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Screening and Adverse Selection in Frictional

Markets

∗

Benjamin Lester

Federal Reserve Bank of Philadelphia

Ali Shourideh

Carnegie Mellon University

Venky Venkateswaran

NYU – Stern School of Business

Ariel Zetlin-Jones

Carnegie Mellon University

September 19, 2018

∗

We thank Gadi Barlevy, Hanming Fang, Mike Golosov, Piero Gottardi, Veronica Guerrieri, Ali Hor-

tacsu, Alessandro Lizzeri, Guido Menzio, Derek Stacey, Robert Townsend, Randy Wright, and Pierre

Yared, along with seminar participants at the Spring 2015 Search and Matching Workshop, 2015 CIGS Con-

ference on Macroeconomic Theory and Policy, 2015 annual meeting of the Society for Economic Dynamics,

2015 meeting of the Society for the Advancement of Economic Theory, 2015 Norges Bank Conference on

Financial Stability, 4th Rome Junior Conference on Macroeconomics (EIEF), 2015 Summer Workshop on

Money, Banking, Payments and Finance at the Federal Reserve Bank of St. Louis, 2015 West Coast Search

and Matching, 2015 Vienna Macro Workshop, NYU Search Theory Workshop, European University Insti-

tute, Toulouse School of Economics, University of Pennsylvania, Columbia University, the Federal Reserve

Bank of Cleveland, and the Banque de France for useful discussions and comments. The views expressed

here are those of the authors and do not necessarily reﬂect the views of the Federal Reserve Bank of

Philadelphia or the Federal Reserve System.

Manuscript (tex file) Click here to

access/download;Manuscript;LSVZ_revision2_final.tex

Please use DOI when citing or quoting. DOI: 10.1086/700729

This content downloaded from 185.216.093.030 on September 29, 2018 14:07:37 PM

All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).

1 Introduction

Many important markets suffer from adverse selection, including the markets for insur-

ance, credit, and certain ﬁnancial securities. There is mounting evidence that many of

these markets also feature some degree of imperfect competition.

And yet, perhaps

surprisingly, the effect of imperfect competition on prices, allocations, and welfare in

markets with adverse selection remains an open question.

Answering this question is important for several reasons. For one, many empirical

studies attempt to quantify the effects of adverse selection in the markets mentioned

above.

A natural question is to what extent these estimates—and the conclusions that

follow—are sensitive to the assumptions imposed on the market structure. There has

also been a recent push by policymakers to make these markets more competitive and

less opaque.

Again, a crucial, but underexplored question is whether these attempts

to promote competition and reduce information asymmetries are necessarily welfare-

improving.

Unfortunately, the ability to answer these questions has been constrained by a short-

age of appropriate theoretical frameworks.

A key challenge is to incorporate nonlinear

pricing schedules—which are routinely used to screen different types of agents—into

a model with asymmetric information and imperfect competition. This paper delivers

such a model: we develop a novel, tractable framework of adverse selection, screening,

and imperfect competition.

The key innovation is to introduce a search-theoretic model of imperfect competition

For evidence of market power in insurance markets, see Brown and Goolsbee (2002), Dafny (2010),

and Cabral et al. (2014). For evidence of market power in various credit markets, see, e.g., Ausubel (1991),

Calem and Mester (1995), and Crawford et al. (2015). In over-the-counter ﬁnancial markets, a variety

of data suggest that dealers extract signiﬁcant rents; indeed, this ﬁnding is hard-wired into workhorse

models of this market, such as Dufﬁe et al. (2005).

See the seminal paper by Chiappori and Salanie (2000), and Einav et al. (2010a) for a comprehensive

survey.

Increasing competition and transparency in health insurance markets is a cornerstone of the Afford-

able Care Act, while the Dodd-Frank legislation addresses similar issues in over-the-counter ﬁnancial

markets. In credit markets, on the other hand, legislation has recently focused on restricting how much

information lenders can demand or use from borrowers.

As Chiappori et al. (2006) put it, “there is a crying need for [a model] devoted to the interaction

between imperfect competition and adverse selection.”

Please use DOI when citing or quoting. DOI: 10.1086/700729

This content downloaded from 185.216.093.030 on September 29, 2018 14:07:37 PM

All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).

