Can Information Heterogeneity Explain the Exchange Rate ...kkasa/bacchetta06.pdf · preventing...

Can Information Heterogeneity Explain the Exchange RateDetermination Puzzle?

By PHILIPPE BACCHETTA AND ERIC VAN WINCOOP*

Empirical evidence shows that most exchange rate volatility at short to mediumhorizons is related to order flow and not to macroeconomic variables. We introducesymmetric information dispersion about future macroeconomic fundamentals in adynamic rational expectations model in order to explain these stylized facts.Consistent with the evidence, the model implies that (a) observed fundamentalsaccount for little of exchange rate volatility in the short to medium run, (b) over longhorizons, the exchange rate is closely related to observed fundamentals, (c) ex-change rate changes are a weak predictor of future fundamentals, and (d) theexchange rate is closely related to order flow. (JEL F3, F4, G0, G1, E0)

The poor explanatory power of existing the-ories of the nominal exchange rate is most likelythe major weakness of international macroeco-nomics. Richard A. Meese and Kenneth Rogoff(1983) and the subsequent literature have foundthat a random walk predicts exchange ratesbetter than macroeconomic models in theshort run. Richard Lyons (2001) refers to theweak explanatory power of macroeconomicfundamentals as the “exchange rate determi-nation puzzle.”

This puzzle is less acute for long-run ex-change rate movements, since there is extensiveevidence of a much closer relationship betweenexchange rates and fundamentals at horizons oftwo to four years (e.g., see Nelson C. Mark,1995). Recent evidence from the microstructureapproach to exchange rates suggests that in-vestor heterogeneity might play a key role in

explaining exchange rate fluctuations. In partic-ular, Martin D. D. Evans and Lyons (2002b)show that most short-run exchange rate volatil-ity is related to order flow, which in turn isassociated with investor heterogeneity.1 Sincethese features are not present in existing theo-ries, a natural suspect for the failure of currentmodels to explain exchange rate movements isthe standard hypothesis of a representativeagent.

The goal of this paper is to present an alter-native to the representative agent model that canexplain the exchange rate determination puzzleand the evidence on order flow. We introduceheterogeneous information into a standard dy-namic monetary model of exchange rate deter-mination. There is a continuum of investorswho differ in two respects. First, they havesymmetrically dispersed information about fu-ture macroeconomic fundamentals.2 Second,they face different exchange rate risk exposureassociated with nonasset income. This exposureis private information and leads to hedge tradeswhose aggregate is unobservable. Our main

* Bacchetta: Study Center Gerzensee, 3115 Gerzensee,Switzerland, University of Lausanne, and Swiss FinanceInstitute (e-mail: [email protected]); vanWincoop: Department of Economics, University of Vir-ginia, Charlottesville, VA 22904 and NBER (e-mail:[email protected]). We would like to thank BrunoBiais, Gianluca Benigno, Christophe Chamley, MargaridaDuarte, Ken Froot, Harald Hau, Olivier Jeanne, RichardLyons, Elmar Mertens, two anonymous referees, and manyseminar and conference participants for helpful comments.Financial support from the Bankard Fund for Political Econ-omy and the National Centre of Competence in Research“Financial Valuation and Risk Management” (NCCR FIN-RISK) is gratefully acknowledged. The NCCR FINRISK isa research program supported by the Swiss National ScienceFoundation.

1 See also Evans and Lyons (2002a), Harald Hau et al.(2002), Geir Bjønnes et al. (2005), and Kenneth A. Frootand Tarun Ramadorai (2005).

2 We know from extensive survey evidence that inves-tors have different views about the macroeconomic outlook.There is also evidence that exchange rate expectations differsubstantially across investors. See Takatoshi Ito (1990),Ronald MacDonald and Ian W. Marsh (1996), GrahamElliott and Ito (1999), and Dionysios Chionis and Mac-Donald (2002).

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finding is that information heterogeneity dis-connects the exchange rate from observed mac-roeconomic fundamentals in the short run,while there is a close relationship in the longrun. At the same time there is a close linkbetween the exchange rate and order flow overall horizons.

Our modeling approach integrates severalstrands of literature. First, it has in commonwith most of the existing (open economy)macro literature that we adopt a fully dynamicgeneral equilibrium model, leading to time-in-variant second moments. Second, it has in com-mon with the noisy rational expectationsliterature in finance that the asset price (ex-change rate) aggregates private information ofindividual investors, with unobserved shockspreventing average private signals from beingfully revealed by the price. The latter are mod-eled endogenously as hedge trades in our model.3

Third, it has in common with the microstructureliterature of the foreign exchange market that pri-vate information is transmitted to the marketthrough order flow.4

Most models in the noisy rational expecta-tions literature and microstructure literature arestatic or two-period models.5 This makes themill-suited to address the disconnect between as-set prices and fundamentals, which has a dy-namic dimension since the disconnect is muchstronger at short horizons. Even the few dy-namic rational expectation models in the fi-nance literature cannot be applied in ourcontext. Jiang Wang (1993, 1994) develops aninfinite horizon, noisy rational expectationsmodel with a hierarchical information structure.There are only two types of investors, one ofwhich can fully observe the variables affectingthe equilibrium asset price. We believe that it ismore appropriate to consider cases where noclass of investors has superior information andwhere there is broader dispersion of informa-tion. Several papers make a step in this direction

by examining symmetrically dispersed informa-tion in a multiperiod model, but they examineonly an asset with a single payoff at a terminaldate.6

For the dynamic dimension of our paper, werely on the important paper by Robert M.Townsend (1983). Townsend analyzed a busi-ness cycle model with symmetrically dispersedinformation. As is the case in our model, thesolution exhibits infinitely higher-order expec-tations (expectations of other agents’ expecta-tions).7 We adapt Townsend’s solution procedureto our model. The only application to asset pricingwe are aware of is Kenneth J. Singleton (1987),who applies Townsend’s method to a model forgovernment bonds with a symmetric informationstructure.8

Another feature of our paper is the explicitmodeling of order flow in a general equilibriummodel. This gives a theoretical framework toguide empirical work on order flow. We show,for example, how order flow precedes pricesand thus conveys information. To derive orderflow, we take a different perspective on theequilibrium mechanism. Typically, the equilib-rium price of a competitive noisy rational ex-

3 Some recent papers in the exchange rate literature haveintroduced exogenous noise in the foreign exchange market.They do not, however, consider information dispersionabout future macro fundamentals. Examples are Hau(1998), Mark and Yangru Wu (1998), Michael B. Devereuxand Charles Engel (2002), Olivier Jeanne and Andrew K.Rose (2002), and Robert Kollman (2002).

4 See Lyons (2001) for an overview of this literature.5 See Markus K. Brunnermeier (2001) for an overview.

6 See Hua He and Wang (1995), Xavier Vives (1995), F.Douglas Foster and S. Viswanathan (1996), Michael J.Brennan and H. Henry Cao (1997), or Franklin Allen et al.(forthcoming). Brennan and Cao assume that private infor-mation is symmetrically dispersed among agents within acountry, while there is also asymmetric information be-tween countries.

7 Subsequent contributions have been mostly technical,solving the same model as in Townsend (1983) with alter-native methods. See Thomas J. Sargent (1991) and KennethKasa (2000). Probably as a result of the technical difficultyin solving these models, the macroeconomics literature hasdevoted relatively little attention to heterogeneous informa-tion in the last two decades. This contrasts with the 1970swhere, following Robert E. Lucas (1972), there had beenactive research on rational expectations and heterogeneousinformation (e.g., see Robert G. King, 1982). Recently,information issues in the context of price rigidity have againbeen brought to the forefront in contributions by N. GregoryMankiw and Ricardo Reis (2002) and Michael Woodford(2003).

8 In Singleton’s model there is no information dispersionabout the payoff structure on the assets (in this case, cou-pons on government bonds), but there is private informationabout whether noise trade is transitory or persistent. Theuncertainty is resolved after two periods. John P. Hussman(1992) and Kasa et al. (2004) also study dynamic assetpricing models with infinitely higher-order expectations,but do not adopt a symmetrically dispersed informationstructure.

553VOL. 96 NO. 3 BACCHETTA AND VAN WINCOOP: INFORMATION AND EXCHANGE RATES

pectation model is seen as determined by aWalrasian auctioneer. The equilibrium can alsobe interpreted, however, as the outcome of anorder-driven auction market, whereby marketorders based on private information hit an out-standing limit order book. This characterizationresembles the electronic trading system thatnowadays dominates the interbank foreign ex-change market. As is common in the theoreticalliterature, we define limit orders as orders thatare conditional on public information and the(yet unknown) exchange rate. Limit orders pro-vide liquidity to the market. Market orders takeliquidity from the market and are associatedwith private information. Order flow is equal tonet market orders. Not surprisingly, the weakrelationship in the model between short-run ex-change rate fluctuations and publicly observedfundamentals is closely mirrored by the closerelationship between exchange rate fluctuationsand order flow.9

The dynamic implications of the model forthe relationship between the exchange rate, ob-served fundamentals, and order flow can beunderstood as follows. In the short run, rationalconfusion plays an important role in disconnect-ing the exchange rate from observed fundamen-tals. Investors do not know whether an increasein the exchange rate is driven by an improve-ment in average private signals about futurefundamentals or an increase in unobservedhedge trades. This implies that unobservedhedge trades have an amplified effect on theexchange rate since they are confused withchanges in average private signals about futurefundamentals.10 We show that a small amountof hedge trades can become the dominantsource of exchange rate volatility when infor-

mation is heterogeneous, while it has practicallyno effect on the exchange rate when investorshave common information. Moreover, our numer-ical simulations show that these effects are quan-titatively consistent with empirical evidence.

