Publications
[33] “Intermediation as Rent Extraction,” with Maryam Farboodi, Gregor Jarosch and Ursula Wiriadinata. Journal of Economic Theory, 2025, 227.
The paper shows that intermediation in asset markets may emerge exclusively because of rent extraction motives. Among traders with heterogeneous bargaining skills, those with superior skills become intermediaries and those with inferior skills become final users. Intermediation is privately profitable because agents with superior bargaining skills can take positions and unwind them in the future at a better price than final users could. Intermediation, though, is socially worthless and the resources invested in bargaining skills are wasted. Using a dataset on the Indonesian interbank market, we document that prices vary with the centrality of buyers and sellers in a way that is uniquely consistent with our theory.
[32] “The Alpha Beta Gamma of the Labor Market” with Victoria Gregory and David Wiczer, Journal of Monetary Economics, 2025, 150.
We access a long panel dataset of US workers to document the extent to which individuals are heterogeneous with respect to their pattern of transitions across employment states. We find that heterogeneity is well approximated by three latent types: αs, βs and γs. Workers of type α leave unemployment quickly and, once they find a job, they are likely to keep it for more than 2 years. Workers of type γ find employment slowly and, once they do find a job, they are likely to leave it within 1 year. We use our empirical findings to calibrate a search-theoretic model in which workers are heterogeneous with respect to the parameters governing their employment transitions. We find that αs move quickly out of unemployment to employment because they have large gains from trade, and they are likely to stay on a job for more than 2 years because their productivity is similar in different jobs. In contrast, γs exit unemployment slowly because their gains from trade are small, and they are likely to leave a job within 1 year because they are much more productive in a small fraction of jobs than in the majority of jobs. We find that a negative shock to aggregate productivity leads to a large and persistent increase in unemployment that is mainly driven by γ-workers. The predictions of the model align well with the unemployment dynamics observed during the Great Recession.
[31] “Search Theory of Imperfect Competition with Decreasing Returns to Scale,” Journal of Economic Theory, 2024, 218.
I study a version of the search-theoretic model of imperfect competition by Burdett and Judd (1983) in which sellers operate a production technology with decreasing rather than constant returns to scale. Equilibrium exists and is unique, and its structure depends on the extent of search frictions. If search frictions are large enough, the price distribution is non-degenerate and atomless. If search frictions are neither too large nor too small, the price distribution is non-degenerate with an atom at the lowest price. If search frictions are small enough, the price distribution is degenerate. Equilibrium is efficient if and only if the price distribution is degenerate. Generically, neither the structure nor the welfare properties of equilibrium are the same as in Burdett and Judd (1983). As in Burdett and Judd (1983), however, equilibrium outcomes span the spectrum from pure monopoly to
perfect competition as search frictions decline.
[30] “Production and Learning in Teams,” with Kyle Herkenhoff, Jeremy Lise and Gordon Phillips, Econometrica, 2024, 92 (2): 467-504.
To what extent is a worker’s human capital growth affected by the quality of his coworkers? To answer this question, we develop and estimate a model in which the productivity and the human capital growth of an individual depend on the average human capital of his coworkers. The measured production function is supermodular: The marginal product of a more knowledgeable individual is increasing in the human capital of his coworkers. The measured human capital accumulation function is convex: An individual’s human capital growth is increasing in coworkers’ human capital only when paired with more knowledgeable coworkers, but independent of coworkers’ human capital when paired with less knowledgeable coworkers. Learning from coworkers accounts for two thirds of the stock of human capital accumulated on the job. Technological changes that increase production supermodularity lead to labor market segregation and, by reducing the opportunities for low human capital workers to learn from better coworkers, lead to a decline in aggregate human capital and output.
[29] “Market Freezes,” with Chao Gu, Randall Wright, and Yu Zhu, Journal of Money, Credit and Banking, 2024, 56 (6): 1291-1320.
