Social Value of Public Information Author(S): Stephen Morris and Hyun Song Shin Source: the American Economic Review, Vol

American Economic Association

Social Value of Public Information Author(s): Stephen Morris and Hyun Song Shin Source: The American Economic Review, Vol. 92, No. 5 (Dec., 2002), pp. 1521-1534 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/3083261 Accessed: 31/03/2010 11:50

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http://www.jstor.org Social Valueof Public Information

By STEPHENMORRIS AND HYUN SONG SHIN*

What are the welfare effects of enhanced dissemination of public information through the media and disclosures by marketparticipants with high public visibility? We examine the impact of public informationin a setting where agents take actions appropriate to the underlyingfundamentals, but they also have a coordination motive arising from a strategic complementarityin their actions. Whenthe agents have no socially valuable private information,greater provision of public informationalways increases welfare. However, when agents also have access to independentsources of information,the welfare effect of increased public disclosures is ambiguous. (JEL D82)

The history of speculative bubbles begins more information is generally beneficial. This roughly with the advent of newspapers. conclusion is unaffected by whether the incre- One can assume that, although the record mental informationis public (shared by every- is of these early newspapers mostly lost, one) or private (available only to the relevant they regularly reportedon thefirst bubble the Dutch individual). of any consequence, tulipmania How far does this conclusion extend to social of the 1630s. Although the news media- and broadcast contexts where decision makers are interested newspapers, magazines, in the actions of others?Public informa- media, along with their new outlets on the parties Internet-present themselves as detached tion has attributesthat make it a double-edged observersof marketevents, they are them- instrument.On the one hand, it conveys infor- selves an integral part of these events. mation on the underlying fundamentals,but it Significantmarket events generally occur also serves as a focal point for the beliefs of the only if there is similar thinking among group as a whole. When prevailingconventional and the news me- large groups of people, wisdom or consensus impinge on dia are essential vehicles the people's for spread of decision-making process, public information ideas. serve to reinforce their on individ- Robert Shiller (2002) may impact ual decisions to the detrimentof private infor- For a decision maker facing a choice under mation. The "sunspots"literature has explored uncertainty,greater access to information per- this latter theme by emphasizing the ability of mits actions that are better suited to the circum- public signals to serve as a coordinationdevice. stances. Also, to the extent that one decision Even when the signal is "extrinsic"and has no maker's choice is made in isolation from others, direct bearing on the underlyingfundamentals, its very public nature allows full play to self- beliefs in economic out- * Yale fulfilling determining Morris:Cowles Foundation, University, P.O. Box comes. Costas Azariadis and David 208281, New Haven,CT 06520 (e-mail:stephen.morris@yale. (1981) edu); Shin: London School of Economics, Houghton Street, Cass and Karl Shell (1983) are early references. London WC2A 2AE U. K. (e-mail: [email protected]). Michael Woodford(1990) and Peter Howitt and This paper was previously circulated under the title "The R. Preston McAfee (1992) bolster the case for CNBC Effect: Welfare Effects of Public Information."We how are gratefulto JuanDubra, Tom Sargent,Frank Heinemann, sunspot equilibria by showing they may Mathias Dewatripont,Takashi Ui, and Heinz Herrmannfor arise in the context of individual learning, and theircomments on earlierversions of this paper,and to three how they arise from a variety of economic referees for their encouragement and guidance. The first mechanisms. version of this paper was preparedfor the Bundesbank/CFS However, while the extrinsic nature of sun- conferenceon "Transparencyof MonetaryPolicy," Frankfurt, allows a clean of the coordi- October2000. We also thank participantsat seminarsat the spots expression Bank of England, BIS, IMF, Pompeu Fabra, ECARES, nation role of public information,it fails to do Essex, Cambridge,and the Bank of Japanfor theircomments. justice to the fact that public informationdoes, 1521 1522 THE AMERICANECONOMIC REVIEW DECEMBER2002 in general, convey information on the funda- (i) When the agents have no private informa- mentals, and that such information will be of tion-so thatthe only source of information value to decision makers. Howitt and McAfee for the agents is the public information- note with irony that William Jevons (1884), then greater precision of the public infor- who introduced sunspots to economics, very mation always increases social welfare. much believed them to be partof the fundamen- (ii) However, if the agents have access to some tals of an agricultural economy. Indeed, for private information, it is not always the policy makers in a variety of contexts, it is the case that greaterprecision of public infor- fundamentalsinformation conveyed by public mation is desirable. Over some ranges, in- disclosures that receives all the emphasis. For creased precision of public information is instance,the proposalsto revise the 1988 accord detrimental to welfare. Specifically, the on bank capital adequacy place great emphasis greaterthe precision of the agents' private on the disclosures by banks that allow