Central bank transparency and the signal value of prices.

Morris, Stephen ; Shin, Hyun Song

A CENTRAL BANK must be accountable for its actions, and its decision-making procedures should meet the highest standards of probity and technical competence. In light of the considerable discretion enjoyed by independent central banks, the standards of accountability that they must meet are perhaps even higher than for most other public institutions. Transparency allows for democratic scrutiny of the central bank and hence is an important precondition for central bank accountability. Few would question the proposition that central banks must be transparent in this broad sense.

A narrower debate over central bank transparency considers whether a central bank should publish its forecasts and whether it should have a publicly announced, numerical target for inflation. This narrower notion of transparency also impinges on issues of accountability and legitimacy, but the main focus in this debate has been on the effectiveness of monetary policy.

Proponents of transparency in this narrower sense point to the importance of the management of expectations in conducting monetary policy. A central bank generally controls directly only the overnight interest rate, "an interest rate that is relevant to virtually no economically interesting transactions," as Alan Blinder has put it. (1) The links from this direct lever of monetary policy to the prices that matter, such as long-term interest rates, depend almost entirely upon market expectations, and monetary policy is effective only to the extent that the central bank can shape the beliefs of market participants. Long-term interest rates are influenced in large part by the market's expectation of the future course of short-term rates. By charting a path for future short-term rates and communicating this path clearly to the market, the central bank can influence market expectations, thereby affecting mortgage rates, corporate lending rates, and other prices that have a direct impact on the economy. Having thus gained a lever of control over long-term rates, monetary policy achieves its effects through the IS curve, through quantities such as consumption and investment.

Indeed, it would not be an exaggeration to say that many leading monetary economists today see the management of expectations as the task of monetary policy. For Lars Svensson, "monetary policy is to a large extent the management of expectations"; Michael Woodford puts it similarly: "not only do expectations about policy matter, but, at least under current conditions, very little else matters." (2)

The reasons for this preeminent role of expectations in monetary policy are explained particularly well for a general audience in a policy speech by Ben Bernanke, titled "The Logic of Monetary Policy." (3) Bernanke considers whether monetary policy' s steering of the economy is in some way analogous to driving a car. Monetary policy actions are akin to stepping on the accelerator or the brake, to stimulate or cool the economy as appropriate given its current state. Bernanke notes that, although this analogy is superficially attractive, it breaks down when one notes the importance of market expectations of the central bank's future actions. If the economy is like a car, then it is a car whose speed at a particular moment depends not on the pressure on the accelerator at that moment, but rather on the expected average pressure on the accelerator over the rest of the trip. Woodford employs a similar transport metaphor: "central banking is not like steering an oil tanker, or even guiding a spacecraft, which follows a trajectory that depends on constantly changing factors, but that does not depend on the vehicle's own expectations about where it is heading." Instead, optimal policy is history dependent, in that the central bank commits itself to a rule that takes into account past conditions, including even some that no longer matter for an evaluation of what is possible to achieve from now on. This is so because it was the anticipation of such a rule that determined the market's expectations today. (4)

The pivotal role of market expectations puts the central bank' s communication policy at center stage, and this view has been adopted to some extent by all central banks, but embraced most enthusiastically by those that have adopted explicit inflation-targeting monetary regimes. (5) However, one issue seems to have received less attention than it deserves, namely, the consequences of central bank transparency for the informativeness of prices. In order for the central bank to know how it should manage expectations, it must obtain its cues from signals emanating from the economy, which themselves are the product of market expectations. On the face of it, there is an apparent tension between managing market expectations and learning from market expectations: the central bank cannot manipulate prices and, at the same time, hope that prices yield informative signals. A recent speech by Federal Reserve governor Don Kohn identifies limits to transparency for these reasons. (6)

This tension between managing expectations and learning from them reflects the dual role of a central bank in the conduct of monetary policy. In addition to being an active shaper of events, the central bank must act as a vigilant observer of events, in order to obtain its cues for future actions. The roles are complementary, since only by being a vigilant observer of events can it be effective as an active shaper of outcomes. On the surface at least, there is a worry that an emphasis on the latter role will detract from the former. The central bank holds a mirror up to the economy for cues for its future actions, but the more effective it has been in manipulating the beliefs of the market, the more the central bank will see merely its own reflection.

The dilemma between managing market prices and learning from market prices would disappear if the central bank were omniscient, not having to rely on the information flowing from market prices. Then its only task would be to convey its knowledge to the rest of the economy, thereby aligning market expectations to its own (correct) view. Even if the central bank is far from omniscient, one could argue that it is so much better informed than any other individual agent in the economy that it should convey what it knows forcefully, so as to educate the myriad other actors in the economy. In this view the tension between managing market expectations and learning from market expectations would be resolved in favor of the former.

This way of resolving the tension is implicit in the following argument in another speech by Bernanke, titled "Central Bank Talk and Monetary Policy":</p> <pre> ... when the monetary policy committee regularly provides information about its objectives, economic outlook, and policy plans, two benefits result. First, with more complete information

available, markets will price financial assets more efficiently.

Second, the policymakers will usually find that they have achieved

a closer alignment between market participants' expectations about

the course of future short-term rates and their own views. (7) </pre> <p>Here Bernanke makes two claims:

--When the central bank conveys its own views clearly, market prices will be more informationally efficient.

--When the central bank conveys its own views clearly, the market's expectations will be closer to the central bank's own expectations.

We will argue that there are strong reasons for believing that the second assertion holds true, but that the first assertion is more open to question. In particular, the stronger are the reasons for believing the second assertion, the more doubtful is the first. In short, the first assertion may be false because the second assertion is true.

Informational Efficiency

Informational efficiency can be expected to have large favorable welfare consequences via two broad channels: the allocational role of financial market prices in guiding investment decisions, and the information revealed by market outcomes as a guide to the central bank's optimal control problem. We take each of these in turn.

Financial market prices have a large impact on the level and type of investments undertaken. For central bankers, the allocational role of the yield curve in determining the duration of investment projects is of particular importance. Irving Fisher in his Theory of Interest gives the example of three possible uses for a plot of land: for forestry, farming, or strip mining. (8) The interest rate used to discount future cash flows largely determines the ranking of the three projects. Long-duration projects such as forestry, where the bulk of the payoffs arrive in the distant future, are most attractive in an environment of low interest rates. When interest rates are high, short-duration projects like strip mining dominate. Since investment decisions are often difficult to reverse, distortions to investment incentives can have a lingering effect long after the initial misallocations.

The current debate in the United States on the booming residential housing market and the appearance of "exotic" mortgage products that backload repayments hinges on the correct pricing of long-term cash flows. If long-term interest rates are low, wage income in the distant future is given a large weight, and even exotic mortgage products seem viable when backed by the large present values of lifetime wage income. For central bankers who must also keep a vigilant eye on overall financial stability, the allocational role of financial market prices thus takes on great significance.

This allocational role is not limited to the yield curve as revealed in the prices of fixed-income securities. Equities that promise high payoffs in the distant future, as do, for example, many technology stocks, are a prime example of investments in long-duration projects. In the same way that high prices of long-duration fixed-income assets push down long-term interest rates, high stock prices lower the implicit discount rate on dividends paid by stocks. Christopher Polk and Paolo Sapienza, as well as Qi Chen, Itay Goldstein, and Wei Jiang, document evidence that investment is sensitive to the information conveyed by stock prices. (9) Anecdotal stories of formerly staid power companies venturing into telecommunications and other more fashionable business areas and then coming up short of expectations have been a constant theme since the bursting of the technology bubble a few years ago.

Central bankers have a large impact on financial markets. Indeed, it could be argued that the central bank's impact can sometimes be too large. By the nature of the problem, it is difficult to gauge whether the reactions in the financial market are excessive or justified by the fundamentals. However, the paper by George Perry in this volume provides some rare, tantalizing evidence that market prices may be distorted by anticipation of central bank actions. The evidence comes from the contrasting market reactions to two sets of official data on the labor market: the Current Population Survey of households and the Current Employment Statistics survey of nonfarm business payrolls. Perry shows that the two measures are roughly comparable in terms of their ability to track broad labor market conditions, and a simple average of the two does well in combining the informational content of both series.

However, the financial markets certainly do not accord equal weight to the two series. The nonfarm payroll numbers are given far greater weight and are much anticipated by market participants. Michael Fleming and Eli Remolona document the sometimes dramatic reactions in the bond market to the nonfarm payroll numbers. (10) The fact that the Federal Reserve is known to accord more weight to the nonfarm payroll survey undoubtedly plays on the minds of market participants. Given the importance of others' reactions to news, the fact that other market participants take note of the announcement is reason enough for any one market participant to take note. Thus the contrasting reactions to the two labor market series may be attributable largely to the background presence of the central bank. Keynes's famous "beauty contest" analogy comes to mind, and we will return to this below.