Market freezes are an interesting and theoretically challenging phenomenon —they are observed empirically, but cannot occur in standard models. This paper develops a formal theory of recurrent freezes emphasizing liquidity and self-fulfilling prophecies. While it is well understood how to get hot and cold spells, where prices and quantities fluctuate, we get asset market freezes and thaws where trade completely stops and starts. The simplest specification gets this using negative asset returns. Other specifications use information frictions or fixed costs. We also consider credit freezes, analyze the extent to which the decentralized nature of trade matters, and discuss policy implications.
[28] “Vertical Differentiation in Frictional Product Markets” with James Albrecht and Susan Vroman, Journal of Political Economy: Macro, 2023, 1 (3): 586-632.
We study a search-theoretic model of imperfect competition in product markets where sellers make an ex ante investment in the quality of their variety of the product. Equilibrium exists and is unique. In equilibrium, search frictions not only cause sellers to offer different surpluses to buyers but also cause sellers to choose different qualities for their varieties. Equilibrium is efficient. As search frictions decline, the market becomes more and more unbalanced, as a vanishing fraction of sellers produces varieties of increasing quality, offers increasing surplus to their customers, and captures an increasing share of the market, while a growing fraction of sellers produces varieties of decreasing quality. Gains from trade and welfare grow at constant rates.
[27] “Optimal Product Design: Implications for Competition and Growth under Declining Search Frictions,” Econometrica, 2023, 91 (2): 605-639.
As search frictions in the market for a consumer product decline, buyers are able to locate and access more and more sellers. In response, sellers choose to design varieties of the product that are more and more specialized in order to take advantage of the heterogeneity in buyers’ preferences. I find conditions on the fundamentals of the market under which the increase in specialization exactly offsets the decline in search frictions. Under these conditions, the extent of competition and the extent of price dispersion remain constant over time even though search frictions are vanishing. Buyer’s surplus and seller’s profit, however, grow over time at a constant endogenous rate, as the increase in specialization allows sellers to cater better and better to the preferences of individual buyers.
[26] “Stubborn Beliefs in Search Equilibrium” NBER Macro Annual, 2022, 37, 239-297, edited by M. Eichenbaum, E. Hurst and V. Ramey, University of Chicago Press.
I study a search equilibrium model of the labor market in which workers have stubborn beliefs about their labor market prospects, i.e. expectations about their future job-finding probability and future wages that do not adjust to cyclical fluctuations in fundamentals. Stubborn beliefs dampen the response of bargained wages to shocks and, in turn, amplify the response of labor market tightness, job-finding probability, unemployment and vacancies. The amplification caused by stubborn beliefs is inefficient, and can be corrected by countercyclical employment subsidies. When only a small fraction of workers have stubborn beliefs, the response of wages and labor market outcomes to negative shocks is the same as when all workers are stubborn. In contrast, the response of wages and labor market outcomes to positive shocks is approximately the same as when all workers have rational expectations. Hence, when only a small fraction of workers have stubborn beliefs, wages and labor market outcomes respond asymmetrically to positive and negative shocks.
[25] “Jacks of All Trades and Masters of One: Declining Search Frictions and Unequal Growth,” with Paolo Martellini, American Economic Review: Insights, 2021, 3(3): 339-352.
Declining search frictions generate productivity growth by allowing workers to find jobs for which they are better suited. For “jacks of all trades”—workers whose productivity is similar across different jobs in their labor market—declining search frictions lead to minimal growth. For “masters of one trade”—workers whose productivity varies a great deal across different jobs in their labor market—declining search frictions lead to fast growth. A rudimentary calibration suggests that differential returns to declining search frictions may account for a non-negligible fraction of the wage growth differential between routine and non-routine workers.
[24] “Revisiting the Hypothesis of High Discounts and High Unemployment,” with Paolo Martellini and Ludo Visschers, Economic Journal, 2021, 131(637): 2203-2232.