market information, the more likely it is that in- discipline to operate more effectively (Basel creased provision of public information Committee on Banking Supervision, 1999b); it lowers social welfare. is no less than the third of three "pillars"of the proposed accord. More generally, the policy The detrimentaleffect of public information response to the recent turbulence in interna- arises from the fact that the coordinationmotive tional financial markets has been to call for entails placing too much weight on the public increased transparency through disclosures signal relative to weights that would be used by from governments and other official bodies, as the social planner. The impact of public infor- well as from the major marketparticipants (see mation is large, and so is the impact of any InternationalMonetary Fund, 1998; Basel Com- noise in the public signal that inevitably creeps mittee, 1999a). Thus, assessing the social value in. In short, although public informationis ex- of public information entails recognizing its tremely effective in influencing actions, the dual role-- of conveying fundamentalsinforma- dangerarises from the fact that it is too effective tion as well as serving as a focal point for at doing so. Agents overreactto public informa- beliefs. Our task in this paper is to assess the tion, and thereby magnify the damage done by social value of public informationwhen allow- any noise. Our objective is to show how such ing for this dual role. "overreaction"need not be predicated on any Our investigation centers on a model that is wishful thinking or irrationalityon the part of reminiscent of Keynes's beauty contest exam- agents. ple, and which also shareskey featureswith the The dilemma posed by the potentialfor over- "island economy" model of Edmund Phelps reaction to public informationis a familiar one (1970) and RobertE. Lucas, Jr. (1972, 1973). A to policy makers that command high visibility large populationof agents have access to public in the market. Central bank officials have and private informationon the underlyingfun- learnedto be wary of public utterancesthat may damentals, and aim to take actions appropriate unduly influence financial markets, and have to the underlyingstate. But they also engage in developed their own respective strategies for a zero-sum race to second-guess the actions of communicatingwith the market.In formulating other individuals in which a player's prize de- their disclosure policies, centralbanks and gov- pends on the distance between his own action ernmentagencies face a numberof interrelated and the actions of others. The smaller is the issues concerning how much they should dis- distance, the greateris the prize. This impartsa close, in what form, and how often. Frequent coordinationmotive to the decision makers as and timely disseminationwould aid the decision- well as the desire to match the fundamentals. making process by putting currentinformation When there is perfect information concerning at the disposal of all economic agents, but this the underlying state, the unique equilibriumin has to be set against the fact that provisional the game between the agents also maximizes estimates are likely to be revised with the ben- social welfare. However, when there is imper- efit of hindsight. By their nature, economic fect information, the welfare effects of in- statistics are imperfect measurementsof some- creased public informationare more equivocal: times imprecise concepts, and no government VOL. 92 NO. 5 MORRISAND SHIN: SOCIALVALUE OF PUBLIC INFORMATION 1523 agency or central bank can guarantee flawless nating role of central bank disclosures has the information. This raises legitimate concerns potential to do good, then by the same token it about the publication of preliminaryor incom- also has the potentialto do ill if expectationsare plete data, since the benefit of early release may coordinatedaway from the fundamentals.Argu- be more than outweighed by the disproportion- ably, central bank intentions are something on ate impact of any error.This trade-off between which the centralbankers have very good infor- timely but noisy informationand slow but more mation, and so the coordinatingrole of disclo- accurate information is a familiar theme, as sures would be effective in aligning beliefs to witnessed by the debate in Japanabout whether fundamentals. On other matters, such as the preliminary GDP figures should be published. appropriatelevel of equity prices, it is far from Australia moved from a monthly calendar in clear that central bankers are better placed to reportingits balance of trade figures to a quar- judge. Nevertheless, their coordinatingrole will terly calendarbecause it was felt that the noise imply a disproportionateimpact of their judg- in the monthly statistics were injecting too ments on the final outcome, whetherfor good or much volatility into the price signals from fi- ill. If their judgment is faulty, the consequent nancial markets.1The flaws in the U.K.'s earn- detrimentalimpact will be that much larger. ings data have been credited with provoking Before turningto our analysis, it is important unjustifiably tight credit conditions in the to place our contributionin the broadercontext United Kingdom in the spring and summer of of the literatureon public information.As well 1998.2 The challenge for central banks and as the sunspots literature already alluded to, other official bodies is to strikethe right balance there are several bodies of work that should be between providingtimely and frequentinforma- borne in mind. The literature on herding and tion to the private sector so as to allow it to informationcascades focuses on the