(a la Burdett and Judd, 1983) into an otherwise standard model with asymmetric infor-

mation and nonlinear contracts. Within this environment, we provide a full analytical

characterization of the unique equilibrium, and then use this characterization to study

both the positive and normative issues highlighted above.

First, we show how the structure of equilibrium contracts—and hence the relation-

ship between an agent’s type, the quantity that he trades, and the corresponding price—

is jointly determined by the severity of the adverse selection problem and the degree of

imperfect competition. In particular, we show that equilibrium offers separate different

types of agents when competition is relatively intense or adverse selection is relatively se-

vere, while they typically pool different types of agents in markets where principals have

sufﬁcient market power and adverse selection is sufﬁciently mild. Second, we explore

how total trading volume—which, in our environment, corresponds to the utilitarian

welfare measure—responds to changes in the degree of competition and the severity of

adverse selection. We show that increasing competition or reducing informational asym-

metries is only welfare-improving in markets in which both market power is sufﬁciently

concentrated and adverse selection is sufﬁciently severe.

Before expanding on these results, it is helpful to lay out the basic ingredients of the

model. The agents, whom we call “sellers,” are endowed with a perfectly divisible good

of either low or high quality, which is private information. The principals, whom we

call “buyers,” offer menus containing price-quantity combinations to potentially screen

high- and low-quality sellers.

Sellers can accept at most one contract, i.e., contracts are

exclusive. To this otherwise canonical model of trade under asymmetric information, we

introduce imperfect competition by endowing the buyers with some degree of market

power. The crucial assumption is that each seller receives a stochastic number of offers,

with a positive probability of receiving only one. Hence, when a buyer formulates

an offer, he understands that it will be compared with an alternative offer with some

probability, which we denote by π, and it will be the seller’s only option with probability

The use of the labels “buyers” and “sellers” is merely for concreteness and corresponds most clearly

with an asset market interpretation. These monikers can simply be switched in the context of an insurance

market, so that the “buyers” of insurance are the agents with private information and the “sellers” of

insurance are the principals.

Please use DOI when citing or quoting. DOI: 10.1086/700729

This content downloaded from 185.216.093.030 on September 29, 2018 14:07:37 PM

All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).

1 − π. This formulation allows us to capture the perfectly competitive case by setting

π = 1, the monopsony case by setting π = 0, and everything in between.

For the general case of imperfect competition, with π ∈ (0, 1), the equilibrium in-

volves buyers mixing over menus according to a nondegenerate distribution function.

Since each menu is comprised of two price-quantity pairs (one for each type), the main

equilibrium object is a probability distribution over four-dimensional offers. An impor-

tant contribution of our paper is developing a methodology that allows for a complete,

yet tractable, characterization of this complicated equilibrium object.

We begin by showing that any menu can be summarized by the indirect utilities it of-

fers to sellers of each type. Next, we establish an important property: in any equilibrium,

all menus that are offered by buyers are ranked in exactly the same way by both low-

and high-quality sellers. This property, which we call “strictly rank-preserving,” implies

that all equilibrium menus can be ranked along a single dimension. The equilibrium,

then, can be described by a distribution function over a unidimensional variable—say,

the indirect utility offered to low-quality sellers—along with a strictly monotonic func-

tion mapping this variable to the indirect utility offered to the high-quality seller. We

show how to solve for these two functions, obtaining a full analytical characterization

of all equilibrium objects of interest, and then establish that the equilibrium is unique.

Interestingly, our approach not only avoids the well-known problems with existence of

equilibria in models of adverse selection and screening, but also requires no assumptions

on off-path beliefs to get uniqueness. We then use this characterization to explore the

implications of imperfect competition in markets suffering from adverse selection.

First, we show that the structure of menus offered in equilibrium depends on both the

degree of competition, captured by π, and the severity of the adverse selection problem,

which is succinctly summarized by a single statistic that is largest (i.e., adverse selection

is most severe) when: (i) the fraction of low-quality sellers is large; (ii) the potential

Mixing is to be expected for at least two reasons. First, this is a robust feature of nearly all models

in which buyers are both monopsonists and Bertrand competitors with some probability, even without

adverse selection or nonlinear contracts. Second, even in perfectly competitive markets, it is well known

that pure strategy equilibria may not exist in an environment with both adverse selection and nonlinear

contracts.

Please use DOI when citing or quoting. DOI: 10.1086/700729

This content downloaded from 185.216.093.030 on September 29, 2018 14:07:37 PM

All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).

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