We revisit the hypothesis that cyclical fluctuations in unemployment are caused by shocks to the discount rate. We use a simple but rich search-theoretic model of the labour market in which the UE, EU and EE rates are all endogenous. Analytically, we show that an increase in the discount rate lowers the UE rate and, under some natural conditions, it lowers the EU rate. Quantitatively, we show that an increase in the discount rate from 4 to 10% generates a 3.5% decline in the UE rate and a 6% decline in the EU rate. These findings are at odds with the actual behaviour of the US labour market over the business cycle, which features a negative comovement between the UE and EU rates.
[23] “Declining Search Frictions, Unemployment and Growth,” with Paolo Martellini, Journal of Political Economy, 2020, 128 (12): 4387-4437. Lead Article.
For a search-theoretic model of the labor market, we seek conditions for the existence of a Balanced Growth Path (BGP), an equilibrium in which unemployment, vacancy, and worker’s transition rates remain constant in the face of improvements in the production and search technologies. A BGP exists iff firm-worker matches are inspection goods, and the idiosyncratic component of productivity of a match is drawn from a Pareto distribution. Declining search frictions contribute to the growth of the economy with an intensity that depends on the tail coefficient of the Pareto distribution. A corollary of the theory is that market size does not affect unemployment, vacancy and worker’s transition rates even with non-constant returns to scale in search. We develop a strategy to measure the rate of decline of search frictions, the returns to scale in search, and their contribution to growth.
[22] “Pandemic Recession: L or V Shaped?” [post publication] with Victoria Gregory and David Wiczer, Quarterly Review, 2020, 40: 1-28.
We develop and calibrate a search-theoretic model of the labor market in order to forecast the evolution of the aggregate labor market during and after the coronavirus pandemic. The model is designed to capture the heterogeneity of the transitions of individual workers across states of unemployment, employment and across different employers. The model is also designed to capture the trade-offs in the choice between temporary and permanent layoffs. Under reasonable parametrizations of the model, the lockdown instituted to prevent the spread of the novel coronavirus is shown to have long-lasting negative effects on unemployment. This is so because the lockdown disproportionately disrupts the employment of workers who need years to find stable jobs.
[21] “Agency Business Cycles,” with Mikhail Golosov, Theoretical Economics, 2020, 15: 123-158.
We develop a theory of endogenous and stochastic fluctuations in economic activity. Individual firms choose to randomize over firing or keeping workers who performed poorly in the past to give them an ex ante incentive to exert effort. Different firms choose to correlate the outcome of their randomization to reduce the probability with which they fire nonperforming workers. Correlated randomization leads to aggregate fluctuations. Aggregate fluctuations are endogenous—they emerge because firms choose to randomize and they choose to randomize in a correlated fashion—and they are stochastic—they are the manifestation of a randomization process. The hallmark of a theory of endogenous and stochastic fluctuations is that the stochastic process for aggregate “shocks” is an equilibrium object.
[20] “Intra Firm Bargaining and Shapley Values” with Bjoern Brugemann and Pieter Gautier, Review of Economic Studies, 2019: 86 (2): 564-592.
We study two wage bargaining games between a firm and multiple workers. We revisit the bargaining game proposed by Stole and Zwiebel (1996a). We show that, in the unique Subgame Perfect Equilibrium, the gains from trade captured by workers who bargain earlier with the firm are larger than those captured by workers who bargain later, as well as larger than those captured by the firm. The resulting equilibrium payoffs are different from those reported in Stole and Zwiebel (1996a) as they are not the Shapley values. We propose a novel bargaining game, the Rolodex game, which follows a simple and realistic protocol. In the unique no-delay Subgame Perfect Equilibrium of this game, the payoffs to the firm and to the workers are their Shapley values.
[19] “Relative Price Dispersion: Evidence and Theory,” with Greg Kaplan, Leena Rudanko and Nicholas Trachter, American Economic Journal: Microeconomics, 2019, 11 (3).