In the long run there is a close relationshipbetween the exchange rate, observed fundamen-tals, and cumulative order flow. First, rationalconfusion gradually dissipates as investors learnmore about future fundamentals.11 The impactof unobserved hedge trades on the equilibriumprice therefore gradually weakens, leading to acloser long-run relationship between the ex-change rate and observed fundamentals. Sec-ond, when the fundamental has a permanentcomponent, the exchange rate and cumulativeorder flow are closely linked in the long run.Private information about permanent futurechanges in the fundamental is transmitted to themarket through order flow, so that order flowhas a permanent effect on the exchange rate.

The remainder of the paper is organized asfollows. Section I describes the model and so-lution method. Section II considers a specialcase of the model in order to develop intuitionfor our key results. Section III discusses theimplications of the dynamic features of themodel. Section IV presents numerical resultsbased on the general dynamic model and Sec-tion V concludes.

I. A Monetary Model with InformationDispersion

A. Basic Setup

Our model contains the three basic buildingblocks of the standard monetary model of ex-change rate determination: (a) money marketequilibrium, (b) purchasing power parity, and(c) interest rate arbitrage. We modify the stan-dard monetary model by assuming incompleteand dispersed information across investors.Before describing the precise informationstructure, we first derive a general solution to

9 In recent work closely related to ours, Evans and Lyons(2004) also introduce microstructure features in a dynamicgeneral equilibrium model in order to shed light on ex-change rate puzzles. There are three important differences incomparison to our approach. First, they adopt a quote-driven market, while we model an order-driven auctionmarket. Second, they assume that all investors within onecountry have the same information, while there is asymmet-ric information across countries. Third, their model is not inthe noisy rational expectations tradition.

10 The basic idea of rational confusion can already befound in the noisy rational expectation literature. For exam-ple, Gerard Gennotte and Hayne Leland (1990) and DavidRomer (1993) argued that such rational confusion played acritical role in amplifying noninformational trade during thestock-market crash of October 19, 1987.

11 Another recent paper on exchange rate dynamicswhere learning plays an important role is Pierre-OlivierGourinchas and Aaron Tornell (2004). In that paper, inwhich there is no investor heterogeneity, agents learn aboutthe nature of interest rate shocks (transitory or persistent),but there is an irrational misperception about the secondmoments in interest rate forecasts that never goes away.

554 THE AMERICAN ECONOMIC REVIEW JUNE 2006

the exchange rate under heterogeneous infor-mation, in which the exchange rate dependson higher-order expectations of future macro-economic fundamentals. This generalizes thestandard equilibrium exchange rate equationthat depends on common expectations of futurefundamentals.

Both observable and unobservable funda-mentals affect the exchange rate. The observ-able fundamental is the ratio of money supplies.We assume that investors have heterogeneousinformation about future money supplies. Theunobservable fundamental takes the form of anaggregate hedge against nonasset income in thedemand for foreign exchange. This unobserv-able element introduces noise in the foreignexchange market in the sense that it preventsinvestors from inferring average expectationsabout future money supplies from the price.12

This trade also affects the risk premium in theinterest rate arbitrage condition. Notice that theunobserved hedge trades are true aggregate fun-damentals that drive the equilibrium exchangerate, but they are typically not called fundamen-tals by macroeconomists because they cannotbe directly observed.

There are two economies. They produce thesame good, so that purchasing power parityholds:

(1) pt � p*t � st .

Local currency prices are in logs and st is thelog of the nominal exchange rate (home perforeign currency).

There is a continuum of investors in bothcountries on the interval [0, 1]. We assume thatthere are overlapping generations of agents wholive for two periods and make only one invest-ment decision. Before dying, investor i passeson his or her private information to the nextinvestor i born the following period. This my-opic agent setup significantly simplifies the pre-sentation, helps in providing intuition, andallows us to obtain an exact solution to themodel.13

Investors in both economies can invest infour assets: money of their own country, nom-inal bonds of both countries with interest rates itand i*t, and a technology with fixed real return rthat is in infinite supply. We assume a smallopen-economy setting. The Home country islarge and the Foreign country infinitesimallysmall; variables from the latter are starred. Bondmarket equilibrium is therefore entirely deter-mined by investors in the large Home country,on which we will focus. We also assume thatmoney supply in the large country is constant. Itis easy to show that this implies a constant pricelevel pt in equilibrium, so that it � r. For ease ofnotation, we just assume a constant pt. Moneysupply in the small country is stochastic.

The wealth wti of investors born at time t is

given by a fixed endowment. At time t � 1these investors receive the return on their in-vestments plus income yt�1

i from time t � 1production. We assume that production dependsboth on the exchange rate and on real moneyholdings mt

i through the function yt�1i �

�tist�1 � mt

i(ln(mti) � 1)/�, with � � 0.14 The

coefficient �ti measures the exchange rate expo-

sure of the nonasset income of investor i. Weassume that �t

i is time varying and known onlyto investor i. This will generate an idiosyncratichedging term. Agent i maximizes

�Etie��ct � 1

i

subject to

ct � 1i � �1 � it �wt

i � �st � 1 � st � i*t � it �bFti

� itmti � yt � 1

i ,

where bFti is invested in foreign bonds and

st�1 � st � i*t � it is the log-linearized excessreturn on investing abroad.

Combining the first-order condition formoney holdings with money market equilib-rium in both countries, we get

12 For alternative modeling of “noise” from rational be-havior, see Matthew Spiegel and Avanidhar Subrahmanyam(1992), Wang (1994), and James Dow and Gary Gorton(1995).

13 See Singleton (1987) for the same setup. In an earlierversion of the paper, Bacchetta and van Wincoop (2003),

we also consider an infinite-horizon version. While thissignificantly complicates the solution method, numericalresults are almost identical.

14 By introducing money through production rather thanutility, we avoid making money demand a function ofconsumption, which would complicate the solution.


(2) mt � pt � ��it

(3) m*t � p*t � ��i*t ,

where mt and m*t are the logs of domestic andforeign nominal money supply.

The demand for foreign bonds by investor iis:15

(4) bFti �

Eti�st � 1 � � st � i*t � it

��t2 � bt

i,

where the conditional variance of next peri-od’s exchange rate is �t

2, which is the samefor all investors in equilibrium. We focus onequilibria where the conditional variance ofnext period’s exchange rate is time-invariant.The hedge against nonasset income is repre-sented by bt

i � �ti.

We assume that the exchange rate exposure isequal to the average exposure plus an idiosyn-cratic term, so that bt

i � bt � �ti. We consider the

limiting case where the variance of �ti ap-

proaches infinity, so that knowing one’s ownexchange rate exposure provides no informationabout the average exposure. This assumption ismade only for convenience and our results donot qualitatively change when we assume afinite, but positive, variance of �t

i. The key as-sumption is that the aggregate hedge componentbt is unobservable. We assume that bt follows anAR(1) process:

(5) bt � b bt � 1 � �tb,

where �tb � N(0, �b

2). While bt is an unobservedfundamental, the assumed autoregressive pro-cess is known by all agents.

B. Market Equilibrium and Higher-OrderExpectations

Since bonds are in zero net supply, marketequilibrium is given by �0

1 bFti di � 0. One way

to reach equilibrium is to have a Walrasianauctioneer to whom investors submit their de-

mand schedule bFti . We show below that the

same equilibrium can also be implemented byintroducing a richer microstructure in the formof an order-driven auction market.

Market equilibrium yields the following in-terest rate arbitrage condition:

(6) E� t �st � 1 � � st � it � i*t � ��t2bt ,

where E� t is the average rational expectationacross all investors. The model is summarizedby (1), (2), (3), and (6). Other than the risk pre-mium in the interest rate arbitrage condition, as-sociated with nonobservable trade, these equationsare the standard building blocks of the monetarymodel of exchange rate determination.

Defining the observable fundamental as ft �(mt � m*t ), in Appendix A we derive the fol-lowing equilibrium exchange rate:

(7) st �1

1 � ��

k � 0

� �

1 � ��k

E� tk� ft � k � ��t � k

2 bt � k�,

where E� t0(xt) � xt, E� t

1(xt�1) � E� t(xt�1) andhigher-order expectations are defined as

(8) E� tk�xt � k � � E� tE� t � 1

... E� t � k�1 �xt � k �.

Thus, the exchange rate at time t depends onthe fundamental at time t, the average expectationat t of the fundamental at time t � 1, the averageexpectation at t of the average expectation at t �1 of the fundamental at t � 2, etc. The law ofiterated expectations does not apply to averageexpectations. For example, E� tE� t�1(st�2) �E� t(st�2).16 This is a basic feature of asset pricingunder heterogeneous expectations: the expectationof other investors’ expectations matters.17 In adynamic system, this leads to the infinite regress

15 Here we implicitly assume that st�1 is normally dis-tributed. We will see in Section ID that the equilibriumexchange rate indeed has a normal distribution.

