ADVERSE SELECTION WITH HETEROGENEOUSLY INFORMED AGENTS

• DOI: http://doi.org/10.1111/iere.12458
• Published date: 01 August 2020
• Author: Seyed Mohammadreza Davoodalhosseini
• Date: 01 August 2020

INTERNATIONAL ECONOMIC REVIEW

Vol. 61, No. 3, August 2020 DOI: 10.1111/iere.12458

ADVERSE SELECTION WITH HETEROGENEOUSLY INFORMED AGENTS∗

BYSEYED MOHAMMADREZA DAVOODALHOSSEINI1

Bank of Canada, Ottawa, Canada

A model of over-the-counter markets is proposed. Some asset buyers are informed in that they can identify

high-quality assets. Sellers with private information choose what type of buyers they want to trade with. When

the measure of informed buyers is low, a unique equilibrium exists, and interestingly, price, trading volume and

welfare typically decrease with more informed buyers. When the measure of informed buyers is intermediate,

multiple equilibria arise. A switch from one equilibrium to another can lead to large drops in liquidity, price,

trading volume, and welfare, like a financial crisis. Implications of an endogenous measure of informed buyers

are also studied.

1. INTRODUCTION

Many assets, such as corporate bonds and derivatives, are traded over-the-counter (OTC). In

OTC markets, agents must search to find a trading partner, and terms of trade are determined

through bilateral negotiations. Many of these markets suffer from adverse selection in that

sellers have superior information about the value of the assets relative to buyers.2Some buyers,

such as venture capitalists, hedge funds, trusts, and investment banks, are sophisticated, so they

may identify the quality of assets better than other buyers. A natural, important question in

these markets is whether more information is preferred or not. More specifically, what are the

implications on markets if the relative number of sophisticated buyers increases?

To address these questions, I study a model of OTC markets where traders have heteroge-

neous information about the assets. Sellers have private information about the quality of their

asset and their reservation value. Some buyers, called informed buyers, can identify high-quality

assets, whereas other buyers, called uninformed buyers, cannot. Informed and uninformed buy-

ers trade in different markets. Markets are segmented in that sellers choose which type of buyers

they want to meet. Meetings are bilateral. When a seller gets to match with a buyer, the terms

of trade are determined through a bargaining protocol.

There are two main insights from the article. The first insight is that more information has

typically adverse effects on price, trading volume and welfare. A similar result arises in various

environments (e.g., Hirshleifer, 1971; Morris and Shin, 2002), but the mechanism in my article

is new: As the measure of informed buyers increases, the incentive of high-quality sellers

∗Manuscript received February 2018; revised September 2019.

1I wish to gratefully acknowledge the help of Neil Wallace, Kala Krishna, Jonathan Chiu, and Russel Wong. I would

also like to thank the editor, two anonymous referees, Kalyan Chaterjee, Antonio Diez de los Rios, Manolis Galenianos,

Veronica Guerrieri, David Jinkins, Ricardo Lagos, Shouyong Shi, Venky Venkateswaran, Randall Wright, and the

participants in several seminars and conferences at Penn State; EconCon (Princeton University); Summer Workshop

on Money, Banking, Payments, and Finance (FRB Chicago); Mid-West Macro (Purdue University); North American

Summer Meeting of the Econometric Society (University of Pennsylvania); and Bank of Canada for their helpful

comments and suggestions. The views expressed in this article are solely those of the author and no responsibility

for them should be attributed to the Bank of Canada. Please address correspondence to: Seyed Mohammadreza

Davoodalhosseini, Department of Funds Management, and Banking, Bank of Canada, 234 Wellington St. W., Ottawa,

ON K1A 0G9, Canada. Phone: +1 613 782 7725. E-mail: davo@bankofcanada.ca.

2There is evidence that markets for nonagency mortgage-backed securities were subject to adverse selection. See

Guerrieri and Shimer (2014) and Demiroglu and James (2012) for more detailed discussion.

1307

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(2020) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1308 DAVOODALHOSSEINI

to meet uninformed buyers decreases. Thus, the price that uninformed buyers are willing to

pay falls, encouraging high-quality sellers further to meet informed buyers. Consequently, the

congestion increases in the market in which informed buyers trade, more high-quality sellers

are left unmatched, and average price, trading volume, and welfare all decrease.

The second insight is that multiplicity of equilibria arises naturally in this environment on

two levels. First, with a fixed measure of informed buyers, there are multiple equilibria with

different prices when the measure of informed buyers is intermediate. Second, when the buyers

endogenously choose to become informed by incurring a cost, there are multiple equilibria

with different measures of informed buyers. The mechanism through which multiplicity arises

here is new and comes from the strategic complementarity between the choice of high-quality

sellers in meeting different types of buyers. An individual high-quality seller is more willing

to meet an uninformed buyer when the aggregate measure of high-quality sellers who meet

uninformed buyers increases. This is because the price that uninformed buyers are willing to

pay is increasing in the average quality of assets that uninformed buyers face, which in turn is

increasing in the measure of high-quality sellers who choose to meet uninformed buyers. This

strategic complementarity can generate multiple equilibria.

An interesting implication of the model is the coexistence of liquid and illiquid markets for the

same asset. Sellers of high-quality assets face a tradeoff between price and liquidity (probability

of matching for sellers), and their heterogeneous reservation values lead them to self-select

into different markets. High-quality sellers with high reservation values go to the more illiquid

market, consisting of informed buyers, and high-quality sellers with low reservation values go

to the more liquid market, consisting of uninformed buyers, because they do not want to get

stuck with their assets. Of course, the price in the liquid market is lower because buyers get a

combination of low- and high-quality assets.

