working papers

Assortative Matching and Wages: The Role of Selection
April 2024
(with Katarina Borovickova, FRB Richmond)

We develop a random search model of the labor market with two-sided heterogeneity and match-specific productivity shocks.  Our model has two main predictions: i) there is positively assortative matching and ii) the average log wage that a worker receives is increasing in the worker's and firm's productivity and is submodular. Sorting and wages are driven by selection. All workers are equally likely to meet all firms, but low (high) productivity workers have a higher average log wage offer in low (high) productivity firms.  The high wage offer meetings result in matches more frequently, generating positive assortative matching. Since only meetings that result in matches are observed in administrative wage data, such data contain only a selected subset of wage offers, and those turn out to be increasing and submodular. We show that our findings are consistent with results in the empirical literature and argue that the selection mechanism affects the interpretation of findings in that literature. First, firm fixed effects in wage equations do not have structural interpretation as firm wage premia because they are estimated with a bias due to selection. Second, while matching patterns are informative about productive complementarities, average log wages are not.

Unpaired Kidney Exchange: Overcoming Double Coincidence of Wants without Money
December 2023
(with Mohammad Akbarpour, Julien Combe, Yinghua He, Victor Hiller, and Olivier Tercieux )
Forthcoming, Review of Economic Studies
Online Appendix

For an incompatible patient-donor pair, kidney exchanges often forbid receipt-before-donation (the patient receives a kidney before the donor donates) and donation-before-receipt, causing a double-coincidence-of-wants problem. Our proposal, the Unpaired kidney exchange algorithm,  uses "memory" as a medium of exchange to eliminate these timing constraints. In a dynamic matching model, we prove that Unpaired delivers a waiting time of patients close to optimal and substantially shorter than currently utilized state-of-the-art algorithms. Using a rich administrative dataset from France, we show that Unpaired achieves a match rate of 57 percent and an average waiting time of 440 days. The (infeasible) optimal algorithm is only slightly better (58 percent and 425 days); state-of-the-art algorithms deliver  less than 34 percent and more than 695 days. We draw similar conclusions from the simulations of two large U.S. platforms. Lastly, we propose a range of solutions that can address the potential practical concerns of Unpaired.

Assortative Matching with Private Information
September 2023
(with Liangjie Wu, EIEF)
We study matching between heterogeneous agents when their types are private information. Competing platforms post terms of trade. Agents with private information choose where to search and form matches. Positively assortative matching arises when each market attracts only one type of agent.  We characterize an equilibrium with positively assortative matching when one exists, and provide sufficient conditions to ensure that matching is positively assortative in a limit with a vanishing role for platforms.  When more desirable partners have a higher willingness-to-pay for matches, they pay high fees to platforms to avoid less desirable types.  When more desirable partners have a lower willingness-to-pay, they match at a low rate to keep out less desirable types.

Decomposing Duration Dependence in a Stopping Time Model
August 2023
(with Fernando Alvarez, University of Chicago and Katarina Borovickova, NYU)
Forthcoming, Review of Economic Studies

We develop an economic model of transitions in and out of employment.  Heterogeneous workers switch employment status when the net benefit from working, a Brownian motion with drift, hits optimally-chosen barriers.  This implies that the duration of jobless spells for each worker has an inverse Gaussian distribution.  We allow for arbitrary heterogeneity across workers and prove that the distribution of inverse Gaussian distributions is partially identified from the duration of two non-employment spells for each worker. We estimate the model using Austrian social security data and find that dynamic selection is a critical source of duration dependence.

Consistent Evidence on Duration Dependence of Price Changes
July 2023
(with Fernando Alvarez, University of Chicago, and Katarina Borovickova, FRB Richmond)
Revise and Resubmit, American Economic Review

We develop a linear GMM estimator of the discrete time mixed proportional hazard (MPH) model of duration with unobserved heterogeneity.  We allow for competing risks, observable characteristics, and censoring.  With repeated spell data, our estimator is consistent and robust to the unknown shape of the frailty distribution. We apply our estimator to the duration of price spells. We find substantial unobserved heterogeneity with economically meaningful implications for the response of output to a monetary policy shock in a model with time-dependent pricing rules and for the degree of state dependence in a model of price plans.

High Wage Workers Work for High Wage Firms
February 2020
(with Katarina Borovickova, FRB Richmond)

We propose a new measure of the correlation between the types of matched workers and firms and show that this captures sorting in a variety of structural models. We also propose an estimator of the correlation and prove that the estimator is consistent when the number of workers and firms grows to infinity even if each worker only has a small number of jobs and each firm only employs a small number of workers. Model simulations also confirm that our estimator is accurate in small data sets.  Using administrative data from Austria, we find that the correlation between worker and firm types lies between 0.4 and 0.6.  In contrast, the Abowd, Kramarz, and Margolis (1999) fixed effects estimator suggests no correlation in our data set.  This reflects a combination of biases in the AKM correlation estimator and limitations of the AKM correlation as a measure of sorting.