16 See Bacchetta and van Wincoop (2004a) and Allen etal. (forthcoming).

17 Notice that the higher-order expectations are of adynamic nature, i.e., today’s expectations of tomorrow’sexpectations. This contrasts with most of the literature thatconsiders higher-order expectations in a static context withstrategic externalities, e.g., Stephen Morris and Hyun SongShin (2002) or Woodford (2003).


problem, as analyzed in Townsend (1983): as thehorizon goes to infinity, the dimensionality of theexpectation term goes to infinity.

C. The Information Structure

We assume that at time t investors observe allpast and current ft, while they receive privatesignals about ft�1, ... , ft�T. More precisely, weassume that investors receive one signal eachperiod about the observable fundamental T pe-riods ahead. For example, at time t investor ireceives a signal

(9) vti � ft � T � �t

vi, �tvi � N�0, �v

2�,

where �tvi is independent from ft�T and other

agents’ signals.18 As usual in this context, weassume that the average signal received by in-vestors is ft�T, i.e., �0

1 vti di � ft�T.19

We also assume that the observable funda-mental’s process is known by all agents andconsider a general process:

(10) ft � D�L��tf, �t

f � N�0, �f2�,

where D(L) � d1 � d2L � d3L � ... and L is thelag operator. Since investors observe currentand lagged values of the fundamental, knowingthe process provides information about the fun-damental at future dates.

D. Solution Method

In order to solve the equilibrium exchangerate, there is no need to compute all the higher-order expectations it depends on. The key equa-tion used in the solution method is the interestrate arbitrage condition (6), which captures for-eign exchange market equilibrium. It involvesonly a first-order average market expectation.We adopt a method of undetermined coeffi-cients, conjecturing an equilibrium exchangerate equation and then verifying that it satisfiesthe equilibrium condition (6). Townsend (1983)

adopts a similar method for solving a businesscycle model with higher-order expectations.20

Here we provide a brief description of the so-lution method, leaving details to Appendix B.

We conjecture the following equilibrium ex-change rate equation that depends on shocks toobservable and unobservable fundamentals:

(11) st � A�L��t � Tf � B�L��t

b,

where A(L) and B(L) are infinite order polyno-mials in the lag operator L. The errors �t

iv do notenter the exchange rate equation as they averageto zero across investors. Since at time t inves-tors observe the fundamental ft, only the inno-vations �f between t � 1 and t � T areunknown. Similarly shocks �b between t � Tand t are unknown. Exchange rates at time t �T and earlier, together with knowledge of �f attime t and earlier, reveal the shocks �b at timet � T and earlier.21

Investors solve a signal extraction problemfor the finite number of unknown innovations.Both private signals and exchange rates fromtime t � T � 1 to t provide information aboutthe unknown innovations. The solution to thesignal extraction problem leads to expectationsat time t of the unknowns as a function ofobservables, which in turn can be written as afunction of the innovations themselves. One canthen compute the average expectation of st�1.Substituting the result into the interest rate ar-bitrage condition (6) leads to a new exchangerate equation. The coefficients of the polynomi-als A(L) and B(L) can then be derived by solvinga fixed point problem, equating the coefficientsof the conjectured exchange rate equation tothose in the equilibrium exchange rate equation.Although the lag polynomials are of infinite

18 This implies that, each period, investors have T signalsthat are informative about future observed fundamentals.Note that the analysis could be easily extended to the casewhere investors receive a vector of signals each period.

19 See Anat R. Admati (1985) for a discussion.

20 The solution method described in Townsend (1983)applies to the model in section 8 of that paper where theeconomy-wide average price is observed with noise.Townsend (1983) mistakenly believed that higher-order ex-pectations are also relevant in a two-sector version of themodel where firms observe each other’s prices withoutnoise. Joseph G. Pearlman and Sargent (2005) show that theequilibrium fully reveals private information in that case.

21 Here we implicitly assume that the B(L) polynomial isinvertible, which is the case when the roots of B(L) � 0 areoutside the unit circle. This assumption holds for all theparameterizations of the model considered below. See Ap-pendix B.3 for a discussion.


order, for lags longer than T periods the infor-mation dispersion plays no role and an analyti-cal solution to the coefficients is feasible.22

A couple of comments about multiplicity ofequilibria are in order. Models with heteroge-neous information do not necessarily lead tomultiple equilibria.23 Multiple equilibria canarise when the conditional variance of next pe-riod’s asset price is endogenous, as shown byStephen McCafferty and Robert Driskill (1980).But that applies to both common knowledgeand heterogeneous information models. In thecontext of our model, the intuition is that ahigher conditional variance of next period’s ex-change rate leads to a bigger impact of hedgetrades on the exchange rate through the risk-premium channel, which indeed justifies thehigher conditional variance. For the special caseT � 1 we discuss below, analytical results canbe obtained. It is easy to check in that case thatfor a given �2 there is a unique solution to theexchange rate equation. But when allowing forthe endogeneity of �2 we find that there arealways two equilibria, a low and a high �2

equilibrium.24 For the more general case whereT � 1, we confirm numerically that there aretwo equilibria.25 In Bacchetta and van Wincoop(2003) we show that the high variance equilib-rium is unstable. Our numerical analysis in thepaper, therefore, always focuses on the lowvariance equilibrium.

E. Order Flow

Evans and Lyons (2002b) define order flowas “the net of buyer-initiated and seller-initiated

orders.” While each transaction involves abuyer and a seller, the sign of the transaction isdetermined by the initiator of the transaction.The initiator of a transaction is the trader (eitherbuyer or seller) who acts based on new privateinformation. In our setup, this includes bothprivate information about the future fundamen-tal and private information that leads to hedgetrades. The passive side of trade varies acrossmodels. In a quote-driven dealer market, such asmodeled by Evans and Lyons (2002b), the quot-ing dealer is on the passive side. The foreignexchange market has traditionally been charac-terized as a quote-driven multi-dealer market,but the recent increase in electronic trading(e.g., EBS) implies that a majority of interbanktrade is done through an auction market. In thatcase the limit orders are the passive side oftransactions and provide liquidity to the market.The initiated orders are referred to as marketorders that are confronted with the passive out-standing limit order book.

In the standard noisy rational expectationsliterature, the order flow plays no role, while theasset price conveys information. But how canthe price convey information when the price isunknown at the time asset demand orders areplaced? This is possible only when investorssubmit demand functions that are conditional onthe price. One can think of those demand func-tions being submitted to an implicit auctioneer,who then finds the equilibrium price.

There is an alternative interpretation, how-ever, of how the equilibrium price is set in suchmodels, which connects more closely to theexplicit auction market nature of the presentforeign exchange market. Investors submit theirdemand functions for foreign bonds in two com-ponents, market orders (order flow) and limitorders. Limit orders depend on available publicinformation and are conditioned on the exchangerate itself. These are passive orders that are exe-cuted only when confronted with market orders.Market orders are associated with the private in-formation component of asset demand.26

22 In Bacchetta and van Wincoop (2003), we solve themodel for the case where investors have infinite horizons.The solution is then complicated by the fact that investorsalso need to hedge against changes in expected future re-turns. This hedge term depends on the infinite state space,which is truncated to obtain an approximate solution. Nu-merical results are almost identical to the case of overlap-ping generations.

23 Peter DeMarzo and Costis Skiadas (1998) show thatthe well-known heterogeneous information model of San-ford J. Grossman (1976) has a unique equilibrium.

24 A technical appendix that is available from the authorson request proves these points for T � 1.

25 We check this by searching over a very wide space ofpossible �2. There is an equilibrium only when the conjec-tured �2 is equal to the conditional variance implied by theresulting exchange rate equation.

26 One way to formalize this separation into limit andmarket orders is to introduce foreign exchange dealers towhom investors delegate price discovery. Dealers are sim-ply a veil, passing on customer orders to the interdealermarket, where price discovery takes place. Customers sub-mit their demand functions to dealers through a combinationof limit and market orders. Dealers can place both types of


To be more precise, let Iti be the private

information set available to agent i at time t, andItp the public information set available to all

investors at the time market orders are submit-ted. The exchange rate st is not part of theinformation set at the time orders are placed, butinvestors can submit limit orders that are con-ditional on the exchange rate. After computingthe expected exchange rate next period as afunction of the information set and of st, it iseasy to show that there are parameters �1 , �2 ,and �3 such that the demand for foreign bondscan be rewritten as

(12) bFti � �1 It

p � �2 st � �3 Iti.

Market orders are defined as the pure privateinformation component of asset demand, whichis equal to

(13) �xti � �3 It

i � E��3 Iti�It

p�.

Note that we do not condition on the exchangerate st since it is not known at the time themarket orders are placed; only limit orders canbe conditioned on the exchange rate. Limit or-ders consist of the remaining component of as-set demand, which depends on the exchangerate and public information. Defining E(�3It

i�Itp) �

�4Itp, limit orders are

(14) ��1 � �4 �Itp � �2 st .

The aggregate order flow is �xt � �01 �xt

i di.Imposing market equilibrium �0

1 bFti di � 0,

which is equivalent to the sum of aggregateorder flow and limit orders being zero, the equi-librium exchange rate is

(15) st � �1

�2��1 � �2�It

p �1

�2�xt .

When demand shifts are due only to publicinformation arrival, the order flow term is zeroand executed limit orders will be zero as well. Ashift in demand can therefore bring about achange in the exchange rate without any actualtrade. Only shifts in demand due to privateinformation lead to trade.

