Paper # Author Title
Are nominal prices sticky because menu costs prevent sellers from continuously adjusting their prices to keep up with inflation or because search frictions make sellers indifferent to any real price over some non-degenerate interval? The paper answers the question by developing and calibrating a model in which both search frictions and menu costs may generate price stickiness and sellers are subject to idiosyncratic shocks. The equilibrium of the calibrated model is such that sellers follow a (Q,S,s) pricing rule: each seller lets inflation erode the effective real value of the nominal prices until it reaches some point s and then pays the menu cost and sets a new nominal price with an effective real value drawn from a distribution with support [S,Q], with s < S < Q. Idiosyncratic shocks short-circuit the repricing cycle and may lead to negative price changes. The calibrated model reproduces closely the properties of the empirical price and price-change distributions. The calibrated model implies that search frictions are the main source of nominal price stickiness. Download Paper
This paper develops a theory of asset intermediation as a pure rent extraction activity. Agents meet bilaterally in a random fashion. Agents differ with respect to their valuation of the asset's dividends and with respect to their ability to commit to take-it-or-leave-it offers. In equilibrium, agents with commitment behave as intermediaries, while agents without commitment behave as end users. Agents with commitment intermediate the asset market only because they can extract more of the gains from trade when reselling or repurchasing the asset. We study the extent of intermediation as a rent extraction activity by examining the agent's decision to invest in a technology that gives them commitment. We find that multiple equilibria may emerge, with different levels of intermediation and with lower welfare in equilibria with more intermediation. We find that a decline in trading frictions leads to more intermediation and typically lower welfare, and so does a decline in the opportunity cost of acquiring commitment. A transaction tax can restore efficiency. Download Paper
Using data from the Employment Opportunity Pilot Project, we examine the relationship between the starting wage paid to the worker filling a vacancy, the number of applications attracted by the vacancy, the number of candidates interviewed for the vacancy, and the duration of the vacancy. We find that the wage is positively related to the duration of a vacancy and negatively related to the number of applications and interviews per week. We show that these surprising findings are consistent with a view of the labor market in which firms post wages and workers direct their search based on these wages if workers and jobs are heterogeneous and the interaction between worker’s type and job’s type in production satisfies some rather natural assumptions. Download Paper
We use a large dataset on retail pricing to document that a sizeable portion of the cross-sectional variation in the price at which the same good trades in the same period and in the same market is due to the fact that stores that are, on average, equally expensive set persistently different prices for the same good. We refer to this phenomenon as relative price dispersion. We argue that relative price dispersion stems from sellers’ attempts to discriminate between high-valuation buyers who need to make all of their purchases in the same store, and low-valuation buyers who are willing to purchase different items from different stores. We calibrate our theory and show that it is not only consistent with the extent and sources of dispersion in the price that different sellers charge for the same good, but also with the extent and sources of dispersion in the prices that different households pay for the same basket of goods, as well as with the relationship between prices paid and the number of stores visited by different households. Download Paper
We propose a new business cycle theory. Firms need to randomize over firing or keeping workers who have performed poorly in the past, in order to give them an ex-ante incentive to exert effort. Firms have an incentive to coordinate the outcome of their randomizations, as coordination allows them to load the firing probability on states of the world in which it is costlier for workers to become unemployed and, hence, allows them to reduce overall agency costs. In the unique robust equilibrium, firms use a sunspot to coordinate the randomization outcomes and the economy experiences endogenous, stochastic aggregate fluctuations. JEL Codes: D86, E24, E32. Keywords: Unemployment, Moral Hazard, Endogenous Business Cycles. Download Paper
We develop a search-theoretic model of the product market that generates price dispersion across and within stores. Buyers differ with respect to their ability to shop around, both at different stores and at different times. The fact that some buyers can shop from only one seller while others can shop from multiple sellers causes price dispersion across stores. The fact that the buyers who can shop from multiple sellers are more likely to be able to shop at inconvenient times induces causes price dispersion within stores. Specifically, it causes sellers to post different prices for the same good at different times in order to discriminate between different types of buyers. Download Paper
The paper studies equilibrium pricing in a product market for an indivisible good where buyers search for sellers. Buyers search sequentially for sellers, but do not meet every sellers with the same probability. Specifically, a fraction of the buyers’ meetings lead to one particular large seller, while the remaining meetings lead to one of a continuum of small sellers. In this environment, the small sellers would like to set a price that makes the buyers indifferent between purchasing the good and searching for another seller. The large seller would like to price the small sellers out of the market by posting a price that is low enough to induce buyers not to purchase from the small sellers. These incentives give rise to a game of cat and mouse, whose only equilibrium involves mixed strategies for both the large and the small sellers. The fact that the small sellers play mixed strategies implies that there is price dispersion. The fact that the large seller plays mixed strategies implies that prices and allocations vary over time. We show that the fraction of the gains from trade accruing to the buyers is positive and non-monotonic in the degree of market power of the large seller. As long as the large seller has some positive but incomplete market power, the fraction of the gains from trade accruing to the buyers depends in a natural way on the extent of search frictions. Download Paper