Unions and Unemployment
May 2014
(with Fernando Alvarez, University of Chicago)

This paper examines the impact of unions on unemployment and wages in a dynamic equilibrium search model. We model a union as imposing a minimum wage and rationing jobs to ensure that the union’s most senior members are employed. This generates rest unemployment, where following a downturn in their labor market, unionized workers are willing to wait for jobs to reappear rather than search for a new labor market. Introducing unions into a dynamic equilibrium model has two implications, which others have argued are features of the data: the hazard of exiting unemployment at long durations is very low when the union-imposed minimum wage is high; and a high union-imposed minimum wage generates a compressed wage distribution and a high turnover rate of jobs.

Optimal Taxation of Consumption Externalities with Search Unemployment
October 2013
(previously titled "A Framework for Valuing the Employment Consequences of Environmental Regulation"

How should the optimal tax on a dirty good, for which pollution is a by-product of production, depend on the presence of search unemployment?  Consumption or production taxes lower the demand for the good and induce workers to move to other sectors of the economy.  The optimal tax on the good depends on individual preferences over consumption of the dirty good and pollution but does not depend on the production side of the economy, including the extent of or cost of search unemployment.  In contrast, optimal regulation of the production of the dirty good depends on these details.  When search is more costly or time-consuming and the dirty sector is initially suboptimally large, optimal regulation will only gradually reduce the production of the dirty good.

Unemployment and Human Capital
July 2012
(with Fernando Alvarez, University of Chicago)

The paper explores the interaction between sector-specific human capital accumulation and sector-specific productivity or demand shocks. Our objective is to better understand the determinants of skill and experience premia, the costs of displacement for workers with long job tenure, and the nature of unemployment among such workers. For example, our model suggests why skilled workers can remain unemployed indefinitely even though low wage jobs are readily available and are acceptable to unskilled workers..

On the Optimal Timing of Benefits with Heterogeneous Workers and Human Capital Depreciation (screen version)(print version)
April 2006
(with Ivan Werning, MIT)
This paper studies the optimal timing of unemployment insurance subsidies in a McCall search model. Risk-averse workers sequentially sample random job opportunities. Our model distinguishes unemployment subsidies from consumption during unemployment by allowing workers to save and borrow freely. When the insurance agency faces a group of homogeneous workers solving stationary search problems, the optimal subsidies are independent of unemployment duration. In contrast, when workers are heterogeneous or when human capital depreciates during the spell, the optimal subsidy is no longer constant. We explore the main determinants of the shape of the optimal subsidy schedule, isolating forces for subsidies to optimally or fall with duration.

Search Intensity
April 2004
Standard theories of labor market search predict that workers should search less when the returns to search are low, yielding the counterfactual prediction that labor market participation and other measures of search intensity should be strongly procyclical and unemployment should be acyclical or even procyclical. I argue that this is a consequence of how search intensity is modelled. In a discrete time setting, I model search intensity as a worker's choice of the number of simultaneous applications to make. My main result is that when the cost of making an application is small, a worker who has at least an eighty percent probability of getting a job responds to an adverse shock by increasing his search intensity. Workers who are less likely to get jobs become discouraged, reducing their search intensity.

The Planning Solution in a Textbook Model of Search and Matching: Discrete and Continuous Time
February 2004

Assignment and Unemployment
July 2003
(paper prepared for Tinbergenweek, Rotterdam, April 2003)

Dynamics in a Model of On-the-Job Search
June 2003
(paper presented at the SED meetings, Paris, June 2003)

Nonstationary Search
October 2001
(with Lones Smith, University of Michigan
This paper explores optimal matching policies in constant returns to scale search economies with heterogeneous agents. We look for a policy that maximizes the present value of output in the economy, taking the search frictions as given. Our main result is that if agents' characteristics are complements in production, an optimal policy may be nonstationary, with a nontrivial asymptotic limit cycle or possibly chaotic behavior, even though the model has no extrinsic uncertainty. This finding holds for a generic set of parameter values. It is due to a trading externality (Diamond 1982) that is inherent in heterogeneous agent economies. The same forces also generate a continuum of perfect foresight equilibria.

Much of this material is based upon work supported by the National Science Foundation under Grants 9709881, 0079345, and 0351352 and 0648842 and 0962354 and 1326068. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.