Silver Signals: Twenty-Five Years of Screening and Signaling

Journal of Economic Literature Vol. XXXIX (June 2001) pp. 432–478

Journal of EconomicRiley: Literature, Silver Vol. XXXIX Signals(June 2001)

Silver Signals: Twenty-Five Years of Screening and Signaling

JOHN G. RILEY1

1. Introduction dix, Vickrey even provided a foundation for modern auction theory. Ten years HY IS IT so hard to get a good price later James Mirrlees (1971), in his Won a used car? Why is the annuity analysis of optimal income taxation, market so thin? Why do firms offer lower provided subtle insights into the trade- premiums per unit of coverage to in- off between efficiency (the incentive to surees who accept deductibles? Why do work) and redistribution. Around the firms continue to pay dividends, even same time, George Akerlof (1970) though shareholders are subject to dou- showed how trade can almost com- ble taxation? Under what conditions can pletely collapse when agents on one amonopolyprofitablydeterentrybyset- side of a market know only the distri- ting a low “limit price” rather than the bution of product quality, rather than monopoly price? These are just a few of the quality of each item traded.3 Finally the vast array of questions that economic Michael Spence (1973) asked whether, theory was in no position to answer until in a competitive marketplace, sellers of the development of new theoretical above-average quality products could foundations. “signal” this fact by taking some costly With the benefit of hindsight, there action. On the other side of the market, were four pioneer papers that set the could the uninformed buyers use the stage for an unprecedented research costly action as a way to “screen” for effort that continues to this day.2 The quality? remarkable paper by William Vickrey In today’s terminology, the papers by (1961) examined a range of issues in the Vickrey and Mirrlees focussed on the provision of incentives when agents design of an incentive scheme by an im- have private information. In the appen- perfectly informed monopolist. Despite having an informational disadvantage, it 1 Department of Economics, UCLA. I am in- debted to Sara Castellanos and Felipe Zurita for is typically the case that the monopolist their assistance in the citation search, which has an incentive to offer a set of alter- served to guide the selection of articles to be natives that (at least partially) separates included, and for their useful summaries. The extensive and most helpful comments and sugges- out agents with different characteristics. tions of Hongbin Cai, Jack Hirshleifer, Beverly In Mirrlees’ case, more able workers Lowe, the editor, and three referees are also very gratefully acknowledged. 3 As evidence of how unusual Akerlof’s ideas 2 Even long after all of these papers were written, were perceived to be, his paper was rejected by the very strong links were not fully understood. two leading journals of the time. 432 Riley: Silver Signals 433 choose to earn higher income even on applications in industrial organiza- though they know they will pay higher tion, section 5 in labor markets, and taxes. And in a Vickrey auction, buyers section 6 in finance. Section 7 provides with higher valuations have an incentive a brief introduction to related papers in to bid higher. Akerlof and Spence ex- macroeconomics. amined models with a very similar formal structure. Imperfectly informed 2. Introduction to the Theory agents make offers, taking into account 2.1 Hidden Knowledge and Adverse the heterogeneity on the other side of Selection the market. However, there is a key difference. Instead of a single uninformed Central to traditional equilibrium agent, there is now competition among theory is the idea that an economy such agents. Thus, while Vickrey and guided by prices economizes on infor- Mirrlees study optimal incentive mation. In a private goods world, indi- schemes, Akerlof and Spence examine vidual agents need to know nothing incentive schemes that will survive the about the other agents in the market- competitive forces of the marketplace, place, and yet Walrasian equilibrium that is, equilibrium incentive schemes. prices result in a Pareto-Efficient allo- One of the great theoretical contro- cation. Critical to the ideal functioning versies of this vast literature is the char- of the invisible hand, however, is the acterization of conditions under which requirement that agents have the same equilibrium incentive schemes exist. information about the characteristics of This is a focus of section 2, which pre- the commodities being traded. When sents the basic theory of “screening.” this assumption fails, how to take full Section 2 also considers situations in advantage of the potential gains to trade whichaninformedagentmustfirst“sig- becomes a much more subtle issue. nal” by taking a costly action, without Akerlof (1970) provides the first for- observing the terms under which he mal model, illustrating how dramatically will be able to trade. The critical ques- asymmetric information can affect equi- tion is then how uninformed potential librium trades. Consider a population of trading partners will interpret the in- car owners, each of whom must choose formed agent’s action. Such a model whether to purchase a new car or hold can only have strong predictive power if onto the old one. While used cars look it is possible to place strong restrictions alike to potential buyers, the actual on equilibrium beliefs. quality varies. Only the current owner Additional theoretical subtleties are knows the actual quality of his car. examined in section 3. The next four From the experience of prior periods, sections look at many of the key buyers correctly anticipate the average applications of the theory and attempt quality of used cars that are traded. The to test the theory.4 Section 4 focuses market price of a used car thus reflects the average quality of a car on the mar- 4 The reader who is primarily interested in a ket. If quality differences are large, particular applied field may wish to go directly those with cars of sufficiently high qual- from section 2 to the appropriate later section. In almost every field, the literature is just too large to ity find it better to keep their old cars survey comprehensively. A primary criterion for rather than sell, thereby lowering the selecting one paper to comment upon and not average quality of cars being traded. As another was the interest generated by the paper as measured by its citation count in the Social Akerlof emphasized, this incentive to Science Citation Index. withdraw from the market can lead to 434 Journal of Economic Literature, Vol. XXXIX (June 2001) an equilibrium in which none but the very more about family longevity than the in- worst cars (the “lemons”)aretraded. surance company (the buyer of the risk.) To understand this, consider a The sellers with the greatest longevity stripped-down version of Akerlof’s stand to gain the most from the annuity model. The market value of a car of since they expect a longer stream of pay- quality t is V(t)=α+βt,wheret is uni- ments. But, from the viewpoint of the formly distributed on [0,1]. Given the buyers, these are the bad risks since they uniform distribution, the average qual- will cost the most. As a result, annuities ity of used__ cars that are of quality t or are expensive and the market is thin. ( )=α+1β lower is V t 2 t. Suppose that the Obviously, a necessary condition for expected consumer surplus from the such a market failure is that the cost of purchase of a new car is s. Suppose establishing a reputation for honesty is also that only those used cars of quality too high. Development economists have t′ or lower are traded. Then the__ average noted that such problems tend to be more market value of these cars is V(t′).Ifa prevalent in economies where market type t seller holds on to his used car institutions are more decentralized, and then his payoff is V(t). If he sells, he there are large numbers of direct sales gets the consumer surplus associated by small sellers.5 In more highly devel- with the purchase of a new car and, for oped markets, it is the low frequency of his used car, a price equal to_ the_ average trades by any single seller that makes market value of such cars, V(t′). Thus, reputation-building prohibitively costly. his total payoff from selling__ his old car We now illustrate adverse selection and buying a new one is V(t′) + s.Typet more formally in a richer model of in- is therefore better off holding on__ rather surance. An insurance contract X =(r,m) is than selling if and only if V(t)>V( t′) + s, an agreement by the insurer that in β( − 1 ′) > that is, t 2t s. In equilibrium, the return for receiving a premium m it marginal seller must be just indifferent will provide coverage r in the event of a between holding and selling. Thus type loss L.Letpt be the probability of loss t′ is the equilibrium marginal seller if for a type t individual. For simplicity, 1β ′= ∈ 2 t s. All those with higher quality cars suppose that t {1,2} and that the higher are better off opting out of the market. indexedtypeisabetterrisk(lowerloss In the limiting case, when s ⁄β is very probability.) Given an initial wealth W,and small, it follows that the marginal type t′ strictly concave von Neumann-Morgenstern is small. Therefore the market for used utility function v(⋅), expected utility of cars essentially dries up, with only the very type t is low-quality cars being traded. While such Ut(X)=Ut(r,m)=(1 − pt)v(W − m) an extreme outcome is possible, the im- + ( − + − ) portant observation is that it is the sell- ptv W L r m . ers of the higher quality items who opt It is readily confirmed that expected util- out of the market. Asymmetric informa- ity is a strictly concave function of the tion therefore adversely affects both the contract terms X = (r,m). The indiffer- volume and quality of the items traded. ence curve for each type through the ^ This phenomenon has long been under- contract X is depicted in figure 1.6 stood by the insurance industry. Consider, The slope of this indifference curve is the for example, the purchase of an annuity marginal willingness to pay an additional upon retirement. While an insurance com- 5 See, for example, Robert Klitgaard (1991). pany can check current health, the cus- 6 For consistency with later diagrams, the axes tomer (the seller of the risk) knows have been inverted in this figure. Riley: Silver Signals 435

Unbroken indifference curve of high risk type

coverage O r

Dashed indifference preference curve of low risk type directions

U2(X) = U2(X)

∏(X) ≥ 0

m = pr U1(X) = U1(X) m premium Figure 1. Single Crossing Property and Adverse Selection premium as the coverage increases. “single-crossing property” of the prefer- Intuitively, the lower the probability of ence maps of different types is abso- loss, the smaller the additional premium lutely central to models of informational an individual is willing to pay for greater asymmetry. − coverage. Thus, the dashed indifference Let p be the probability of loss aver- curve of the low-risk type is flatter than aged over the good and bad risks. Ig- the unbroken indifference curve of the noring administrative expenses, the ex- high-risk type.7 As we shall see, this pected profit on the contract X = (m,r) for an individual selected at random 7 It is readily confirmed that the slope of the from the population is then indifference curve at X = (m,r) − Π( )= − − ∂ X m pr. Ut Expected probability  ∂ = premium − × coverage dm r profit of loss __ =− dr ∂ Ut Ut − ∂m In figure 1, expected profit Π(X) is p v′(W − L + r − m) positive in the interior of the shaded re- = t − ′( − + − )+( − ) ′( − ) , = ptv W L r m 1 pt v W m gion below the zero profit line m pr. Note that the indifference curve of the increases with p . Note also that the slope exceeds t low-risk group is sufficiently flatter that pt if and only if coverage is incomplete. 436 Journal of Economic Literature, Vol. XXXIX (June 2001)

O r

U2(X) = U2(O)

∏ 2(X) = 0 m = p2r ∗ X1

∏ 1(X) = 0 U1(X) = U1(X1) m m = p1r premium Figure 2. Single Crossing and Screening it lies below the no-insurance point X = contract for a high-risk type.9 This is (0,0).8 Thus, low-risk types choose not depicted in figure 2. to insure, leaving only the high-risk As in the previous figure, indiffer- types. This is another illustration of ence curves (and the zero-profit line) Akerlof’slemonsprinciple.However, for the low-risk type are shown as there is now a continuum of possible dashed curves. Note that the dashed in- levels of coverage. A complete analysis difference curve for the low-risk type thus requires that we consider different U2(X) = U2(O) goes through the no- levels of coverage. We begin by suppos- insurance point O and lies above the ∗ ing that adverse selection has taken contract X1. Thus, the low-risk types are place and that the high-risk types are indeed better off out of the market the only ones getting insurance. Given than purchasing the insurance contract ∗ competition among insurance companies X1. (and assuming insurance companies are 2.2 Screening risk neutral), the equilibrium contract ∗ X1 is the utility-maximizing zero profit We will now argue that insurance companies have an incentive to “screen” 8 If the loss probabilities are similar, the indifference curve lies above the origin. Thus, for for low-risk types by offering a second adverse selection to occur, the range of loss ∗ 9 = ( ) Π ( )≥ probabilities must exceed some threshold level. That is, X1 arg Max{U1 X | 1 X 0}. X Riley: Silver Signals 437

Dashed indifference curve of low risk type coverage r O

X ∏ 2(X) = 0

U2(X) = U2(X)

∏(X) = 0 U1(X) = U1(X)

premium m Figure 3. No Pooling Nash Equilibrium insurance policy that provides lower tionally consistent equilibrium contracts. coverage. Consider the contracts in the If firms offer these two contracts based interior of the shaded area in figure 2. on the belief that types will separate, These lie below the indifference curve then these expectations are fulfilled. ∗ U1(X)=U1(X1) and above the indiffer- Moreover, the expected profit on each ence curve U2(X)=U2(O). Thus, they are contract is zero. Of course, exactly the attractive only to the low-risk types. same argument holds for all points on Moreover, they also lie below the zero the upper boundary of the shaded re- expected profit line Π2(X)=0 for the gion. This led to Spence’s controversial low-risk group. Thus any such contract conclusion that there was a continuum screens for the low-risk types and is of informationally consistent equilibria. strictly profitable. While the idea of an informationally Consider next the insurance contract consistent set of contracts appears to be X2 on the zero profit line Π2(X)=0 a natural generalization of Walrasian bounding the shaded region of profit- equilibrium, it is incomplete in a num- able screening. Spence (1973) in his ber of ways. First, there is no competition seminal thesis argued that pairs of con- in the screening dimension. Second, the ∗ tracts such as X1 and X2 were informa- timing of actions is not spelled out. 438 Journal of Economic Literature, Vol. XXXIX (June 2001)