Since st�1 is part of Itp, it follows that there

are parameters 1 and 2 such that

(16) �st � 1 Itp � 2�xt .

Equation (16) is important. It breaks downchanges in exchange rates associated with pub-lic information (the first term) and private in-formation (the second term). The two terms areorthogonal since order flow is defined to beorthogonal to public information. This also im-plies that a regression of the change in theexchange rate on order flow will lead to anunbiased estimate of 2 and an unbiased mea-sure of the contribution of order flow to ex-change rate volatility. There is no simultaneitybias in such a regression. Causality runs fromquantity (order flow) to price (the exchangerate), not the other way around. Order flowdecisions are made before the equilibrium ex-change rate is known. This differs from theimplicit auctioneer interpretation, where quan-tities and prices are set simultaneously by theauctioneer. We want to emphasize though thatthe equilibrium exchange rate is the same underthese two interpretations of price setting. The ex-plicit auction market interpretation simply has theadvantage to connect more closely to existinginstitutions and to evidence on the relationshipbetween order flow and exchange rate.

II. Model Implications: A Special Case

In this section we examine the special casewhere T � 1, which has a relatively simplesolution. This example is used to illustrate howinformation heterogeneity disconnects the ex-change rate from observed macroeconomic fun-damentals, while establishing a close relationshipbetween the exchange rate and order flow.

One aspect that simplifies the solution forT � 1 is that higher-order expectations are thesame as first-order expectations. This can be seenas follows. Bacchetta and van Wincoop (2004a)show that higher-order expectations are equal tofirst-order expectations plus average expectations

orders in the interdealer electronic auction market, but needto place the limit orders before customer orders are known.If we introduce an infinitesimal trading cost in the inter-dealer market that is proportional to the volume of executedtrades, dealers will submit limit orders that are equal to theexpected customer orders based on public information. Theunexpected customer orders are associated with private in-formation and are submitted as market orders to the inter-dealer market. This formalization also connects well to theexisting data, which is for interdealer order flow.


of future market expectational errors. For example,the second-order expectation of ft�2 can be writtenas E� t

2ft�2 � E� t ft�2 � E� t(E� t�1 ft�2 � ft�2). WhenT � 1, investors do not expect the market tomake expectational errors in the next period. Aninvestor may believe at time t that he has dif-ferent private information about ft � 1 thanothers. That information is no longer relevantnext period, however, since ft�1 is observed att � 1.27

While not critical, we make the further sim-plifying assumptions in this section that bt and ftare i.i.d., i.e., b � 0 and ft � �t

f. Replacinghigher-order with first-order expectations, equa-tion (7) then becomes

(17) st �1

1 � � � ft ��

1 � �E� t ft � 1�

��

1 � ��2bt .

Only the average expectation of ft�1 appears.We have replaced �t

2 with �2 since we willfocus on the stochastic steady state where sec-ond-order moments are time-invariant.

A. Solving the Model with HeterogenousInformation

When T � 1, investors receive private signalsvt

i about ft�1, as in (9). Therefore, the aver-age expectation E� t ft�1 in (17) depends on theaverage of private signals, which is equal to ft�1itself. This implies that the exchange rate stdepends on ft�1, so that the exchange rate be-comes itself a source of information about ft�1.The exchange rate is not fully revealing, how-ever, as it also depends on unobserved aggre-gate hedge trades bt. To determine the informationsignal about ft�1 provided by the exchange rate,we need to know the equilibrium exchange rateequation. We conjecture that

(18) st �1

1 � �ft � �f ft � 1 � �b bt .

Since an investor observes ft, the signal hegets from the exchange rate can be written

(19)st

�f� ft � 1 �

�b

�fbt,

where st � st � (1/(1 � �)) ft is the “adjusted”exchange rate. The variance of the error of thissignal is (�b/�f)

2�b2. Consequently, investor i

infers Etift�1 from three sources of information:

(a) the distribution of ft�1; (b) the signal vti; and

(c) the adjusted exchange rate (i.e., (19)). Sinceerrors in each of these signals have a normaldistribution, the projection theorem implies thatEt

ift�1 is given by a weighted average of thethree signals, with the weights determined bythe precision of each signal. We have

(20) Eti ft � 1 �

�vvti � �sst /�f

D,

where �v � 1/�v2, �s � 1/(�b/�f)

2�b2, �f � 1/�f

2,and D � 1/var( ft�1) � �v � �f � �s. For theexchange rate signal, the precision is complexand depends both on �b

2 and �b/�f, the latterbeing endogenous. By substituting (20) into(17) and using the fact that �0

1 vti di � ft�1 in

computing E� t ft�1, we get:

(21) st �1

1 � �ft � z

�

�1 � ��2

�v

Dft � 1

� z�

1 � ��2bt ,

where z � 1/(1 � (�/(1 � �)2)(�s/�fD)) � 1.Equation (21) confirms the conjecture (18).Equating the coefficients on ft�1 and bt in (21)to �f and �b, respectively, yields implicit solu-tions to these parameters.

We will call z the magnification factor: theequilibrium coefficient of bt in (21) is the directeffect of bt in (17) multiplied by z. This mag-nification can be explained by rational confu-sion. When the exchange rate changes, investorsdo not know whether this is driven by hedgetrades or by information about future macroeco-nomic fundamentals by other investors. There-fore, they always revise their expectations offundamentals when the exchange rate changes(equation (20)). This rational confusion magni-fies the impact of the unobserved hedge tradeson the exchange rate. More specifically, from(17) and (20), we can see that a change in bt hastwo effects on st. First, it affects st directly in(17) through the risk-premium channel. Second,

27 See Bacchetta and van Wincoop (2004a) for a moredetailed discussion of this point.


this direct effect is magnified by an increase inE� t ft�1 from (20).

The magnification factor can be written as28

(22) z � 1 ��s

�v .

The magnification factor, therefore, depends onthe precision of the exchange rate signal relativeto the precision of the private signal. The betterthe quality of the exchange rate signal, the moreweight is given to the exchange rate in formingexpectations of ft�1, and therefore the larger themagnification of the unobserved hedge trades.

Figure 1 shows the impact of two key param-eters on magnification. A rise in the privatesignal variance �v

2 at first raises magnificationand then lowers it. Two opposite forces are atwork. First, an increase in �v

2 reduces the pre-cision �v of the private signal. Investors there-fore give more weight to the exchange ratesignal, which enhances the magnification factor.Second, a rise in �v

2 implies less informationabout next period’s fundamental and therefore a

lower weight of ft�1 in the exchange rate. Thisreduces the precision �s of the exchange ratesignal, which reduces the magnification factor.For large enough �v

2 this second factor domi-nates. The magnification factor is therefore larg-est for intermediate values of the quality ofprivate signals. Figure 1 also shows that ahigher variance �b

2 of hedging shocks alwaysreduces magnification. It reduces the precision�s of the exchange rate signal.

B. Disconnect from Observed Fundamentals

In order to precisely identify the channelsthrough which information heterogeneity dis-connects the exchange rate from observed fun-damentals, we now compare the model to abenchmark with identically informed investors.The benchmark we consider is the case whereinvestors receive the same signal on future ft’s,i.e., they have incomplete but common knowl-edge on future fundamentals. With commonknowledge, all investors receive the signal

(23) vt � ft � T � �tv, �t

v � N�0, �v,c2 �,

where �tv is independent of ft�T.

28 Substitute �f � z(�/(1 � �)2)(�v/D) into z � 1/(1 �(�/(1 � �)2)(�s/�fD)) and solve for z.

FIGURE 1. MAGNIFICATION FACTOR IN MODEL WITH T � 1

Notes: This figure is based on the simulation of the model for T � 1, with both bt and ft i.i.d.The qualitative results do not depend on other model parameters. We set � � 10, � � 50, andall standard deviations of the shocks equal to 0.1, unless varied within the figure.


Defining the precision of this signal as �v,c 1/�v,c

2 , the conditional expectation of ft�1 is

(24) Etift � 1 � E� t ft � 1 �

�v,cvt

d,

where d 1/vart( ft�1) � �v,c � �f. Substitu-tion into (17) yields the equilibrium exchangerate:

(25) st �1

1 � �ft � �vvt � �b

cbt ,

where �v � (�/(1 � �)2)�v,c/d, and �bc � �(�/

(1 � �))��c2. Here, �c

2 is the conditional vari-ance of next period’s exchange rate in thecommon knowledge model. In this case theexchange rate is fully revealing, since by observ-ing st investors can perfectly deduce bt. Thus, �b

c isequal to the direct risk-premium effect of bt givenin (17).

We can now compare the connection betweenthe exchange rate and observed fundamentals inthe two models. In the heterogeneous informa-tion model, the observed fundamental is ft,while in the common knowledge model it alsoincludes vt. We compare the R2 of a regressionof the exchange rate on observed fundamentalsin the two models. From (18), the R2 in theheterogeneous information model is defined by

(26)R2

1 � R2 �

1

�1 � ��2 �f2

�f2�f

2 � z2� �

1 � ��2

�2�4�b2

.

From (25) the R2 in the common knowledgemodel is defined by

(27)R2

1 � R2 �

1

�1 � ��2 �f2 � �v

2��f2 � �v,c

2 �

� �

1 � ��2

�2�c4�b

2

.

