Optimal disclosure decisions when there are penalties for nondisclosure

• Date: 01 August 2017
• DOI: http://doi.org/10.1111/1756-2171.12197
• Author: Ronald A. Dye
• Published date: 01 August 2017

RAND Journal of Economics

Vol.48, No. 3, Fall 2017

pp. 704–732

Optimal disclosure decisions when there

are penalties for nondisclosure

Ronald A. Dye∗

We study a seller of an asset who is liable for damages if the seller fails to disclose to buyers an

estimate of the asset’s value he knew prior to the sale. Our results include as either the “damages

multiplier” that determines the size of the damages the seller must pay buyers increases, or as

the probability the seller is caught withholding his estimate from buyers increases, the seller

discloses his estimate less often, and as the precision of the seller’s estimate increases, he sells a

larger fraction of the asset.

1. Introduction

Grossman (1981) and Milgrom (1981) made what was, at the time of publication, the

surprising observation that information asymmetry between buyers and sellers of a product need

not cause any difficultyin the operation of the market for the product, notwithstanding the previous

insights of Akerlof (1970), as long as antifraud statutes are strong enough so that sellers of the

product are confined to making truthful (but costless) disclosures of their private information

about the product. Their key insight, the so-called unravelling result, was that the sellers of better

quality products would have an incentive to make disclosures about their products that could not

be truthfully replicated by sellers of inferior quality products.

Grossman’s and Milgrom’s conclusion gave rise to a quandary, as in practice, information

asymmetry between buyers and sellers sometimes does interfere with markets, with buyers

occasionally being surprised postsale about the realized utility or performance of the products

they buy, and sellers of inferior products sometimes successfully selling products at prices that

would not prevail werebuyers as well informed about their products’ attributes as the sellers are.

This quandary led researchers to study what assumption(s) underlying the Grossman-Milgrom

analyses might be violated in practice that could be responsible for information asymmetry

between buyers and sellers continuing to play a key role in the performance of markets, even

when antifraud statutes prevent sellers from making false claims about their private information.

One key assumption is that buyers know when sellers are withholding information. In the

unravelling result, if buyers know that sellers have private information about their products that

they have not disclosed,then buyers must infer that the only reason the sellers have not disclosed

∗Northwestern University; rdye@kellogg.northwestern.edu.

I would like to thank the Editor, Kathryn Spier,and two anonymous referees, as well as workshop participants at UCLA

and Carnegie-Mellon University,for comments on a previous draft of the manuscript.

704 C2017, The RAND Corporation.

DYE / 705

their information is that disclosing the information would reduce the product’s selling price. Aware

of this, buyers should adopt a posture of “sophisticated skepticism” (Milgrom and Roberts, 1986)

and revise downward the price they propose to pay for the product until sellers find it in their

self-interest to disclose their information.

The preceding logic does not apply when sellers sometimes have no private information

about their products but the sellers cannot credibly convince buyers of that fact. In that case,

a posture of sophisticated skepticism by buyers is inappropriate, because sellers who make no

disclosure are not necessarily withholding unfavorable information: they may simply have no

information to disclose. However, this possibility opens the door for sellers with sufficiently

unfavorable information to mimic the behavior of sellers who possess no information by making

no disclosure. In short, it allows sellers who receive private, but sufficiently negative, information

about their products in equilibrium to “pool” with sellers who received no information. Dye

(1985), Farrell (1986), Jung and Kwon (1988), Shavell (1994), Hughes and Pae (2004), and

Hughes and Pae (2014), among others, have developed models based on this last observation.

The present article contains a model of a seller’s disclosure decision that preserves the

central features of both the Grossman-Milgrom (GM) and Dye-Farrell (DF), etc., models (a seller

of a product/asset only sometimes privately receives information about the asset’s value; if the

seller discloses his information, that disclosure must be truthful) and then goes beyond the GM

and DF models by determining the consequences of the seller facing a requirement to disclose

his information when he receives it. The “duty to disclose” requirement is imperfectly enforced

by some fact finder (auditor, reporter, investigator, etc.) who sometimes, but not always, detects

when the seller withheld information he received from buyers prior to sale. When the fact finder

detects the seller’s withholding, the seller is obliged to make damages payments to buyers. The

damages payments are taken to be a, possibly fractional, multiple of the buyers’ overpayment for

the asset (called the “damages multiplier” in the following), where the overpayment is defined

as the difference between the amount buyers actually paid for the asset and the (counterfactual)

amount they would have paid for the asset had the seller disclosed his information to them prior

to sale.

Westudy a base model along with three extensions of the base model: in the base model, the

asset being sold is indivisible, the seller cannot takeany action before sale that influences the value

of the asset to buyers, and the probability the seller acquires information is exogenously given. In

the first extension, we endogenize the probability that the seller receives information. This first

extension is motivated bythe obser vationthat there are two distinct ways a seller, confronted with

a duty to disclose his private information, can escape liability: disclose information whenever

he receives information or not acquire information. The base model does not entertain the latter

possibility. In the second extension, the asset continues to be indivisible, but we allow the seller

to enhance the asset’s value to buyers by taking some action (that is unobservable to buyers) prior

to sale. This is a practically important problem, as sellers of used cars, businesses, etc., often face

moral hazard in their use, care, etc., of their assets before passing the assets on to others, and

it is useful in such settings to understand how credible voluntary disclosures can ameliorate the

seller’s presale moral hazard in making these action choices. In the third extension, the seller also

can make some value-enhancing investment in the asset prior to sale (as in the second extension),

but the asset is now taken to be divisible, and so the seller can decide whatfraction of the asset to

retain for himself and what fraction to sell to buyers. This third extension is natural for studying

disclosures in an initial public offering (IPO) context, where the founder of a firm retains a

nontrivial fraction of his firm post the IPO, and is also relevant in the modern “sharing” economy

where the owners of an asset can exploit the fact that they intend to use only a limited portion of

the asset’s capacity, and so they can sell off, or rent, to other parties the portion of the asset they

don’t use.

Weobtain a variety of results concerning the seller’sequilibrium disclosure behavior. Among

these results, at least four stand out. To describe the first result, call the seller’s disclosure decision

nonmyopic (resp., myopic) if he takes into account (resp., ignores) the potential liability he is

C

The RAND Corporation 2017.