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 show that relative price dispersion might stem 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.
[18] “The (Q,S,s) Pricing Rule,” with Kenneth Burdett, Review of Economic Studies, 2018, 85 (2), 892-928.
We introduce menu costs in the search-theoretic model of imperfect competition of Burdett and Judd (1983). When menu costs are not too large, the equilibrium is such that sellers follow a (Q,S,s) pricing rule. According to the 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 resets the real value of its nominal price to a point randomly drawn from a distribution with support [S,Q], where s<S<Q. A (Q,S,s) equilibrium differs with respect to a standard (S,s) equilibrium: (i) In a (Q,S,s) equilibrium, sellers sometimes keep their nominal price constant to avoid paying the menu cost, other times because they are indifferent to changes in the real value of their price. An exploratory calibration reveals that menu costs account less than half of the observed duration of nominal prices. (ii) In a (Q,S,s) equilibrium, higher inflation leads to higher real prices, as sellers pass onto buyers the cost of more frequent price adjustments, and to lower welfare.
[17] “Equilibrium Price Dispersion Across and Within Stores,” with Nicholas Trachter, Review of Economic Dynamics, 2018, 28 (2), 205-220.
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 multiple times 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.
[16] “Evidence on the Relationship between Recruiting and Starting Wage,” with Jason Faberman, Labour Economics, 2018, 50 (1), 67-79.
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.
[15] “The (Q,S,s) Pricing Rule: A Quantitative Analysis,” with Kenneth Burdett, Research in Economics, 2017, 71 (4), 784-797.
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.
[14] “Shopping Externalities and Self-Fulfilling Unemployment Fluctuations,” with Greg Kaplan, Journal of Political Economy, 2016, 124 (3), 771-825.
We propose a novel theory of self-fulfilling unemployment fluctuations. When a firm increases its workforce, it increases the demand facing other firms—as employed workers spend more than unemployed workers—and decreases the extent of competition facing other firms—as employed workers have less time to search for low prices than unemployed workers. In turn, the increase in demand and the decline in competition induces other firms to hire more labor in order to scale-up their presence in the product market. The feedback between employment and product market conditions generates multiple equilibria—and the possibility of self-fulfilling fluctuations—if the differences in the shopping behavior of employed and unemployed workers are large enough. Empirical evidence on spending, shopping and prices paid suggests that this is the case.
[13] “Directed Search over the Life Cycle,” with Irina Telyukova and Ludo Visschers, Review of Economic Dynamics, 2016, 19 (1), 38-62.
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 effect of age variation in work-life expectancy, human capital and match quality.
[12] “Equilibrium Price Dispersion with Sequential Search,” with Nicholas Trachter, Journal of Economic Theory, 2015, 160 (6), 188-215.
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.
[11] “The Morphology of Price Dispersion,” with Greg Kaplan, International Economic Review, 2015, 56 (4), 1165-1206.
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.
[10] “Taxation and Redistribution of Residual Income Inequality,” with Mikhail Golosov and Pricila Maziero, Journal of Political Economy, 2013, 121 (6), 1160-1204.
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.
[9] “Monetary Theory with Non-Degenerate Distributions,” with Shouyong Shi and Hongfei Sun, Journal of Economic Theory, 2013, 148 (6), 2266-2312.
We construct and analyze 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.
[8] “Sticky Prices: A New Monetarist Approach,” with Allen Head, Lucy Qian Liu and Randall Wright, Journal of the European Economic Association, 2012, 10 (5), 939-973 (Lead article).
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.
[7] “Efficient Search on the Job and the Business Cycle,” with Shouyong Shi, Journal of Political Economy, 2011, 119 (3), 468-510.