Third, the information sets of the agents Π2(X)=0, must be as depicted. Note are not fully specified. These issues that any offer such as X^,intheinterior were independently addressed by Riley _of_ the shaded region, is preferred over (1975) and Michael Rothschild and X by only the low-risk type. Since such Joseph Stiglitz (1976). The latter paper offers also lie below Π2(X)=0,theyare makes a more radical departure from strictly profitable. We have therefore Spence’s analysis by proposing that the shown that it is always profitable and model should be viewed as a noncoop- feasible for an insurance company to erative game between the uninformed screen and “skim the cream” from the pool. insurance companies and the consumers. 2.5 Uniqueness 2.3 Rothschild-Stiglitz Screening Game10 We now show that there is at most one Nash equilibrium pair of contracts. The game is defined thus: First, the The informationally consistent contract uninformed players announce offers. ∗ pair (X1,X2) from figure 2 is redrawn in Second, each informed type chooses the figure 4. Consider the insurance con- offer which is best for him. The offers tract X^. Low-risk types are strictly bet- are a Nash equilibrium set of contracts ^ ter off choosing X rather than X2, while if, given the strategies of the other play- ∗ ^ high-risk types strictly prefer X1 over X. ers, each uninformed agent’s strategy is Thus, the new offer successfully screens a best response. for the low-risk types. Since X^ also lies The three key conclusions about the below the zero-profit line for the low- (pure strategy) Nash equilibria of this risk types, it is strictly profitable. Then game are that: (i) different types are al- ∗ the pair of contracts (X1,X2) is not a ways separated, (ii) there is at most one Nash equilibrium. Exactly the same separating equilibrium, and (iii) equi- argument holds for any point to the librium exists if and only if the propor- ∗ northeast of X2 on the zero-profit line tion of high-value (low-risk) types is bounding the shaded region. Thus, if sufficiently low. We now look at each of there is a Nash equilibrium, it must be these points in turn. ∗ ∗ the pair (X1,X2). Combining these arguments, we have shown that if there is an 2.4 No Pooling ∗ ∗ equilibrium (X1,X2) it has the following It is easy to see that there can be no ∗ properties: (i) X1 is the best zero-profit Nash equilibrium that pools the dif- contract for the high-risk types, and (ii) ferent types. Consider figure__ 3 and ∗ X2 is the best zero-profit contract for the suppose that the contract X is a Nash low-risk types, which is just separating.11 equilibrium. If it were strictly profitable, an insurance company could offer a 2.6 Equilibrium slightly smaller premium and__ attract everyone in the pool. Then X must just Thus far we have established that if break even. It follows that the flatter there is an equilibrium it must be the zero-profitlineforthelow-risktype, separating pair of contracts with the minimum separation of the two types. 10 In the early literature, the terms “screening” The final step is to determine conditions and “signaling” are used almost interchangeably. More recently, it has become common to refer to under which there are no profitable de- the game in which the uninformed agents move fections from these contracts. Rather than first as a “screening game” and a game in which the informed agents move first as a “signaling 11 This conclusion generalizes immediately to game.” We shall follow this convention. the n type case. Riley: Silver Signals 439

U2(X) = U2(X2) coverage r r O

∗ X2 m X π m = 2r

∏ 2(X) = 0 π m = 1r

∗ X1

∏ (X) = 0 1 premium m Figure 4. Minimum Separation of Types continue with the insurance example, it dividual with education level z.The will be convenient to switch to a simple worker’s utility Ut(X)=Ut(z,w) is an in- version of Spence’s labor market model. creasing function of w and a decreasing Atypet individual has a productivity of function of z. Formally this model is Vt(z)12 whichisincreasinginbothhis identical in structure to the insurance type and his level of education, z.An model. However, for expositional reasons, employment contract X = (z,w)isan we follow Spence and make the further agreement to pay a wage w to an in- assumption that utility can be expressed in the separable form Ut(z,w)=w − ct(z). 12 While the literature simply takes marginal Then the slope of an indifference curve product as given, the model is readily generalized. for type t is: Let Vt(z) be the number of efficiency units of labor supplied by a type t worker. Then if the firm ∂ hires Lf efficiency units of labor, and the output Ut price is p, the marginal value product of a type t ∂ ≡ dw z worker is Vt(z) pMPL(Lf)vt(z). Assuming price- __ =− = c′t(z). taking behavior, the firm adds workers until the dz ∂ Ut Ut marginal value product of type t is equal to his ∂ market wage w(zt). w 440 Journal of Economic Literature, Vol. XXXIX (June 2001)

∗ U1(X) = U1(X1) ∗ w U2(X) = U2(X2) wage ∏ 2(X) = 0 w2 (w = V2 (z)) X2 ∗ w2 ∗ X2

∏ (X) = 0 1 (w = V (z)) 1

∗ w1 ∗ X1 Preference directions

z ∗ ∗ z1 z2 z z2 education Figure 5. Labor Market Screening

The single-crossing property holds if the equilibrium is that in which the low marginal cost of education is lower for productivity worker is offered his best more productive workers. This is de- zero-profit contract and the level of picted in figure 5 for the simplest case of the educational screen is set just high two types. enough to deter low-productivity work- ∗ ∗ In graphical terms, the dashed indif- ers. These two contracts X1 and X2 are ference curves of a high-productivity as depicted in figure 6. (type 2) worker are flatter. Given our To complete the analysis, we need to assumptions, the profit on a type t ask whether the unique candidate pair ∗ ∗ worker who accepts the contract (z,w)is of contracts X1 and X2 is a Nash equilib- Πt(X)= Vt(z)−w. The zero profit curves rium. Figure 6 provides the answer. As are also depicted in figure 5. The analy- depicted, the equilibrium indifference sis then proceeds exactly as in the insur- curve for the high-quality workers cuts ance example. The only potential Nash below the zero-expected profit line for Riley: Silver Signals 441

w U1(X) = U1(X) wage U2(X) = U2(X)

∗ X w = V (z) ∗ 2 2 w2

w = V (z)

w2 X

∗ X1

z z z2 education Figure 6. Nonexistence of a Screening Equilibrium a worker drawn at random from the en- sized by Rothschild and Stiglitz, a tire population. Note that this will be necessary and sufficient condition for the case if and only if the fraction of equilibrium is that the proportion of high-quality workers is sufficiently__ high. high-quality workers should not be too For then the curve w = V(z) lies just un- high. der the corresponding curve for the Riley (1985) extends the analysis by high-quality workers w = V2(z).Allcon- asking what sort of assumptions about tracts in the interior of the shaded re- preferences are sufficient for equilib- gion are strictly preferred by both types rium. Suppose that we fix the technol- of worker and generate strictly positive ogy, the distribution of types and the expected profits. Thus, the separating preferences of low-quality workers. ∗ ∗ ^ pair of contracts, X1 and X2 is not a Consider the contract X in__ figure 6. This Nash equilibrium. Therefore, as empha- lies below the curve w = V(z) if and only 442 Journal of Economic Literature, Vol. XXXIX (June 2001)

∗ if the vertical distance w2 − w^2 is suffi- cepts and X1. Thus his offer must be on ∗ ciently large relative to w2 − w^1. But the or above the heavy dashed indifference ∗ ^ contracts X2 and X lieonthesameindif- curve. The monopolist then maximizes ference curve for a high productivity type. profit on a type 2 worker Π2(X) = V2(z) − Thus, w subject to the constraint that U2(X) ≥ U (X ). ( ∗ ∗)= ∗ − ( ∗) 2 1 U2 z2,w2 w2 c2 z2 Note that at Xt, t = 1,2, the slope of = ^ − (^ )= (^ ^ ) w2 c2 z2 U2 z,w2 , the indifference curve c′1(z) is equal to ′ ( ) ∗ − ^ = ( ∗)− (^) the slope of the iso-profit curve V t z . and therefore w2 w2 c2 z2 c2 z .A Thus both contracts are efficient. We symmetrical identical argument for type ∗ will now argue that the monopolist can 1workersestablishesthatw2 − w^1 = ( ∗)− (^) always do better by lowering the educa- c1 z2 c1 z . Therefore tional requirement for the low type. ∗ ∗ M w2 − w^2 c2(z2)−c2(^z) The resulting pair of contracts is X1 and = M ∗ ∗ . X . Note that this change reduces the w − w^ c (z )−c (^z) 2 2 1 1 2 1 profit on low-productivity workers and We have argued that equilibrium fails raises the profit on high productivity to exist if and only if the left-hand side workers. But, starting from the contract is sufficiently large. Thus, for equilib- X1 and moving around the type 1 reser- rium, the ratio of educational costs vation indifference curve, the iso-profit must be sufficiently small. This will be curve and indifference curves are locally the case if the marginal cost of educa- of the same slope. Thus, in the neigh- tion is sufficiently lower for the high borhood of X1, the loss in profit on a quality type. The central conclusion is type 1 worker is of second order, while that it is not enough for preferences to thegaininprofitonatype2workeris satisfy the single crossing property. of first order. Instead, the preference maps of the dif- As is the case for the R-S screening ferent types should vary sufficiently model, the monopolist maximizes profit rapidly with type. by separating low- and high-quality workers. However, there is an impor- 2.7 Monopoly Screening tant difference. Note that now it is the With a single uninformed agent, the high-productivity worker who is offered optimal screening mechanism is super- an efficient contract while the low- ficially very similar. Consider our labor productivity worker achieves a sub- market example once more. Suppose there optimal education. The opposite con- is a small supply of low-productivity clusion holds for the Nash equilibrium workers so that the monopolist maxi- of the R-S screening game. In the mizes profit by hiring both types of monopoly model, the firm sacrifices worker. For simplicity, suppose both efficiency at low-quality levels in order types have the same reservation wage to extract more surplus from high- wR. The monopolist maximizes profit on productivity workers. In the “competi- type 1 workers by maximizing profit, tive” screening model, firms sacrifice Π1(z,w) = V1(z) – w, subject to the con- efficiency at high-quality levels in or- straint that U1(z,w) ≥ wR.Thisisthe der to separate high- from low-quality contract X1 in figure 7. workers. To be incentive compatible, a high- The earliest formal modeling of mo- quality (type 2) worker must be at least nopoly screening is Mirrless’ (1971) indifferent between the offer he ac- remarkable paper on income taxation. Riley: Silver Signals 443

w wage

U2(X) = U2(X1)

≥ U1(X) wR X2

X1 M X2

M X1

∏ ∏ 2(X) = 2(X2) w R ∏ ∏ 1(X) = 1(X1)

O z education Figure 7. Monopoly Screening

Suppose we reinterpret the vertical axis 2.8 Signaling of figure 7 as gross income and the horizontal axis as tax. Then, as Mirrlees In the R-S screening model, it is the observed, the trade-off between income uninformed agents who have the critical and taxation differs, because individuals role. They use their knowledge of dif- of differing ability have different oppor- ferences in preferences to screen for tunity costs of leisure. Then the tax different quality levels. The informed authority chooses among incentive com- agents simply respond to the offers patible tax-income pairs (X1,X2)to made by the uninformed. But what if it achieve its social objective. This paper is the informed agent or agents who and the closely related work by Vickrey must move first? For example, what if a (1961) on auction choice has since firm has developed a new product or spurred a vast literature on the design service whose quality is not easily evalu- of incentive schemes by an unin- ated by potential buyers? Is there some formed “principal.” Much of this litera- way that the firm can, through a costly ture has at its core the single crossing action, “signal” to buyers that it is selling property. a high-quality product? 444 Journal of Economic Literature, Vol. XXXIX (June 2001)

To answer these questions, we return “sequential” (Kreps and Robert Wilson to Spence’s labor market model and ex- 1982). In the signaling game, this re- plore the implications, under the new quires that the second movers assign a assumption that it is the informed agent probability distribution over types for who must move first.13 In this signaling every possible action by the first mover game, firms are seeking to hire a new and, hence, a best response wbr(z)to type of technology consultant who may every feasible signal z. Given these best be of high or low quality. Consider fig- responses, the Nash equilibrium is se- ure 5 once more and the pair of educa- quential if the first mover has no incen- ∗ tion levels z1 and z2. Suppose that the tive to change his strategy. Consider ∗ consultant’s strategy is to choose the then the Nash equilibrium strategies z1 higher education level if and only if his and z2 in figure 5. If firms believe that quality is high. If firms believe this, it is low productivity consultants are suffi- a Nash-equilibrium best response to ciently more likely to take some out-of- pay a wage equal to the perceived mar- equilibrium level of the signal z,the ginal product. Thus a consultant with best responses will be low wage offers. ∗ education level z1 is offered a wage Given these low wage offers, it follows ∗ ∗ w1 = V1(z1), while a consultant with edu- that a high quality consultant is worse cation level z2 is offered a wage w2 = off deviating. Thus, there is a continuum V2(z2).Givensuchoffers,itisclear of (sequential) Nash equilibria. from figure 5 that the consultant is bet- Cho and Kreps (1987) argue that out- ter off choosing the higher education of-equilibrium beliefs should be further level if and only if he has a high mar- refined. If a consultant takes an out-of- ∗ ginal product. The pair of contracts X1 Nash-equilibrium action ^z ,thenfirms and X2 are thus Nash equilibrium con- go through the following “intuitive” tracts. By the same argument, there is a exercise. continuum of equilibria with the high- (1) If all the uninformed firms believe it quality contract lying on the curve ∗ is a type t consultant who chose ^z , Π (X) = 0, between X and X . Indeed, 2 2 2 what will be the highest wage of- as In-Koo Cho and David Kreps (1987) fered? Let the resulting contract be showed, all the equilibria discussed by X^ =(^z,w^). Spence are Bayesian-Nash equilibria of (2) Would a type t consultant be strictly this game. better off with the contract X^ than With the better-informed agent mov- with his Nash equilibrium contract? ing first, the critical issue is how a less- (3) Is it also the case that no other informed agent will respond to some type would be better off switching to unanticipated action by the first mover. contract X^? Unfortunately, there is nothing in the formal description of a Nash equilib- If the answer to both (2) and (3) is yes, rium to restrict such beliefs. One of the Cho and Kreps argue that a type t con- key innovations of modern game theory sultant has an incentive to deviate. That ∗ is the development of ways to “refine” is, the pair of contracts X1 and X2 fails beliefs. Among the least controversial of their “intuitive criterion.” these ideas is that the equilibrium be In figure 5, any education level z2 ∗ strictly greater than z2 fails the intuitive 13 We will consider signaling games in which criterion. If firms believe that the devia- there is more than one uninformed agent. Having ^ only a single agent changes the outcome, but not tion to z is by a high-quality consultant, the method of analysis. they will bid his wage up to w = V2(^z). Riley: Silver Signals 445