inefficien- pursue its goals, but to recognize the inherent cies both in the generation of new information limitations in any disclosure and to guard when free-ridingdecision makersfail to engage against the potential damage done by noise. in socially valuableexperimentation, and also in Central bank disclosures in the conduct of the dissemination of informationwhen private monetarypolicy have become especially impor- informationfails to find an expression through tant in recent years as monetary targeting has the actions of decision makers. Abhijit V. Ban- given way to interestrate targeting.In the latter erjee (1992) and Sushil Bikhchandani et al. regime, monetarypolicy works mainly through (1992) are early references. Henry Cao and variables that are driven by market expecta- David Hirshleifer (2000) develop a model that tions, such as asset prices, long-dated yields, allows full play to both types of inefficiency. and exchange rates. The link from the very The insights from this literature are comple- short-terminterest rates that are controlled by mentaryto that gained from ours. In both cases, the central bank to these financial variables is access to noisy public information results in through market expectations, where these ex- socially valuableprivate information being lost. pectations are, in turn, influenced by central However, the mechanisms are very different. bank disclosures. Alan Blinder (1998) and Jack Hirshleifer's(1971) paperis an instance Blinder et al. (2001) argue that this expecta- of how public information may be damaging tional mechanism works best in an environment because it removes insurance possibilities. of central bank transparency.Since market ex- There is also a large literaturein industrialor- pectations are shaped in part by the future ganization and related strategic contexts where course of action of the central bank, monetary the smoothingeffects of uncertaintyaffect play- policy is more effective if it is more effective in ers' actions. When the unique equilibrium is coordinatingmarket expectations. inefficient, the smoothing effect of uncertainty However, if the effectiveness of the coordi- may improve welfare. Siew Hong Teoh (1997) shows an instance of this in a game of voluntary contribution to public goods. Michael Raith reviews a literatureon and 1 We are grateful to Philip Lowe for this example. (1996) private pub- 2 See, for instance, "Garbage in, Garbage out." The lic information in oligopoly. Simon Messner Economist, October 15, 1998. and Xavier Vives (2000) examine the welfare 1524 THE AMERICANECONOMIC REVIEW DECEMBER2002 propertiesof a rationalexpectations equilibrium agents, indexed by the unit interval [0, 1]. Agent in which the price serves as a public signal of i chooses an action ai E fR,and we write a for the distributionof costs among producers,and the action profile over all agents. The payoff show how this informationmay be detrimental function for agent i is given by to welfare. The "global games" literaturehas examined (1) ui(a, 0) the impact of public informationin binary ac- - tion coordinationgames where agents have both -(1 r)(ai- 0)2- r(Li- L) private and public signals about some underlying state (see Morris and Shin, 1999, 2000; where r is a constant, with 0 < r < 1 and ChristianHellwig, 2000; ChristinaMetz, 2000). Here, if privateinformation is sufficientlyaccu- rate relative to public information, there is a Li (aj - ai)2dj unique equilibriumin a setting where multiple 0o equilibriawould exist with common knowledge of fundamentals.The comparativestatics of the precision of public informationreveal complex L- Ljdj. the effects that arises from interplay between o better fundamentals information and shifts in strategic uncertainty.One virtue of the simple The loss function for individual i has two com- model proposedin this paperis that equilibrium ponents. The first componentis a standardqua- is unique irrespectiveof the parameters,so that draticloss in the distancebetween the underlying we are able to examine the impact of public state 0 and his action ai. The second component signals and obtain cleaner welfare implications. is the "beauty contest" term. The loss Li is The plan for the rest of the paper is as fol- increasing in the average distance between i's lows. We introduceour model in the next sec- action and the action profile of the whole pop- tion, and solve for the unique equilibrium, ulation. There is an externality in which an highlighting along the way the distinctive chan- individualtries to second-guess the decisions of nels throughwhich public informationoperates. other individuals in the economy. The parame- The core of the paper is Section II, which ex- ter r gives the weight on this second-guessing amines the welfare effects of shifts in the pre- motive. The larger is r, the more severe is the cision of public information. A number of externality. Moreover, this spillover effect is extensions and variations of our model are socially inefficient in that it is of a zero-sum discussed in Section III, although the details nature. In the game of second-guessing, the of these extensions are presented separately in winners gain at the expense of the losers. Social an Appendix, availableonline at the AEA web welfare, defined as the (normalized)average of site (http://www.aeaweb.org/aer/contents).The individual utilities, is purpose of these extensions is both to demon- stratethe robustnessof our main conclusions to in the but also 1 r1 changes modeling assumptions, W 0)(a,) u(a, 0) di to delve deeper into the underlyingmechanisms 1 -r for the theoreticalresults. We conclude by pur- N0 suing some of the policy issues on disclosures further. - (ai - 0)2 di