The paper develops a model of directed search on the job where transitions of workers between unemployment, employment and across employers are driven by heterogeneity in the quality of firm-worker matches. The equilibrium is such that the agents’ value and policy functions are independent of the distribution of workers across employment states. Hence, the model can be solved outside of steady-state and used to measure the effect of cyclical productivity shocks on the labor market. Productivity shocks are found to generate large fluctuations in workers’ transitions, unemployment and vacancies when matches are experience good, but not when matches are inspection goods.
[6] “Job Search with Bidder Memories,” with Carlos Carrillo-Tudela and Eric Smith, International Economic Review, 2011, 52 (3), 639-655.
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.
[5] “Inflation and Unemployment in the Long Run,” with Aleksander Berentsen and Randall Wright, American Economic Review, 2011, 101 (1), 371-398.
We study the long-run relation between money (inflation or interest rates) and unemployment. We document positive relationships between these variables at low frequencies. We develop a framework where money and unemployment are modeled using explicit microfoundations, providing a unified theory to analyze labor and goods markets. We calibrate the model and ask how monetary factors account for labor market behavior. We can account for a sizable fraction of the increase in unemployment rates during the 1970s. We show how it matters whether one uses monetary theory based on the search-and-bargaining approach or on an ad hoc cash-in-advance constraint.
[4] “Worker Replacement,” with Espen Moen, Journal of Monetary Economics, 2010, 57 (6), 623-636 (Lead article).
Consider a labor market in which firms want to insure existing employees against income fluctuations and, simultaneously, want to recruit new employees to fill vacant jobs. Firms can commit to a wage policy, i.e. a policy that specifies the wage paid to their employees as a function of tenure, productivity and other observables. However, firms cannot commit to employ workers. In this environment, the optimal wage policy prescribes not only a rigid wage for senior workers, but also a downward rigid wage for new hires. The downward rigidity in the hiring wage magnifies the response of unemployment to negative shocks.
[3] “Directed Search on the Job, Heterogeneity and Aggregate Fluctuations,” with Shouyong Shi, American Economic Review, 2010, 100 (2), 327-332.
In this paper, we prove the existence of a Block Recursive Equilibrium for a model of directed search on the job in which workers are ex-ante heterogeneous with respect to some observable characteristic such as education.
[2] “Block Recursive Equilibria for Stochastic Models of Search on the Job,” with Shouyong Shi, Journal of Economic Theory, 2010, 145 (4), 1453-1494.
We develop a general stochastic model of directed search on the job. Directed search allows us to focus on a Block Recursive Equilibrium (BRE) where agents’ value functions, policy functions and market tightness do not depend on the distribution of workers over wages and unemployment. We formally prove existence of a BRE under various specifications of workers’ preferences and contractual environments, including dynamic contracts and fixed-wage contracts. Solving a BRE is as easy as solving a representative agent model, in contrast to the analytical and computational difficulties in models of random search on the job.
[1] “A Theory of Partially Directed Search,” Journal of Political Economy, 2007, 115 (5), 748-769.
This paper studies a search model of the labor market where firms 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 offer 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.
Working Papers
“Markups: A Search-Theoretic Perspective,” NBER Working Paper 32888, Revise and Resubmit at the Journal of Political Economy (April 2025).
I derive a formula for the equilibrium distribution of markups in the search-theoretic model of imperfect competition of Butters (1977), Varian (1980), and Burdett and Judd (1983). The level of markups and the sign of the relationship between a seller’s markup and its size depends on the extent of search frictions, as well as on other deep parameters. Markups are efficient. Markups are positive even though the varieties produced by sellers are perfect substitutes. Markups are heterogeneous even when all sellers operate the same production technology. Markups depend on size, even though the substitutability between a variety and the others does not depend on how much of that variety is consumed. Interpreting these markups through the lens of the monopolistic competition model of Dixit and Stiglitz (1977) would lead one to recover incorrect and unstable buyers’ preferences. Interpreting these markups through the lens of the Dixit-Stiglitz model would also lead to incorrect policy recommendations. These results are a cautionary note on recent work in macroeconomics.