Perry' s findings echo a similar phenomenon from an earlier era, namely, the exaggerated reactions to announcements of money stock aggregates during the period after 1979, when the Federal Reserve began to emphasize growth of the money stock as an indicator of the monetary stance. (11) Although the Federal Reserve had published weekly estimates of monetary aggregates for some time (and continues to do so today), the announcements in the early 1980s became particularly significant with the added importance that the Federal Reserve placed on these aggregates at the time. These money stock announcements became one of the focal events in financial markets, if for no other reason than that significant movements in interest rates were associated with sizable unanticipated changes in the money stock. The market's reactions to such announcements were noticeably larger during the period following the shift in the monetary regime in 1979 than in that preceding it. Roley shows that, "over the 1 1/2-hour intervals spanning the weekly announcements the variance of the change in the three-month Treasury bill yield in the three years following October 1979 is more than thirty times larger than that in the previous two-year period." (12) In particular, the variance of the change in the three-month Treasury bill rate from 3:30 p.m. to 5 p.m. on the announcement day (the announcement always came at 4:10 p.m. on Friday) was 0.0016 for the period from 1977 to September 1979, but then jumped to 0.0536 between October 1979 and October 1982.

When the market understands that the central bank itself is watching the money stock for its policy stance, the strategic interactions among market participants will take center stage. The actual magnitudes will matter less than the fact that the announcements make the numbers common knowledge. The forces at work are similar to the forces that move markets after breaking news stories. The news itself may not be a surprise to some market participants, but the fact that it has become commonly known is news. It is this news that serves as the lightning rod that moves markets.

We now turn to the second channel through which informational efficiency may have an impact on economic welfare. In order for the central bank to steer the economy, it must have good information on the current state of the economy; in particular, it must know how close the economy is to full capacity. If the signals reaching the central bank are not informative, the control problem will be made more difficult.

The flattening of the Phillips curve in many countries in the 1990s is perhaps one indication that this signal value of aggregate prices has deteriorated. Flint Brayton, John Roberts, and John Williams note how the main feature of the Phillips curve--that inflation rises when labor markets tighten--was turned on its head during the economic expansion in the 1990s, when the unemployment rate fell below its long-run average of around 6 percent and then fell below 5 percent, even as inflation fell. (13) (Figure 1 depicts the unemployment-inflation relation from 1967 to 2002 in both the United States and the United Kingdom.) Replacing unemployment with a measure of capacity utilization does little better to rescue the Phillips curve. Although a flattening of the Phillips curve could be interpreted as a shift in the natural rate of unemployment itself, the authors conclude that the explanation that best fits the evidence is that firms' price-cost margins, rather than prices themselves, have taken the brunt of the adjustment. To the extent that costs are part of the fundamentals, and prices are expected to signal cost conditions, the fact that price-cost margins bear the brunt of the adjustment indicates that the signal value of aggregate prices has changed in recent years for the worse. (Here the informational efficiency of prices pertains to goods prices rather than asset prices.)

A telltale sign of the deterioration of the information value of signals would be large revisions to past data. The larger are the revisions to official data, the larger was (in retrospect) the uncertainty about economic conditions at the time.

The Bank of England's experience with data revisions in 2005 is revealing in terms of the difficulties of trying to steer the economy without good information about where the economy is at the moment. Figure 2 shows two fan charts for GDP growth as published in two consecutive issues of the Bank's Inflation Report. (14) It is immediately evident that GDP growth in early 2005 was revised sharply downward, so that the realized outcome in the first quarter of 2005 fell in the outer tail of the projected distribution of outcomes as given by the top panel. This led to some scrutiny and comment from the press. (15)

[FIGURE 2 OMITTED]

Another evident difference is in the shape of the fan chart for the August 2005 report: here the short-range forecasts are given much larger dispersion--the shape is more like a hammer than a fan. The change was introduced to emphasize the uncertainties surrounding current economic conditions. The larger range of outcomes permissible in the short run anticipates possible data revisions.

The August 2005 report describes the divergence between official statistical estimates of GDP and those obtained through business surveys, especially for the services sector. If the survey respondents put excessive weight on the prevailing conventional wisdom about the level of economic activity, it would make the surveys far less informative about current conditions than otherwise. Christopher Sims' notion that economic agents exercise "rational inattention," economizing on their information gathering, would exacerbate this deterioration of information value. (16)

Greater uncertainty about current conditions would be a telltale sign of the deterioration of signal values, and the new convention of drawing a fan chart with a "fatter" base could be seen as an indication of greater awareness of such uncertainty. Strictly speaking, the base of the fan ought to start in the distant past--after all, there is great uncertainty even about the past. The broadening of the base at the current period is a nod to the convention of drawing the fan chart as if current conditions were known. The more the information value of central bank signals deteriorates, the wider will be the base of the fan. Thus one of the key questions we will address is how the precision of the central bank's information changes as it shifts from one disclosure regime to another.

Much evidence has accumulated recently that the publication by central banks of numerical targets for inflation has been associated with a more effective anchoring of inflation expectations. (17) By squeezing out the corrosive and insidious effects of inflation expectations from the economy, the anchoring of inflation expectations brings large welfare gains. But, we would argue, the flipside of "well-anchored" is "uninformative": price signals that are well anchored are also price signals that have little signal value. They reveal very little to observers looking to them for signs of underlying shifts or trends in the economy. When informational efficiency emerges as a concern, well-anchored expectations cease to be unambiguously desirable.

Gregory Mankiw, Ricardo Reis, and Justin Wolfers examine the dispersion of inflation expectations in survey data and find that inflation expectations have become more concentrated around the mean. (18) Andrew Levin, Fabio Natalucci, and Jeremy Piger investigate how well the mean inflation expectations have been anchored, also from survey data. (19) They examine data on inflation forecasts from Consensus Forecasts, Inc., who poll market forecasters twice a year on their forecasts of inflation one to ten years ahead. Levin, Natalucci, and Piger conclude that long-term inflation expectations (looking six to ten years into the future) for a group of inflation-targeting countries (Australia, Canada, New Zealand, Sweden, and the United Kingdom) have become delinked from actual inflation outcomes, but that there is evidence that they still respond to actual outcomes in the United States and the euro area. They reach their conclusions by running regressions of the following form:

(1) [DELTA][[pi].sup.q.sub.it] = [[lambda].sub.1] + [beta][DELTA][bar.[[pi].sub.it]] + [[epsilon].sub.it],

where [[pi].sup.q.sub.it] is the expectation (formed at date t) of inflation q years ahead in country i, and [[pi].sub.it] is a three-year moving average of inflation in country i ending at date t. The coefficient [beta] is the focus of the investigation, since it measures the extent to which expectations of future inflation are influenced by the experience of recent inflation. The authors' results indicate that [beta] is small and insignificant in the formal inflation-targeting countries, but positive, large, and significant for the non-inflation-targeting countries.

A similar picture emerges from studies that examine the expectations embedded in financial market prices. Refet Gurkaynak, Levin, and Eric Swanson use daily data to examine the market's compensation for expected future inflation as revealed in the difference between forward rates on nominal government bonds and inflation-indexed bonds. (20) The authors apply this measure of forward inflation compensation to interest rates for U.S., Swedish, and U.K. government bonds to extract estimates of long-run inflation expectations. (Sweden and the United Kingdom are inflation-targeting countries, but the United States is not.) For all three countries the authors find stable long-run inflation expectations, but there are revealing differences. For the United States long-term inflation expectations appear to be influenced by recent experiences of inflation, whereas no such dependence is observed for the United Kingdom or Sweden. These results echo those obtained by Levin, Natalucci, and Piger. They imply that such "excessive" dependence, relative to the baseline model, in the forward inflation premium in the United States occurs because the Federal Reserve does not have a numerical objective for inflation to help tie down long-term inflation expectations. In addition, Gurkaynak, Levin, and Swanson show that long-term forward yield differences in the United States respond excessively to economic news, including surprises in the federal funds rate, a result that the authors attribute to shifts in market participants' views of the Federal Reserve's long-term inflation objectives. (21) To contrast their results for the United States with those for the inflation-targeting countries, the authors show that such excess sensitivity in long-term inflation expectations disappears in the United Kingdom after May 1997, when the Bank of England gained operational independence and monetary policy moved to a formal inflation-targeting regime.

The nature of the problem makes it difficult to bring empirical evidence to bear on whether the central bank's information has, indeed, deteriorated. Thus, at best, our argument is conjectural and speculative. However, we show below that the precision of the central bank's information will depend, in general, on the disclosure regime. The more the central bank discloses, the less precise the signals it receives will be. The fan charts of central bank forecasts become fatter, sometimes considerably so, when it chooses to disclose more. We also return, in closing, to the Bank of England's experience in 2005 for some clues as to what kind of evidence one might look for to help answer the question of informational precision for the central bank.

The theme explored in this paper is the tension between managing expectations and the impaired signal value of both financial market prices and goods prices when expectations are managed. We argue that the quality of the central bank' s information is endogenous, and that a central bank that attempts to steer the market's beliefs more vigorously will suffer a greater deterioration in the information value of its signals. We will begin by outlining some technical considerations in developing our argument. But first we revisit a much older debate in economics between Hayek and his socialist contemporaries on the informational role of prices and the role of the market mechanism in aggregating the distributed information of economic agents.

