incomplete wage posting we consider a directed search model in which workers differ in productivity productivity becomes observable to firms after assessing their workers on the job but it is not verifiable firms with vacancies choose between posting a noncontingent wage and leaving wages subject to bargaining with the worker under wage bargaining firms cannot optimize the trade off between paying higher wages and having a larger probability of filling vacancies but wage bargaining makes wages increasing in worker productivity and so may allow firms to attract better workers into the vacancy when workers heterogeneity is large and bargaining powers come close to satisfying hosios s rule firms opt for bargaining yet equilibria with bargaining fail to maximize aggregate net income and sometimes are not constrained pareto optimal

limits of exact equilibria for capacity constrained sellers with costly search abstract this paper studies finite versions of competitive matching models in which sellers announce prices and buyers understand the relationship between price and probability of trade two equilibrium concepts are studied for finite games subgame perfect equilibrium and rational expectations equilibrium it is shown that the distribution of prices offered by sellers under both equilibrium concepts converges weakly to the same competitive equilibrium distribution of prices furthermore the payoffs that sellers face in both kinds of equilibrium have the market utility property in the limit journal of economic literature classification numbers c78 d41 d45

competitive search equilibrium in monetary economies abstract competitive search was recently introduced in monetary economics by rocheteau and wright money in search equilibrium in competitive equilibrium and in competitive search equilibrium econometrica 73 2005 175 203 we extend their work by eliminating the restriction that the fees market makers charge to enter a submarket must be either non negative or identical for buyers and sellers without this restriction buyers pay a positive fee to enter the submarket they visit and nothing else when they meet a seller sellers are remunerated by the market makers from the entry fees collected from the buyers this trading arrangement allows buyers to perfectly predict their expenses so the opportunity cost of holding idle money balances is eliminated

wage vacancy contracts and coordination frictions abstract we consider a directed search model with risk averse workers and risk neutral entrepreneurs who can set up firms that post wage vacancy contracts i e contracts where firms can make payments to more than one applicant and where the payments can be different for each applicant and be contingent on the number of applicants we establish that the type of contracts the literature focuses on are not offered if firms can post wage vacancy contracts we show that there exists an equilibrium satisfying a monotonic expected utility property which is efficient furthermore we investigate the role of wage vacancy contracts on welfare and competition

optimal contracts under adverse selection and moral hazard a continuous time approach this article presents a continuous time agency model in the presence of adverse selection and moral hazard with a risk averse agent and a risk neutral principal under the model setup we show that the optimal controls are constant over time and thus the optimal menu consists of contracts that are linear in the final outcome we also show that when a moral hazard problem adds to an adverse selection problem the monotonicity condition well known in the pure adverse selection literature needs to be modified to ensure the incentive compatibility for information revelation the model is applied to a few managerial compensation problems involving managerial project selection and capital budgeting decisions we argue that in the third best world the relationship between the volatility of the outcome and the sensitivity of the contract depends on interactions between the managerial cost and the firm s production functions contrary to conventional wisdom sometimes the higher the volatility the higher the sensitivity of the contract the firm receiving good news sometimes chooses safer projects or invests less than it does with bad news we also examine the effects of the observability of the volatility on corporate investment decisions copyright 2005 oxford university press

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

the first best sharing rule in the continuous time principal agent problem with exponential utility abstract the continuous time principal agent model with exponential utility developed by holmstrom and milgrom admits a simple closed form solution the second best sharing rule is a linear function of aggregated output here we show that the first best sharing rule is also linear in aggregated output the result follows immediately from the separability of the problem and the fact that principal and agent both have cara utility journal of economic literature classification numbers d82 j33

continuous time methods in finance a review and an assessment i survey and assess the development of continuous time methods in finance during the last 30 years the subperiod 1969 to 1980 saw a dizzying pace of development with seminal ideas in derivatives securities pricing term structure theory asset pricing and optimal consumption and portfolio choices during the period 1981 to 1999 the theory has been extended and modified to better explain empirical regularities in various subfields of finance this latter subperiod has seen significant progress in econometric theory computational and estimation methods to test and implement continuous time models capital market frictions and bargaining issues are being increasingly incorporated in continuous time theory the roots of modern continuous time methods in finance can be traced back to the seminal contributions of merton 1969 1971 1973b in the late 1960s and early 1970s merton 1969 pioneered the use of continuous time modeling in financial economics by formulating the intertemporal consumption and portfolio choice problem of an investor in a stochastic dynamic programming setting merton 1973b also showed how such a framework can be used to develop equilibrium asset pricing implications thereby significantly extending the asset pricing theory to richer dynamic settings and expanding the scope of applications of continuous time methods to study problems in financial economics 1 within a span of about 30 years from the publication of merton s inf luential papers continuous time methods have become an integral part of financial economics indeed in certain core areas in finance such as e g asset pricing derivatives valuation term structure theory and portfolio selection continuoustime methods have proved to be the most attractive way to conduct research and gain economic intuition the continuous time approach in these areas has produced models with a rich variety of testable implications the econometric theory for testing continuous time models has made rapid strides in the last decade and has thus kept pace with the impressive progress on the theoretical front one hopes that the actual empirical investigations and estimation using the new procedures will follow suit soon