“A Quantitative Theory of Heterogeneous Returns to Wealth,” with Saverio Spinella, NBER Working Paper 33868 (May 2025).
Recent empirical evidence documents that different individuals earn systematically different rates of return, even after controlling for portfolio composition. We propose a general equilibrium theory of residual heterogeneity in rates of return on wealth by embedding a financial market with search frictions into a monetary incomplete-market model. We show that the distribution of rates of return offered in the financial market is endogenous and depends on the marginal product of capital, the return on fiat money, and the joint distribution of households across wealth and financial human capital. When calibrated, the model succeeds in reproducing the extent of residual dispersion in returns to wealth across individuals. We use the calibrated model to study various policies and counterfactuals, with a particular focus on monetary policy.
“Efficient Imperfect Competition with an Application to International Trade,” NBER Working Paper 33253 (December 2024).
I study the equilibrium and the welfare effects of international trade when product markets are imperfectly competitive due of search frictions—as in Burdett and Judd (1983)—rather than product differentiation—as in Dixit and Stiglitz (1977). Markups are positive, even though there are multiple firms producing identical goods. Markups depend negatively on the number of firms producing identical goods, which, in turn, determines the extent of competition in the market. Markups may be increasing, constant, decreasing or non-monotonic in firm’s size, depending on the extent of competition and on the distribution of marginal costs. The entry of firms and the quantity of output produced by each firm are efficient, even though the market is imperfectly competitive. International trade increases the measure of firms in the market, intensifies competition, lowers markups, and unambiguously increases welfare. These “natural” effects of trade emerge generically in the Burdett-Judd model of imperfect competition. In the Dixit-Stiglitz model of imperfect competition, these effects are an artifact of particular specifications of preferences.
“A Delegation Approach to Regulating Hiring Discrimination,” with Paolo Martellini, NBER Working Paper 32018 (January 2024).
We approach the design of anti-discriminatory labor market regulation as a delegation problem. A private firm (the agent) is repeatedly faced with the opportunity of hiring one among several applicants to fill its vacancies. The firm is biased against applicants from some demographic group, and it is neutral towards applicants from some other group. Applicants differ not only with respect to their demographic characteristics, but also with respect to the idiosyncratic quality of their match with firm. A benevolent and unbiased labor market authority (the principal) enacts a hiring regulation (a direct-revelation mechanism without transfers) in order to reduce the impact of the firm’s bias on its hiring behavior. The hiring regulation is constrained by the fact that the quality of the match between any particular applicant and the firm is privately observed by the firm. We characterize the optimal mechanism.
“More on onetary Economics,” with Saverio Spinella, Manuscript (July 2025).
In the theory of heterogeneous returns to wealth of Menzio and Spinella (2025), monetary policy affects equilibrium outcomes even when real money balances are negligible and nominal rigidities are absent. Holding money is the households’ investment option outside the financial market. Monetary policy affects the rate of return on holding money, the value of the households’ option outside the financial market and, in turn, the rates of return inside the financial market. This is true even when the fraction of households that do exercise the outside option is negligible and, hence, even when real money balances are arbitrarily small. Quantitatively, monetary policy has a large impact on economic outcomes even in the cashless limit. These findings echo Lagos and Zheng (2022). They imply that one cannot use the observation that money balances are low (and may become even lower) as a justification to use models that abstract from the role of money as a store of value to assess monetary policy.
“Private and Social Learning in Frictional Product Markets,” with Sephorah Mangin, Manuscript (February 2024).