I. Model so that a social planner who cares only about Our model is based on a game that induces social welfare seeks to keep all agents' actions strategic behavior in the spirit of the "beauty close to the state 0. From the point of view of contest" example mentioned in Keynes's Gen- agent i, however, his action is determined by eral Theory (1936). There is a continuum of the first-ordercondition: VOL.92 NO. 5 MORRISAND SHIN: SOCIALVALUE OF PUBLIC INFORMATION 1525

(2) ai = (1 - r)Ei(O) + rEi(a) for all i; expected welfare, conditional on 0, is where a is the average action in the population E(WI 0) -E[(y- 0)21 0] (i.e., a = f j ajdj) and Ei() is the expectation operator for player i. Thus each agent puts = 2 positive weight on the expected state and the expected actions of others. Note, however, that Thus,the smallerthe noise in the publicsignal, the if 0 is common knowledge, the equilibriumen- higheris social welfare.We will now contrastthis tails ai = 0 for all i, so that social welfare is with the generalcase in which agentshave private maximized at equilibrium. So, when there is informationas well as public information. perfect information,there is no conflict between individually rational actions and the socially B. Private and Public Information optimal actions. We now examine the case where 0 is not known with certainty. Consider now the case where, in addition to the public signal y, agent i observes the realiza- A. Public InformationBenchmark tion of a private signal:

Consider the case where agents face uncer- (7) Xi = 0 + ei tainty concerning 0, but they have access to public information.The state 0 is drawnfrom an where noise terms si of the continuumpopula- (improper)uniform prior over the real line, but tion are normally distributed with zero mean the agents observe a public signal and variance o<, independentof 0 and r1, so that E(Sisj) = 0 for i : j. The private signal of one (3) y= +rl agent is not observableby the others. This is the sense in which these signals are private. where 7 is normallydistributed, independent of 0, As before, the agents' decisions are made with mean zero and varianceo2&. The signal y is after observing the respective realizations of "public"in the sense that the actualrealization of their private signals as well as the realizationof y is commonknowledge to all agents.They choose the public signal. Denote by their actions after observingthe realizationof y. The expected payoff of agent i at the time of (8) ai(li) decisionis thengiven by theconditional expectation: the decision by agent i as a functionof his infor- (4) E(uily) mationset Ii. The informationset Ii consistsof the pair (y, xi) thatcaptures all the informationavail- where E( * |y) is the common expectation op- able to i at the time of decision.3 erator. Conditional on y, both agents believe Let us denote by a the precision of the public that 0 is distributednormally with mean y and information, and denote by j3 the precision of variance o&2.Hence, the best reply of i is the private information,where

1 1 = = - + r (9) a 2 (5) ai(y) (1 r)E(Oly) E(ajly) dj 77 ' o 1 where ai(y) denotes the action taken by agent i /~- 2. as a function of y. Since E(O0y) = y and since the strategies of both agents are measurable with to we have = so respect y, E(ajly) aj(y), 3 The notation in that in the (8) makes explicit that the strategy of unique equilibrium, agent i in the imperfect-informationgame is a function that maps the information IJ to the action ai. For any given strategy,ai is thereforea randomvariable that is measurable (6) ai(y) = y on the partitiongenerated by Ii. 1526 THE AMERICANECONOMIC REVIEW DECEMBER2002

Then, based on both private and public infor- 13(rK + 1 - r) mation, i's value of 0 is K= agent expected a+/3

ay + f3xi (10) a+/3 fromwhich we can solve for where we have used the shorthandEi(') to de- K - note the conditional expectation E( * |Ii). P(l r) + a

C. Linear Equilibrium Thus, the equilibriumaction ai is given by

We will now solve for the unique equilib- ay +3(l - r)Xi rium. We do this in two We first (13) steps. solve for ,~a+/3(1-r) a linearequilibrium in which actions are a linear function of signals. We will follow this with a D. Uniqueness of Equilibrium demonstrationthat this linear equilibriumis the unique equilibrium.Thus, as the first step, sup- The argumentpresented above establishesthe pose that the populationas a whole is following existence of a linearequilibrium. We will follow a linear strategy of the form this by showing (througha "bruteforce" solution method)that the linearequilibrium we have iden- (11) aj(I) = KX+ (1 -K)y. tified is the unique equilibrium.In doing so, we establishthe role of higher-orderexpectations in Then agent i's conditionalestimate of the aver- this model. In particular,we note that,if someone age expected action across all agents is observes a public signal that is worse than her privatesignal, then her expectationof others'ex- + pectationsof 0 is lower thanher expectationof 0 Kay(ay ++ f / -K) Ei(a) E^-a)= = + ) -+ (1-)( K)y (i.e., it is closer to the public signal than her own expectation).This in turnimplies that if we look at nth orderexpectations about 0 (i.e., some- - one's expectationof others' expectationsof oth- (21) Xi + a+1 ) (1 - ers' expectationsof [n times] of 0), then this Thus agent i's optimal action is approachesthe public signal as n becomes large. Higher-orderexpectations depend only on public (12) signals. - Recall that player i's best response is to set ai(i) = (1 r)Ei(0) + rEi(a) ai= (1 - r)Ei(O) + rEi(a). = ay + ( 1- r) + xi- aya px,\ Substitutingand writing E(0) for the average expectation of 0 across agents we have +r K B ) K+BI (14) a = (1 - r)Ei(0) + (1 - r)rEi(E(0))