Hayek Revisited

Friedrich von Hayek's 1945 essay "The Use of Knowledge in Society" has remarkable resonance for today's debate on the informational role of prices. (22) As is well known, Hayek was arguing against his socialist con

temporaries and other advocates of Soviet central planning. However, his comments are equally relevant for today's debate on central bank transparency. He poses the problem in the following terms:</p> <pre>

The peculiar character of the problem of a rational economic order

is determined precisely by the fact that the knowledge of the circumstances of which we must make use never exists in concentrated or integrated form, but solely as the dispersed bits of incomplete and frequently contradictory knowledge which all the separate individuals possess. The economic problem of society is thus not merely a problem of how to allocate "given" resources--if "given" is taken to mean given to a single mind which deliberately solves the problem set by these "data." It is rather a problem of how to secure the best use of resources known to any of the members of society, for ends whose relative importance only these individuals know. Or, to put it briefly, it is a problem of the utilization of knowledge not given to anyone in its totality. (23) </pre> <p>Hayek was directing his argument against his contemporaries who argued, from Paretian optimality principles, for the superiority of a centrally planned economy. Chief among this group was Oskar Lange, who developed his arguments in his paper "On the Economic Theory of Socialism," published in two parts in the fledgling Review of Economic Studies in 1936 and 1937. (24) Lange was an economist in the Paretian tradition who, together with contemporaries such as Abba Lerner and John Hicks, provided the formal apparatus for the development of modern welfare economics. Lange presented one of the first formal arguments for what economists now know as the "two fundamental theorems" of welfare economics. But rather than seeing these results as buttressing the case for the market system, Lange saw them as compelling arguments in favor of central planning and socialism.

For Lange, following Pareto's lead, prices are merely rates of exchange of one good for another, and it is immaterial whether they are set by the central planner or determined in the market by supply and demand. The central planner, however, has the advantage that he or she can act "as if" the Walrasian auctioneer were setting prices, thereby overcoming the distortions of the market economy resulting from imperfect competition, transactions costs, and externalities and achieving a superior allocation of resources.

It was into this debate that Hayek weighed in. Prices, he argued, are not merely the rates of exchange between goods. They have a second role, that of conveying information on the fundamentals of the economy and the shocks that constantly buffet it. In more modern parlance, price systems are mappings from states of the world to observed market prices, and, as such, they convey information on the shifting fundamentals of the economy that is not available to any one agent or subset of agents. Hayek's argument for the superiority of the market mechanism rests on the premise that the information revealed in prices is likely to be far more illuminating and timely than that which any central planner could possibly hope to amass, let alone maintain and update in a timely manner in line with shifting fundamentals and continuing shocks to the economy.

Hayek's emphasis on the informational role of prices anticipates the modern microeconomic literature on rational expectations equilibria. (25) His argument is also relevant for the issue of central bank transparency and monetary policy. If the central bank aims to manipulate market expectations in its own image, it cannot at the same time expect the market outcome to serve as the aggregator of the "dispersed bits of incomplete and frequently contradictory knowledge which all the separate individuals possess." The more important the informational role of prices, the greater the tension between managing market expectations and learning from market expectations.

Hayek was not disputing that the central planner may be relatively better informed than any other particular agent in the economy. Indeed, the central planner could have an absolute advantage in this respect over any particular agent. But that is not the point. The point is that prices reveal the collective wisdom of all agents in the economy, by aggregating the diverse information they possess individually. Thus Christina Romer and David Romer's finding that central bank forecasters are better informed than their private sector counterparts is not sufficient to conclude that the central bank does not face the dilemma posed above (although, as we will show later, any formal calculus of the effects must consider the relative informational prowess of the central bank over the individual agents). (26) The corner shopkeeper serving a small clientele would be hard pressed to match the insights of the central bank forecasting department. However, the shopkeeper is best placed to observe the economic fundamentals ruling in his or her small sliver of the real world. These small slivers, across geographical regions and sectors of the economy, when pieced together in mosaic fashion, may reveal a far clearer picture than any central planner can hope to achieve.

To be sure, the modern central bank has an awesome array of expertise and technical resources at its disposal. Sims describes vividly how central bank forecasts are the culmination of a major logistical effort, drawing together the results of formal modeling from an array of models as well as the unquantifiable insights of experts on individual sectors. (27) In this respect, central bank forecasting departments bear some resemblance to the economic planning ministries that Hayek has in his sights. Hayek argues, "We cannot expect that this problem will be solved by first communicating all this knowledge to a central board which, after integrating all knowledge, issues its orders." (28) The central bank's resources and expertise, as formidable as they are, may fail to match the collective wisdom of the economically active population as a whole.

The Double-Edged Nature of Public Information

The fundamental debate over the relative superiority of the market mechanism versus central planning that raged in Hayek's time reminds us that the stakes in the economic debate were once much higher than they are today. However, some of the lessons from the Hayek-Lange debate are applicable even in the more modest arena of central bank transparency and monetary policy. Rather than presenting a stark choice between socialism and the market economy, the issues arise in the role of public information in an economy with distributed knowledge--an economy where each agent has a "window" on the world, each with a slightly different perspective, and each with a possible relative advantage in ascertaining the truth about some smaller sliver of the real world.

In general, an individual facing a choice under uncertainty will benefit from gaining greater access to information that reduces the uncertainty, since better information permits actions that are better suited to the circumstances. This conclusion is unaffected by whether the incremental information is public (in the sense of being shared by everyone) or private (available only to that individual).

But there are reasons why improved public information, although privately valuable to the decisionmaker receiving it, might not be valuable to society. If the private information of some market participants is to be revealed to others, that information must be reflected in market outcomes. But if public information leads market participants to ignore or downplay their own private information in their actions, the market will reveal less new information about market conditions. Thus public signals generate an informational externality.

This effect is further exacerbated if decisionmakers' interests are intertwined in such a way that a decisionmaker is an interested party in the actions taken by others. Public information in such contexts has attributes that make it a double-edged instrument. On the one hand, public information conveys information concerning the underlying fundamentals, as before. However, it also serves as a focal point for the beliefs of the group as a whole and thus serves a powerful coordination role. The "sunspots" literature has emphasized how even signals that are "extrinsic," having no direct bearing on the underlying fundamentals, may nevertheless serve to coordinate the actions of individual agents because of their very public nature. To the extent that public information allows coordination on good outcomes, greater precision of public information may be beneficial. But, equally, that coordination could be coordination on less desirable outcomes. With sunspots, some indeterminacy would always rule.

In most cases of interest, public information about monetary policy is not merely a sunspot, however; it conveys important information concerning the economic fundamentals. The question then is how the coordination effect of public information will affect the inferences drawn by individual economic agents, and how their intertwined interests will affect their individual incentives and the collective outcome that results from their acting on these incentives.

When there is the potential for a strong consensus to prevail or a conventional wisdom to take hold, individual incentives may become distorted in such a way as to reduce the informational value of economic outcomes. Central bank pronouncements may then serve as a lightning rod, reinforcing the conventional wisdom or consensus and suppressing dissent from those individuals whose own private signals tell them that the conventional wisdom is flawed. When individual incentives are thus eroded, the signals that would otherwise emerge from dissenting voices to undermine the flawed consensus may be muted, serving to perpetuate the flawed consensus.

In an earlier paper, (29) we explored the trade-offs that result in such a setting by examining the outcome of a collective decision problem reminiscent of Keynes' s celebrated metaphor of the beauty contest. Keynes drew a parallel between financial markets and a form of newspaper competition of his day that invited readers to pick the six prettiest faces from 100 photographs. (30) Readers won by picking the set of faces that "most nearly corresponds to the average preferences of the competitors as a whole." Under these rules, Keynes noted, a reader would win by anticipating which faces would become the popular choice, rather than by choosing those that the reader found most attractive. If individual readers voted on the basis of their own sincerely held judgments, the aggregate outcome would reveal much about the true collective judgment of the contestants as a whole. However, the more the contestants vote on the basis of "anticipating what average opinion expects average opinion to be," the more the aggregate vote will reflect the outcome of this second-guessing game among the contestants.

Now imagine how much worse the distortion would be if a widely watched authority figure were to weigh in, offering his or her public judgment on the faces in the photographs. The authority's judgment may or may not be sound. What counts is that his or her pronouncements reach a wide audience, and that everyone knows that his or her pronouncements reach a wide audience. For this reason alone, the authority's public judgment would serve as a powerful rallying point around which average opinion could coalesce. Once the public pronouncement has been issued, it would be futile for any reader to expend effort in scouring the faces in the photographs, to form an independent opinion of their fundamental attributes. Knowing that others would likewise regard this as futile and will not gainsay the authority figure, such a reader would have little incentive to expend effort in reaching an independent judgment. The aggregate outcome would thus reveal little about the genuine collective judgments of the individual contestants, but instead would be dominated by the public pronouncement. The signal value of the aggregate vote would thus be severely impaired.

Arguably, central bank transparency raises similar issues. When the central bank issues regular pronouncements on the economic outlook and publishes its forecasts of the output gap and the path of its policy rate, such pronouncements provide a powerful rallying point around which market expectations can coalesce. The more market participants consider the beliefs of other market participants, the greater will be the impact of the central bank's pronouncements in determining the aggregate market outcome.