If the conditional variance of the exchange rateis the same in both models, the R2 is clearlylower in the heterogeneous information model.Two factors contribute to this. First, the contri-bution of unobserved fundamentals to exchangerate volatility is amplified, as measured by themagnification factor z in the denominator of(26). Second, the average signal in the hetero-geneous information model, which is equal to

the future fundamental, is unobserved andtherefore contributes to reducing the R2. It alsoappears in the denominator of (26). In contrast,the signal about future fundamentals is observedin the common knowledge model, and thereforecontributes to raising the R2. The variance of thissignal, �f

2 � �v,c2 , appears in the numerator of (27).

The conditional variance of the exchange rate alsocontributes to the R2. It can be higher in eithermodel, dependent on assumptions about parame-ter values and quality of the public and privatesignals.29

C. Order Flow

It is straightforward to implement for thisspecial case the general definition of order flowand limit orders discussed in Section I. Using(4), (18), and (20), we can write demand forforeign bonds as

(28) bF,ti �

1 � �

��2z � 1

1 � �ft � st�

��v

�1 � ��2Dvt

i � bti.

Limit orders are captured by the first term,while order flow is captured by the sum of thelast two terms. Note that the variables vt

i and bti

in the private information set are unpredictableby public information at the time market ordersare placed.30

Aggregate order flow is then

(29) �xt ��v

�1 � ��2Dft � 1 � bt .

29 While we focus here on the exchange rate determina-tion puzzle, which is about the disconnect between ex-change rates and observed fundamentals, it is easy to showthat in the heterogeneous information model the exchangerate is more disconnected from fundamentals “f” generally(both observed and future fundamentals) than in the com-mon knowledge model. In that case the term �f�f

2 movesfrom the denominator to the numerator of (26). When theconditional variance of next period’s exchange rate is thesame in both models, the R2 remains lower in the hetero-geneous information model due to the amplification ofunobserved hedge trades.

30 In terms of the notation introduced in Section I,E(It

i�Itp) � 0.


Taking the aggregate of (28), imposing marketequilibrium, we get

(30) st �1

1 � �ft � z

�

1 � ��2�xt .

Equation (30) shows that the exchange rate isrelated in a simple way to a commonly observedfundamental and order flow. The order flowterm captures the extent to which the exchangerate changes due to the aggregation of privateinformation. The impact of order flow is largerthe bigger the magnification factor z. A higherlevel of z implies that the order flow is moreinformative about the future fundamental.

It is easily verified that in the commonknowledge model

(31) st �1

1 � �ft � �vvt �

�

1 � ��2�xt .

In that case order flow is driven only by hedgetrades.31 Since these trades have no informationcontent about future fundamentals, the impactof order flow on the exchange rate is smaller(not multiplied by the magnification factor z). Acomparison between (30) and (31) clearlyshows that the exchange rate is more closelyconnected to order flow in the heterogeneousinformation model and more closely connectedto public information in the common knowl-edge model.

III. Model Implications: Dynamics

In this section, we examine the more complexdynamic properties of the model when T � 1.There are two important implications. First, itcreates endogenous persistence of the impact ofnonobservable shocks on the exchange rate.Second, higher-order expectations differ fromfirst-order expectations when T � 1. Even forT � 2 expectations of infinite order affect theexchange rate. We show that higher-order ex-pectations tend to increase the magnificationeffect, but have an ambiguous impact on thedisconnect. We now examine these two aspectsin turn.

A. Persistence

When T � 1, even transitory nonobservableshocks have a persistent effect on the exchangerate. This is due to the learning of investors whogradually realize that the change in the ex-change is not caused by a shock to future fun-damentals.32 The exchange rate at time tdepends on future fundamentals ft�1, ft�2, ... ,ft�T, and therefore provides information abouteach of these future fundamentals. A transitoryunobservable shock to bt affects the exchangerate at time t and therefore affects the expecta-tions of all future fundamentals up to time t �T. This rational confusion will last for T periods,until the final one of these fundamentals, ft�T, isobserved. Until that time, investors will con-tinue to give weight to st in forming their ex-pectations of future fundamentals, so that btcontinues to affect the exchange rate.33 As in-vestors gradually learn more about ft�1,ft�2, ... , ft�T, both by observing them andthrough new private signals and exchange ratesignals, the impact on the exchange rate of theshock to bt gradually dissipates.

The persistence of the impact of b-shocks onthe exchange rate is also affected by the persis-tence of the shock itself. When the b-shockitself becomes more persistent, it is more diffi-cult for investors to learn about fundamentals upto time t � T from exchange rates subsequent totime t. The rational confusion is therefore morepersistent, and so is the impact of b-shocks onthe exchange rate.

B. Higher-Order Expectations

The topic of higher-order expectations is adifficult one, but it has potentially importantimplications for asset pricing. Since a detailedanalysis falls outside the scope of this paper, we

31 Note that aggregate hedge trade bt is not in the publicinformation set at the time orders are submitted. It is re-vealed only after the price is known.

32 Persistence can also arise in models with incompletebut common knowledge, such as Michael Mussa (1976).When agents do not know whether an increase in an ob-served fundamental is transitory or persistent, a transitoryshock will have a larger and more persistent effect becauseof gradual learning.

33 This result is related to findings by David P. Brownand Robert H. Jennings (1989) and Bruce D. Grundy andMaureen McNichols (1989), who show in the context oftwo-period noisy rational expectations models that the assetprice in the second period is affected by the asset price inthe first period.


limit ourselves to a brief discussion regardingthe impact of higher-order expectations on theconnection between the exchange rate and ob-served fundamentals. We apply the results ofBacchetta and van Wincoop (2004a), where weprovide a general analysis of the impact ofhigher-order expectations on asset prices.34 Westill assume that b � 0.

Let s�t denote the exchange rate that wouldprevail if the higher-order expectations in (7)are replaced by first-order expectations.35 InBacchetta and van Wincoop (2004a), we showthat the present value of the difference betweenhigher- and first-order expectations depends onaverage first-order expectational errors aboutaverage private signals. In Appendix C we showthat in our context this leads to

(32) st � s� t �1

1 � ��

k � 2

T

�k �E� t ft � k � ft � k �.

The parameters �k are defined in the Appendixand are positive in all numerical applications.Higher-order expectations therefore introduce anew asset price component, which depends onaverage first-order expectational errors aboutfuture fundamentals.

Moreover, the expectational errors E� tft�k �ft�k depend on errors in public signals, i.e.,observed fundamentals and exchange rates;based on private information alone, these aver-age expectational errors would be zero. Thereare two types of errors in public signals. First,there are errors in the exchange rate signals thatare caused by the unobserved hedge trades attime t and earlier. This implies that unobservedhedge trades receive a larger weight in the equi-librium exchange rate. The other type of errorsin public signals are errors in the signals basedon the process of ft. These errors depend nega-tively on future innovations in the fundamental,which implies that the exchange rate dependsless on unobserved future fundamentals. Tosummarize, hedge shocks are further magnifiedby the presence of higher-order expectations,while the overall impact on the connection be-

tween the exchange rate and observed funda-mentals is ambiguous.36

IV. Model Implications: Numerical Analysis

We now solve the model numerically to il-lustrate the various implications of the modeldiscussed above. We first consider a benchmarkparameterization and then discuss the sensi-tivity of the results to changing some keyparameters.

A. A Benchmark Parameterization

The parameters of the benchmark case arereported in Table 1. We assume that the observ-able fundamental f follows a random walk,whose innovations have a standard deviation of�f � 0.01. We assume a high standard deviationof the private signal error of �v � 0.08. Theunobservable fundamental b follows an AR pro-cess with autoregressive coefficient of b � 0.8and a standard deviation �b � 0.01 of innova-tions. Although we have made assumptionsabout both �b and risk-aversion �, they entermultiplicatively in the model, so only theirproduct matters. Finally, we assume T � 8, sothat agents obtain private signals about funda-mentals eight periods before they are realized.

Figure 2 shows some of the key results fromthe benchmark parameterization. Panels A andB show the dynamic impact on the exchangerate in response to one-standard-deviationshocks in the private and common-knowledgemodels. In the heterogeneous-agent model,there are two shocks: a shock �t�T

f ( f-shock),

34 Allen et al. (forthcoming) provide an insightful anal-ysis of higher-order expectations with an asset price, butthey do not consider an infinite horizon model.

35 That is, s�t � (1/(1 � �)) ¥k�0 (�/(1 � �))kE� t( ft�k �

��t�k2 bt�k).

36 In Bacchetta and van Wincoop (2004a), we show thatthe main impact of higher-order expectations is to discon-nect the price from the present value of future observablefundamentals.

TABLE 1—BENCHMARK PARAMETERIZATION

Parameter Value

�f 0.01�b 0.01�v 0.08b 0.8� 10� 500T 8


which first affects the exchange rate at time t,and a shock �t

b (b-shock). In the common-knowledge model there are also shocks �t

v,which affect the exchange rate through the com-monly observable fundamental vt. In order tofacilitate comparison, we set the precision of thepublic signal such that the conditional varianceof next period’s exchange rate is the same as inthe heterogeneous-information model. This im-plies that the unobservable hedge trades havethe same risk-premium effect in the two models.

We will show below that our key results do notdepend on the assumed precision of the publicsignal.