+ 1- (3(rK r) + (1 - r)r2E(E2()) + ... Xi V[ a+3

+ 1 - - + I 3(rK r)) (1 r) E rkEi(Ek(0)). +t1- a+X y. k=O

Comparing coefficients in (11) and (12), we In order to evaluate this expression, and check thereforehave that the infinite sum is bounded, we must solve VOL 92 NO. 5 VOLMORRIS92NO. 5 AND SHIN: SOCIALVALUE OF PUBLIC INFORMATION 121527 explicitly for Ej(E( 0)). Recall that player i's and expected value of 0 is k + k~(E()) =(1 ayky f3xi) ? /3xi (15) E =ay0 f3 a+ = 1-gk?l)y + ijk+l1Xi

Thbus,thle average expectation of 0 acrossagents is which proves Lemma 1. Now substituting the expression from Lemma 1 into equation (14), we obtain 1 ~~ay+f3O E(0) = Ei(0)di a= - a= (1 r) I rk[(l tLk?l)y ? ,llk+lXi] k =O Now player i's expectation of the average ex- - - of 0 across is g(l r) g(l r) pectation agents - y + I - - Xi I rg I rg (ay ? 0 Ei (E(0))=Eik a + 3 ay + 131-r)xi a?f3(1r)

ay+ 0 a(yf3 i) This is exactly the unique linear equilibrium we identified earlier.

E. Lucas-Phelps Island Economy Model _((a +f3)2-f2)y +f32X~ -(a +1) We conclude this section by drawing out the parallels between the equilibriumin our model and the average expectation of the average ex- and featuresof the celebratedLucas-Phelps "is- pectation of 0 is land economy" model.4 To do this, let each index i refer an island whose supply ys of the is E = E(E(O)) single consumption good given by

_((a +(3)2-(32)y +f320 ys=b[ai-Eia] 2 (a ?13) where ai is the price on island i, a-is the average price across all islands, and b > 0 is a supply More generally, we have the following lemma. parameter.The demand yd' on island i is given by LEMMAl1: For any k, E()(1~ )+ k+1)k ?~k+ I gkOadE-k(o)) = (1 c[Ei(6) -ai] where ji = f31(a + 13). where 0 is the money supply and c > 0 is the PROOF: slope parameter for demand. Market-clearing The proof is by induction on k. We know then implies from (15) that the lemma holds for k = 1. Suppose that it holds for k - 1. Then, ai= (1 - r)Ej(0) ? rEi(ai)