This is strictly preferable for a high- offered? Let the resulting contract quality consultant, but strictly worse for be X^ =(^z,w^). a low-quality consultant. Thus, the be- (2) Would any consultant of type t ∈ S be lief that it is a high-quality consultant is strictly better off with the contract X^ sustained. than with his Nash equilibrium Similar arguments establish that there contract? can be no pooling equilibrium when the (3) Is it also the case that no other type intuitive criterion is applied. Thus the would be better off switching to unique Nash equilibrium pair of con- contract X^ ? tracts, which also satisfies the intuitive ∗ ∗ criterion, is the pair X1 and X2. If the answer to both (2) and (3) is yes, The intuitive criterion has dominated Grossman and Perry (G-P) argue that a the literature in the years since its in- consultant whose type is in S indeed has troduction. From the perspective of ap- an incentive to deviate. Of course, if the plied research, it is easy to understand subset S is a singleton, the G-P criterion why. Gone are the problems of non- reduces to the intuitive criterion. existence that make applied theorists In figure 6, let the subset S be both uneasy about the Rothschild-Stiglitz types. As long as the probability of a game. Gone also is the continuum of se- high type is sufficiently high, there is a quential Nash equilibria. Instead, given shaded region of profitable responses the single-crossing property, the theory which are strictly preferred by both yields a well-specified prediction of full types. Thus the unique Cho-Kreps separation of types. Unfortunately, the equilibrium fails the G-P criterion. It theory is not as tidy as it might appear. follows that there is no equilibrium Consider figure 6. Applying the intui- satisfying the G-P criterion. Indeed, an tive criterion yields the unique separat- equilibrium of the signaling game fails ∗ ∗ ing equilibrium contracts X1 and X2. to exist in precisely those situations Suppose the consultant deviates and where there is no equilibrium of the chooses education level ^z . Suppose also Rothschild-Stiglitz screening game. that there is only a very small prob- Myviewonallofthisisthatitisvery ability that the consultant is of__ low hard to make a case in favor of the Cho- quality. Then the heavy curve w = V(z) Kreps criterion without also providing representing the average productivity support for the more stringent G-P across the two quality levels is ex- criterion. Since I find the intuitive cri- tremely close to the high-quality zero terion persuasive, I am unable to reject profit curve w = V2(z). How will firms the G-P criterion. I am therefore forced respond to such a deviation? Sanford to conclude that there will not always Grossman and Motty Perry (1986) ar- be a credible equilibrium. This should gueasfollows.LetT be the set of all not be too surprising. In traditional types (here T = {1,2})andletS be some equilibrium theory, problems for equi- subset of T. In the spirit of the intuitive librium often occur whenever there are criterion, the following questions need externalities. Here it is the preferences to be asked. of the low-quality types which constrain the profitable alternatives of higher (1) If all the uninformed firms believe it quality types. The more similar are the is a type from S who chose ^z ,and preferences of the two types, the update their beliefs using Bayes greater the negative informational ex- Rule, what will be the highest wage ternality. As we have already seen, it 446 Journal of Economic Literature, Vol. XXXIX (June 2001) is possible to characterize conditions w(zs(t)) = V(t) (3) under which there exists a separating To close the model we need to determine equilibrium under the more stringent the signal chosen by the lowest type. G-P criterion. The critical requirement But, we can argue exactly as with two is that the rate at which the marginal types, that the only feasible education cost of signaling declines with quality level for type α is the full-information must be sufficiently high. efficient level zs(α). We now establish that the separating 3 Further Theoretical Developments wage function w(z) satisfying these conditions is not a Nash equilibrium.14 3.1 Screening with Many Types Choose w^ so that type t is indifferent s One of the limitations of the basic model between his separating contract (z (t), s ( s(α) ^) is the assumption that there are only w(z (t)) and z ,w .Thatis, two types. It is natural to ask whether ( s(α) ^)≡^ − ( s(α)) U t,z ,w w C t,z (4) the difficulties are compounded as the = w(zs(t)) − C(t,zs(t)). number of types increases. To illustrate the issues involved, we focus on a sim- Given the single crossing property, such a wage offer is strictly preferred__ by all ple labor market example in which ( ) there is a continuum of types. Consider typeslessthant. Let V t be the ex- the R-S screening game. Suppose that pected marginal product of types less productivity of type t is V(t), that is, the than t. Substituting from equation (4), the expected profitability of this offer is signal has no direct effect on produc- __ __ tivity. Suppose also that types are con- − Π(t)=V(t)−w^ = V(t)−w(zs(t)) tinuously distributed with support [α,β]. + C(t,zs(t)−C(t,zs(α)). Thecostofaneducationlevelz is C(t,z), where the marginal cost of Differentiating by t and collecting terms, __ education is a decreasing function of −  ∂  dzs Π′( )= ′( )− ′( s( )) − ( s( )) type. t V t w z t C t,z t   ∂z  dt As in the two-type case, it is not diffi-  ∂ ∂  cult to characterize the equilibrium +  C(t,zs(t)) − C(t,zs(α)) . (assuming it exists.) First, arguing as in ∂t ∂t  the two-type case, there can be no From the first order condition, (2), the equilibrium pooling. We then seek a first bracketed expression is zero. In separating equilibrium. Given a wage func- the limit, as t approaches α, the second tion w(z), type t chooses his education s bracketed expression is zero. Thus, level z (t) to maximize his payoff − __ ( )= ( )− ( ) Π′(α) = V′(α) > 0. U t,z,w w z C t,z . (1) − Π(α) = For complete separation, zs(t) is strictly Since 0, it follows that at the s α increasing and satisfies the first order education level z ( ), any wage which α condition, exceeds V( ) and is sufficiently close ∂ generates positive expected profits. ′( s( )) − ( s( )) = (2) This general nonexistence result is, at w z t ∂ C t,z t 0. z first sight, devastating to the theory. In equilibrium, the marginal profit on each type is zero. Thus, the wage that 14 The argument below does not seem to have appeared in print. The result was discussed, how- type t chooses must be equal to his mar- ever, in unpublished drafts of Riley (1975) and ginal product; that is, Rothschild and Stiglitz (1976). Riley: Silver Signals 447

However, the result hinges on the as- rium if, for any additional offer X (or sumption that all types would enter the set of offers) that is strictly profitable, industry under full information. Sup- when the full set of offers is W ∪ X,the pose instead that there is an equilib- new offer loses money when unprofit- rium threshold for the types who able offers in W are dropped. Wilson choose to signal. For example, suppose proved a general existence result and that each worker has a reservation wage showed that, whenever there is no Nash wR (an opportunity in some different in- separating equilibrium, the Wilson dustry). If this wage wR = V(γ) > V(α), equilibrium (i) has fewer offers than there is an interval of types [α,γ]who types so there is some pooling and (ii) are better off in the other industry. Pareto dominates any fully separating (Remember that, in a separating equi- set of zero-profit contracts. librium, each type is paid his marginal A similar argument along these lines product.) Then the lowest wage among produces a quite different result. In a those who choose to signal is V(γ). It reactive equilibrium, firms react by follows that raising the wage at zs(α)at- adding new profitable contracts rather tracts all those who would otherwise ac- than dropping old ones. Starting from a cept the reservation wage. If this pool is separating set of zero-profit contracts, sufficiently large, the offer loses money. any additional offer, X, involves pooling Thus far I have focused on the criti- of different types. But, if the pool is cal problem at the lower endpoint of profitable, profits on the best in the the wage distribution. As long as this pool are even more profitable. As Riley problem can be dealt with satisfactorily, (1979) showed, there are always screen- it is possible to derive sufficient condi- ing reactions that skim the cream and tions for existence for a fairly general result in losses for the offer X.Asetof version of the basic Spencian model, offers, R, is a reactive equilibrium, if, with a continuum of types (Riley 1979b, for any additional offer X that is profit- 1985). The key insight is that there ex- able, that contract loses money when ists a Nash equilibrium, as long as the rate firms add profitable “reactive” offers. It at which the marginal cost of signaling turns out that the Pareto dominating set declines with type is sufficiently high. of separating zero-profit contracts is the Moreover, this equilibrium is unique unique reactive equilibrium. and completely separates the different Rather than weaken the equilibrium types. concept, Martin Hellwig (1987) changes the rules of the game. He shows that 3.2 Alternative Equilibrium Concepts the Wilson equilibrium is a Nash Equi- Given the nonexistence results for librium of a game in which the unin- the simple static model, Charles Wilson formed have two rounds of play. In the (1977) began the exploration for sta- first round each uninformed agent offers tionary points of a dynamic adjustment as many contracts as he wishes. The full process. He noted that if new profitable set of contracts is then made public. In offers lead to losses for other offers, the the second round each uninformed agent latter might be quickly withdrawn. then has an opportunity to withdraw as Based on this idea, he then weakened the many of his first round offers as he Nash Equilibrium concept by requiring wishes. The informed agents then select that any new offer remain profitable af- from the set of contracts remaining after the withdrawal of loss-making offers. ter the second round. At least for the A set of contracts W is a Wilson equilib- two-type case, it is easy to see that the 448 Journal of Economic Literature, Vol. XXXIX (June 2001)

