Adverse selection, seller effort, and selection bias.

• Author: Wimmer, Bradley S.

1. Introduction

   Researchers use several approaches to identify adverse selection. (1) Genesove (1993) tests the proposition that, in a lemons market, prices inversely relate with observable seller characteristics that correlate with seller incentives to select goods adversely. Genesove examines the proposition in used automobile auctions. Chezum and Wimmer (1997) examine the proposition in thoroughbred racehorse markets, arguing that sellers with a high propensity to race horses should receive, on average, lower prices. Both Genesove (1993) and Chezum and Wimmer (1997) use data limited to market transactions. Wimmer and Chezum (2003) model adverse selection as a case of Heckman's (1979) sample selection bias and examine the correlation between errors in participation and price equations to study how third party certification could alleviate the effect of adverse selection in thoroughbred auctions. (2)

   In this paper, we extend the work of Genesove (1993) and Chezum and Wimmer (1997) and Wimmer and Chezum (2003) by characterizing adverse selection as a sample selection problem in a setting in which sellers possess (1) an informational advantage over buyers and (2) characteristics that correlate with both seller incentives to select goods adversely and the quality of goods produced. In such a setting, the relationship between prices and seller characteristics proves ambiguous, and researchers cannot easily disentangle adverse selection from quality effects. We show that Heckman's sample selection framework disentangles the correlation between a seller's characteristic and the effect of the selection decision on price from the correlation between a seller's characteristic and the quality of goods produced by a seller.

   The notion that the decision to sell goods relates to the quality of goods produced is not new. For example, Kim (1985) developed an adverse selection model in which car owners' maintenance and upkeep decisions affected the quality of used cars. Kim showed that allowing owners to affect the quality of goods could, under certain conditions, lead to an equilibrium in which the expected quality of used cars sold exceeds the expected quality of cars not sold. Similarly, we develop a theoretical model that extends a standard adverse selection specification by allowing owners (potential sellers) to improve a good's quality by expending unobserved effort. We show that owner effort only affects the adverse selection equilibrium when owners choose effort before they make the sell-retain decision.

   Owners decide whether to sell or retain a good once they observe their good's innate quality. Because buyers do not observe owner effort, the owner's dominant strategy is to expend zero effort on goods they will surely sell. Essentially, the model collapses to a standard moral hazard model, such as a fixed wage contract, in which employers cannot observe employee effort, and employees exert the necessary minimum effort to avoid dismissal. Because equilibrium effort equals zero, quality effects do not alter seller selection decisions and, therefore, the adverse selection equilibrium.

   Owners who must exert effort before they observe innate quality know only the probability that they will sell their goods and that the expected return to effort increases in the probability of retaining those goods. Because the probability of retention increases in seller incentives to select goods adversely, sellers who more likely select goods adversely also exert more effort. In this version of the model, no clear relationship exists between the expected quality of goods sold and the seller characteristics that Genesove (1993), and Chezum and Wimmer (1997) use to measure adverse selection. The model shows that uncertainty about whether a good will be sold partially solves the hidden action problem, in which owners underprovide effort and lessen the effect of adverse selection on markets.

   The notion that both adverse selection and moral hazard are important in markets affected by asymmetric information is well understood. Stewart (1994) modeled competitive insurance markets characterized by both adverse selection and moral hazard, showing that the two problems could partially offset one another. Jullien, Salanie, and Salanie (1999) and de Meza and Webb (2001) showed, theoretically, that standard adverse selection results might not hold when risk preferences affect both the policy selected and prevention activities. In an empirical study, Bradley (2002) showed that both moral hazard and adverse selection played important roles in health insurance markets. In related work, Abbring, Chiappori, and Pinquet (2003) used dynamic panel data to separate the effects of adverse selection from moral hazard, whereas Edelberg (2004) examined similar issues using consumer loan data. This paper extends this literature by examining the potential effect hidden action concerns can impose on adverse selection equilibrium in a goods market.