-(k l(O)) =(1 - 11~k)y + p.kXi so 4We are indebted to Tom Sargent and to R. Preston (1 - ? Ek(0) = gk)y W o McAfee for pointing out this connection. 1528 THE AMERICANECONOMIC REVIEW DECEMBER2002 where r = bl(b + c), so that we have the levels and fundamentalsmay have some welfare equation (2) that characterizes equilibrium in consequences. However, the analysis of the the beauty contest model. A question that arises welfare consequences of our beauty contest in this context is how the profile of prices { ai game can be undertakenmore systematically across the economy are affected by the shifts in thanks to the explicit welfare function. We turn informationon money supply. Does greaterin- to this in the following section. A more system- formation precision on the money supply 0 atic discussion of alternativewelfare criteria is mean that the prices { ai are tied closer to the presentedin the separateAppendix to our paper, fundamentals0? Phelps (1983) posed this ques- available on the AEA web site. tion in the context of an economy in which the central bank is determinedto combat the inflation expectations of the private sector agents, II. WelfareEffect of Public Information and noted that the answer depends on subtle ways on the, interaction of beliefs between We are now ready to address the main ques- agents. Our analysis below may be regardedas tion of the paper.How is welfare affected by the a formal solution of the original problem posed precisions of the agents' signals? In particular, by Phelps in his 1983 paper. will welfare be increasing in the precision a of A disanalogy between our model and the the public signal? From the solution for ai, we island economy is that there is no clear formal can solve for the equilibriumstrategies in terms counterpartto the social welfare function in the of the basic randomvariables 0, rj, and {e }. latter.For this reason, we prefer to conduct our main analysis within the terms of reference of (16) ai = 0 + + (-r) the beauty contest. Nevertheless,even without a a+ 3(l - r) formal welfare criterion, the distance between the set of prices {ai} across islands and the If r = 0, the two types of noise (private and underlyingfundamentals given by 0 (the money public) would be given weights that are com- supply) will be of some interest. When this mensuratewith their precision. That is, r would distance is written as be given weight equal to its relative precision a/(a + 83), while Ei would be given weight equal to its relative precision /3(a + /3). How- - (ai 0)2 di ever, the weights in (16) deviate from this. The o noise in the public signal is given relatively more weight, and the noise in the private signal then the resultsthat follow in the next section on is given relatively less weight. This feature re- the welfare effects of public informationhave a flects the coordinationmotive of the agents, and direct bearing on the question of what effect reflects the disproportionateinfluence of the greaterpublic informationon the money supply public signal in influencing the agents' actions. has on the tightness of the relationshipbetween The magnitudeof this effect is greaterwhen r is prices and money supply. large. What effect does this have on welfare? In general, any welfare conclusions will de- Expected welfare at 0 is given by pend on the desirability of having the price levels aligned with the "fundamentals."In a (17) E[W(a, 0)10] world where only relative prices matter, the price levels per se will not be of much conse- a2E(rn2) + 2(1 -r)2[E(e2)] But in a world with infor- quence. incomplete [a + /3(1 - r)]2 mation where monetary policy works through the of the market(as expectations suggested by a + (1 - r)2 Blinder et al. [2001], mentionedin the introduc- + tion), price levels convey informationabout fu- [a 3(1 -r)]2 ture financial conditions and hence their tightness with the underlyingfundamentals may By examining (17), we can answer the compar- matter. If so, the distance between the price ative statics questions concerning the effect of \

VOL. 92 NO. 5 MORRISAND SHIN: SOCIALVALUE OF PUBLIC INFORMATION 1529 increased precision of private and public information. Welfare is always increasing in the precision of the private signals. We can see this by dif- ferentiating(17) with respect to 3, the precision of the private signals. We have 0

aE(WI0) ,\ We (18) ine \(Wl)