w 2, it is always possible to skim the wage W cream with an additional offer. This U1(X) = U1(X ) leaves the bad workers choosing X and so the defecting firm ends up with V2 losses. One difficulty with modifying the rules of the game in this way is that it is W X U2(X) = U2(X ) hard to know when to stop. A third pos- sibility would be to allow firms to either V add or drop offers in the second round. XW I conjecture that both the Wilson and reactive equilibria are Nash equilibrium V 1 of this new game. z More fundamentally, telling a story education about a hypothetical adjustment process Figure 8. Wilson Equilibrium to justify a static equilibrium is a poor substitute for a formal dynamic model. Spence, in his early work, suggested that Wilson equilibrium is a Nash equilib- if competition were sufficiently fierce, rium of this two-round game. Consider the outcome would most likely be some thecaseoftwofirms.Themarginal form of cycle. Recently, theorists have product of type 2 is V2 and the expected begun analyzing screening using simple marginal product of a worker_ drawn_ evolutionary dynamics. Building on the randomly from the population is V.We work of M. Kandoori, George Mailath, will argue that the Nash equilibrium of and Rafael Rob (1993) and Peyton this game is the Wilson pooling equilib- Young (1993), Georg Noldeke and rium XW. Suppose that firm A chooses the Larry Samuelson (1997) built a formal contract X^ in round 1 and round 2, evolutionary model for the two-type case. rather than XW. To be profitable, firm They show that if there is no Nash equi- 1’s offer must lie in the shaded region librium of the Rothschild-Stiglitz one- in figure 8. Since this leaves only type 1 shot game, the evolutionary dynamical accepting the offer XW,thelatterisun- system does not have a stationary point. profitable and so firm B’s best response Instead there is an equilibrium two- in round two is to drop its offer. Then period cycle that is stable in the face of all accept the remaining contract X^.But low-frequency perturbations. The high- XW is a zero-profit contract thus X^ must value types always choose the more yield losses. It follows that firm A is costly action zH while the low types W strictly better off choosing X . switch back and forth between zH and For the two-type case, it is easy to some less costly action zL. Suppose that see that the reactive equilibrium can in period t all workers choose zH.Then also be viewed as the equilibrium of a firms__ find that the average productivity multi-round game. The only difference is V(zH). Firms base their offers next is that players get an opportunity to period on this period’s observations__ and make additional offers in the second thus offer a wage wH(t + 1) = V(zH).This round, rather than drop offers. Let is sufficiently low that low-quality work- ( R R) X1 ,X2 be the reactive (separating) ers are better off choosing zL and re- equilibrium. Any profitable deviation X ceiving a wage wL(t + 1) = VL(zL).The must pool the two types. Then, in round productivity of workers choosing zH Riley: Silver Signals 449 then rises to VH(zH). Firms observing equilibrium in which__ they are all this outcome then offer a wage treated alike. Let V234 be the expected wH(t + 2)= VH(zH) and the cycle begins productivity of a consultant of types 2, again. While this seems to be a poten- 3, and 4. Since the conditional prob- tially promising research program, much ability is high that he__ is type 2 rather work remains to be done. In particular, then types 3 or 4, V2 − V234 is small. it will be important to understand the Consider the pair of contracts ∗ ∗ conditions under which equilibria can (X1,X234) in figure 9. Since X1 is a best be readily characterized with more than response for type 1 and X234 is a best two types. Moreover, surely the simple response for the other types, both con- ∗ adaptive expectations model is too tracts just break even. Thus (X1,X234) is a naive. Presumably firms would begin to Nash equilibrium. understand the cycle and thus make Suppose that the consultant chooses wage offers based on the expectation of the out-of-equilibrium signal ^z .Asde- a continuing cycle. picted, even if firms were to pay the high marginal product (the contract X^ 3.3 Signaling in figure 9) type 1 would be worse off ∗ With the informed agents moving choosing ^z rather than z1. Thus by the first, we have seen that there is a con- intuitive criterion, only types 2, 3, and 4 tinuum of Nash signaling equilibria. could possibly gain. However, the crite- For equilibrium theory, the central rion is silent as to what restrictions question is whether it is possible to should be placed on beliefs about the place sensible restrictions on beliefs likelihood that it is a type 2 consultant that then support a much smaller set of rather than a type 3 or type 4.15 equilibria. As noted in section 2, it is The “properness” criterion proposed typical to appeal to the Cho-Kreps in- by Roger Myerson (1978) focuses on tuitive criterion. Unfortunately, while this the relative advantage to doing so. In a criterion successfully selects a unique proper equilibrium almost all the equilibrium in the basic signaling weight is placed on the type who gains model, it needs to be strengthened to the most from the defection. Since type have any bite when the assumptions of 4 has a larger marginal cost than types 2 the model are relaxed only slightly. and 3, properness assigns almost all the Consider the simple consulting exam- weight to type 4. Given such beliefs, it ple. As in the basic two-type model, follows that firms would offer a wage too each type has a marginal product that is low to be attractive to any type. Then high or low. A type 1 consultant has a the Nash equilibrium is proper. Indeed low marginal product and a high cost of any separating Nash equilibrium is signaling, while a type 2 consultant has proper. a high marginal product and a low mar- Rather than look directly at payoffs, ginal cost of signaling. There is also a Jeffrey Banks and Joel Sobel (1987) small probability that the consultant is compare the sets of responses that of type 3 or type 4. Type 3 has a mar- would make the worker better off. If ginal cost of signaling slightly lower the set for type 4 is strictly larger than than type 2 and type 4 has a marginal for type 2, Banks and Sobel require that cost of signaling slightly higher than the revised probability that the worker type 2. Both have a low marginal product. Since types 2, 3, and 4 have very 15 An almost identical argument holds for signals similar signaling costs, we look for an greater than z234. 450 Journal of Economic Literature, Vol. XXXIX (June 2001)

w wage ∗ U4(X) = U4(X234) U1(X) = U1(X1)

U2(X) = U2(X234)

V2 X U3(X) = U3(X234)

∗ X234 w2 = V234 X234

w1 = V1 ∗ X1

z O ∗ ∗ z1 z234 z z234 signal Figure 9. Continuum of Equilibria is type 4 rather than type 2 should not that the players can choose either to fall below the prior probability. In this play the game in round 1 or choose not example, all wages above w^4 make type to play and then play the game in round 4 better off and all wages above 2. This modified game is depicted below. w^2 make type 2 better off. Thus the Let the game in the box be the sim- probability placed on type 4 must rise. ple consulting example with the four In particular, the Banks-Sobel criterion different types (whose preferences are does not rule out the belief that it is as depicted in figure 9.) Suppose that ∗ highly likely that the defector is type 4. the Nash equilibrium (X1,X234) is played With such a belief, the response is a low in the upper box in figure 10. Consider wage offer. Thus, just as with properness, a type who chooses “Don’tPlay” in there is a continuum of Banks-Sobel (or round 1 and then the signal ^z .Sincethe “Divine”) equilibria. high marginal product is V2,themost Elon Kohlberg and Jean-Francois that any firm will offer in response is a ^ Mehrtens (1986) propose to restrict the wage w^ = V2.ThisisthecontractX in set of Nash equilibria to those that are figure 9. As depicted, type 1 strictly equilibria of the entire family of games prefers his Nash equilibrium payoff to that have the same normal form as the this contract. That is, his Nash equilib- original game. In particular, suppose rium payoff strictly dominates (“Don’t Riley: Silver Signals 451

lem. To me, the simplest way out of the Play maze is to employ the stronger Gross- game Game man-Perry approach and then seek conditions that are sufficient to ensure ex- 16 consultant istence. If there is an equilibrium that satisfies the stronger criterion, it is Don’t Play the Pareto dominating separating equi- play consultant Game librium. As I have emphasized, the critical requirement is that, for the signals chosen in this Nash equilibrium, Figure 10. Modified Game with Identical Normal the marginal cost of signaling should Form decline sufficiently rapidly with type.

4. Industrial Organization Play,” ^z . The firm then infers that the signaler is type 2, 3, or 4. However, as There has been a remarkably rich set with the other qualitative criteria, stabil- of applications of signaling in the indus- ity places no restriction on the condi- trial organization field. In many cases, tional probability that the signal ^z was papers are not simply straightforward sent by type 2. In particular, we are applications, but have advanced the free to assign a very low conditional theory significantly. The earliest litera- probability. Given such beliefs, each ture focuses on the role of advertising firm responds with a wage offer too low as a signal of product quality. Phillip to be preferred by any of the types. Nelson (1974) contrasts advertising of Then all consultant types are worse off goods that must be consumed before choosing the out-of-equilibrium signal they can be fully appreciated with goods ^z . It follows that the Nash equilibrium that can be evaluated in the shop. He is stable. Indeed all the Nash equilibria concludes that advertising of “experi- that separate type 1 from the other ence goods” is much more focussed on three types are “stable.” attracting attention to the brand than Suppose instead that Bayes’ Rule is providing information about product used to update beliefs. Then, in re- quality. While he did not attempt a formal sponse to the deviation to ^z ,thewage model, he argues that high advertising offered to types 2, 3, and 4 will be bid expenditures on brands are seen by up__ to their expected marginal product consumers as a signal of product quality. V .Ifthisisthecase,types2–4 indeed 234 Benjamin Klein and Keith Leffler have an incentive to deviate. As in the (1981) and Paul Milgrom and John two-type case, only the Pareto dominat- Roberts (1986) build closely related ing equilibrium that separates out type models of repeat purchasing that yield 1 survives. Nelson’s conjectures. To illustrate the Of course, as illustrated in section 2, we know that such Grossman-Perry up- 16 For a contrary view see Mailath, Masahiro dating of beliefs can lead to nonexis- Okuno-Fujiwara, and Andrew Postlewaite (1993), who argue that if an out-of-equilibrium action is tence. The example makes clear how observed, the revised beliefs should be fully difficult it is to find a refinement of consistent with some other equilibrium. Positive Nash equilibrium that has enough bite probability is assigned only to those types who are better off in the alternative equilibrium. The to rule out a continuum of equilibria, Pareto dominant Nash signaling equilibrium is without also creating an existence prob- then the unique “undefeated” equilibrium. 452 Journal of Economic Literature, Vol. XXXIX (June 2001) central issues, we will consider a tomers by mimicking in period 1. That stripped-down version of the Milgrom- is, it can also choose A and the intro- Roberts model. Suppose there are two ductory price pH(q). If it does, it has a quality levels, high and low. In a world present value of of full information, the firm would sell ( )=Π ( )− + 1Π ( ) to one group of customers when it had a UM q,qL,A M q A L qL r high-quality product (at a high price) 1 (5) and another group when its product was =ΠH(q)+(cH − cL)q − A + ΠL(qL). of low quality. Each potential customer r buys at most one unit per period. Thus, The low-quality firm thus prefers to in the high-end market, with demand mimic if, for some (q,A),UM(q,qL,A) ≥ UL. price function pH(q), the quantity q is Assuming diminishing marginal revenue, the number of high-end customers. this region must be as depicted in figure Similarly in the low-end market, if the 11. Also depicted is an indifference ^ price is set at pL(q), the quantity q is the curve UH(q,A)=UH for some high-quality number of low-end customers. Suppose firm. Since the present value of the firm that in period one, buyers do not know is linear in A, all the high-quality indif- quality. However, if advertising is suffi- ference curves are vertically parallel with ciently intensive, then they will infer turning points at the profit maximizing ∗ that quality is high. After period one, output level qH. Moreover, from (5), as information on advertising is forgotten, long as the lower-quality firm has lower ∗ − but all those who have purchased know costs, it must be the case that qH < q.It product quality. Thus, if and only if follows from the figure that the profit- quality is indeed high, the firm will maximizing separating point is (qs,As).17 maintain its high-end customer base. As Note that the signaling quantity is set a result, there is a payoff to signaling in lower than the monopoly output under the short- and long-run for a firm with a full information. Thus, the introductory price high-quality product. A low-quality pro- set by the monopoly with a high-quality ducer makes a short-run killing if he product is above the full-information mimics but must lower his price on all monopoly price. repeatsalesafterperiodone,when This argument is extended by Birger quality is known. Wernerfelt (1988), who argues that Let r be the interest rate and assume firms may often be able to signal quality an infinite horizon. If the firm is be- more cheaply by building a reputation lieved to be selling a low-quality prod- for a range of products all benefiting uct, the present value of its profit from the “umbrella” reputation of the stream is the first-period profit plus the firm itself. That is, instead of advertis- discounted future stream of profits ing product by product, there are U ( )=Π (q ) + 1Π (q ) L qL L L r L L ,whereqL is economies of scale in branding a group chosen to maximize profit RL(q)–cLq. of products as all belonging to the same If the high-quality firm chooses price part of the quality spectrum. pH(q) and advertising expenditures A, All these models focus on the oppor- which is high enough to signal high tunity for signaling by a single firm in quality, the present value of its profit order to exploit its monopoly power U ( A)= Π (q)−A + 1Π (q)= stream is H q, H r H 1 + r 17 ΠH(q) − A. Given beliefs about the All points outside the shaded region, which r generate a non-negative payoff, are Nash signaling signal conveyed by the advertising, a low- equilibria. Applying the standard refinements quality firm can fool high-quality cus- yields the unique equilibrium S. Riley: Silver Signals 453

advertising

S AS UM(q, qL A) = UL (qL)

UH(q, A) = UH

q S ∗ q qH q output of high quality firm

Figure 11. Advertising as a Signal of Product Quality under imperfect information. Richard revenue is decreasing so that the profit Kihlstrom and Michael Riordan (1984) function is strictly concave with a single ∗ show that if firms are price takers, turning point at qt . Then maximized ∗ ∗ ∗ there can be no such equilibrium with profit is Πt = pt(qt )(qt − ct).Ifalow-cost advertising. Firms get zero profits if firm can trick all consumers into believ- they are separated, thus it is always ad- ing it is selling a high-quality product, it vantageous for a low-quality firm to faces a demand price pH(q) and thus has mimic over the initial “experience” period. aprofitof A closely related line of research ex- Πm(q)=p (q)(q − c ) plores conditions under which a high L H L (6) introductory price can alone be a signal = ΠH(q) + (cH − cL)q. of product quality. For this to be the case, there must be some heterogeneity Suppose next that a fraction f of the con- in the ability of consumers to distin- sumers are informed and so do not pur- guish quality prior to purchase. Kyle chase when a low-quality firm mimics Bagwell and Riordan (1991) assume the high-quality firm by announcing an that some consumers have full informa- introductory price p(q).Theprofitofthe tion while others know only the prior mimicking firm is then reduced to ( − )Πm( ) (exogenous) distribution of product 1 f L q . Now it pays to mimic if and quality. Let pH(q) be the demand price only if function when it is believed that quality Π∗ > Πm( )> L (7) is high. Let cL and cH cL be the unit L q − . costs of a low- and high-quality firm. 1 f Then the profit of a firm of quality level Since the unit cost of production is lower m t is Πt(q)=pt(q)(q − ct),t = L,H. We as- for the mimicking firm, Π (q) has a L ∗ m sume that, for each type, marginal unique turning point at q > qH.It 454 Journal of Economic Literature, Vol. XXXIX (June 2001) ∏

Profit

VH(z) – CH (z)

∏ m L = VH (z) – CL (z)