The dilemma for monetary policy transparency is that such pronouncements by the central bank will, invariably, also offer genuine and valuable insight on the current and future state of the economy. But, however sound as a guide to the underlying fundamentals, the central bank's pronouncements are even better as guides to what average opinion will be. As a result, traders give the opinions of central bankers undue weight and place less weight on their own independent assessments of the economy. Public pronouncements can thus crowd out private opinions, and the market may cease to function as a way of aggregating and revealing diverse, private judgments about the world in the way that Hayek envisaged.

Most interestingly (and most disturbingly), consider how the problem is altered when the central bank becomes even better informed. Suppose that the central bank, in light of the disappointing performance of its forecasts, decides to beef up its forecasting effort by recruiting yet more experts and pouring in yet more resources. Paradoxically, the problem may become worse, not better, when the central bank's competence in reading the economy improves. There are two countervailing effects. On the one hand, the improved ability of the central bank to read the economy will provide better-quality information to other economic agents. However, the better the central bank becomes at reading the economy, the more authority it gains in the eyes of those other agents. As the central bank's pronouncements become more authoritative, its ability to serve as the rallying point for coordinating market expectations becomes stronger, suppressing further the channel through which dissenting agents can express their views. The net effect of improved central bank transparency is thus ambiguous. This is one aspect of what might be called the "paradox of transparency."

Elements of a Theory

The simplest way to motivate the problem is in terms of a decision problem akin to Keynes's beauty contest, although it will be important to show how real-world economic decisions can be understood within a similar framework. We will return to the economic applications after seeing how the key effects enter in a simpler, abstract decision.

Suppose that there are many small agents, each of whom faces the problem of tailoring his or her action to the underlying state [theta], but also tries to second-guess the decisions of the other agents. Suppose that each agent i follows the decision rule

(2) [a.sub.i] = (1 - r)[E.sub.i]([theta]) + r[E.sub.i]([bar.a]),

where [bar.a] is the average action in the population, and [E.sub.i](*) is the expectations operator for player i. Each agent puts a positive weight on the expected fundamental state E([theta]) and on the expected actions of others and chooses a weighted average of the two. The parameter r, where 0 < r < 1, indicates the extent to which agent i is motivated by the concern to second-guess the actions of others. If r is large (close to 1), decisions are influenced predominantly by anticipation of what others do, rather than by one' s own perception of the fundamentals.

The Public Information Benchmark

In the simplest case, if [theta] is commonly known, equilibrium entails [a.sub.i] = [theta] for all i. When instead agents face uncertainty concerning [theta] but have access to a source of information shared by all, their actions approximate [theta] most closely when uncertainty is small. Suppose [theta] is drawn from an (improper) uniform prior over real numbers, but agents observe the single public signal

(3) y = [theta] + [eta],

where [eta] is normally distributed and independent of [theta], with mean zero and variance [[sigma].sup.2.sub.[eta]]. The signal y is "public" in the sense that the actual realization of y is common knowledge among all agents. They choose their actions after observing the realization of y. Conditional on y, all agents believe that [theta] is distributed normally with mean y and variance [[sigma[.sup.2.sub.[eta]]. Hence, agent i's optimal action is

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where [a.sub.i](y) denotes the action taken by agent i as a function of y. Since E([theta]|y) = y, and since everyone can condition on y, we have E([a.sub.j]|) = [a.sub.j](y), so that

(5) [a.sub.i](y) = y

for all i. The average action is then y, and the distance between [a.sub.i] and [theta] is

E[[(y - [theta]).sup.2]|[theta]] = [[sigma].sup.2.sub.[eta]].

Thus the less noise in the public signal, the closer is the action to the fundamentals. We will now contrast this with the Hayekian case in which each agent has his or her own "window on the world."

The Hayekian Case

Consider now the case where, in addition to the public signal y, agent i observes the realization of a private signal:

(6) [x.sub.i] = [theta] + [[epsilon].sub.i],

where noise terms [[epsilon].sub.i] are normally distributed with zero mean and variance [[sigma].sup.2.sub.[epsilon]], independent of [theta] and [eta], so that E([[epsilon].sub.i][[epsilon].sub.j]) = 0 for i [not equal to] j. The private signal of one agent is not observable by the others; each agent has a privileged view of his or her own small sliver of the world.

As before, the agents' decisions are made after observing their signals. Denote by [alpha] and [beta] the precision of the public and the private information, respectively, where

(7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Then, based on both private and public information, agent i's expected value of [theta] is

(8) [E.sub.i]([theta]) = [alpha]y + [beta][x.sub.i]/[alpha] + [beta].

One simple way to solve for the equilibrium is to posit that actions are a linear function of signals. We will follow this with a demonstration that this linear equilibrium is the unique equilibrium, which also gives important insights into the double-edged nature of public information. Thus, as the first step, suppose that each agent follows a linear rule,

(9) [a.sub.j] = [kappa][x.sub.j] + (1 - [kappa])y

for some constant [kappa]. Then agent i's conditional estimate of the average expected action across all agents is

[E.sub.i]([bar.a]]) = [kappa] ([alpha]y + [beta][x.sub.i]/[alpha] + [beta]) + (1 - [kappa])y

= ([kappa][beta]/[alpha] + [beta])[x.sub.i] + (1 - [kappa][beta]/[alpha] + [beta])y.

Agent i's optimal action is

(10) [a.sub.i] = (1 - r)[E.sub.i]([theta]) + r[E.sub.i]([alpha]) = (1 - r) ([alpha]y + [beta][x.sub.i]/[alpha] + [beta]) + r[([kappa][beta]/[alpha] + [beta])[x.sub.i] + (1 - [kappa][beta]/[alpha] + [beta])y]

= [[beta](r[kappa] + 1 - r)/[alpha] + [beta]][x.sub.i] + [1 - [beta](r[kappa] + 1 - r)/[alpha] + [beta]]y.

Comparing coefficients in equations 9 and 10, we therefore have

[kappa] = [beta](r[kappa] + 1 - r)/[alpha] + [beta],

from which we can solve for [kappa]. The equilibrium action [a.sub.i] is given by

(11) [a.sub.i] = [alpha]y + [beta](1 - r)[x.sub.i]/[alpha] + [beta](1 - r),

and the average action is

(12) [a.sub.i] = [alpha]y + [beta](1 - r)[theta]/[alpha] + [beta](1 - r).

First observe that the larger is [alpha], the further away is the average action from [theta]. This is true even if r = 0. However, if r > 0, even less weight is put on the true state and even more weight on the public signal.

Together with Franklin Allen, we have developed this theme in an asset pricing model where the price of an asset today is the average expectation of tomorrow's price. (31) Average expectations fail to satisfy the "law of iterated expectations." That is to say, the average expectation today of the average expectation tomorrow of future payoffs is not the same thing as the average expectation of future payoffs. In a Hayekian environment, the failure of the law of iterated expectations follows a systematic pattern that puts too much weight on shared information--conventional wisdom or other public signals, including past prices. Past prices, in particular, receive too much weight relative to the statistically optimal weight in a frictionless world. Given the importance of the failure of the law of iterated expectations, it is illuminating to dwell briefly on how the example sketched above can be shown to be an example of such a failure.

Higher- Order Beliefs

Recall that agent i's decision rule is

(13) [a.sub.i] : (1 - r)[E.sub.i]([theta]) + r[E.sub.i]([bar.a]).

Substituting and writing [bar.E]([theta]) for the average expectation of 0 across agents, we have

(14) [a.sub.i] = (1 - r)[E.sub.i]([theta]) + (1 - r)r[E.sub.i]([bar.E]([theta])) + (1 - r)[r.sup.2][E.sub.i]([[bar.E].sup.2]([theta]))+ ... = (1 - r)[[infinity].summation over k=0][r.sup.k][E.sub.i]([[bar.E].sup.k]([theta])).

To evaluate this expression, one must solve explicitly for [E.sub.i]([[bar.E].sup.k]([theta])). Recall that agent i's expected value of [theta] is

(15) [E.sub.i]([theta]) = [alpha]y + [beta][x.sub.i]/[alpha] + [beta].

Thus the average expectation of [theta] across agents is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

31. Allen, Morris, and Shin (forthcoming).

Now agent i's expectation of the average expectation of [theta] across agents is

[E.sub.i]([bar.E]([theta])) = [E.sub.i]([alpha]y + [beta][theta]/[alpha] + [beta])

and the average expectation of the average expectation of 0 is

[[bar.E].sup.2]([theta]) = [bar.E]([bar.E]([theta]))

= [[([alpha] + [beta]).sup.2] - [[beta].sup.2]]y + [[beta].sup.2][theta]/[([alpha] + [beta]).sup.2].