(1 - r)[(l + r)a + ( - r)2j3] > [a + 3(1 -r)]3 aCE Thus, increasedprecision of privateinformation FIGURE1. SOCIALWELFARE CONTOURS enhances welfare unambiguously. The same cannot be said of the effect of increased preci- Even if greater precision of public informa- sion of the public signal. The derivative of (17) tion can be obtained relatively cheaply, there with respect to a is may be technical constraintsin achieving precision beyond some upper bound. For instance, - - - 9E(Wl0) a (2r 1)(1 r)3 the social plannermay be restrictedto choosing (19) - a from some interval In this [ + (1 r)]3 given [0, a]. case, even if the choice of a entails no costs, we will so that see a "bang-bang"solution to the choice of optimal a in which the social optimum entails aE(WI0) either providing no public information at all (20) doeaa O (i.e., setting a = 0), or providing the maximum feasible amount of public information(i.e., set- if and only if ting a = a). The better informed is the private sector, the higher is the hurdle rate of precision of informationthat would make it wel- ( 1 public fare enhancing. a- (2r- 1)(1 - r) Figure 1 illustratesthe social welfare contours in (a, 3)-space.The curves are the set of points When r > 0.5, there are ranges of the param- that satisfy E(WO0)= C, for constantsC. As can eters where increased precision of public infor- be seen fromFigure 1, when ( > a/[(2r - 1)(1 - mation is detrimental to welfare. Increased r)], the social welfare contours are upward- precision of public information is beneficial sloping, indicatingthat welfare is decreasing in only when the private informationof the agents the precisionof public information. is not very precise. If the agents have access to What is the intuition for this result? Observe very precise information(so that , is high), then that equation (13) can be rewrittenas any increase in the precision of the public information will be harmful. Thus, as a rule of ay + 3(1 - r)xi when the sector are al- (21) ai= (-r) thumb, private agents a + (1-r) ready very well informed, the official sector would be well advised not to make public any ay + 3xi more information, unless they could be confi- + - a+/3 (y xi) dent that they can provide public informationof very great precision. If a social planner were choosing ex ante the optimal precision of public Pr ( - informationand increasingthe precision of pub- c + \ a + ((1 r)' lic informationis costly, then corer solutions at a = 0 may be common. This equation shows well the added impact of 1530 THE AMERICANECONOMIC REVIEW DECEMBER2002 public informationin determiningthe actions of beliefs. This feature of higher-order beliefs is the agents. In additionto its role in forming the a consequence of the underweighting of pri- conditional expectation of 0, there is an addi- vate information. tional (positive) term involving the public sig- Arguably,the role of sharedknowledge goes nal y, while there is a correspondingnegative far beyond economics. Michael S. Y. Chwe term involving the private signal xi. Thus, the (2001) argues for the importance of shared agents "overreact"to the public signal while knowledge in a wide variety of social settings. suppressingthe informationcontent of the pri- For example, he documents the high per unit vate signal. The impact of the noise 'r in the cost of reaching a viewer when the audience is public signal is given more of an impact in the large, and shows that goods that have a promi- agents' decisions than it deserves. nent "social" dimension are more likely to re- Perhaps a more illuminating intuition is ob- ceive the benefit of such high-cost advertising. tained by considering the role of higher-order Having establishedthe possibility that public expectations in our model. This intuition also information may be detrimental, we now ad- brings out well the unease expressed by Phelps dress a numberof extensions and variationsof (1983) (justified, it turns out) concerning the our model. The purpose is both to gauge the overly simplistic treatment of iterated expec- robustnessof our conclusions, and also to delve tations. The key to our result is the fact that deeper into the results. the "average expectations" operator E(.) vio- lates the "law" of iterated expectations. In our III. Extensions and Variations model, The linear-normalsolution of our model is an (22) E(0) + E(E(0)) attractively simple illustration of our main ideas, but the general conclusions are robust to Ei(E(O)) - Ei(O). alternative specifications. In the separate Ap- pendix to this paper (available online at the These propertiesare key,_sinceif we had equal- AEA web site), we illustrateseveral extensions ity between E(0) and E(E(0)) and between and variations.The first example is for a model Ei(E(O)) and E(0) then all higher-order-level where signals have two realizations, in which expectations collapse to the first order, so that we show overreactionto public informationrel- (14) would become ative to the welfare benchmark.Indeed, the key result that increasingly higher-order expecta- oc tions of a random variable converges to the E,(E(0))(1 - r) E rk= Ei(E(0)) expectation with respect to public information k=O only is a robust feature of differentialinforma- tion economies (see Dov Samet, 1998). Thus, = Ei(0) neither the normality nor the improperprior is essential for our results. which coincides with the socially efficient ac- A more immediate question is how our re- tion. Thus, it is this failure of the law of iterated sults vary with alternative specification of the expectations for the expectations operatorsthat payoffs. In our model, the overreactionto public injects genuine strategic uncertainty into the information arises from the positive spillover problem, and which entails the overreactionto effects of individual actions. What if actions public information. The importance of shared were strategic substitutes, rather than strategic knowledge in the promulgationof policy was complements?The solution for the unique equi- emphasized by Phelps in his 1983 paper, and libriumcan be obtainedfrom the same methods our results could be seen as giving this asser- used above. Suppose that the best-reply function formal backing. More recently, Wood- tion for i is given by ford (2001) has argued that the persistence exhibited by many macroeconomic time se- a, Ei(0)- pE,(a) ries can be explained by the relative inertia of higher-orderbeliefs as compared to first-order for some constantp > 0. Then the unique linear VOL. 92 NO. 5 MORRISAND SHIN: SOCIALVALUE OF PUBLIC INFORMATION 1531 equilibriumcan be obtainedfrom the method of deviation of the aggregate level of activity from comparing coefficients to yield the true state 0. Consider a finite player version of our frameworkwhere the principal's objec- 1 /(1 + p) tive is to minimize (23) ai l+ p a + p3(1 + p) Xi - aj- a \ y + a + ( + p) so thatthe objective for the principalis to set the The symmetric-informationbenchmark solution average action as close as possible to 0. Sup- is when ai = aj for all i, j which gives ai = pose that all agents follow a linear strategy and Ei(a), so that set their action according to 1 + (/3xi+ay) = + - (24) ai =1 p a ai KXi (1 K)y