Magnification.—The magnification factor inthe benchmark parameterization turns out to besubstantial: 7.2. This is visualized in Figure 2 bycomparing the instantaneous response of theexchange rate to the b-shocks in the two modelsin panels A and B. The only reason the impactof a b-shock is so much bigger in the heteroge-

FIGURE 2. RESULTS FOR THE BENCHMARK PARAMETERIZATION

Note: See Table 1 for parameter assumptions.


neous information model is the magnificationfactor associated with information dispersion.

Persistence.—We can see from panel A thatafter the initial shock the impact of the b-shocksdies down almost as a linear function of time.The half-life of the impact of the shock is threeperiods. After eight periods the rational confusionis resolved and the impact is the same as in thepublic information model, which is close to zero.

The meaning of a three-period half-life de-pends of course on what we mean by a period inthe model. What is critical is not the length of aperiod, but the length of time it takes for uncer-tainty about future macro variables to be re-solved. For example, assume that this length oftime is eight months. If a period in our model isa month, then T � 8. If a period is three days,then T � 80. We find that the half-life of theimpact of the unobservable hedge shocks on theexchange rate that can be generated by the modelremains virtually unchanged as we change thelength of a period. For T � 8, the half-life is aboutthree, while for T � 80 it is about 30.37 In bothcases the half-life is three months. Persistence istherefore driven critically by the length of time ittakes for uncertainty to resolve itself. Deviationsof the exchange rate from observed fundamentalscan therefore be very long-lasting when it takes along time before expectations about future funda-mentals can be validated, such as expectationsabout the long-term technology growth rate of theeconomy.

Exchange Rate Disconnect in the Short andthe Long Run.—Panel C reports the contribu-tion of unobserved hedge trades to the varianceof st�k � st at different horizons. In the heter-ogeneous information model, 70 percent of thevariance of a one-period change in the exchangerate is driven by the unobservable hedge trades,while in the common-knowledge model it is a

negligible 1.3 percent (such a small effect istypical of standard portfolio-balance models).While in the short run unobservable fundamen-tals dominate exchange rate volatility, in thelong run observable fundamentals dominate.For example, the contribution of hedge trades tothe variance of exchange rate changes over aten-period interval is less than 20 percent. Asseen in panel A, the impact of hedge trades onthe exchange rate gradually dies down as ratio-nal confusion dissipates over time.

In order to determine the relationship be-tween exchange rates and observed fundamen-tals, panel D reports the R2 of a regression ofst�k � st on all current and lagged observedfundamentals. In the heterogeneous-informationmodel, this includes all one-period changes inthe fundamental f that are known at time t � k:ft�s � ft�s�1, for s k. In the common-knowledge model, it also includes the corre-sponding one-period changes in the publicsignal v. The R2 is close to one for all horizonsin the common-knowledge model, while it ismuch lower in the heterogeneous-informationmodel. At the one-period horizon it is only 0.14;it then rises as the horizon increases to 0.8 for a20-period horizon. This is consistent with ex-tensive findings that macroeconomic fundamen-tals have weak explanatory power for exchangerates in the short to medium run, starting withMeese and Rogoff (1983), and findings of acloser relationship over longer horizons.38

Two factors account for the results in panelD. The first is that the relative contribution ofunobservable hedge shocks to exchange ratevolatility is large in the short run and small inthe long run, as illustrated in panel C. Thesecond factor is that, through private signals, theexchange rate at time t is also affected by inno-vations �t�1

f , ... , �t�Tf in future fundamentals

that are not yet observed today. In the long runthese become observable, again contributing toa closer relationship between the exchange rateand observed fundamentals in the long run.

Exchange Rate and Future Fundamentals.—Recently Engel and Kenneth D. West (2005)and Froot and Ramadorai (2005) have reported

37 When we change the length of a period, we also needto change other model parameters, such as the standarddeviations of the shocks. In doing so we restrict parameterssuch that (a) the contribution of b-shocks to var(st�1 � st)is the same as in the benchmark parameterization, and (b)the impact of b-shocks on exchange rate volatility remainslargely driven by information dispersion (large magnifica-tion factor). For example, when we change the benchmarkparameterization such that T � 80, �v � 0.26, �f � 0.0016,and � � 44, the half-life is 28 periods. The magnificationfactor is 48.

38 See MacDonald and Mark P. Taylor (1993), MenzieD. Chinn and Meese (1995), Mark (1995), Mark and Dong-gyu Sul (2001), Froot and Ramadorai (2005), and Gourin-chas and Helene Rey (2005).


evidence that exchange rate changes predict fu-ture fundamentals, but only weakly so. Ourmodel is consistent with these findings. Panel Eof Figure 2 reports the R2 of a regression ft�k �ft�1 on st�1 � st for k � 2. The R2 is positive,but is never above 0.14. The exchange rate isaffected by the private signals of future funda-mentals, which aggregate to the future funda-mentals. Most of the short-run volatility ofexchange rates, however, is associated with un-observable hedge trades, which do not predictfuture fundamentals.

Exchange Rate and Order Flow.—Order flowis computed as discussed in Section IE. Appen-dix D discusses further details for the casewhere the fundamental f is a random walk. Withxt defined as cumulative order flow, panel Freports the R2 of a regression of st�k � st onxt�k � xt. The R2 is large. At a one-periodhorizon it is 0.84, so that 84 percent of thevariance of one-period exchange rate changescan be accounted for by order flow as opposedto public information. The relationship betweencumulative order flow and exchange rates getseven stronger as the horizon k increases, withthe R2 rising to 0.97 for k � 40. As k approachesinfinity, the R2 approaches a level near 0.99, sothat there is a very close long-run relationshipbetween cumulative order flow and exchangerates.39

It is important to point out that the close re-lationship between the exchange rate and orderflow in the long run is not inconsistent with theclose relationship between the exchange rateand observed fundamentals in the long run.When the exchange rate rises due to privateinformation about permanently higher futurefundamentals, the information reaches the mar-ket through order flow. Eventually the future

fundamentals will be observed, so that there is alink between the exchange rate and the observedfundamentals. But most of the informationabout higher future fundamentals is aggregatedinto the price through order flow. Order flowassociated with information about future funda-mentals has a permanent effect on the exchangerate.

Our results can be compared to similar re-gressions that have been conducted based on thedata. Evans and Lyons (2002b) estimate regres-sions of one-day exchange rate changes on dailyorder flow. They find an R2 of 0.63 and 0.40 for,respectively, the DM-$ and the yen-$ exchangerate, based on four months of daily data in 1996.Evans and Lyons (2002a) report results for ninecurrencies. They point out that exchange ratechanges for any currency pair can also be af-fected by order flow for other currency pairs.Regressing exchange rate changes on order flowfor all currency pairs, they find an average R2 of0.67 for their nine currencies.

The pictures for the exchange rate and cumu-lative order flow reported in Evans and Lyons(2002b) for the DM-$ and yen-$ exchange ratesuggest that the link is even stronger over ho-rizons longer than one day, although their data-set is too short for formal regression analysis.These pictures look very similar to their theo-retical counterparts, which are reported in Fig-ure 3 for four simulations of the model over 40periods.40 The simulations confirm a close linkbetween the exchange rate and cumulative orderflow at both short and long horizons.

While not reported in panel F, the R2 ofregressions of exchange rate changes on orderflow in the public-information model is close tozero. Two factors contribute to the much closerlink between order flow and exchange rates inthe heterogeneous-information model. First, inthe heterogeneous-information model both pri-vate information about future fundamentals andhedge trades contribute to order flow, while inthe public-information model only hedge tradescontribute to order flow. Second, the impact onthe exchange rate of the order flow due to hedgetrades is much larger in the heterogeneous in-formation model. The reason is that order flowis informative about future fundamentals in the

39 The relationship between st�k � st and xt�k � xt doesnot always get stronger for longer horizons. For low valuesof T, the R2 declines with k and then converges asymptot-ically to a positive level. Appendix D shows that cumulativeorder flow and exchange rates are not cointegrated, whichexplains why the R2 never approaches one as k approachesinfinity. The Appendix shows that there is a cointegratingrelationship between st, xt, and bt � ¥s�0

�t�T�sb . Shocks to

the fundamental f have a permanent affect on both theexchange rate and cumulative order flow. Hedge trade in-novations affect cumulative order flow permanently, buttheir effect on the exchange rate dies out when hedge tradeshocks are temporary (b � 1).

40 Both the log of the exchange rate and cumulative orderflow are set at zero at the start of the simulation.


heterogeneous-information model. As illus-trated in Section IIC, the magnification factor zapplied to the impact of b-shocks on the ex-change rate also applies to the impact of orderflow on the exchange rate.

B. Sensitivity to Model Parameters

In this subsection, we consider the parametersensitivity of two key moments: the R2 of aregression of st�1 � st on observed fundamen-tals at t � 1 and earlier, and the R2 of a regres-sion of st�1 � st on order flow xt�1 � xt. Theseare the moments reported for k � 1 in panels Dand F of Figure 2.