Higher-order expectations put more weight on the (noisy) public information at the expense of the truth. Not only does the law of iterated expectations fail; it fails in a systematic way where higher-order expectations are less informative about [theta]. By induction we have [[bar.E].sup.k]([theta]) = (1 - [[mu].sup.k])y + [[mu].sup.k][theta], where [mu] = [beta]/([alpha] + [beta]), and

[a.sub.i] = (1 - r)[[infinity].sub.k=0][r.sup.k][(1 - [[mu].sup.k+1])y + [[mu].sup.k+1][x.sub.i]] = [1 - [mu](1 - r)/1 - r[mu]]y + [[mu](1 - r)/1 - r[mu]][x.sub.i] = [alpha]y + [beta](1 - r)[x.sub.i]/[alpha] + [beta](1 - r).

This is exactly the unique linear equilibrium we identified earlier.

Economic Interpretations of the Decision Rule

The decision rule in equation 2, which was motivated by the beauty contest analogy, can be given more familiar macroeconomic underpinnings by appealing to the "island economy" model of Robert Lucas and Edmund Phelps, (32) although, for reasons to be discussed below, we favor another interpretation of the decision rule. Suppose that there are a large number of small islands, which can be interpreted either as distinct geographical regions or as different sectors of the economy. There is a single good in this archipelago, and the supply of this good on island i is denote by [q.sup.s.sub.i]. The supply of the good is increasing in the difference between the price on island i and the perceived average price across all islands. In particular, we take the linear supply function

(16) [q.sup.s.sub.i] = b[[p.sub.i] - [E.sub.i]([bar.p])],

where Pi is the price on island i, [bar.p] is the average price across all islands, and b > 0 is a supply parameter. The expectations operator [E.sub.i](x) denotes the expectation with respect to the information available to residents of island i.

The demand for the good on island i is a decreasing linear function of the price on the island, but it also depends on the best estimate of some underlying fundamental variable [theta]. In the original treatment of this problem by Lucas and Phelps, [theta] is construed as being the money supply and is under the central bank's control. Demand on island i is thus given by

(17) [q.sup.d.sub.i] = [E.sub.i]([theta]) - [p.sub.i],

where [theta] is the money supply. Market clearing then implies

(18) [p.sub.i] = (1 - r)[E.sub.i]([theta]) + r[E.sub.i]([bar.p]),

where r = b/(b + 1). This is the pricing rule obtained by Phelps, (33) which extends the standard Lucas-Phelps island economy model by incorporating a role for the expectations of prices set on other islands. Thus we retrieve the beauty contest decision rule.

Although the outward form of equation 18 conforms to the beauty contest decision rule, the fundamental variable [theta] in the original version of the island economy model is something that the central bank has full control over. Thus learning about [theta] is not an issue, and so the informational role of prices has no part to play in the analysis.

A more appropriate interpretation of the pricing rule in equation 1 8 is in terms of the price-setting decisions of firms that have some market power due to imperfect substitutability between goods. (34) In this context [theta] represents the underlying marginal cost conditions for the firms, which also correspond to the output gap under some simplifications. (35) Firms care about the prices set by other firms because there is price competition across firms. Woodford considers pricing rules for firms of the form

(19) [p.sub.i] = [E.sub.i](p) + [xi][E.sub.i](x),

where [p.sub.i] is the (log) price set by firm i, p is the average price across firms, is marginal cost (in real terms), and [xi] is a constant between 0 and 1.36 The operator [E.sub.i] denotes the conditional expectation with respect to firm i's information set. The parameter [xi] is related to the elasticity of substitution between goods, and it becomes small as the economy becomes more competitive. (37) An active literature has developed exploring the Hayekian theme in the context of an imperfectly competitive economy. (38)

Rewriting equation 19 in terms of nominal marginal cost, defined as [theta] [equivalent to] - x + P, we have

(20) [p.sub.i] = (1 - [xi])[E.sub.i](p) + [xi][E.sub.i]([theta]),

yielding another way to derive the beauty contest decision rule.

The examples above pertain to the pricing of goods, but many of the properties of beauty contests arise also in the context of financial market pricing. Financial market prices present the additional complication that they are forward looking: the price today equals the discounted expected payoff at some future date. Nevertheless, the excessive impact of public information can be shown, at the cost of some additional apparatus. Allen, Morris, and Shin derive asset pricing formulas of the form

(21) [p.sub.t] = [[bar.E].sub.t][[bar.E].sub.t+1] ... [bar.E].sub.t+h][[theta].sub.t+h] - [omega][s.sub.t],

where [p.sub.t] is the price of a financial asset at time t, [[theta].sub.t+h] is the fundamental payoff at time t + h, [omega] is a constant, and s, is the asset supply, with a mean of zero. (39) Thus the price of an asset today is the average expectation today of the average expectation tomorrow, and so on, of the eventual realized fundamentals.

The law of iterated expectations fails also in this context, and the direction of the failure is toward excessive influence of public information. Asset pricing applications present some technical difficulties, such as the fact that past (and even current) prices constitute public signals that enter into the information sets of traders. Thus the innocuous-looking notation Et actually conceals much subtlety.

However, the broad conclusions are the same as for the static beauty contest. Public information has a disproportionate impact on financial market prices. The precise sense in which this is true is that the market price deviates systematically from the average expectation of the fundamental value, and the bias is always toward commonly shared information, including past prices. More formally,

(22) [p.sub.t] = [[bar.E].sub.t][ [bar.E].sub.t+1] ... [[bar.E].sub.t+h][[theta].sub.t+h] - [omega][s.sub.t] [not equal to] [[bar.E].sub.t]([[theta].sub.t+h]) - [omega][s.sub.t],

and the distance between Pt and the expectation of [[theta].sub.t+h] based purely on public information is smaller than the distance between [[bar.E].sub.t][[theta].sub.t+h] and the expectation of [[theta].sub.t+h] based purely on public information. Thus the key features of the overreaction to public information apply to financial markets also.

The Precision of Endogenous Information

So far we have treated the precision [alpha] of public information as given. But the information available to central banks derives from outcomes in the economy itself and hence is the result of actions taken by individual economic agents. To the extent that individuals' decisions are affected by public information, we can expect the signal values of the resulting outcomes to be sensitive to the disclosure regime.

We show that this is indeed the case. The information precision of a central bank that issues regular forecasts is lower than that of a central bank that simply tracks the evolution of the fundamentals through its signals. We postpone a discussion of the potential welfare effects of such impaired signal precision until the next section, and instead concentrate here on why the information value deteriorates when a central bank discloses more.

Time is discrete and indexed by t [member of] {..., -2, -1, 0, 1, 2, ...}. The fundamentals {[[theta].sub.t]} evolve as a Gaussian random walk:

(23) [[theta]t = [[theta].sub.t-1] + [[phi].sub.t],

where {[[phi].sub.t]} are independent standard normal innovations.

At each date a new generation of private sector actors observe a noisy signal of the fundamentals as of that date, together with any present and past disclosures by the central bank. Individual i's noisy signal in generation t is given by

[[x.sub.it] = [[theta].sub.t] + [[member of].sub.it],

where [[epsilon].sub.it], are independently and identically distributed (i.i.d.) normal across individuals and across generations with precision [beta].

We assume a sparse information set for the individual at date t (for instance, there is no access to the private information of previous generations). But we do this as a way of setting the basic level of information to which the central bank can add by disclosing its own estimates and forecasts, if it chooses to. Extending the model to encompass richer settings would be worthwhile for specific applications.

The private sector agents play a beauty contest game, following the decision rule

(24) [a.sub.it] = (1 - r)[E.sub.it]([[theta].sub.t]) + r[E.sub.it]([[bar.a].sub.t]),

where [[bar.sub.a].sub.t] is the average action across individuals at date t.

The central bank observes a noisy signal about what the private sector individuals did in the previous period. At date t that signal is

(25) [z.sub.t] = [[bar.a].sub.t-1] + [[phi].sub.t],

where {[[phi].sub.t]} are i.i.d. Gaussian noise terms independent of all other random variables, and with variance 1/[gamma].

The central bank's information set at date t is the collection of all past signals {... , [z.sub.t-2], [z.sub.t-1], [z.sub.t]}. We are interested in the central bank's information precision at date t as measured by

Var([[theta].sub.t]|[z.sub.t], [z.sub.t-1], ...).

Compare two possible regimes. In the first the central bank makes no disclosures but simply tracks the fundamentals through its signals. In the second the central bank discloses its best estimates of the fundamentals. Since the fundamentals follow a random walk, the disclosure of the central bank' s estimate of [theta] is tantamount to issuing forecasts of future values of [theta] at all horizons.

The Case without Disclosure

In the first case, since there is a continuum of private sector agents, and they receive i.i.d, signals conditional on the fundamentals, the average action [[bar.a].sub.t] fully reveals the true fundamental state [[theta].sub.t]. Thus the central bank' s signals are given by

[z.sub.t] = [[theta].sub.t-1] + [[phi].sub.t].

We write [z.sub.t] as the linear estimate of [[theta].sub.t], based on {[z.sub.t], [z.sub.t-1], [z.sub.t-2], ...}, and let [[alpha].sub.t], be the precision of this estimate as measured by 1/Var([[theta].sub.t]|[z.sub.t], [z.sub.t-1], ...). Then, on observing [z.sub.t+1] at date t + 1, the linear estimate of [[theta].sub.t] is

(26) [[alpha].sub.t][z.sub.t] + [gamma][z.sub.t+1]/[[alpha].sub.t] + [gamma],

with precision [[alpha].sub.t] + [gamma]. Since [[theta].sub.t+1] = [[theta].sub.t] + [[phi].sub.t+1], we have a recursive formula for the central bank's information precision over time, namely,

(27) 1/[[alpha].sub.t+1] = Var([[theta].sub.t+1]|[z.sub.t+1],[z.sub.t])

= 1 + 1/[[alpha].sub.t] + [gamma].