   We test the theoretical model using data that include goods retained and sold by their original owners. We estimate a price equation using Heckman's standard correction for self-selection, separating the adverse selection effect on price from the effect of potential effort by including a proxy for each seller's preference for the goods in both the selection and price equations. Evidence of adverse selection exists when our proxy for the seller's preference for the good reduces the probability that a good is sold, and the inverse Mills ratio receives a negative coefficient. A positive coefficient on our proxy for a seller's preference for the good in the price equation, holding the selection effect constant, implies the presence of an effort effect.

   Empirically, we compare standard ordinary least squares (OLS) regressions with the Heckman specification. Our OLS results contradict the findings of Chezum and Wimmer (1997), who used data from a single thoroughbred sale, and found that sellers who participate more intensively in the racing end of the business, on average, receive lower prices. With the use of data from a random sample of sales, and a similar specification, we find no significant relationship between price and a seller's racing intensity in standard OLS regressions. Correcting for sample selection, the data support the hypothesis that adverse selection plays an important role in the market for thoroughbred racehorse prospects. Our findings also support the prediction that sellers who are more likely to retain goods exert more effort.

   The remainder of the paper is outlined as follows. Section 2 constructs a theoretical model that accounts for both hidden actions and adverse selection, showing that sellers for whom adverse selection is more severe may produce higher quality goods. Section 3 illustrates how Heckman's selection bias model can separate the effects of adverse selection from hidden seller actions. Section 4 discusses the data. Section 5 presents the results. We find that both adverse selection and our measure of hidden effort produce statistically significant effects on prices in the market for thoroughbred racehorse prospects. Section 6 offers concluding remarks.

2. Theoretical Framework

   This section develops a three-period model that examines a goods market with asymmetric information. The market considered consists of m heterogeneous owners (potential sellers) and n identical buyers (n > m). Owners and buyers are risk-neutral expected utility maximizers. In period 1, owners are randomly allocated a single unit of a good with innate quality q + g([??]), where [??] is a vector of observable mean shifters, g'([??]) > 0 and q is stochastic. (3) The stochastic component of innate quality, q, is drawn from the cumulative distribution F(q) with support [[q.sub.L], [q.sub.H]], where 0 0, c"(e) > 0, with c(0) = c'(0) = 0--and is common knowledge. The realized quality of goods at the end of period 2 equals the sum of innate quality and owner effort (i.e., [q.sup.R] = q + g[[??]] + e). (5) In period 3, owners observe realized quality, and the market opens. (6) The market is a standard lemons market, in which owners possess an informational advantage over buyers.

   Following Genesove (1993), heterogeneous owners differ in the utility they receive from retained goods. At the time of sale, buyers cannot observe the realized quality of goods, but observe owner characteristics, and the distribution of innate quality. Owners choose the level of effort and whether to retain the good. Buyers choose whether to bid for a unit of the good and the amount they will bid.

   If the good is retained, owners endowed with quality q + g([??]) exerting effort e receive utility [U.sub.0] = v + s[q + g([??]) + e] - c(e), (7) where s is an owner's marginal rate of substitution of quality for other goods, and v is a numeraire good. (8) The utility that owners receive from retaining goods increases in the value of s. If the good is sold, the owner receives utility [U.sub.0] = v + P - c(e), where P is the market price. Owners maximize utility by choosing effort and whether to sell goods.

   Buyers, who purchase a unit of the good at price P receive expected utility: [U.sub.B] = v + bE[q + g([??]) + e] - P, where the expectation of quality forms over the distribution of quality, whereas, as shown below, the expectation of e is conditional on seller type. Buyers receive [U.sub.B] = v if they do not buy a good. The parameter b is a buyer's marginal rate of substitution of quality for other goods. To ensure that all trades are mutually beneficial, we assume that b > s > 0 for all potential values of s. (9,10) Buyers maximize utility by submitting price bids to owners. Price bids reflect buyer expectations on the realized quality of goods sold, and depend on the distribution of innate quality and the owner's valuation s, which is common knowledge.

   An owner's decision to sell a good depends on the realization of the stochastic...