs about one another the equilibrium illustrates one of the reasons why contracts that are employed in practice may not be as finely tuned to beliefs as the theory of mechanism design says that they should be the answer is simply that contracts are not offered in a vacuum sellers in the model studied in this paper need to compete with one another in order to attract buyers highly tuned mechanisms tend to extract buyer surplus in such an environment sellers are able to attract many buyers by offering to use cruder mechanisms that leave some surplus for buyers in this paper sellers are allowed to have different costs for the commodity that is being traded nonetheless the equilibrium for the limit economy in which there are infinitely many buyers and sellers is such that every seller offers a second price auction and publicizes a reserve price equal to his cost in a standard monopoly auction the optimal reserve price for the seller exceeds his cost by an amount that depends on his beliefs about buyers valuations myerson 1981 a seller who raises his reserve price has his profits affected in two distinct ways by raising his reserve price the seller makes it unprofitable for some buyer types to participate in his auction the seller therefore loses any surplus that he might have earned by trading with these buyers the buyers who still find it profitable to participate in the seller s auction will end up having to pay a higher price when they win because of this increase in the seller s reserve price this means that the seller will be able to extract a bit more surplus from buyers who continue to participate the seller raises the reserve price until the marginal cost associated with raising the reserve price is just equal to the marginal gain associated with the ability to extract more surplus from remaining buyers competition mitigates this argument since there is a limit to the amount of surplus that the seller can extract from remaining buyers before they decide that they should instead choose one of the alternative auctions that are being held on the market with

wage differentials employer size and unemployment the unique equilibrium solution to a game in which a continuum of individual employers choose permanent wage offers and a continuum of workers search by sequentially sampling from the set of offers is characterized wage dispersion is a robust outcome provided that workers search while employed as well as when unemployed the unique nondegenerate equilibrium distribution of wage offers is constructed for three cases 1 identical workers and employers 2 identical employers and an atomless distribution of worker supply prices and 3 identical workers and an atomless distribution of job productivities copyright 1998 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

sectoral shifts and interindustry wage differentials the observed differences in wages across industries may arise from a lack of worker mobility particularly among experienced workers allowing the effects of industry shocks to persist for some time although young workers arbitrage wage shocks they will have little effect on the dispersion of experienced workers wages if young and old workers are poor substitutes in production this explanation is investigated using the five censuses of population between 1940 and 1980 the evidence strongly suggests that differences in pay are not temporary phenomena the data provide some support for the role of human capital and ability