A first issue is that the precision of the publicsignal in the common knowledge model doesnot play an important role in the comparisonwith the heterogeneous-information model. Inparticular, it has little influence on the starkdifference between the two models regardingthe connection between the exchange rate andobserved fundamentals. Consider the R2 of aregression of a one-period change in the ex-change rate on all current and past observedfundamentals, as reported in Figure 2D. In the

heterogeneous-information model it is 0.14,while in the public-information model it variesfrom 0.97 to 0.99 as we change the variance of thenoise in the public signal from infinity to zero.41

We now consider sensitivity analysis to fourkey model parameters in the heterogeneous-information model: �v, �b, b, and T. The re-sults are reported in Figure 4. Not surprisingly,the two R2’s are almost inversely related as wevary parameters. The larger the impact of orderflow as a channel through which information istransmitted to the market, the smaller is theexplanatory power of commonly observedmacro fundamentals.42

41 In Figure 2, we have assumed that the precision of thepublic signal is such that the conditional variance of theexchange rate is the same in the two models. This implies astandard deviation of the error in the public signal of 0.033.

42 The two lines do not add to one. The reason is thatsome variables that are common knowledge are not in-cluded in the regression on observed fundamentals. Theseare past exchange rates and hedge demand T periods ago.Past exchange rates are not included since they are nottraditional fundamentals. Hedge demand T periods ago canbe indirectly derived from exchange rates T periods ago andearlier, but is not a directly observable fundamental.

FIGURE 3. FOUR MODEL SIMULATIONS EXCHANGE RATE AND CUMULATIVE ORDER FLOW


An increase in �v, implying less preciseprivate information, reduces the link betweenthe exchange rate and order flow and in-creases the link between the exchange rateand observed fundamentals. In the limit, asthe noise in private signals approaches infin-ity, the heterogeneous-information model ap-proaches the public-information model (withuninformative signals).

Somewhat surprisingly, an increase in thenoise originating from hedge trades, by eitherraising the standard deviation �b or the persis-tence b, tends to strengthen the link betweenthe exchange rate and observed fundamentalsand reduce the link between the exchange rateand order flow. The effect is relatively small,however, due to offsetting factors. Order flowbecomes less informative about future funda-mentals with more noisy hedge trades. Thisreduces the impact of order flow on the ex-change rate. On the other hand, the volatility of

order flow increases, which contributes posi-tively to the R2 for order flow. The former effectslightly dominates.

It is also worthwhile pointing out that theassumed stationarity of hedge trades in thebenchmark parameterization is not responsiblefor the much weaker relationship between theexchange rate and observed fundamentals in theshort run than the long run. Even if we assumeb � 1, so that unobserved aggregate hedgetrades follow a random walk as well, this find-ing remains largely unaltered. The R2 for ob-served fundamentals rises from 0.21 for a one-period horizon to 0.85 for a 40-period horizon.

The final panel of Figure 4 shows the impactof changing T. Initially, an increase in T leads toa closer link between order flow and the ex-change rate and a weaker link between observedfundamentals and the exchange rate. The reasonis that as T increases, the quality of privateinformation improves because agents have sig-

FIGURE 4. R2 OF REGRESSION OF st�1 � st ON (A) OBSERVED FUNDAMENTALS AND (B) ORDER FLOW: SENSITIVITY ANALYSIS

Notes: Order flow: R2 of regression of st�1 � st on xt�1 � xt (same as Figure 2F for k � 1). Observed fundamentals: R2 ofregression st�1 � st on all ft�s � ft�s�1 for s 1 (same as Figure 2D for k � 1). The figures show how the explanatorypower of order flow and observed fundamentals changes when respectively �v, �b, T, and b are varied, holding constant theother parameters as in the benchmark parameterization.


nals about fundamentals further into the future.This implies that the impact of order flow on theexchange rate increases. Moreover, order flowitself also becomes more volatile as more pri-vate information is aggregated. Beyond a cer-tain level of T, however, the link between theexchange rate and order flow is weakened whenT is raised further. The reason is that the im-proved quality of information reduces the con-ditional variance �2 of next period’s exchangerate. This reduces the effect of order flow on theexchange rate, as can be seen from (30).

V. Conclusion

The close relationship between order flowand exchange rates, as well as the large volumeof trade in the foreign exchange market, suggestthat investor heterogeneity is key to understand-ing exchange rate dynamics. In this paper we haveexplored the implications of information disper-sion in a simple model of exchange rate determi-nation. We have shown that these implications arerich and that investors’ heterogeneity can be animportant element in explaining the behavior ofexchange rates. In particular, the model can ac-count for some important stylized facts on therelationship between exchange rates, fundamen-tals, and order flow: (a) fundamentals have littleexplanatory power for short- to medium-run ex-change rate movements, (b) over long horizonsthe exchange rate is closely related to observedfundamentals, (c) exchange rate changes are aweak predictor of future fundamentals, and (d) theexchange rate is closely related to order flow.

The paper should be considered only as a firststep in a promising line of research. While wehave mostly focused on the implications of themodel for the relationship between exchangerates, fundamentals, and order flow, future workalong this line should also consider the impli-cations for other outstanding exchange rate puz-zles such as the forward discount puzzle andexcess volatility puzzle.43 More broadly speak-ing, a natural next step is to link the theory to

the data. While the extent of information dis-persion and unobservable hedge trades is notknown, both affect order flow. Some limiteddata on order flow are now available and willhelp tie down the key model parameters. Themagnification factor may be quite large. Back-of-the-envelope calculations by Gennotte and Leland(1990) in the context of a static model for the U.S.stock market crash of October 1987 suggest thatthe impact of a $6 billion unobserved supplyshock was magnified by a factor of 250 due torational confusion about the source of the stockprice decline. In the context of foreign exchangemarkets, Carol L. Osler (2005) presents evidencethat trades that are uninformative about futurefundamentals have a large impact on the price.

There are several directions in which themodel can be extended. The first is to explicitlymodel nominal rigidities as in the “new openeconomy macro” literature. In that literature,exchange rates are entirely driven by commonlyobserved macro fundamentals. Conclusions thathave been drawn about optimal monetary andexchange rate policies are likely to be substan-tially revised when introducing investor het-erogeneity. Another direction is to consideralternative information structures. For example,the information received by agents may differ inits quality or in its timing. There can also beheterogeneity about the knowledge of the un-derlying model. For example, in Bacchetta andvan Wincoop (2004b), we show that if investorsreceive private signals about the persistence ofshocks, the impact of observed variables on theexchange rate varies over time. The rapidlygrowing body of empirical work on order flowin the foreign exchange microstructure litera-ture is likely to increase our understanding ofthe nature of the information structure, provid-ing guidance to future modeling.

APPENDIX

A. Derivation of Equation (7)

It follows from (1), (2), (3), and (6) that

(A1) st �1

1 � �ft �

�

1 � ��t

2bt

��

1 � �E� t

1�st � 1 �.

43 See Bacchetta and van Wincoop (2003) for somediscussion of the excess volatility puzzle in the context ofthis model. The current model yields a forward discountbias of the correct sign, but the magnitude falls short of whatis found in empirical evidence. See Bacchetta and vanWincoop (2005) for an explanation of the bias based on adifferent type of information heterogeneity.


Therefore

(A2) E� t1�st � 1 � �

1

1 � �E� t

1� ft � 1 �

��

1 � ��t � 1

2 E� t1�bt � 1 � �

�

1 � �E� t

2�st � 2 �.

Substitution into (A1) yields

(A3)

st �1

1 � � � ft � ��t2bt �

�

1 � �E� t

1� ft � 1

� ��t � 12 bt � 1 ��

1 � ��2

E� t2�st � 2 �.

Continuing to solve for st this way by forwardinduction and assuming a no-bubble solutionyields (7).

B. Solution Method with Two-PeriodOverlapping Investors

The solution method is related to Townsend(1983, sect. VIII). We start with the conjecturedequation (11) for st and check whether it isconsistent with the model, in particular withequation (6). For this, we need to estimate theconditional moments of st�1 and express themas a function of the model’s innovations. Finally,we equate the parameters from the resulting equa-tion to the initially conjectured equation.

B.1. The Exchange Rate Equation.—From(1)–(3), and the definition of ft, it is easy to seethat i*t � it � ( ft � st)/�. Thus, (6) gives (for aconstant �t

2)

(B1)

st ��

1 � �E� t �st � 1 � �

ft

1 � ��

�

1 � ��bt�

2.

We want to express (B1) in terms of current andpast innovations. First, we have ft � D(L)�t

f.Second, using (5) we can write bt � C(L)�t

b,where C(L) � 1 � bL � b

2L2 � ... . What re-mains to be computed are E� (st�1) and �2.

Applying (11) to st�1, writing A(L) � a1 �a2L � a3L2 � ... and B(L) � b1 � b2L � b3L2

� ... , we have

(B2) st � 1 � a1�t � T�1f � b1�t � 1

b � ��t

� A*�L��tf � B*�L��t � T

b ,

where ��t � (�t�Tf , ... , �t�1

f , �tb, ... , �t�T�1

b ) rep-resents the vector of unobservable innovations,�� (a2, a3, ... , aT�1, b2, ... , bT�1), andA*(L) � aT�2 � aT�3L � ... (with a similardefinition for B*(L)). Thus, we have (since �j

f

and �j�Tb are known for j t)

(B3) Eti�st � 1 � � ��Et

i��t�

� A*�L��tf � B*�L��t � T

b

and

(B4) �2 � vart �st � 1 � � a12�f

2

� b12�b

2 � ��vart��t��.

We need to estimate the conditional expecta-tion and variance of the unobservable �t as afunction of past innovations.