∏ ∗ L VL (z) – CL (z)

z ∗ ∗ S zL zH zH Warranty Figure 12. Warranty as a Signal follows that there is a unique pair of are assumed to be risk neutral, thus an quantities q′ and q′′,whereq′ q′,theleastcostly Let Vt(z) t ∈ {L,H} be the expected value separating price is either q′ or q′′.But of the product to consumers if the Πm( ′) = Πm( ′′) ( ) L q L q . It follows immediately warranty level is z. Let Ct z be the ex- from (6) that ΠH(q′) > ΠH(q′′).Hencethe pected unit cost of producing the good least costly means of avoiding mimick- and providing such a warranty. The ex- ing is for the high-quality firm to pected payoff to a consumer if the choose the quantity q′. That is, it sets an monopolist charges a price P is then ∗ introductory price p(q′) > p(qH). Ut(z,P) = Vt(z) – P. With complete in- Another line of research explores the formation about the firm’stype,the role of warranties as signals of product monopoly solution is depicted in figure quality. The earliest papers by Spence 12. The firm extracts all of the surplus (1977a) and Grossman (1981) use many so that the profit Πt(z) = Vt(z) – Ct(z)is ∗ of the ideas from the signaling literature maximizedbysettingawarrantylevelzt ∗ ∗ but are really risk-spreading stories. In and price Pt = Vt(zt ). But if buyers do each case firms sell items of uncertain not observe quality, a low-quality firm quality to risk-averse individuals. Firms can mimic and charge a price P = VH(z). Riley: Silver Signals 455

The profit of the low-quality firm is then challenge to the theory, it should be Πm( )= ( )− ( ) Πm( ∗ ) L z VH z CL z .Inthefigure, L zL noted that neither directly address the exceeds the full information profit, point of the theoretical papers which is so mimicking is profitable. The high- primarily that firms will seek to signal quality firm then must increase its war- quality when introducing new experience s ranty level to zH in order to eliminate goods. the incentive to mimic. Joshua Wiener (1985) uses Consumer Nancy Lutz (1989) provides an alter- Reports data on automobiles to see native description of signaling in a whether higher priced cars have better Spence/Grossman insurance model of warranties. He finds that indeed there warranties. Consumers exhibit moral is a strong positive correlation, lending hazard in taking care of the product, support to the idea that warranties do thus insurance coverage is only partial. signal quality. Finally, Daniel Ackerberg As in the model above, the costs of pro- (1996) presents structural and reduced- viding this partial coverage are higher form estimates of a dynamic learning for a low-quality firm, thus the extent of model. One of the central questions he the warranty is again a potential signal. asks is whether the effect of advertising Despite the plethora of theories argu- a new product primarily signals quality ing that introductory prices, advertis- (a “persuasive” effect) or primarily pro- ing, and warranties can signal high qual- vides information about the product. ity, there is remarkably little applied For the particular product studied (the work seeking empirical support. More- introduction of a new yogurt) he is over, the papers that do attempt to look unable to find a significant persuasive at the data draw mixed conclusions. effect. This paper is a valuable first step Gerstner (1985) examines the relation- in what seems to be a field ripe for de- ship between price and quality using tailed empirical investigation, especially data from the Consumers Union Buying as firms begin to seek ways to exploit Guide. Using the Guide’s quality rank- the vast amounts of sales data stored ing as a proxy for quality, Gerstner finds electronically. only weak support for the hypothesis 4.1 Limit Pricing that higher quality is correlated with higher price. C. Hjorth-Andersen (1991) Another area in which signaling mod- extends this analysis by introducing a els have been central is in the analysis vector of quality indicators and leaving of entry. Consider the case of a monop- the data to speak for itself on the nature olist who faces a potential entrant. One of the overall connection between these important source of informational asym- indicators and product price. His test is metry is that each firm is likely to be whether there is a positive relationship uncertain about the unit cost of its between the different quality rankings. potential competitor. Given this infor- Using both Consumer Reports data and mational asymmetry, might an incum- Danish data, he again concludes that bent profitably deter entry by setting a there is at best only a weak link be- “limit price” rather than the monopoly tween quality and price. He also consid- price prior to entry? As Milgrom and ers Wernerfelt’s argument about um- Roberts (1982) showed, this may indeed brella branding and finds only a very weak be the case. To illustrate the issues, correlation of quality indicators across consider a simple two-period model. In different products produced by the the first period, the incumbent with same firm. While these results are a unit cost c1 is the only firm in the 456 Journal of Economic Literature, Vol. XXXIX (June 2001) market. The entrant, with unit cost cE, crossing property holds. Therefore “limit observes the first-period price and then pricing” can signal an incumbent’s makes an irrevocable decision whether toughness. or not to enter. In period 2, if there is One of the points emphasized by Mil- entry, the resulting competition yields a grom and Roberts is that in a separating duopoly profit to the incumbent of equilibrium the types of firms that do Π1(c1,cE). In the absence of entry, the enter are exactly those that would enter incumbent sets the monopoly price in if the entrant could directly observe the ∗ period 2 and his profit is Π (c1). In the incumbent’s type. Thus, limit pricing first period his profit is q(p)(p – c1). does not discourage entry relative to a Suppose that the entrant’scostisc or world of full information. Instead, limit less with probability FE(c). If all en- pricing is a mechanism the incumbent trants with costs higher than c are suc- uses to discourage entry of those firms cessfully discouraged from entering, the that would otherwise enter because of incumbent’sprofitis asymmetric information. ∗ One assumption of the Milgrom- U(p,y,c1)=q(p)(p − c1)+(1 − FE(z))Π (c1) c Roberts model is that the cost of the potential entrant is uncorrelated with + ∫Π1(c1,cE)dFE(cE). 0 the cost of the incumbent. Joseph Har- rington (1986) extends the analysis to The question is whether the incumbent the case of correlated costs. Suppose encourages more firms to stay out by that only after he enters will the entrant setting a lower “limit price” in the first know his cost with certainty. If costs are period.Formally,isitpossibletocharac- positively correlated, information about terize a mapping cs(p), from the incum- the incumbent’s cost will affect the en- bent’s price to the cost of the marginal try decision. The incumbent thus has an entrant, such that the lower the equilib- incentive to signal that his cost is high rium price, the lower is the cost of the and thereby discourage entry. Har- marginal entrant? If this is the case, in- rington shows that if costs are suffi- cumbents will be separated. Thus, the ciently highly correlated, the optimal critical entrant has a cost c, satisfying strategy of the firm is to choose a price Π (c ,c) = 0. The pairs (c,z) satisfying E 1 higher than the monopoly price, this condition are depicted in the left thereby signaling that his cost is high. half of figure 13. Whether or not types In a further follow-up paper, Bagwell are separated hinges on whether an in- and Garey Ramey (1988) consider the cumbent with a higher cost has a steeper further implications if advertising has a indifference map. That is, for a separat- direct effect on demand. They show ing equilibrium, we require that the that it is efficient for the incumbent to single-crossing property be satisfied. combine the limit pricing strategy with Mathematically we require that asecondsignal—advertising beyond the ∂U1 level that would prevail in the absence dc ∂p of the informational symmetry. __ =− dp ∂ Roberts (1986) offers a model very U1 U1 ∂ similar in spirit to explain the “preda- c tory pricing” of an incumbent firm. The increases with the incumbent’scost. informational structure of the model is While this is not automatically satisfied, the same. Here, though, the entrant it is easy to find cases where the single- moves first, choosing whether to enter. Riley: Silver Signals 457

cI cost of marginal entrant ∏ E (cI, c) = 0 cs (p)

UI (p, cI, cE) = UI

cI p incumbent’s cost price set by incumbent Figure 13. Limit Price Signaling

If it does, the incumbent and entrant be the strategies of the incumbent and competeforoneperiod.Theentrant entrant. In the first period, the entrant must decide whether to continue or to observes its profit and then uses its own withdraw and leave the market to the profit ΠE(s1,sE) to make an inference ^ incumbent in period 2. Again it is not about its total cost C = C(ΠE(s1,sE),sE). too difficult to build a model in which Since the incumbent’s strategy is not the opportunity cost of flooding the observable, his strategy has a direct ef- market in the first period (and driving fect on his own profit and an informa- price down) is lower for a tougher in- tional effect on his opponent’s inference. cumbent. Thus, the resulting period 1 This gives the incumbent an incentive price is a signal of the incumbent’s to lower price. Note that the entrant is toughness.18 not fooled since he can infer the incum- Drew Fudenberg and Jean Tirole bent’s equilibrium strategy. It is simply (1986) offer an alternative explanation the non-observability of the strategy of predation by an incumbent firm. In that increases the incentive to lower price. their model, the entrant is uncertain Of course, to the extent that the entrant about how costly it will be to operate in is uncertain about the incumbent’scost, the market. It also does not observe the this “signal-jamming” effect and the choice of the incumbent.19 Let s1 and sE signaling effect are reinforcing.20 LeBlanc (1992) has shown that by 18 If the incumbent faces an infinite sequence of potential entrants, fairly standard “folk theorem” adding slightly to the dynamic structure arguments show that there is an equilibrium in of these games, both limit pricing and which weaker incumbents mimic the strongest predatory pricing can emerge as equi- incumbent in responding to entry. As Milgrom and Roberts (1982) and Kreps and Wilson (1982b) librium signals. In the initial round the show, mimicking remains equilibrium behavior in the initial periods even if there is a long finite 20 Kirman and Masson (1986) consider the role horizon. of capacity signals as a deterrent of entry. In their 19 This could be the quantity sold or the secret paper the entrant is uncertain about the degree discount on the listed price offered to “loyal” to which the incumbent oligopolists operate as a customers. cartel and respond collusively. 458 Journal of Economic Literature, Vol. XXXIX (June 2001) limit pricing conveys strength. It is used ated product. In period 1 neither knows if the incumbent is very strong and the its opponent’s cost. Thus a naive choice prior belief is that this is very unlikely. would be to maximize first-period ex- However, if the prior belief is that the pected profit. If firm B’s strategy is to B( B) incumbent is likely to be strong and set a price p1 c , the naive best re- A( A) the entrant is likely to be weak, then sponse of firm A is to choose p1 c to A A B ~B the incumbent would prefer only to sig- solve Max E{Π1 (p1 ,p1 (c ),cA)}. However, the pA B nal his strength in the unlikely event first-period1 C decision will be used by that the entry actually takes place. In firm B to draw an inference about firm this situation, there is predatory pricing A’s actual cost. Assuming that the equi- rather than limit pricing. librium is monotonic, firm B can invert A A A B A B While I am not aware of a paper that and infer that c = c (p1 ).Letp2 (c ,c ) formally models the capacity decision of be firm B’s equilibrium price in pe- the entrant as a signal of strength (low riod 2, given full information. Then if unit cost), it is intuitively clear that such firm A chooses a first-period price of A A A B ~B A a model could be easily developed along p1 , its total profit is E{Π1 (p1 ,p1 (c ),c )+ cB A A B A A ~B A the lines of the limit pricing model. Π2 (p2 ,p2 (c (p1 ),c ),c )}. Since the choice While the timing is different, such a of firm A’s first-period price signals its model would seem to flow naturally from unit cost, there is an informational ef- the earlier work on equilibrium conjec- fect that the firm must take into ac- tures by potential entrants. Building such count in order to maximize profit. In a model would be useful as a part of an standard differentiated duopoly models, evaluation of the relative efficiency of firm B responds to a higher cost by rais- different methods of signaling strength. ing its price, recognizing that firm A One paper, which does focus on will also price higher. Thus firm A has capacity signals, provides a rare analysis an incentive to push up its first-period of entry when the incumbents are mem- price, which induces a higher second- bers of an oligopoly rather then a mo- period price for firm B. In equilibrium, nopoly. (This is another area crying out neitherfirmisfooled.However,thein- for further study.) William Kirman and centive that results from information being Robert Masson (1986) consider a model signaled leads to higher first-period in which the entrant is uncertain about prices.21 the degree to which the incumbent oli- Finally, two papers consider the en- gopolists operate as a cartel and then dogenous timing of decisions. Mailath respond collusively. In the model the (1993) considers a Cournot game in weak oligopoly responds with a round of which the firm with less information competitive price cuts. Such behavior about demand moves in period 2. The discourages entry. Thus the collusive better-informed firm can choose period oligopoly has an interest in mimicking 1orperiod3.Ifitleads,thenitschoice the weak oligopoly. This it can do by signals its information to its opponent. adding enough capacity to simulate the Despite this, at least in the model con- weak oligopoly outcome. sidered, the unique equilibrium satisfy- Mailath (1989) does consider simulta- ing plausible refinements has the in- neous signaling among oligopolists. His formed firm moving first. Andrew focus is not on deterrence per se, but Daughety and Jennifer Reinganum on the effects of each firm drawing 21 As Mailath notes, there are existence and inferences about its opponents’ costs. uniqueness issues that are non-trivial in oligopoly Consider two firms selling a differenti- models. Riley: Silver Signals 459