The steady-state information precision in the nondisclosure case is thus the value of [alpha] that solves

(28) [alpha](1 + 1/[alpha] + [gamma]) = 1.

The Case with Disclosure

In the second case, where the central bank discloses its signals to the individual agents, the information set of agent i in generation t is

(29) {[x.sub.it], [z.sub.t], [z.sub.t-1], ... }.

Let [z.sub.t] be the linear estimate of [[theta].sub.t] based on the central bank's disclosures only, and let [[alpha].sub.t], be the precision of this estimate. Then this individual will take action as follows:

(30) [a.sub.it] = [[alpha].sub.t][z.sub.t] + (1 - r)[beta][x.sub.it]/[[alpha].sub.t] + (1 - r)[beta].

By taking the average across individuals in equation 30, the average action is

Solving for [[theta].sub.t] as a function of [z.sub.t], [z.sub.t+1],

[[theta].sub.t] = [1 + [[alpha].sub.t]/(1 - r)[beta]][z.sub.t+1] - [[alpha].sub.t]/(1 - r)[beta][z.sub.t] - [1 + [[alpha].sub.t]/(1 - r)[beta]][psi].sub.t+1].

Thus the incremental information value to the central bank from observing [z.sub.t+1] comes from the signal

(31) [s.sub.t+1] [equivalent to] [1 + [[alpha].sub.t]/(1 - r)[beta]][z.sub.t+1] - [[alpha].sub.t]/(1 - r)[beta][z.sub.t],

which is orthogonal to {[z.sub.[tau]}.sub.[tau][less than or equal to]t]. The precision of [s.sub.t+1] is

[gamma][[1 + [[alpha].sub.k]/(1 - r)[beta]].sup.-2],

which we denote by [[gamma].sub.t].

Since [[gamma].sub.t] [less than or equal to] [gamma], we can conclude that the incremental information value to the central bank of observing its signal [z.sub.t+1] is lower in the disclosure case. Moreover, this incremental information value is lower, the higher was the central bank's overall precision [[alpha].sub.t] in the previous period. In other words, raising the central bank's overall information precision has the effect of lowering the value of its subsequent signal. The intuition is that increased precision at t intensifies the beauty contest and reduces the information value of the average action. This then lowers the information precision of the signal arriving at t + 1.

At date t + 1 the central bank's linear estimate of [[theta].sub.t] is

(32) [[alpha].sub.t][z.sub.t] + [[gamma].sub.t][s.sub.t+1]/[[alpha].sub.t] + [[gamma].sub.t],

with precision [[alpha].sub.t] + [[gamma].sub.t]. Since [[theta].sub.t+1] = [[theta].sub.t+1] + [[phi].sub.t+1], we have a recursive formula for the central bank's information precision in the disclosure case:

(33) 1/[[alpha].sub.t+1] = 1 + 1/[[alpha].sub.t] + [[gamma].sub.t]

= 1 + 1/[[alpha].sub.t] + [gamma][(1 - r)[beta]/[[[alpha].sub.t] + (1 - r)[beta]].sup.2].

The steady-state information precision in the disclosure case is the value of [alpha] that solves

(34) [alpha]{1 + 1/[alpha] + [gamma][[(1 - r)[beta]/[alpha] + (1 - r)[beta]].sup.2]} = 1.

Comparing the Regimes

Comparing the steady-state information precision levels in the two regimes given by equations 28 and 34, we can see that steady-state precision is lower under the disclosure regime, since the value of the expression in curved brackets in equation 34 is greater than 1 + [1/([alpha] + [gamma])]. For parameter values r = 0.85 and [beta] = 1, (40) we can plot in figure 3 the steady-state information precision [alpha] as a function of the variance 1/[gamma] of the noise term [psi]. The central bank has higher information precision in the nondisclosure case. In both cases this precision can be raised to the upper bound of 1 by reducing the variance of the noise, but the disclosure case requires very little noise to get close to the upper bound.

It is worth noting that the deterioration of the central bank's signal value under the disclosure regime holds even when r = 0, so that there are no coordination elements, although coordination elements exacerbate the effect. We return to this issue below.

It is also apparent from the implicit formula in equation 34 for steady-state [alpha] that the central bank's information precision is a function of the private sector agents' information precision. This is intuitively clear, since the central bank learns by observing what the individual agents do. The reason [beta] enters in this relation is that the aggregate actions [[bar.[alpha]].sub.t] are revealing only to the extent that private agents put weight on their own private signals. The more informative their private signals, the greater the information value of the aggregate action. In this sense the central bank's information value is dependent on (and derivative of) the private sector agents' information precision.

Figure 4 plots [alpha] as a function of [beta] for varying values of the noise [[psi].sub.t], in the central bank's signal (holding other parameter values the same as in figure 3). The central bank's information precision is increasing in the private sector's information precision, but [alpha] can lie below [beta], especially when [beta] is large. One reason is that, whereas private sector agents have contemporaneous information about [[theta].sub.t] from their signals (say, by observing a signal about their current marginal cost), the central bank's signal comes with some delay, and the innovation to [[beta].sub.t] increases the central bank's uncertainty.

Finally, it is worth noting that the forecasting rule for the central bank will change if it moves from a nondisclosure regime to a disclosure regime. Since 0, follows a random walk, the linear estimates given by equations 26 and 32 are also forecasts of all future values of [theta]. Needless to say, if the central bank continues to use the old (nondisclosure) forecasting rule under the new (disclosure) regime, its forecast will be off the mark. One could view this as a variation of the Lucas critique as applied to central bank transparency. The time-series properties of aggregate actions will change as the disclosure regime changes.

Welfare Effects of Transparency

The impaired signal value for the transparent central bank will impinge on any control problem that it faces, and it poses greater challenges in making decisions under uncertainty. Thus the central bank will face a trade-off between the welfare gains that result from being able to steer the future beliefs of economic agents, and the impaired signal value that results from disclosure of its forecasts. Evaluating the terms of such a trade-off is an important topic for future investigation. Furthermore, the degree of transparency itself emerges as one dimension of the optimal control problem: one can expect to see a future debate on "optimal transparency." We believe these issues to be the key to resolving the welfare effects of transparency in the spirit of the Hayek-Lange debate.

The debate to date, however, has concentrated on the one-shot model of beauty contests sketched earlier, where [alpha] is taken as given. Although the current debate sheds no light on the endogenous nature of central bank information, it is nevertheless illuminating in outlining some of the other dimensions of the debate.

Welfare Effects in the Static Analysis

Recall that, under the equilibrium decision rule (equation 12), the average action of individuals was equal to

[alpha]y + [beta](1 - r)[theta]/[alpha] + [beta](1 - r)

Expressed in terms of basic random variables [theta] and [eta], we have

(35) [bar.a] = [theta] + [alpha][eta]/[alpha] + [beta](1 - r).

Thus increases in [alpha] and increases in r unambiguously reduce the informativeness of the average action as a signal of [theta]. In particular, public information always reduces the informativeness of average actions, even if r = 0, but strategic complementarities exacerbate the effect. Although we have not formally modeled the social value of information about [theta], we have focused on the importance of the information aggregation role of prices in private investment decisions and in the forecasting of the central bank. The welfare losses come not from coordination itself, but rather from the externalities imposed by the agents playing the beauty contest on those other agents who rely on prices to be informationally efficient. There is a market failure in which agents fail to internalize the externalities flowing from uninformative prices.

Some recent debates on the social value of information have focused on the welfare of the coordinating players themselves (rather than their external effect on others learning from their actions). In a previous paper we assumed that the beauty contest element of the individuals' decision is socially wasteful, entering only as a zero-sum component in payoffs, so that social welfare depends only on the variation of individual actions around [theta]. (41) In this case social welfare is enhanced only to the extent that individuals' actions approximate the fundamental state [theta]. In such a formulation, increased precision of public information is not guaranteed to raise welfare. Expected welfare in that paper is given by

(36) E[W|[theta]] = [[alpha].sup.2]E([[eta].sup.2]) + [[beta].sup.2][(1 - r).sup.2][E([[epsilon].sup.2.sub.i])]/[[[alpha] + [beta](1 - r)].sup.2]

= - [alpha] + [beta][(1 - r).sup.2]/[[[alpha] + [beta](1 - r)].sup.2], since Var([eta]) = 1/[alpha]

and Var([[epsilon].sub.i]) = E([[epsilon]2.sup.u.sub.i]) = 1/[beta].