the costs of worker displacement this study identifies part of the social loss attendant upon displacement as the remaining value of the assets specific to the severed employment relationship a bargaining model is used to link wage tenure profiles to the amount of information firms and workers possess about the duration of that relationship if information is good the profile will flatten as displacement approaches using psid data for workers separated between 1977 and 1981 wage tenure profiles are found not to change this suggests that either workers or both firms and workers are surprised by the displacement the present value of that part of the social loss attributable to the worker s share of firm specific capital is around 7 000 1980 dollars

equilibrium wage dispersion and interindustry wage differentials this paper develops a search theoretic explanation of interindustry wage differentials given coordination problems in the labor market the probability of filling a vacancy is an increasing function of the wage offered in equilibrium firms that find vacancies more costly will offer higher wages the model thus explains the persistence of interindustry wage differentials and their correlation with industry average capital labor ratio and profitability additionally the model predicts that high wage firms will receive more applications per job opening and that wages in the labor market will behave as strategic complements

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

bidding for money we analyze monetary exchange in a model that allows for directed search and multilateral matches we consider environments with divisible goods and indivisible money and compare the results with those in models that use random matching and bilateral bargaining two different pricing mechanisms are used ex ante price posting and ex post bidding auctions also we consider settings both with and without lotteries we find that the model generates very simple and intuitive equilibrium allocations that are similar to those with random matching and bargaining but with different comparative static and welfare properties

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 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

optimal risk sharing with effort and project choice we consider first best risk sharing problems in which the agent can control both the drift effort choice and the volatility of the underlying process project selection in a model of delegated portfolio management it is optimal to compensate the manager with an option type payoff where the functional form of the option is obtained as a solution to an ordinary differential equation in the general case the optimal contract is a fixed point of a functional that connects the agent s and the principal s maximization problems we apply martingale duality methods familiar from optimal consumption investment problems

market power and efficiency in a search model we build a theoretical model to study the welfare effects and resulting policy implications of firms market power in a frictional labor market our environment has two main characteristics wages play a role in allocating labor across firms and there is a finite number of agents we find that the decentralized equilibrium is inefficient and that the firms market power results in the misallocation of workers from the high to the low productivity firms a minimum wage forces the low productivity firms to increase their wage leading them to hire even more often thereby exacerbating the inefficiencies moderate unemployment benefits can increase welfare because they limit firms market power by improving the workers outside option

ex ante price offers in matching games non steady states a matching problem is considered in which sellers can publicly commit to a trading price that differs from the price at which buyers expect to trade elsewhere in the market when demand and supply are nearly equal the equilibrium ex ante price offer lies below the price associated with the nash bargaining split this relationship reverses when the level of excess demand is large sellers always have an incentive to make ex ante offers when prices elsewhere are determined by nash bargaining this can be interpreted to mean that nash bargaining is an unstable pricing institution copyright 1991 by the econometric society

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

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

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

linearity with project selection and controllable diffusion rate in continuous time principal agent problems i extend holmstrom and milgrom s model by allowing the agent to control privately or publicly the diffusion rate process and show that the optimal contract is still linear i discuss the conditions under which conflicts over the choice of diffusion rate do and do not arise as an application i examine project selection problems of a firm conflicts between the manager and investors arise because giving the manager too much incentive to work to increase the profit from ongoing operations can induce him to be too conservative in project selection possibly resulting in optimal contracts with low sensitivities

implicit labor contracts and free entry the model investigated here is an adaptation of the free entry model introduced in kihlstrom laffont 1979 in that model the only labor market is one in which employers pay workers an ex ante guaranteed wage in the model of this paper there is also a spot market for labor in the earlier sections of the paper the existence of the equilibrium is established and its efficiency is investigated in this analysis it is assumed that all individuals are identical in the later sections we drop this assumption and investigate conditions under which employers are more risk averse than workers

on the equivalence of walrasian and non walrasian equilibria in contract markets the case of complete contracts this paper explores two models of an economy in which contracts are exchanged in the first model contracts are exchanged on a competitive market in which traders expectations concerning conditions that prevail within specific markets adjust until markets clear in the second model contract designers compete directly against one another by offering alternate contracts it is shown that walrasian allocations correspond with the equilibrium allocations in the model with direct competition when the number of traders is made large furthermore the expectational assumptions that drive the walrasian analysis coincide with off the equilibrium path conjectures in the problem with direct competition