(1994) take this a step further and allow (other firms) use this as a signal of in- firms to choose whether to acquire information learned on the job by the cur- formation. In equilibrium, a firm knows rent employer. The third group of papers whether its opponent is informed and looks at labor-management contract thus how much information is conveyed issues. by its future decisions. An agent must 5.1 Educational Screening then decide whether and when to seek information, knowing that this choice Both the human capital model and will influence the nature of the signal- the screening model imply that earnings inggame.Thegameitselfistherefore should increase with education. Thus determined endogenously. As in standard simply estimating an earnings function signaling models, the intuitive criterion is not likely to shed much light on the is employed to obtain a unique separat- screeningroleofeducation.Letz be an ing equilibrium in each possible realiza- individual’s educational achievement. tion of the information acquisition game. Let θ be an unobserved variable repre- In the duopoly production game ana- senting the individual’s ability. Suppose lyzed in the paper, the two players are an individual of type θ and education ex ante identical. For certain parameter level z has a marginal product of values, however, the information acqui- v = V(θ,z)+ε,whereε is a realization of ~ sition phase of the game has only asym- the independent random variable ε metric equilibria. Thus, asymmetry is which has a zero mean. The cost of endogenously induced and a signaling achieving education level z is C(θ,z). In game is then played out. The players also the human capital story, informational choose whether to act simultaneously or problems are of second order. A type θ sequentially (leader-follower.) individual chooses z∗(θ) to maximize his The model is illustrative rather than net payoff U(θ,z,w) = w – C(θ,z), where conclusive. However, issues of timing w = V(θ,z) +ε. Under weak assump- are important, and making them a part tions, the choice z∗(θ) is monotonic. In- of the solution rather than imposing verting this, we may write θ=θ∗(z). He timing assumptions is another fruitful then earns a wage of w = V(θ∗(z),z)+ε. avenue for further research. The observed distribution of wages is thus ~ w~(z)=V(θ∗(z),z)+ε. (8) 5. Labor As discussed in section 2, firms that As in industrial organization, the ba- do not observe marginal product (in the sic theory has been used to explain a early years on the job) will pay a wage wide range of theoretical puzzles. How- based on educational credentials. A type θ individual solves Max{w(z)−C(θ,z)}.In ever, there is considerably more empha- z sis on empirical verification. Rather than a screening equilibrium, higher types attempt to cover everything, this section choose more education. Inverting, there focuses primarily on three areas which is a monotonic relationship between edu- θs have attracted considerable interest. The cation and the unobserved ability (z). first series of papers attempts to test Firms bid wages up to expected mar- Spence’s educational screening hy- ginal productivity so that the expected pothesis against the traditional human wage is s( )= (θs( ) )+ε~ = (θs( ) ) capital explanation of educational choice. w z E{V z ,z } V z ,z . (9) The second group examines the impli- Early empirical work (e.g., Paul cations for promotion when outsiders Taubman and Terence Wales 1973) was 460 Journal of Economic Literature, Vol. XXXIX (June 2001) hampered by the absence of an equilib- is lower than that of a representative in- rium model of screening. Since dividual from the class. When income is Spence’s papers, much of the empirical regressed against years of college edu- work starts with the assumption that cation plus a “sheepskin” dummy, the screening is more important in some latter picks up the difference in the rate sectors than in others. Richard Layard and of capital accumulation among drop- George Psacharopoulos (1974) compare outs and the rest of the class. There- earnings functions of students who fore, if data on dropouts are to be used achieve some educational credential as evidence, one necessary preliminary (say a bachelor of arts degree) with step is to provide a theory of why some those who do not. They argue that the students drop out. credential should have strong explana- Of all the empirical work that builds tory power only in a screening world. on the theory, the most creative is by For the data that they consider, there is Kevin Lang and David Crop (1986). To no such strong effect. While, on its illustrate their central point, consider face, this is evidence against educa- the following special case of the screen- tional screening, the data is far from ing model described above. The mar- ideal. The sample is a set of World War ginal product of a type θ individual who II veterans who were getting a deferred achieves an education level z is V(θ,z)= education in a booming job market. θz, while his cost of education is (θ )=1 2 θ Presumably many were “pulled” from C ,z 2z / . Suppose that every type education rather than dropped out. has the same outside opportunity to Thomas Hungerford and Gary Solon earn a wage r with no college educa- (1987) use Current Population Survey tion. With full information, type θ is (CPS) data to further test the “sheep- paid a wage equal to his marginal prod- skin effect.” They find a significant uct. He therefore chooses an education ∗ 1 z (θ) = argMax{θz − z2/θ . positive effect as implied by screening level z 2 } It is read- theory. John Heywood (1994) analyzes ily confirmed that z∗(θ) =θ2, and hence ∗(θ) = 1θ3 additional CPS data and again finds a that his net payoff is U 2 .Since significant sheepskin effect. However, all types can earn r in another industry, this effect is significant only in the private the lowest type, θo, who enters the in- non-union sector and not elsewhere. It dustry is just indifferent between doing ∗ 1 3 is far from clear that a screening story so and earning r. Thus U (θo)= θo = r 1 2 can be easily constructed to explain the and hence θo =(2r)3. It follows that the absence of screening in other sectors. minimum education level and wage is ( )=(( )2 ) A serious problem with these studies zo,wo 2r 3,2r . (10) is that they do not spell out which vari- For all higher types, the wage of type θ ant of the traditional human capital is w∗(θ) = V(θ,z∗(θ)) =θ3. Then, since model or screening model is to be z∗(θ) =θ2, the observed “wage function” tested. In the human capital model, the is productivity of a college graduate is a ∗( )= 3 ≥ ( ) function of what he has learned at col- w z z2, z zo r . (11) lege. This is positively related to his Next consider a screening equilib- grades and the quality of the college rium. From section 2 we know that the that he attends. Presumably, those who outcomeisexactlythesameforthelow- drop out do so because they find the est type who chooses a college educa- going tough and their grades are low. tion. That is, (zo,wo) satisfies condition Thus, the productivity of the dropouts (10). Given a wage function w(z), each Riley: Silver Signals 461 higher type chooses zs(θ)tosolve ability. Then a subset of types must be Max ( )−1 2 θ z {w z 2z / }. It is readily confirmed indifferent between working in the that the first-order condition is “screened” and “unscreened” sectors. w′(z)=z/θ. In equilibrium, each type has The only way this can occur is if, when a wage equal to his marginal product, holding ability constant, jobs in the un- thus w =θz. Combining these two con- screened sector involve less education. ditions yields the differential equation, In addition, holding education constant, w(z)w′(z)=z2, with end-point condition wages in the unscreened sector are (10). Direct integration and substitution higher. This observation is then used to yields the screening equilibrium wage separate jobs (as classified in the CPS function data) into an “unscreened” group with low education and above-average wages 2 2 3 1 2 w (z)= z + wo, z ≥ zo, z ≥ zo(r), and a second “screened” groupwithhigh 3 3 (12) where wo = 2r. education and below-average wages. The test of the screening hypothesis is The important thing to note is that whether there are other differences while a change in the outside opportu- between the two groups, which can be nity affects the minimum entry level, it predicted by screening theory. does not affect wages for higher types One crucial issue for potential testing in the full-information world. However, is how quickly firms begin to identify in the screening equilibrium, the entire true productivity and subsequently ad- wage function rises with an increase just wages to reflect this new informa- in the outside wage. The intuition is tion.Injobswherescreeningisimpor- relatively straightforward. With the im- tant, one would expect the earnings proved outside opportunity, the mini- function to explain wages very well mum type to enter college is greater early in the life cycle. In the extreme than before. Therefore, the necessity case, represented by the wage function for a type to signal that he is better than in equation (9), education and wage are all lower types in the market is reduced. perfectly correlated in the screened As a result, over-investment in educa- sector, whereas the correlation is tion falls and everyone is made better weaker in the unscreened sector (see off. This can only be achieved by a rise equation 8). in the equilibrium wage function. If, in addition, firms accumulate in- Effectively, the same argument ap- formation about true productivity over plies when the mandated minimum the early years in the work force, the educational credential is increased. explanatory power of education should Lang and Crop look at the effects of decline. Thus the ratio of unexplained changes in compulsory attendance laws. residuals for the screened group over They conclude that there is a significant that for the “unscreened” group should “ripple effect” as predicted by the rise over time. Riley observes such an screening model. effect. Another approach, which builds on Kenneth Wolpin (1981) also takes the the theory, begins with the observation two-sector approach using the NBER- that screening will be most important in Thorndike data first used by Taubman those sectors where productivity is rela- and Wales (1973) and then by Layard tively hard to measure. In Riley (1979a) and Pscharopoulos (1974). All the men the key assumption is that the different in this sample were given extensive sectors are not segregated according to ability tests. If these tests are unbiased 462 Journal of Economic Literature, Vol. XXXIX (June 2001) estimates of true ability, one can then tion about natural ability, there is no compare the education levels of the two reason for firms to wait until gradu- groups to see whether ability is lower ation. Firms can look instead at lower for dropouts. Wolpin finds only small division grades and recruit from the ability differences and therefore con- freshman class! However, once students cludes that the data provide little understand that the cost of signaling support for screening theory. However, is only the cost of getting high grades as already noted, traditional human for a couple of quarters, the signaling capital theory yields precisely the same equilibrium collapses.22 prediction. Noldeke and Eric van Damme (1990) Eric Friedland and Roger Little examine this informal argument in a (1981) use National Longitudinal Sur- simple two-type model. Their key inno- vey data to explore the difference be- vation is the assumption that the labor tween the self-employed and salaried market is open continuously. Suppose workers. At least in this sample, the one firm does start recruiting from the self-employed have higher average edu- freshman class. As they note, it is a best cational achievement and incomes than response of other firms to immediately salaried workers. The inference is that follow the leader. If this response is suf- this group is a high-ability group and ficiently rapid, there is no reason for a thus the tests that appeal to overlapping student to accept the first offer be- ability levels no longer apply. This sug- cause, by waiting a very short interval, gests that new theoretical predictions he will get a better offer. The “instanta- are necessary before the self-employed neous reaction” thus sustains the stan- can be used in tests for screening. dard equilibrium. Noldeke and van Finally, Wim Groot and Hessel Oos- Damme then consider a discrete time terbeek (1994) use Dutch longitudinal version of the model and show that data to see what happens to students there is a unique equilibrium. In the who either skip a year of school or are limit, as the time between offers gets held back and forced to repeat a year. smaller, the equilibrium approaches the Screening theory would surely expect “instantaneous reaction” equilibrium. the former to be a positive and the lat- The problem with such an argument ter a negative signal. Since these effects is that instantaneous responses greatly are not observed in the data, the reduce incentives to innovate. In real- authors conclude that this is strong evi- ity, much of the incentive for change dence against the screening hypothesis. comes from the inability of potential Ideally one would like wage data early competitors to react immediately. Thus, in the life cycle. However, in the data it seems to me that the Weiss critique examined, there is a thirty-year gap cannot be so easily overcome. What one between the early collection of school would really like is a model in which data and wage data. Thus the absence education is not simply a credential but of a significant effect may be simply also adds to human capital. A more due to overwhelming noise. Still, this complete model of the educational pro- does seem a fruitful avenue for further cess would surely also allow colleges to empirical investigation. choose how to bundle courses into con- One criticism of the educational centrations (degrees). In this case, much screening hypothesis is that if the main of the value of the education may lie in role of (say) graduating with a higher GPAfromUCLAistoconveyinforma- 22 See Andrew Weiss (1983). Riley: Silver Signals 463 such concentrations. Then dropping out Dan Bernhardt and David Scoones early might be very costly. (1993) extend this argument, noting that the current employer can discourage 5.2 Employment Status as a Signal the investment in information-gathering As workers gain experience on the by offering an especially outstanding job, their employers gather information worker a preemptive wage. The wage is about them. This information will typi- credible if it is sufficiently high to be cally be better than information avail- unprofitable unless offered only to those able to outsiders. The employer can very close to the top of the ability distri- therefore hold down wage increases and bution. As long as the support of these so earn rents from above-average qual- abilities is sufficiently small, it is not ity workers. However, if it becomes profitable for outsiders to incur the cost necessary to promote high-quality expe- of pre-auction information gathering. rienced workers into higher level jobs, the The authors find informal confirming promotion becomes a signal to outsiders. evidence in academic job markets, In the first paper to explore this is- where promotion to tenure is a strong sue, Michael Waldman (1984) assumes positive signal of quality. Even though that workers accumulate firm-specific many candidates fail to get tenure, ini- human capital on the job. With full in- tial salary increases of those achieving formation, an individual is switched tenure are typically in the modest to from job A to job B (“promoted”)ifhis moderate range. Salaries several years marginal product is higher in job B. after promotion are then determined by Consider a worker of type θ whose pro- the strength of the auction. Less com- ductivity is the same in the two jobs. monly, exceptional faculty are given large With full information, firms would be raises with tenure, thus discouraging indifferent as to whether or not to the opening of an auction.23 promote. With asymmetric information, A closely related paper by Milgrom outsiders bid up the wages of those and Sharon Oster (1987) contrasts the promoted to the average productivity of promotion of different skill levels when this group. Thus the type θ worker has part of the population is “visible” (abil- a productivity below the equilibrium ity is recognized) and part is invisible wage in job B. Hence he will not be (ability known only to the current em- promoted. It follows that asymmetric ployer). In contrast to Waldman, a key information results in fewer workers underlying assumption is that the mar- being promoted. In a second paper ket observes the actual ability of anyone (Waldman 1990), it is assumed that who is promoted. Again the question is workers accumulate general human who among the insiders, if anyone, will capital. Then, if an individual is pro- be promoted. It is shown that the moted, outside firms have an incentive higher rents earned on unpromoted in- to expend resources to obtain a noisy siders leads to promotion of intermedi- estimate of the employee’s actual pro- ate quality workers rather than the most ductivity. The promoted worker gets a able. small initial wage increase and then Similar arguments have been made outsiders compete for his services in an about the implications of the decision auction. Again this has the effect of raising the quality of individuals pro- 23 While I certainly know of universities where this story has a ring of truth, it really would be helpful moted above that which would prevail to have some serious empirical investigation of the with full information. phenomenon. 464 Journal of Economic Literature, Vol. XXXIX (June 2001) to lay off workers. Robert Gibbons and equilibrium payoffs (discounted to the Lawrence Katz (1991) note that with time of each agent’s first offer) are = = V asymmetric information, termination is U1 U2 1 +δ. Finally, discounting agent a negative signal of worker quality when 2’s first offer to the first period, the  V δV  ( )=  the terminating firm is a viable opera- equilibrium payoffs are U1,U2 1 +δ , 1 +δ . tion.Thisisnottrueiftheentirefirmis Note that the total gains to the two par- closing down. They then look at data ties sum to V. This can only be the case from the Displaced Worker Supple- if there is no time cost through de- ments to the Current Population Survey lay. Thus the equilibrium strategy is for and find strong supporting evidence. agent 1 to ask for a fraction 1 of the 1 +δ Finally, Ching-to Ma and Weiss (1993) total pie and for agent 2 to accept this use a signaling argument to explain the immediately. length of unemployment spells. In their Explanations for the delays observed model, a laid-off worker who accepts a in bargaining typically introduce a cen- poor job is sending a sufficiently nega- tral role for sorting. Suppose that the tive signal about his productivity that firm has private information about the relatively more able workers choose to profit level. In the “screening” ver- be unemployed. sion,24 the union starts with high offers, knowing that if profits are high, the cost 5.3 Bargaining of delay is high and so the firm will be willing to accede. Each round that the The equilibrium theory of bargaining firm refuses the union’s offer, the union between two agents initiated by Ariel revises downwards its beliefs about the Rubinstein (1982) has been fruitfully profits of the firm. Suppose that in applied to union management negotia- round t beliefs about the future round tions. In the basic noncooperative bar- imply an expected wage bill (discounted gaining model, the two parties make to period t + 1) of wt + 1. Given these be- alternative offers. Suppose the two liefs, the firm will accept any wage offer parties are bargaining over whether the wt satisfying V − wt ≥δ(V − wt + 1).Re- profits of V should be retained by the arranging, the firm will accept a wage firm or distributed to the workers as satisfying the constraint wages. The critical idea is that if the wi ≤(1 −δ)V +δwt + 1. (13) agent making the first offer (agent 1) looks ahead to the next time he makes This inequality is depicted in figure 14 an offer, he can reason as follows: If my for valuations of VH, VM,andVL.Ifthere equilibrium payoff is U1 and if I get to is sorting, then by period 3, it is a com- makeanoffertwoperiodsfromnow,I monbeliefthatthefirm’s profit level is should be able to use my equilibrium VL. Appealing to Rubinstein’sresult, strategy from then on and get at least there is a unique equilibrium wage offer U1 at that time. Discounting back one w3(VL). Now consider a firm with profit period, my opponent will realize that VM. Given this period 3 wage, the firm in period 2, when he makes his first will accept any period 2 wage satisfying counteroffer, I can command a dis- (13). Thus the best period 2 offer by the counted payoff of δU1. Then the best he workers is w2(VM) where the constraint is can do is ask for the remaining surplus just satisfied. The first period wage offer U2 =V– δU1. A symmetric argument is similarly computed. Whether or not for agent 2 establishes that U1 = V – 24 See, for example Grossman and Perry δU2. Combining these two results, the (1986a), and Sobel and Ichiro Takahashi (1983). Riley: Silver Signals 465