Welfare is increasing in the precision of the private signals, as we can see by differentiating equation 36 with respect to [beta]:

(37) [differential]E(W|[theta])/[differential][beta] = (1 - r)[(1 + r)[alpha] + [(1 - r).sup.2][beta]]/[[[alpha] + [beta](1 - r)].sup.3]

However, the derivative of equation 36 with respect to [alpha] is

(38) [differential]E(W|[theta])/[differential][alpha] = [alpha] - (2r - 1)(1 - r)[beta]/[[[alpha] + [beta](1 - r)].sup.3],

so that

(39) [differential]E(W|[theta])/[differential][alpha] [less than or equal to] 0 if and only if r [greater than or equal to] 0 if and only if r [greater than or equal to] 1/2 and [beta]/[alpha] [greater than or equal to] 1/(2r - 1)(1 - r).

When r > 0.5, there are ranges of the parameters where increased precision of public information is detrimental to welfare.

If [alpha] is restricted to some interval [0, [bar.[alpha]]] for technical feasibility reasons, we can expect a corner solution to the optimization of [alpha], in which the social optimum entails either providing no public information at all (that is, setting ([alpha] = 0) or providing the maximum feasible amount of public information (setting [alpha] = [bar.[alpha]]). The better informed is the private sector, the higher the hurdle rate of the precision of public information that would make it welfare enhancing.

However, the zero-sum nature of the coordination element in payoffs is crucial to our 2002 result. If instead the coordination itself has some social value, the ambiguous effect of [alpha] disappears. Woodford describes utility functions that give rise to the same linear decision rule (equation 2) but allow for a social value of coordinated action; (42) in this case welfare is no longer given by equation 36 but rather by

(40) -[alpha] + [beta](1 - [r.sup.2])/[[[alpha] + [beta](1 - r)].sup.2].

Woodford points out that this function is globally increasing in [alpha], and so greater precision of public information cannot be harmful.

In the same spirit, George-Marios Angeletos and Alessandro Pavan propose a microfounded model that incorporates coordination elements in the welfare function. (43) The coordination element comes from an investment problem with positive spillover effects, and so an explicit coordination premium is built into the problem. In particular, the welfare effects are closely tied to the fact that better public information allows the agents to eliminate the inefficiencies associated with coordination failure.

The coordination element in Hellwig's analysis is more subtle. (44) Hellwig presents a macroeconomic model with monopolistic competition based on the Dixit-Stiglitz aggregators for consumption and price. In particular, the average price for the economy as a whole is given by the index

(41) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.],

where [theta] > 1 is the elasticity of substitution between goods, and [p.sup.i.sub.t] is the price charged by firm i at date t. In effect, the average price is a generalized harmonic mean of prices. (45) This has important consequences. Although profit is increasing in [P.sub.t], it is decreasing in price dispersion, reflecting the fact that the harmonic mean always lies below the arithmetic mean. Thus a firm's expected profit increases when price dispersion is reduced. In turn, the form of the price index reflects the preference for variety implicit in the Dixit-Stiglitz utility function. For other specifications of preferences, an alternative perspective is to note that a consumer's indirect utility (utility as a function of prices at the optimum) is a convex function of prices, reflecting the ability of consumers to switch away from expensive goods in favor of cheaper ones. Price dispersion then has a beneficial effect. It would be desirable to understand more generally how welfare effects in Hellwig's model depend on attitudes to price dispersion.

Our original results are thus sensitive to the microfoundation given to the coordination motive. We highlighted this sensitivity in the online appendix to our 2002 paper. (46) A recent paper by Angeletos and Pavan provides a unified analysis of the value of public information strategic problems with quadratic payoff. (47) Their analysis makes use of a comparison of equilibrium behavior with an "efficient" outcome, corresponding to a constrained planner's problem, where the planner can mandate players' actions as a function of their signals but cannot observe the signals. Their analysis highlights that the results in our 2002 paper rely on both the lack of externalities in payoffs and that the equilibrium involves an inefficiently high level of coordination. Thus continuing work on the welfare analysis of public information with a microfounded coordination motive is clearly valuable. However, we have emphasized elsewhere in this paper that the dynamic effects of information revelation may be important and that one should not rely too heavily on the one-shot version of the beauty contest model in drawing conclusions about the desirability of greater transparency.

Relative Precision

In a reply to our 2002 paper, Lars Svensson raises another issue. (48) Taking our payoffs at face value, he makes two observations. First, the result that welfare is locally decreasing in the precision of public information holds only with restrictions on the information parameters that are empirically very restrictive ([alpha] has to be small relative to [beta]). Second, even on a global analysis, when the precision of the public signal is no lower than that of the private signal, welfare is higher with the public signal than without it.

Svensson's point can be explained by referring back to welfare as given by equation 36, but expressed as a function of [alpha]. Let us denote this by V([alpha]). Thus,

(42) V([alpha]) = - [alpha] + [beta][(1 - r).sup.2] / [[alpha] + [beta][(1 - r)].sup.2]

On the assumption that withholding the public signal is equivalent to setting [alpha] = 0, the ex ante welfare in the absence of the public signal is thus

(43) V(0) = - 1/[beta].

There is a hurdle rate [bar.[alpha]] for the precision of the public signal such that welfare with the public signal is lower than welfare without it if and only if [alpha] < [[bar.[alpha]]. The hurdle rate is the value of [alpha] that solves V([alpha]) = V(0) and is given by

(44) [bar.[alpha]] = [beta](2r - 1).

Since 0 < r < 1, the hurdle rate is lower than the precision [beta] of the private information. Thus, for the benchmark case where the precision of public information is no lower than that of private information (that is, where [alpha] [greater than or equal to] [beta]), welfare is higher with the public signal than without it.

Without taking fully into account the endogenous nature of [alpha], it would be difficult to come to a firm conclusion on the relative sizes of [alpha] and [beta]. We can see from figure 3 above that, when good public information depends on a high precision of private information, choosing one has implications for the other.

[FIGURE 3 OMITTED]

The evidence from Romer and Romer that the Federal Reserve' s Greenbook forecasts outperform the forecasts of the Federal Reserve's private sector counterparts is often cited as evidence that [alpha] is greater than [beta]. (49) However, private sector forecasters are not the typical "economic agent" studied in most economic models. Rather they are special types of agents who try to mimic the central bank's decision problem, but with fewer resources. Thus [beta] should be understood to refer to the information precision of genuine economic agents who learn about the current state of the economy from their own transactions. For instance, in the price setting game version of the beauty contest rule, each economic agent is a firm trying to balance the competitive effects of price changes with the need to keep price above marginal cost. Here [beta] is the precision of the firm's estimate of its own marginal cost. The stylized model in our 2002 paper also suffers from the fact that it imposes independence of the signals conditional on [theta]. The online appendix to that paper dealt with a more general case that allows for correlated signals, and Morris, Shin, and Hui Tong present an example, in a reply to Svensson, (50) showing the variety of welfare effects that may arise away from the simple benchmark case, and in particular that public information may be damaging even at high levels of public precision.

The debates formulated in the static model have extended our understanding along several dimensions, but the limited nature of the static framework and the sensitivity of the results to the assumed payoffs suggest that we have come close to the limits of useful debate within the confines of such a restrictive framework. Much more important would be the endogenous nature of public information precision itself. It is this issue that lies at the heart of the debate between Hayek and his socialist contemporaries, and the largest stakes in the monetary policy transparency debate lie here.

Implications for Monetary Policy

One of the pitfalls of engaging in any debate is that of overselling one's case and making possibly untenable claims. The dangers are large, especially if the issue is something as basic and desirable as the transparency of a prominent and influential public institution. Thus it is worth taking a deep breath and a larger perspective. The arguments presented in this paper do not address the question of whether any particular forecast or other information should or should not be disclosed. Rather, the objective has been to review arguments about the trade-offs involved in the choice of framework for communicating with diverse economic actors. Nor do we claim that transparency (or inflation targeting, or publication of forecasts) is undesirable. Our aim is the much more modest one of drawing attention to the two-sided nature of the debate.