This paper is a study of the shape and structure of the distribution of prices at which an identical good is sold in a given market and time period. We find that the typical price distribution is symmetric and leptokurtic, with a standard deviation between 19% and 36%. Only 10% of the variance of prices is due to variation in the expensiveness of the stores at which a good is sold, while the remaining 90% is due, in approximately equal parts, to differences in the average price of a good across equally expensive stores and to differences in the price of a good across transactions at the same store. We show that the distribution of prices that households pay for the same bundle of goods is approximately Normal, with a standard deviation between 9% and 14%. Half of this dispersion is due to differences in the expensiveness of the stores where households shop, while the other half is mostly due to differences in households’ choices of which goods to purchase at which stores. We find that households with fewer employed members pay lower prices, and do so by visiting a larger number of stores, rather than by shopping more frequently. Download Paper
We study the effect of menu costs on the pricing behavior of sellers and on the cross-sectional distribution of prices in the search-theoretic model of imperfect competition of Burdett and Judd (1983). We find that, when menu costs are small, the equilibrium is such that sellers follow a (Q, S, s) pricing rule. According to a (Q, S, s) rule, a seller lets inflation erode the real value of its nominal price until it reaches some point s. Then, the seller pays the menu cost and changes its nominal price so that the real value of the new price is randomly drawn from a distribution with support [S,Q], where Q is the buyer’s reservation price and S is some price between s and Q. Only when the menu cost is relatively large, the equilibrium is such that sellers follow a standard (S; s) pricing rule. We argue that whether sellers follow a (Q, S, s) or an (S, s) rule matters for the estimation of menu costs and seller-specific shocks. Download Paper
We propose a novel theory of self-fulfilling fluctuations in the labor market. A firm employing an additional worker generates positive externalities on other firms, because employed workers have more income to spend and have less time to shop for low prices than unemployed workers. We quantify these shopping externalities and show that they are sufficiently strong to create strategic complementarities in the employment decisions of different firms and to generate multiple rational expectations equilibria. Equilibria differ with respect to the agents’ (rational) expectations about future unemployment. We show that negative shocks to agents’ expectations lead to fluctuations in vacancies, unemployment, labor productivity and the stock market that closely resemble those observed in the US during the Great Recession. Download Paper
This paper studies the optimal redistribution of income inequality caused by the presence of search and matching frictions in the labor market. We study this problem in the context of a directed search model of the labor market populated by homogenous workers and heterogeneous firms. The optimal redistribution can be attained using a positive unemployment benefit and an increasing and regressive labor income tax. The positive unemployment benefit serves the purpose of lowering the search risk faced by workers. The increasing and regressive labor tax serves the purpose of aligning the cost to the firm of attracting an additional applicant with the value of an application to society. Download Paper
We develop a life-cycle model of the labor market in which different worker-firm matches have different quality and the assignment of the right workers to the right firms is time consuming because of search and learning frictions. The rate at which workers move between unemployment, employment and across different firms is endogenous because search is directed and, hence, workers can choose whether to seek low-wage jobs that are easy to find or high-wage jobs that are hard to find. We calibrate our theory using data on labor market transitions aggregated across workers of different ages. We validate our theory by showing that it correctly predicts the pattern of labor market transitions for workers of different ages. Finally, we use our theory to decompose the age profiles of transition rates, wages and productivity into the effects of age variation in work-life expectancy, human capital and match quality. Download Paper
Dispersion of money balances among individuals is the basis for a range of policies but it has been abstracted from in monetary theory for tractability reasons. In this paper, we fill in this gap by constructing a tractable search model of money with a non-degenerate distribution of money holdings. We assume search to be directed in the sense that buyers know the terms of trade before visiting particular sellers. Directed search makes the monetary steady state block recursive in the sense that individuals’ policy functions, value functions and the market tightness function are all independent of the distribution of individuals over money balances, although the distribution affects the aggregate activity by itself. Block recursivity enables us to characterize the equilibrium analytically. By adapting lattice-theoretic techniques, we characterize individuals’ policy and value functions, and show that these functions satisfy the standard conditions of optimization. We prove that a unique monetary steady state exists. Moreover, we provide conditions under which the steady-state distribution of buyers over money balances is non-degenerate and analyze the properties of this distribution. Download Paper
Why do some sellers set prices in nominal terms that do not respond to changes in the aggregate price level? In many models, prices are sticky by assumption. Here it is a result. We use search theory, with two consequences: prices are set in dollars since money is the medium of exchange; and equilibrium implies a nondegenerate price distribution. When money increases, some sellers keep prices constant, earning less per unit but making it up on volume, so profit is unaffected. The model is consistent with the micro data. But, in contrast with other sticky-price models, money is neutral Download Paper
This paper revisits the no-recall assumption in job search models with take-it-or-leave-it offers. Workers who can recall previously encountered potential employers in order to engage them in Bertrand bidding have a distinct advantage over workers without such attachments. Firms account for this difference when hiring a worker. When a worker first meets a firm, the firm offers the worker a sufficient share of the match rents to avoid a bidding war in the future. The pair share the gains to trade. In this case, the Diamond paradox no longer holds. Download Paper