Comparing (23) and (24), the introduction of where y is the public signal, and xi is i's private strategicsubstitutability implies that agents now signal. Then the expected loss for the principal overreact to private informationxi relative to at 0 is the symmetric-informationbenchmark. Players 2 - accentuate their differences in order to avoid I n similar actions to other K playing players. E - ( - K)y - 0 0 n xj+ An early paperby Roy Radner(1962) gives a j=l nice instance of this.5 He examines the problem where two members of a team aim to minimize _( > Ln the loss function - =-E E j + (1- K) 0 - - j=l (a1 - 0)2 + (a2 0)2 + 2q(al - 0)(a2 0). K2 (1 - K)2 In otherwords, the loss is increasingin the prod- a uct of the two errors.This gives rise to strategic n/3 substitutabilitybetween the two teammembers, so that the optimaldecisions put less weight on the The value of K that minimizes the principal's publicinformation and more weight on the private loss is informationas comparedto the individualdeci- sion. The choice of in a Courot model output no examined by Robert M. Townsend (1978) also a + falls into this categoryof strategicsubstitutes. 3np' As well as alternativepayoff functionsfor the individualplayers, we could also consider alter- Note that when n is large, the principal would native forms of the welfare function. For in- like the agents to put small weight on the public stance, if we pursue our macroeconomic signal, and base their decision largely on the interpretationof the model as the interaction private signal. Whereas the noise terms { si in between a central bank and the private sector the private signals of the agents tend to cancel agents, one natural way to formulate the prin- each other out, the noise term r1 in the public cipal's objective function is in terms of the signal remains in place irrespectiveof the number of agents. Thus, if the welfare function places weight on some aggregate activity vari- 5 the of the We are grateful to Takashi Ui for this reference. Ui able, overweighting public signal by (2001) shows that Radner'smodel as well as our own model the agents would cause an even greater social here can be analyzed as Bayesian potential games. welfare loss. This example is clearly rather 1532 THEAMERICAN ECONOMIC REVIEW DECEMBER2002 simplistic in the way that it exploits the inde- firms making investment decisions are pendently and identically distributed(i.i.d.) na- startingto emulate the hair-triggerbehav- ture of noise terms.More realistically,we might ior of financial investors. That means a of the be expect that private signals have shared raw in- growing part economy may across the that com- startingto act like a financialmarket, with gredients population impart all that the for correlation structures across implies-like potential plex private bubbles and panics. One could argue that signals. As a simple example, private signals far from the more stable, = + + making economy that have the structure xi 0 ~ ei, where the rapid responses of today's corpora- ( is a common noise term that enters into all tions make their investment in equipment players' private signals will impartcorrelations and software vulnerable to the kind of into the private signals, even if we condition on self-fulfilling pessimism that used to be the true state 0. In the online Appendix we possibleonly for investmentin paperassets. explore two issues in some detail: In terms of the framework of our paper, the (i) We explore alternativespecifications of the increased vulnerabilitymentioned by Krugman welfare function and determine conditions is an entirely rational response by individual that give rise to the result that greaterpublic actors, but is socially inefficient. informationis welfare decreasing. The challenge for central banks and other (ii) We present a general analysis of the two public organizations is to strike the right bal- player version of our model where the play- ance between providing timely and frequent ers can observe many signals, where the informationto the private sector so as to allow signals are multivariatenormal with a gen- it to pursue its goals, but to recognize the in- eral correlation structure.In this context, herentlimitations in any disclosure and to guard we show that correlated noise terms give against the potential damage done by noise. rise to qualitativelysimilar effects as in the This is a difficult balancing act at the best of benchmarkmodel. times, but this task is likely to become even harder. As central banks' activities impinge IV. ConcludingRemarks and Discussion more and more on the actions of marketparticipants, the latter have reciprocatedby stepping Public informationhas attributesthat make it up their surveillanceof central banks' activities a double-edged instrument for public policy. and pronouncements. The intense spotlight Whilst it is very effective at influencing the trainedon the fledgling EuropeanCentral Bank actions of agents whose actions are strategic and the ECB's delicate relationship with the complements, the trouble is that it is too effec- press and private sector market participantsil- tive in doing so. Agents overreact to public lustrate well the difficulties faced by policy information,and hence any unwarrantedpublic makers. news or mistaken disclosure may cause great In the highly sensitized world of today's fi- damage. The underweightingof private infor- nancial markets populated with Fed watchers, mation may be even worse if the acquisition of economic analysts, and other commentatorsof informationis costly for the individual agents. the economic scene, disclosure policy assumes Given the diminished role of private informa- great importance.Our results suggest that pri- tion in the game, the ex ante value of such vate sources of informationmay actually crowd information will be devalued, as would any out the public informationby renderingthe pub- incentive to acquire such information if it is lic information detrimental to the policy costly. maker's goals. The heightened sensitivities of Commentatorssuch as Paul Krugman(2001) the market could magnify any noise in the have raised the possibility that the parameterr public information to such a large extent that in our model-indicating the strength of the public information ends up by causing more strategic motive-may have become larger in harm than good. If the information provider recent years. Commentingon the recent down- anticipates this effect, then the consequence turn in economic activity in the United States, of the heightened sensitivities of the market is he suggests that to push it into reducing the precision of the VOL. 92 NO. 5 MORRISAND SHIN: SOCIALVALUE OF PUBLIC INFORMATION 1533 public signal. In effect, private and public Howitt, Peter and McAfee,R. Preston. "Animal information end up being substitutes, rather Spirits." American Economic Review, June than being cumulative. 1992, 82(3), pp. 493-507. International Monetary Fund. 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