Transparency affords considerable leverage to central bankers in influencing the beliefs of economic agents. But this in turn may reduce the signal value of private sector actions. The Bank of England's recent experience provides a glimpse into the difficulties faced by a central bank when it has poor information on the current state of the economy. At its August 2005 meeting the Monetary Policy Committee voted by a majority of five to four to lower the policy rate. The minutes of the meeting represent the views of the members who voted against the cut as follows:</p>

<pre> For these members, there appeared to be little risk in waiting for further data. Given the difficulty in explaining a reversal of a decision soon after a turning point, should that prove necessary in the light of future data, it was advisable to accumulate a little

more evidence than usual before changing interest rates. (51) </pre> <p>The uncertainty about the current state of the economy clearly played on the minds of all members. Uncertainty as to where the economy actually was at the time was also a prominent theme at the press conference following the publication of the August 2005 Inflation Report. (52)

To the extent that uncertainty about current conditions makes forecasting more difficult, another telltale sign of a drop in signal values would be a deterioration in forecasting performance. Of course, such a deterioration cannot be seen as a clinching argument for a drop in signal values (there may be other culprits), but we have seen that changes in the disclosure regime are associated with changes in the time-series properties of aggregate outcomes, as well as changes in the signal value of those outcomes. When poor signal values conspire with structural change in the economy, forecasting will be extremely difficult. Thus forecasting failures would certainly be consistent with a drop in signal values. There is some recent evidence of a deterioration in the forecasting accuracy of central banks and their private sector counterparts. (53)

At the Federal Reserve, the staff of the Board of Governors prepares a detailed forecast before each scheduled meeting of the Federal Open Market Committee (FOMC). The purpose of this forecast, known as the Greenbook, is to serve as background to the deliberations in the FOMC, and the views expressed are those of the staff rather than individual committee members. Sims provides a detailed description of the process by which the Greenbook forecasts are arrived at. (54) The forecasts are posted on the website of the Federal Reserve Bank of Philadelphia, except for the most recent five-year window, which remains confidential. Peter Tulip's study therefore uses the publicly disclosed data that include forecasts of outcomes up to the end of 2001. (55)

Tulip finds that, even as output fluctuations have moderated substantially in recent years,56 forecast errors have not. The fact that policy responses are endogenous and that output fluctuations have moderated both make forecasting more difficult. Nevertheless, it is notable from Tulip's study that the performance of longer-term forecasts for output (up to eight quarters) has not been encouraging. Since the late 1980s, mean squared prediction errors have been similar to, and sometimes greater than, the variance itself. In other words, the simple sample mean (the most naive forecast) has proved a more accurate guide to GDP growth than the actual forecasts, which is to say that the forecasts have had negative predictive value.

One way to picture this is to consider a regression of the two-year change in GDP on a constant and the corresponding forecast. This regression has a negative coefficient when estimated on the last ten years of the sample (1992 to 2001). C. Goodhart reports findings for the Bank of England's forecast performance, which demonstrate a similar lack of predictive power for longer-term forecasts, but Goodhart points out that, when the central bank acts on the forecasts themselves, the lack of correlation between the initial forecast and the final outcome should be expected. (57) Sean Campbell reports results from private sector forecasts and finds that short-term forecasts of the Survey of Professional Forecasters have a negative R-squared over the period 1984-2003, echoing Tulip's result for the Federal Reserve. (58)

If the central bank does not recognize that signal values are impaired in a world of managed expectations, it may be lulled into a false sense of security when in fact imbalances are building in the economy. Even though consumer goods prices may be stable and the flows in the IS curve are well behaved, asset prices may be buoyed by excessively lax credit conditions, building up problems for the future despite no obvious signs of trouble.

If inflation targeting is practiced flexibly, the output costs of financial distress could figure in the overall calculations. Less easy to overcome would be the political economy hurdles facing a central bank's monetary policy committee whose mandate is interpreted narrowly as inflation and output stabilization over a relatively short horizon. The key issue is whether a monetary policy committee that suspects that imbalances are building up under the radar feels that it can justify departing from the inflation target over the targeting horizon in order to forestall larger problems over a longer horizon.

Australia provides one recent instance where a central bank has acted to lean against the wind, raising interest rates and then keeping them high in the face of an overheating residential property market, even though consumer prices and output were well behaved. The Reserve Bank of Australia (RBA) came under considerable criticism for acting beyond its mandate: critics claimed that it was looking "beyond its horizon" of two years in targeting inflation. By taking such actions, the RBA was undoubtedly risking its own reputation, since the politically more expedient path would have been to stick to a more narrow interpretation of its mandate. In the event, the RBA's preemptive actions proved well advised, and its reputation has been enhanced. Thus, in practice, central bankers have adapted well to the new inflation targeting regime, and debates are frequently conducted in broader terms.

It is beyond the scope of this paper to broach the larger topic of central bank accountability. Transparency in this broader sense is crucial for establishing and maintaining the political legitimacy of the central bank as a public institution. (59) But there is a potential paradox of transparency. One of the inevitable fruits of the success in influencing beliefs is that the central bank has to rely on less informative signals to guide its decisions. If policymakers are to consolidate the successes achieved to date, they will have to turn their attention to how monetary policy should be conducted in an era when prices are less informative.

We thank Benjamin Friedman and Christopher Sims for their comments and guidance. We also thank Marios Angeletos, Alan Blinder, Christian Hellwig, Anil Kashyap, Don Kohn, Chris Kent, Phil Lowe, Ellen Meade, Lars Svensson, and T. N. Srinivasan for comments at various stages of the project.

(1.) Blinder (1998, p. 70).

(2.) Svensson (2004, p. 1); Woodford (2005, p. 3).

(3.) Bernanke (2004b).

(4.) Woodford (2005, p. 2); see also Blinder (1998); Woodford (2003b, chapter 7); Svensson and Woodford (2005).

(5.) See Kuttner (2004) for an overview of the various ways in which inflation targeting has been implemented. Early contributions include Leiderman and Svensson (1995), Bernanke and Mishkin (1997), and Bernanke and others (2001).

(6.) Kohn (2005).

(7.) Bernanke (2004a).

(8.) Fisher (1930).

(9.) Polk and Sapienza (2004); Chen, Goldstein, and Jiang (2005).

(10.) Fleming and Remolona (1999).

(11.) Roley (1983), Cornell (1983), and Roley and Walsh (1985) have documented the heightened reaction to money stock announcements in the early 1980s.

(12.) Roley (1983, p. 344).

(13.) Brayton, Roberts, and Williams (1999).

(14.) Bank of England (2005).

(15.) See Geoffrey Dicks, "Bank of England Needs to Re-examine Its Forecasts," Financial Times, August 10, 2005.

(16.) Sims (2003). See also Mackowiak and Wiederholt (2005), who show how Sims' (2003) framework can be used to explain the simultaneous occurrence of persistent average prices and large price shifts in some subsets of goods.

(17.) Kuttner (2004); Ball and Sheridan (2003).

(18.) Mankiw, Reis, and Wolfers (2004).

(19.) Levin, Natalucci, and Piger (2004).

(20.) Gurkaynak, Levin, and Swanson (2005).

(21.) Gurkaynak, Levin, and Swanson (2005); this result is elaborated in Gurkaynak, Sack, and Swanson (2005).

(22.) Hayek (1945).

(23.) Hayek (1945, pp. 519-20).

(24.) Lange (1936, 1937).

(25.) Grossman (1976); Radner (1979).

(26.) Romer and Romer (2000).

(27.) Sims (2002).

(28.) Hayek (1945, p. 524).

(29.) Morris and Shin (2002).

(30.) Keynes (1936).

(32.) Lucas (1972, 1973); Phelps (1970).

(33.) Phelps (1983).

(34.) Woodford (2003a) has popularized this interpretation of the beauty contest rule.

(35.) Gali and Gertler (1999).

(36.) Woodford (2003a).

(37.) Woodford (2003a). Townsend (1983) discusses similar linear rules but in the context of investment.

(38.) See Adam (2003), Amato and Shin (forthcoming), Hellwig (2002, 2004), and Ui (2003). See also Kasa (2000) and Pearlman and Sargent (2005). The latter show how the problem can sometimes be reduced to the case with common knowledge. Similar issues arise in the context of asset pricing: see Allen, Morris, and Shin (forthcoming) and Bacchella and Van Wincoop (2003, 2004).

(39.) Allen, Morris, and Shin (forthcoming).

(40.) The value r = 0.85 is implied by [xi] = 0.15 in the imperfect competition interpretation of the beauty contest rule. See Woodford (2003b) for a discussion of the magnitude of [xi].

(41.) Morris and Shin (2002).

(42.) Woodford (2005, appendix A).

(43.) Angeletos and Pavan (2004).

(44.) Hellwig (2004).

(45.) More accurately, it is the power mean with a negative power. See, for instance, mathworld.wolfram.com/HarmonicMean.html.

(46.) Morris and Shin (2002); the online appendix is at www.e-aer.org/data/dec02_app_morris.pdf.

(47.) Angeletos and Pavan (2005).

(48.) Svensson (forthcoming).

(49.) Romer and Romer (2000).

(50.) Morris, Shin, and Tong (forthcoming).

(51.) www.bankofengland.co.uk/publications/minutes/mpc/pdf/2005/index.htm, p. 9.

(52.) A video of the press conference is available at the Bank of England website, www.bankofengland.co.uk.

(53.) The evidence is documented in Schuh (2001) and Campbell (2004) for private sector forecasters, and in Goodhart (2004) and Tulip (2005) for the Bank of England and the Federal Reserve, respectively.

(54.) Sims (2002).

(55.) Tulip (2005).

(56.) The moderation in output fluctuations has been documented by McConnell and Perez-Quiros (2000), Kim and Nelson (1999), and Blanchard and Simon (2001).

(57.) Goodhart (2004).

(58.) Campbell (2004).

(59.) Geraats (2002) gives a taxonomy of the different types of transparency.</p>

<pre> Australia: quarterly change in the consumption deflator Percent a year, annualized 2002:1 3.68 2002:2 1.22 2002:3 2.43 2002:4 1.61 2003:1 4.79 2003:2 -1.19 2003:3 0.80 2003:4

1.59 2004:1 3.55 2004:2 1.17 2004:3 1.17 2004:4 2.33 2005:1 2.70 </pre> <p>STEPHEN MORRIS

Princeton University

HYUN SONG SHIN

London School of Economics