We introduce dynamic learning in the static search-theoretic framework of imperfect competition of Butters (1977), Varian (1980) and Burdett and Judd (1983). We consider two forms of learning: memory and word of mouth. In the model with memory, long-lived buyers not only learn about some new sellers in every period, but they also remember some of the sellers about which they learned in the past. In the model with word of mouth, short-lived buyers not only learn about sellers through search, but they also learn about sellers by talking to previous buyers, which refer them to the best seller of which they are aware. Both models are tractable. We establish the existence and uniqueness of equilibrium and characterize the dynamics of the product market. Memory increases the quantity of information available to buyers and, for this reason, leads to higher concentration and competition. Word of mouth increases the quality of information available to buyers and, for this reason, leads to higher concentration, but does not increase competition as much as memory.
“Rolodex Game in Networks,” with Bjoern Brugemann and Pieter Gautier, Manuscript (August 2017).
The paper studies the Rolodex bargaining game in networks. We first revisit the Rolodex game originally proposed in the context of intra firm bargaining, in which a central player bargains sequentially with multiple peripheral players. We show that the unique no-delay SPE of this game yields the Myerson-Shapley value for the star graph in which the central player is linked to all peripheral players. Second, we propose a Rolodex game for a general graph. Links in the graph negotiate sequentially, with one of the linked players making an offer to the other. If the respondent rejects, the link moves to the end of the line and the direction of the offer is reversed for the next negotiation of this link. As in the original Rolodex game, all agreements are renegotiated in the event of a breakdown. We show that the unique no-delay SPE of this game yields the Myerson-Shapley value for the corresponding graph.
“A Search Theory of Rigid Prices,” PIER Working Paper 07-031 (2007).
This paper studies price dynamics in a product markets characterized by: (a) search frictions—in the sense that it takes time for a buyer to find a seller that produces a version of the good he likes; (b) anonymity—in the sense that sellers cannot price discriminate between first-time buyers and returning costumers; (c) asymmetric information—in the sense that sellers are subject to idiosyncratic shocks to their marginal cost of production and privately observe the shocks’ realizations. I find that the joint dynamics of costs and prices may be very different than in a standard Walrasian market. When shocks are i.i.d., the price remains constant in the face of fluctuations in a seller’s marginal cost. When shocks are moderately persistent, the price adjusts slowly and imperfectly in response to changes in a seller’s cost. Finally, when shocks are sufficiently persistent, the price adjusts instantaneously and efficiently as soon as a seller’s production cost varies.
“A Cheap-Talk Theory of Random and Directed Search,” Revised for the Journal of Political Economy as “A Theory of Partially Directed Search” (2006).
This paper studies a search model of the labor market where firms have private information about the gains from trade and post cheap-talk messages to advertise their vacancies before workers decide which location to visit. The surplus of a match is divided ex-post according to the outcome of an alternating-offer bargaining game of asymmetric information. When this bargaining game is fast, I show that the maximum amount of information that can be transmitted through the cheap-talk depends non-monotonically on the tightness of the labor market. In particular, if the ratio of unemployed workers to vacancies is either sufficiently high or sufficiently low, the unique equilibrium has the firms babbling and search is random. If the tightness of the labor market takes on intermediate values, there is also an equilibrium where the cheap-talk is informative, high and low productivity firms post different messages and the search process of the workers is directed.
“High-Frequency Wage Rigidity,” Job Market Paper (2005).
In the context of a frictional model of the labor market with off and on the job search, I advance a novel model of wage determination where contracts are non-binding and firms have private information about the productivity of labor. The characterization of the intra-firm bargaining game leads to a reduced-form model where the firm chooses the wage subject to a non-discrimination and consistency constraints. The fundamental property of the optimal firm-wage policy is high-frequency wage rigidity. While the firm does not respond to productivity shocks whose persistence falls below a critical threshold, the wage is a non-degenerate function of the long-term component of labor productivity. A calibrated version of the model shows that the cyclical behavior of the model is quantitatively consistent with the empirical regularities of the labor market at the business cycle frequency. Among other things, wages are nearly acyclical, the semi-elasticity of the average labor productivity to unemployment is smaller than one, and vacancies are almost perfectly correlated with unemployment.