We build a directed search model of the labor market in which workers’ transitions between unemployment, employment, and across employers are endogenous. We prove the existence, uniqueness and efficiency of a recursive equilibrium with the property that the distribution of workers across employment states affects neither the agents’ values and strategies nor the market tightness. Because of this property, we are able to compute the equilibrium outside the non-stochastic steady-state. We use a calibrated version of the model to measure the effect of productivity shocks on the US labor market. We find that productivity shocks generate procyclical fluctuations in the rate at which unemployed workers become employed and countercyclical fluctuations in the rate at which employed workers become unemployed. Moreover, we find that productivity shocks generate large counter-cyclical fluctuations in the number of vacancies opened for unemployed workers and even larger procyclical fluctuations in the number of vacancies created for employed workers. Overall, productivity shocks alone can account for 80 percent of unemployment volatility, 30 percent of vacancy volatility and for the nearly perfect negative correlation between unemployment and vacancies. Download Paper
This paper studies a search model of the labor market where .rms have private information about the quality of their vacancies, they can costlessly communicate with unemployed workers before the beginning of the application process, but the content of the communication does not constitute a contractual obligation. At the end of the application process, wages are determined as the outcome of an alternating o¤er bargaining game. The model is used to show that vague non-contractual announcements about compensation. such as those one is likely to find in help-wanted ads. can be correlated with actual wages and can partially direct the search strategy of workers.   Download Paper
In this paper, we develop a general stochastic model of directed search on the job. Like in the analogous models of random search on the job, the state of the economy in our model includes the infinite-dimensional distribution of workers across different employment states (unemployment, and employment at different wages). Unlike the analogous models of random search on the job, our model admits an equilibrium in which the agents’ value and policy functions does not depend on the distribution of workers. We refer to this type of equilibrium as a Block Recursive Equilibrium. Therefore, while solving the equilibrium of a random search model in a stochastic environment is a difficult task both analytically and computationally, solving the Block Recursive Equilibrium of our model is as easy as solving a representative agent model. Download Paper
We consider a frictional labor market in which firms want to insure their senior employees against income fluctuations and, at the same time, want to recruit new employees to fill their vacant positions. Firms can commit to a wage schedule, i.e. a schedule that specifies the wage paid by the firm to its employees as function of their tenure and other observables. However, firms cannot commit to the employment relationship with any of their workers, i.e. firms can dismiss workers at will. We find that, because of the firm's limited commitment, the optimal schedule prescribes not only a rigid wage for senior employees, but also a downward rigid wage for new hires. Moreover, we find that, while the rigidity of the wage of senior workers does not affect the allocation of labor, the rigidity of the wage of new hires magnifies the response of unemployment and vacancies to negative shocks to the aggregate productivity of labor. Download Paper
We build a directed search model of the labor market in which workers’ transitions between unemployment, employment, and across employers are endogenous.  We prove the existence, uniqueness and efficiency of a recursive equilibrium with the property that the distribution of workers across employment states does not affect the agents’ values and strategies. Because of this property, we are able to compute the equilibrium outside the non-stochastic steady-state. We use a calibrated version of the model to measure the effect of productivity shocks on the US labor market. We find that productivity shocks generate procyclical fluctuations in the rate at which unemployed workers become employed and countercyclical fluctuations in the rate at which employed workers become unemployed. Moreover, we find that productivity shocks generate large countercyclical fluctuations in the number of vacancies opened for unemployed workers and even larger procyclical fluctuations in the number of vacancies created for employed workers. Overall, productivity shocks alone can account for 80 percent of unemployment volatility, 30 percent of vacancy volatility and for the nearly perfect negative correlation between unemployment and vacancies. Download Paper
We study the long-run relation between money, measured by inflation or interest rates, and unemployment. We first discuss data, documenting astrong positive relation between the variables at low frequencies. We then develop a framework where both money and unemployment are modeled using explicit microfoundations, integrating and extending recent work in macro and monetary economics, and providing a unified theory to analyze labor and goods markets. We calibrate the model, to ask how monetary factors account quantitatively for low-frequency labor market behavior.  The answer depends on two key parameters: the elasticity of money demand, which translates monetary policy to real balances and profits; and the value of leisure, which affects the transmission from profits to entry and employment. For conservative parameterizations, money accounts for some but not that much of trend unemployment — by one measure, about 1/5 of the increase during the stagflation episode of the 70s can be explained by monetary policy alone. For less conservative but still reasonable parameters, money accounts for almost all low-frequency movement in unemployment over the last half century. Download Paper
In this paper, I build a model marketplace populated by a finite number of sellers – each producing its own variety of the good – and a continuum of buyers – each searching for a variety he likes. Using the model, I study the response of a seller’s price to privately observed fluctuations in its idiosyncratic production cost. I find that the qualitative properties of this response critically depend on the persistence of the production cost.  In particular, if the cost is i.i.d., the seller’s price does not respond at all. If the cost is somewhat persistent, the seller’s price responds slowly and incompletely. If the cost is very persistent, the seller’s price adjusts instantaneously and efficiently to all fluctuations in productivity. I argue that these findings can explain why the monthly frequency of a price change is so much lower for processed than for raw goods. Download Paper