The comparative statics presented in Section 3 can be used to study the interaction between

the two liquid and illiquid markets. For example, in the region of parameters where the equilib-

rium is unique, as high-quality sellers become more willing to sell (i.e., their reservation value

decreases in the first-order stochastic sense), more high-quality sellers go to the uninformed

market as this market is more liquid than the informed market. Hence, the price increases in

the uninformed market, and since more sellers go to this market, the liquidity decreases in this

market and increases in the informed market. The total trading volume increases because some

sellers have moved to the more liquid market.

When informed buyers are relatively scarce, the equilibrium is unique. When the measure of

informed buyers is intermediate, multiplicity of equilibria arises for a given measure of informed

buyers as a result of the strategic complementarity. In one equilibrium, relatively many high-

quality sellers meet uninformed buyers and the price that uninformed buyers are willing to pay

is high. In another equilibrium, relatively few high-quality sellers meet uninformed buyers and,

consequently, the price that uninformed buyers are willing to pay is low. Since more high-quality

sellers want to meet informed buyers in the latter relative to the former equilibrium, more sellers

are left unmatched. Trading volume and welfare in the latter equilibrium are lower than those

in the former one. The change from the former to the latter equilibrium shares many features

of a financial crisis in that the price, liquidity, trading volume, and welfare fall considerably.

To study the incentive of buyers to become informed, I then endogenize the measure of

informed buyers by allowing buyers to invest in an information technology that enables them to

identify high-quality assets. For example, financial institutions can hire economists to help them

determine better the underlying value of assets. Interestingly, even if the cost of acquiring the

information technology is identical for all buyers, it may be the case that ex post some buyers

will be informed and some will be uninformed. More interestingly, this version of the model

features endogenous strategic complementarity in acquiring the information technology under

certain parameters. That is, the higher the measure of informed buyers, the higher the incentive

of buyers to become informed. This endogenous complementarity leads to another dimension

of multiplicity, with different measures of informed buyers, but a scheme of tax/subsidy on

ADVERSE SELECTION AND HETEROGENEITY 1309

acquiring the information technology sometimes leads to the unique equilibrium. However, the

choice of the scheme is sensitive to the cost distribution of the information technology.

The model of this article can in principle be applied to any setting with segmented markets.

The most direct application is a financial market where one asset is traded on multiple seg-

ments with potentially more informed traders concentrated in one.3Other applications include

markets for university applicants where some universities can better identify good applicants,

markets for antiques where some buyers can better assess the true value of antiques and markets

for loans where some banks may have superior ability in screening the projects.

The informed buyers in my article can refer to the “other finance” in the language of Philippon

and Skreta (2012). They divide the finance sector into three subsectors: credit intermediation,

insurance, and other finance. Other finance is small but includes sophisticated financial insti-

tutions, such as venture capitalists, hedge funds, trusts, and investment banks. They document

that in other finance, the relative wage has increased enormously since 1980. This finding is

consistent with a finding of my model in both Examples 1 and 3, where the payoff of informed

buyers is increasing in the measure of informed buyers (when the measure of informed buyers

is sufficiently small). Presumably, the cost of information technology in recent years has de-

creased, which has led to an increase in the size of the informed segment of the market and

consequently in their payoff.

The article is organized as follows: In Section 2, I describe the environment. In Section 3,

I present my main results. I characterize the equilibria and discuss the regions of λ∈[0,1]

(denoting the fraction of informed buyers) in which there is uniqueness or multiplicity. I conduct

comparative statics with respect to λand the sellers’ willingness to sell along one equilibrium and

also compare different equilibria for a given λ. In Section 4, I endogenize λ. In Section 5, I discuss

how my article is related to the search literature and three closely related articles: Bolton et al.

(2016), Kurlat (2016), and especially Fishman and Parker (2015). Section 6 concludes. Shorter

proofs come in the main body and the rest is presented in Appendix A.2.

2. MODEL

There is a measure 1 of sellers and a measure n>0 of buyers. Each seller possesses a

single, indivisible asset that is heterogeneous in the buyer’s valuation, uT, where T∈{H,L}

and uH≡h>uL≡>0, and in the seller’s reservation value, v. The measure of sellers with

T=H(high type) is k∈(0,1) and with t=L(low type) is 1 −k. Given T, the reservation

value v∈[0,1] is drawn from a conditional cumulative density function (CDF) FT(v). The

seller’s/asset’s characteristics are summarized by a pair (T,v), and both Tand vare private

information to the seller. Notation-wise, I refer to Tas the type of the asset or type of the seller.

For example, “H seller” refers to the seller with a high-type asset. Buyers are of two types. A

fraction λof buyers, called informed or Ibuyers, have perfect information to distinguish the

type of the asset, and the remaining 1 −λ, called uninformed or Ubuyers, cannot distinguish

the type of the asset. Buyer types are public information.

The timing of actions are as follows: First, sellers learn their (T,v), and then direct their search

to target a particular type of buyers to sell their assets. Second, bilateral matches between buyers

and sellers are realized subject to a matching technology. Finally, the matched sellers and buyers

trade according to a trading protocol.

3Direct evidence that, in markets with an OTC structure, informed traders concentrate in a certain segment of

the market is limited. However, several works have established similar evidence for exchanges. For example, Easley

et al. (1996) provide evidence that the information content of trades in the New York Stock Exchange (NYSE) and

Cincinnati Stock Exchange is significantly different, suggesting that the fraction of informed buyers and uninformed

buyers is different across these two segmented markets. Bessembinder and Kaufman (1997) find similar results when

comparing the NYSE with several regional exchanges. Comparing exchanges with dark pools, Ready (2014) and

Comerton-Forde and Putniņˇ

s (2015) find in their empirical works that informed traders use the exchange, whereas

uninformed traders concentrate in the dark pool.