45˚ line

δ δ wt = (1 – )VH + wt + 1

wt (VH) δ δ wt = (1 – )VM + wt + 1

w2 (VM)

wt + 1 w3 (VL) w2 (VM) w1 (VH) wage in round t + 1 Figure 14. Equilibrium Sorting Offers full sorting of the three types is optimal Anat Admati and Perry (1987) also has depends upon the difference between alternating offers, but each agent can the profit levels and the likelihood of choose how long to wait before present- each. For example, if VM and VL are suf- ing his offer. Suppose that the union ficiently close, it is more profitable to makes the first offer. Again, the fact simply separate out a high-profit firm. that a more profitable firm loses more One theoretical difficulty with this by delaying allows for separation. Sup- model is that it does not explain the de- pose that the firm has either a high- lay if the time between rounds is small. profit VH or a low-profit VL.Ifthefirm Indeed, as Faruk Gull, Hugo Sonnen- does not delay its counter-offer, the schein, and Wilson (1986) show, in the union believes that the profit is high. limit, as the time between bargaining Appealing to Rubinstein’s theorem, the rounds goes to zero, there is no delay.25 union (the agent making the first move) Thesignalingversionofthemodelby will then accept a wage equal to 1 w(0)= VH. If in fact the profit is low, 25 At least this is the case under their stationar- 1 +δ ity assumption. As Lawrence Ausubel and Ray- the firm delays until time z before pre- mond Deneckere (1989) have since shown, delay senting its counteroffer. If this delay is is possible under weaker assumptions. It should an effective signal, the union then be- also be noted that the screening argument rests heavily on the assumption of a fixed order of offers lieves that the profit is low. As the and counteroffers. responder to the offer, the Rubinstein 466 Journal of Economic Literature, Vol. XXXIX (June 2001)

wage

U (z, w) = U (0, w(0)) V L L w(0) = H 1 + δ

U (z, w) = U (0, w(0)) H H

Preference directions

δ V 1 + δ L

z O z∗ delay Figure 15. Signaling Equilibrium equilibrium yields the union a wage the “war of attrition” where each party δ equal to w(z)= VL. The payoff to the tries to wait the other out. Suppose that 1 +δ firm if the wage w is accepted at time z the settlement will be w if it is the − is UH(z,w) =δz(VH – w). The indiffer- union that concedes and w > w− if the ence curve for a high-profit firm firm concedes. Let the firm’s assess- through (0,w(0)) is depicted in figure ment of the probability that the union 15. The high-profit firm strictly prefers will concede by time t be p(t). Then if any offer in the interior of the shaded time t is reached, the conditional region to (0,w(0)). Also depicted are probability that the union will concede the flatter (dashed) indifference curves in the time-interval dt is dp .Then 1 − p(t) of a low-profit firm with payoff function the discounted expected payoff from dp UL(z,w) =δz(VL – w). Thus if the profit conceding at time t + dt is (V − w−) + − 1 − p is low, the firm’s cost minimizing (V − w)(1 − dp )e−rdt.Ifthefirmcon- 1 − p − separating strategy is to delay its cedes at t it has a payoff of V − w.Col- counteroffer until time z∗.26 lecting terms, the expected net gain to A third model of bargaining delay is waiting the extra time interval is dU = ( − ) dp +( − −) = V − w− ( − −) dp − V w V w rdt − [ V w − 1 − p V − w 1 − p 26 It should be noted that the result relies heav- rdt]. Note that the term in square ily on the assumption that the union must wait for bracketsisincreasinginV. Thus if a the firm to counter its original offer, rather then ^ revise its own offer. firm with profit level V is better off Riley: Silver Signals 467 waiting until t + dt, rather than conced- however, there are systematic price effects ing at t, all firms with higher profit lev- of announcements by firms. The signaling els are also. It follows that the equilib- literature argues that these announce- rium strategies are separating with the ments convey inside information to the firms with higher profits staying in the marketplace. competition longer. 6.1 Adverse Selection There is a considerable body of empirical evidence on the duration of One of the early highly influential strikes and the terms of the settle- papers is Stewart Myers and Nicholas ment.27 In a thought-provoking paper, Majluf’s (1984) discussion of adverse John Kennan and Wilson (1989) review selection when raising cash to fund a the data and the implications of the new project. Consider a group of firms, three theories. They conclude that the all of which appear similar to outsider signaling models fare rather poorly investors but differ in their true value; when confronted with the evidence. On that is, firms of lower-than-average the other hand, they argue that both the value are overpriced by the market. attrition model28 and the screening Then equity-holding insiders of low- model are able to explain “many of the value firms will be eager to finance a salient features of the data.” new project through a new issue of equity. On the other hand, any suffi- 6. Finance ciently undervalued firm will be worse off financing through a new offering of Finance has not only a fascinating equity. The market is thus subject to array of applications of screening and adverse selection. signaling theory, but also an impressive Consider the following simple variant set of investigations into their empirical of the Myers-Majluf model. Only the significance. As with the other fields, owners of a firm (the “insiders”)know the literature is vast, and I will focus on thetruevalueofafirmV(t), where some key issues rather than attempt to V′(t)>0 and t ∈[α,β]. Since it will be be comprehensive. The traditional fi- helpful later, we also define the average nance literature assumes that any in- value of all firms__ whose type is no formation that owners and managers greater than t, V(t)=E{V(t~) | t~≤ t}.Anew (“insiders”) have about future firm project requires an injection of funds C performance is known to current and and has a payoff with present value B > prospective shareholders (“outsiders”). C.LetP be the market value of the firm From this follows the famous Miller- after the new equity issue. The new Modigliani Irrelevance Theorem. In such shareholders, who provide C in new a world, changes in capital structure, funds, then have a total shareholding of dividend increases, etc. have no effect C P . Current shareholders of a firm with a on the value of a firm’sassets.Inreality, prior true value of V(t) thus end up with a payoff of U(t,P)=(1 − C)(B + V(t)). 27 See Sheena McConnell (1989) and the refer- P ences therein. In a world of full information, the cur- 28 Kennan and Wilson consider only the sim- rent market value is equal to the pres- plest attrition model in which there is no informa- = + tional asymmetry. Adding asymmetry (as discussed ent value of the firm, that is, P B here) should help to distinguish the attrition from V(t). Substituting into the above expres- the screening models, for in the former it is the sion, U(t,P(t)) = B − C + V(t). Thus, the high-profit firms that continue to hold out, while low-profit firms settle early. In the latter it is the insiders capture all the gains from the high-profit firms that concede more quickly. new issue. 468 Journal of Economic Literature, Vol. XXXIX (June 2001)

value

V(t) U(t, V (t))

V(α) + B – C

V(α)

type αβt∗ t Figure 16. Financial Market Equilibrium

With informational asymmetry, sup- earnings. Two early papers use standard pose that outsiders believe that only signaling arguments. Hayne Leland and those types of firms s ∈ [α,t] will enter David Pyle (1977) point out that if the market for new equity. Then the ex- insiders are risk averse, it is costly to pected__ value of the post-issue firm will commit to holding a sizeable fraction of be B + V(t). Given such beliefs, outsiders theirportfoliosinthefirm,ratherthen will bid up the price of the firm to this be fully diversified. However, the marginal expected value. Then__ the value to insid- cost of holding more shares is higher for ers becomes U(t,V(t)) = (1 − __C )(B _+_ V(t)). insiders who have a low-quality firm. V(t) It is easily confirmed that U(α,V(α)) = Thus, the single-crossing property holds. V(α) + B − C > V(α). Moreover, unless the Stephen Ross (1977) introduces a bonus net__ value of the project is large, (or penalty) scheme for the manager U(β,V(β)) < V(β).Thus,asdepictedin basedonthefirm’s future price relative figure 16, the two curves must intersect to the face value of the debt issued. The at some t∗. In equilibrium, the marginal marginal cost of issuing additional debt firm type t∗ is just indifferent between is lower for a higher quality firm since investing and not investing in the new the probability of paying the penalty is project. All higher types are strictly lower. worse off investing. 6.3 Non-dissipative Signals 6.2 Capital Structure Most of the literature on capital One large set of papers considers structure abstracts from issues of risk and how the firm’s capital structure might managerial incentives and focuses instead signal about otherwise unobservable on the financing of new investment. Riley: Silver Signals 469

Insider µ σ Shareholding U2(D, S) = y2 – C (high , )

µ σ U1(D, S) = y1 – C (low , )

D Debt Figure 17. Efficient Separating Equilibrium

Suppose firm i with i = 1,2 needs to if firm 2 has a higher expected return, raise C in order to finance its invest- the insiders retain a higher equity share. ment plan. This plan will yield earnings Next consider a pure debt financing. ~ yi. Initially we will assume that outsid- The expected return to the debt-holders ~ − − ers have full information. For simplic- is Ui(D,1)=E{Max{yi − D,0}} = Ui = yi − C. ity, we assume that the interest rate is Suppose, following Robert Heinkel zero so that outsiders demand a return (1982), that the firm with the higher of C and so the net expected payoff to mean return is also considerably more − − insiders is Ui = yi − C. The investment is risky. Then the face value of the pure to be financed by a combination of risky debt issue will be higher for firm 2. debt and equity. We define D to be the Given these assumptions, indifference face value of the debt and S to be the curves for the two firms are as depicted final equity share of the current owners. in figure 17. The insiders thus get a fraction S of any Consider any pair of capital struc- income in excess of the debt, that is, tures A and B, one to the left and one ~ − − Ui(D,S)=SE {Max {yi − D,0}} = Ui = yi − C.In to the right of the intersection point, the case of pure equity financing, this along the lower envelope of the two − − − reduces to Ui(0,S)=Syi = Ui = yi − C. Thus, indifference curves. Firm 1 strictly 470 Journal of Economic Literature, Vol. XXXIX (June 2001) prefers to finance at A and firm 2 at B. announcement abnormal returns. Debo- Thus the high-mean/high-variance firm rah Lucas and Robert McDonald (1990) separates by issuing a sufficiently large show that firms typically float a new amount of debt. In contrast to the basic issue after an unusual run-up in stock signaling model in which there is over- price and that the announcement of the investment in the signaling activity new issue depresses the price. On the (relative to a world of full information), other hand, Michael Barclay and Clifford here signaling is efficient. Of course, Smith (1995) argue that the variation of the firms are not limited to the simple debt priority structure of corporate liabilities equity choice illustrated here. As Mi- across firms is much better explained by chael Brennan and Alan Kraus (1987) incentive-contracting arguments than show, any financial instruments with signaling. the property that the outer envelope of 6.4 Dividends as Signals the efficient indifference curves has a segment for each type of firm can be Another puzzle for finance theory is used to induce efficient separation. For why firms offer dividends even though related papers applying this principle, they are double-taxed. Sudipto Bhat- see Gunther Franke (1987), Thomas tacharya (1979) and Kose John and Noe (1989), M. P. Narayaman (1988), Joseph Williams (1985) argue that tax- George Constantinedes and Bruce able dividends signal firm quality. Fol- Grundy (1990), and Gautam Goswami, lowing John and Williams, suppose Noe, and Michael Rebello (1995). firms need to raise a fixed amount of Efficient separation requires more capital to fund operations. This is funded extreme asset structures if firms’ through the sale of equity. The higher earnings distributions can be ordered the firm’s current price, the greater will according to conditional first-order be the insider’s share of the final out- stochastic dominance. Suppose that for put. The firm with a higher expected any pair of realizations y′ and y′′ > y′, final output then gains more from hold- ~ ~ ~ ~ Prob {y2 > y′′ | y2 > y′} > Prob {y1 > y′′ | y1 > ing a higher final share. Thus, a higher y′}. Thus, firm 2 has more probability quality firm is willing to accept a weight at the upper tail of the distri- smaller increase in firm value in return bution. Given this assumption, it can be for accumulating greater tax liabilities shown that the intersection point of the (a higher dividend.) two indifference curves lies to the Morton Miller and Kevin Rock (1985) northeast of the point E,whereS = 1. generalize the model and introduce the Thus efficient separation requires that scale of investment as a choice. Let yi the high-quality firm choose S > 1, that be first period earnings (known only to is, issue debt and retire equity. insiders.) An amount z is distributed as The empirical literature on price a dividend and the remainder I = yi – z effects of new issues and repurchase is invested. Given an investment of I, finds considerable support for the idea the firm can produce an expected that announcements convey inside in- second period output of Q(I). Assuming formation to outsiders, that is, support (for simplicity) that the interest rate is for signaling theory. Theo Vermaelen zero, the present expected value of the (1981) examines the effect of stock firm is Vi(z)=yi − z + Q(I)=z + Q(yi − z). repurchases on prices. He shows that Miller and Rock assume that the man- there is a significant price effect and ager’s objective is to maximize a that this is a predictor of favorable post- weighted average of the current and Riley: Silver Signals 471

Market Price

∗ P2

∗ P1 V2 (z)

V1 (z)

z ∗ ∗ S z1 z2 z2 Dividend Figure 18. Dividend Signaling

future value of the firm, Ui(z,P) = sastry Ambarish, John, and Williams αP +βVi(z). With full information, the (1987) and Williams (1988) allow a firm equilibrium price is the present value. to relax its budget constraint by issuing Thus, the firm’s objective is to solve new equity to finance the investment. Max ( ) = ( ) z {Ui z,P | P Vi z }. The solution for Thus the new equity can act as a signal the low- and high-earnings firms are instead of the dividend. Even when depicted in figure 18 above. With full dividends are taxed, they show that the information, the value of each firm is least costly signal is a combination of a maximized so the equilibrium dividend new issue and dividend. While there is where the curve Vi(z) takes on its is plenty of evidence that dividend ∗ ∗ maximum. Note that (z2,P2), the dividend- changes result in changes in the market price pair for the high-earnings firm, is value of the asset, the appropriate test strictly preferred by the low-earnings is to see whether the announcement is firm over its full information outcome. followed by “surprising” post-dividend Thus, the high-quality firm must in- returns. Empirical research (see, for ex- s crease its dividend to z2 in order to ample, N. J. Gonedes 1978; Larry Lang separate itself. and Robert Litzenberger 1989; and Generalizing this argument, Rama- Aharon Ofer and D. Siegel 1987) is at 472 Journal of Economic Literature, Vol. XXXIX (June 2001) best weak. Thus, the dividend puzzle so that the issue is oversubscribed.29 As remains. Roger Ibbotsen (1975) first showed, the resulting underpricing is large. One ex- 6.5 Convertible Debt planation for this effect is the winner’s Suppose a firm has convertible debt curse (Rock 1986). Suppose that bid- and the market value of stock reaches ders can be divided into those that are the call price. While standard arguments informed and those that are not. The suggest that it is in the firm’s interest to former will not bid on the relatively convert immediately, it is quite com- poor issues so the uninformed have to mon for firms to wait. Milton Harris be compensated with a low asking and Artur Raviv (1985) offer a signaling price in order for an issue to be fully explanation. Suppose that when the call subscribed. becomes feasible the firm has private The largest informational asymmetry, information that earnings will be down. however, seems likely to be between Then the firm will be overvalued and the current owner and potential buyers. there is no reason to delay. On the Ivo Welch (1989) argues that firms will other hand, if the insiders believe that underprice to signal quality if they ex- good news will be forthcoming, the firm pect to go back into the market later to is undervalued. It is then more profit- issue additional equity. The higher the able to delay and thus reduce dilution initial underpricing, the more optimistic of ownership. The immediate conver- the firm is about its growth prospects sion of the debt then conveys bad news (and the need for additional equity). On to the market and the price of the firm the other side of the market, the signal should drop. For those who delay con- of a deeper price discount means that version, the same story continues to buyers are willing to pay more for the hold. Suppose that, given its private in- second issue. formation, a firm is just indifferent be- Welch’s one-parameter model is gen- tween converting and waiting t periods eralized by Franklin Allen and Gerald after the bond conversion can be Faulhauber (1989) to allow for informa- forced. Then with more favorable pri- tion about the project to emerge over vate information, this firm has an incen- time. Mark Grinblatt and Chuan Yang tive to wait longer. Thus for delayed Hwang (1989) generalize the model to conversions the price effect should still allow for uncertainty about multiple un- be negative. observable characteristics. In the latter Ofer and Ashok Natarajan (1987) paper both the mean and variance of a look at post-conversion returns and find firm’s return are unobservable. The two that they decline, as predicted by the characteristics are signaled by the firm’s signaling model. Sankarshan Acharya choice of a price discount at the IPO (1988) directly tests the Harris and and the fraction of the equity retained Raviv model by comparing firms that by the insiders. force immediately with those that The signaling story is then tested choose to delay. Again the data con- by Narasimhan Jegadeesh, Mark Wein- forms well to the signaling explanation stein, and Welch (1993). While they for delay. find the evidence consistent with the signaling story, they also show that 6.6 Initial Public Offerings 29 A recent listing in Hong Kong of a company When firms initially go public, it is doing business in mainland China was 100 times typical for the underwriter to set the price oversubscribed! Riley: Silver Signals 473 returns in the six weeks after the listing sions to lower the cost of the hearing. also effectively signal both a higher As a final example Susanne Lohmann probability of returning to the market (1993) offers an argument on why vot- and a larger seasoned issue. Thus, there ing can be rational despite the extreme is apparently no special role associated unlikelihood of being the swing voter. with the under-pricing itself. Instead, In the signaling equilibrium, leaders the data is broadly consistent with the use the size of the majority on (say) a view that the market is better informed referendum as a cue for political action. than the seller and the underwriter and Then each vote has an impact, and with that IPO under-pricing is simply an the low cost of going to the polls (or underestimate of value by the seller. mailing in), the net benefits from voting are positive. 7. Other Fields The second group of papers uses signaling theory to better understand the While space precludes a complete dis- extent to which an announcement about cussion of applications in other fields, government policy is credible. The two groups of papers deserve particular most-cited early papers are by Robert mention. Both are on the interface of Barro and David Gordon (1983) and economics and politics. The first group David Backus and John Driffil of papers focuses on political competi- (1985a,b), which focus on monetary tion. Banks (1990a) models campaign policy and inflation. Other influential platforms as signals of candidates’ be- contributions are Vickers (1986), Alex havior if elected. The platforms convey Cukierman, and Allan Meltzer (1986), information about future actions, since and Kenneth Rogoff and Anne Siebert the greater the deviation from them, the (1988). more likely a politician is to incur the Dani Rodrik (1998) extends the electorate’s wrath at the end of his analysis of credibility of government to term. A multi-period model with similar issues in trade and financial liberaliza- implications is developed by Harrington tion. A government serious about re- (1993). Banks (1990b) also considers a form can get better aid terms if it can voting game in which the political signal its seriousness and so distinguish authority has private information about itself from would-be mimickers that are the implications if the current proposals simply seeking foreign aid. This is ac- are not voted through. The way the complished by undertaking prior “pain- agenda is set then signals the private ful” trade reform. Since the mimicking information of the political authority. government places a lower value on the Charles Cameron and Peter Rosendorff long-run benefits of the reform, the (1993) ask how congressional commit- early trade reform becomes an equilib- tees with agency oversight authority are rium signal as long as the proposed aid able to affect an agency’splanswhen flow is not too large. A related paper by the committee has no authority to over- Rogoff (1990) offers an equilibrium rule decisions. They argue that the de- model of the business cycle. The politi- cision to hold a formal hearing (costly cal budget cycle (from one election to to all parties) should be viewed as an the next) is part of a process of multi- equilibrium signal that the committee dimensional signaling. Multiple signals majority is resolute. As an immediate are also featured in a paper by Torsten implication, the agency’s equilibrium Persson and Sweder Wijnbergen (1993) response is typically to offer conces- that explores the use of wage-price 474 Journal of Economic Literature, Vol. XXXIX (June 2001) controls to mitigate the credibility second goal has been to emphasize test- problem. It is shown that a stabilization ing of the theory and to suggest that program combining a restrictive mone- further development of the theory will tary policy with wage price controls make this easier. Theoretical models is less costly (more efficient) than one are often of the bare-bones type, where using monetary policy as the only signal. the objective is to demonstrate that in- Last but definitely not least, three formation asymmetry and self-selection empirical studies attempt to seek evi- provides a logically consistent explana- dence that governments do signal credi- tion for some observed behavior. Richer bility. Allan Drazen and Paul Masson models, with somewhat more micro- (1994) use inter-country interest rate economic detail, will provide a founda- differentials as a reflection of the mar- tion for both estimation and calibration. ket’s estimate of the probability of de- Once fitted to the data, it will be possi- valuation. They argue that under the ble to determine whether the equilib- signaling hypothesis an announcement rium costs of screening and signaling are of a continuing “tough” monetary pol- small or large relative to the benefits. If icy, in the presence of continuing un- the cost-benefit ratio is high, there is a employment, will raise the probability strong incentive for the market to seek of a future devaluation, thus leading to alternative means of information trans- a widening spread. The data on adjust- mission. It is likely that in environments ments to the European exchange rate where this is the case, there will be evi- mechanism appear to be broadly consis- dence of direct testing, early monitoring, tent with this prediction. Masson (1995) etc.—all provided to greatly reduce, if draws similar conclusions from British not eliminate, asymmetric information. data prior to the devaluation of the As I look to the future, my hope is British pound in 1992. Finally, Karen that in the applied fields, there will be Lewis (1995) asks whether intervention more effort to derive theoretical foun- in foreign exchange markets by the dations for testing the theory, particu- United States can be understood as a larly in the field of industrial organiza- signal of a toughening stance by the tion.Since,inthesignalingstory,good Federal reserve. If so, such interven- news is conveyed to the market by some tions should have been followed by credit action, this should be reflected in the tightening. For the period analyzed market valuation of the firm. Thus for (1985–90), the data is broadly consis- any publicly traded firm, one should tent with signaling, but the evidence is observe stock price effects of signaling. far from overwhelming. In labor economics, the connection between the theory and testing has 8. Final Remarks often been rather loose. With more careful attention to the underlying In this essay, my primary goal has model, new implications may lead to been to show that a remarkable collec- new tests. In particular, productivity tion of new economic insights has changes in other sectors have quite emerged from the twin theories of different implications for the wage- screening and signaling. In all three of education profile than a traditional the primary areas of application, there human capital wage profile. The con- are now clear explanations of a wide nection between the theory and data range of economic phenomena, where has been explored most fully in the formerly there were just puzzles. My field of finance. While quite a number Riley: Silver Signals 475 of papers report data findings consis- Backus, David and John Driffill. 1985. “Inflation and Reputation,” Amer. Econ. Rev. 75:3, pp. tent with the theory, others find the 530–38. evidence to be less then compelling. 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