B.2. Conditional Moments.—We follow thestrategy of Townsend (1983, p. 556), but use thenotation of James D. Hamilton (1994, chap. 13).First, to focus on the informational content ofobservable variables, we subtract the knowncomponents from the observables st and vt

i anddefine these new variables as s*t and vt

i*. Let thevector of these observables be Yt

i � (s*t,s*t�1, ... , s*t�T�1, vt

i*, ... , vt�T�1i* ). This vector

provides information on the vector of unobserv-ables �t. From (B2) and (9), we can write

(B5) Yti � H��t � wt

i,

where wti � (0, ... , 0, �t

vi, ... , �t�T�1vi )� and

H� � �a1 a2

... aT b1 b2... bT

0 a1... aT � 1 0 b1

... bT � 1

... ... ... ... ... ... ... ...

0 0 ... a1 0 0 ... b1

d1 d2... dT 0 0 ... 0

0 d1... dT � 1 0 0 ... 0

... ... ... ... ... ... ... ...

0 0 0 d1 0 0 ... 0

.

The unconditional means of �t and wti are zero.


Define their unconditional variances as P and R.Then we have (applying equations (17) and (18)in Townsend)

(B6) Eti��t� � MYt

i,

where

(B7) M � PH�H�PH � R��1.

Moreover, P vart(�t) is given by

(B8) P � P � MH�P.

B.3. Solution.—First, �2 can easily be de-rived from (B4) and (B8). Second, substituting(B6) and (B5) into (B3), and averaging overinvestors, gives the average expectation interms of innovations

(B9) E� t �st � 1 � � ��MH��t

� A*�L��tf � B*�L��t � T

b .

We can then substitute E� t(st�1) and �2 into (B1)so that we have an expression for st that has thesame form as (11). We then need to solve afixed-point problem.

Although A(L) and B(L) are infinite lag op-erators, we need only solve a finitely dimen-sional fixed-point problem in the set ofparameters (a1, a2, ... , aT, b1, ... , bT�1). Thiscan be seen as follows. First, it is easily verifiedby equating the parameters of the conjecturedand equilibrium exchange rate equation for lagsT and greater that bT�s�1 � ((1 � �)/�)bT�s ��2b

T�s�1 and aT�s�1 � ((1 � �)/�)aT�s �(1/�)ds for s � 1. Assuming nonexplosive co-efficients, the solutions to these difference equa-tions give us the coefficients for lags T � 1 andgreater: bT�1 � ��2b

T/(1 � � � �b),bT�s � (b)s�1bT�1 for s � 2, aT�1 � (1/�)¥s�1

(�/(1 � �))sds, and aT�s�1 � ((1 ��)/�)aT�s � (1/�)ds for s � 1. When the fun-damental follows a random walk, ds � 1 @s, sothat aT�s � 1 @s � 1.

The fixed-point problem in the parameters(a1, a2, ... , aT, b1, ... , bT�1) consists of 2T � 1equations. One of them is the bT�1 ��2b

T/(1 � � � �b). The other 2T equa-tions equate the parameters of the conjecturedand equilibrium exchange rate equations up tolag T � 1. The conjectured parameters (a1,

a2, ... , aT, b1, ... , bT�1), together with the so-lution for aT�1 above, allow us to compute �,H, M and �2, and therefore the parameters ofthe equilibrium exchange rate equation. We usethe Gauss NLSYS routine to solve the 2T � 1nonlinear equations.

After having found the solution, we can alsoverify that the polynomial B(L) is invertible,which is necessary to extract information abouthedge trade innovations at t � T and earlierfrom exchange rates at t � T and earlier. Usingthat bT�s � (b)s�1bT�1 for s � 2, we have

(B10) B�L� � �i � 1

T

bi Li � 1 � bT � 1 LT �

i � 0

bi Li

� �i � 1

T

bi Li � 1 �

bT � 1 LT

1 � b L.

B(L) is invertible when the roots of the polyno-mial are outside the unit circle. Setting B(L) �0, multiplying by 1 � bL, yields

(B11) b1 � �i � 1

T

�bi � 1 � b bi �Li � 0.

This amounts to solving the roots of an ordinaryT-order polynomial, which is done with theroutine polyroot in Gauss. The roots are indeedoutside the unit circle for all parameterizationsconsidered in the paper. For the benchmarkparameterization, the roots are (rounding to thesecond digit after the decimal point): (�1.43,�1.03 � 0.98i, �1.03 � 0.98i, �0.07 � 1.39i,�0.07 � 1.39i, 0.89 � 0.98i, 0.89 � 0.98i,1.28).

C. Higher-Order Expectations

We show how (32) follows from Proposition1 in Bacchetta and van Wincoop (2004a). Bac-chetta and van Wincoop (2004a) define thehigher-order wedge �t as the present value ofdeviations between higher-order and first-orderexpectations. In our application (assuming b � 0):

(C1) �t � �s � 2

� �

1 � ��s

�E� tsft � s � E� t ft � s �.


Define PVt � ¥s�1 (�/(1 � �))sft�s as the

present discounted value of future observed fun-damentals. Let Vt

i be the set of private signalsavailable at time t that are still informativeabout PVt�1 at t � 1. In our application Vt

i �(vt�T�2

i , ... , vti)�. Let V� t denote the average

across investors of the vector Vti. Proposition 1

of Bacchetta and van Wincoop (2004a) thensays that

(C2) �t � ��t�E� tV� t � V� t�,

where �t � (1/R2)(I � �)�1�, �� Et�1

i PVt�1/�Vti and �� Et�1

i V� t�1/�Vti.

In our context V� t � ( ft�2, ... , ft�T). For b �0 equations (7), (C1), and (C2) then lead to (32)with �/(1 � �) � (�2, ... , �T)�.

D. Order Flow

In this section we describe our measure oforder flow when the observable fundamentalfollows a random walk. Using the notation andresults from Appendix B, we have

(D1)

bFti �

��MYti � ft � nbt � T � st � i*t � it

��t2 � bt

i,

where n � ��2bT�1/(1 � � � �b). Let � �

(�1, ... , �t)� be the last T elements of M��,divided by ��2. The component of demand thatdepends on private information is therefore

(D2) �s � 1

T

�svt � 1�si* � bt

i.

Using that vt�1�si* � �t�1

f � ... � �t�1�s�Tf �

�t�1�svi , (D2) aggregates to

(D3) ��t � bTbt � T ,

where �� (1, ... , 2T) with s � �1 � ... ��s and T�s � �b

s�1 for s � 1, ... , T. Orderflow xt � xt�1 is defined as the component of(D3) that is orthogonal to public information(other than st). Public information that helpspredict this term includes bt�T and s*t�1, ... ,s*t�T�1. Order flow is then the error term of aregression of ��t on s*t�1, ... , s*t�T�1. DefiningHs as rows 2 to T of the matrix H defined in

Appendix B.2, it follows from Appendix B.2that E� t(�t�s*t�1, ... , s*t�T�1) � MsH�s�t, whereMs � PHs[H�sPHs]

�1. It follows that

(D4) xt � xt � 1 � ��I � MsH�s��t .

We can also show that there is a cointegratingrelationship between the exchange rate, cumu-lative order flow, and bt � ¥s�0

�t�T�sb . When

f follows a random walk, the equilibrium ex-change rate can be written as (see AppendixB.3)

(D5) st � ft � �bt � T � ��t .

Order flow is equal to

(D6) xt � xt � 1 � ��t ,

where �� (I � MsH�s). It therefore followsthat cumulative order flow is equal to

(D7) xt � ��1 � ... � �T �ft

� ��T � 1 � ... � �2T �bt � ��t ,

where depends on the parameters in the vec-tor �. It follows from (D5) and (D7) that there isa cointegrating relationship between st, xt, andbt. Note that the latter follows a random walksince bt � bt�1 � �t�T

b . This cointegratingrelationship holds both for b � 1 and b � 1.In the latter case bt�T � bt.

REFERENCES

Admati, Anat R. “A Noisy Rational Expecta-tions Equilibrium for Multi-Asset SecuritiesMarkets.” Econometrica, 1985, 53(3), pp.629–57.

Allen, Franklin; Morris, Stephen and Shin, HyunSong. “Beauty Contests and Iterated Expecta-tions in Asset Markets.” Review of FinancialStudies (forthcoming).

Bacchetta, Philippe and van Wincoop, Eric. “CanInformation Heterogeneity Explain the Ex-change Rate Determination Puzzle?” Na-tional Bureau of Economic Research, Inc.,NBER Working Papers: No. 9498, 2003.

Bacchetta, Philippe and van Wincoop, Eric.“Higher Order Expectations in Asset Pric-ing.” International Center for Financial Asset


Management and Engineering, FAME Re-search Paper Series: No. 100, 2004a.

Bacchetta, Philippe and van Wincoop, Eric. “AScapegoat Model of Exchange-Rate Fluctua-tions.” American Economic Review, 2004b,94(2), pp. 114–18.

Bacchetta, Philippe and van Wincoop, Eric. “Ra-tional Inattention: A Solution to the ForwardDiscount Puzzle.” Unpublished Paper, 2005.

Bjønnes, Geir H.; Rime, Dafinn and Solheim,Haakon O. A. “Liquidity Provisions in theOvernight Foreign Exchange Market.” Jour-nal of International Money and Finance,2005, 24(2), pp. 175–96.

Brennan, Michael J. and Cao, H. Henry. “Inter-national Portfolio Investment Flows.” Jour-nal of Finance, 1997, 52(5), pp. 1851–80.

Brown, David P. and Jennings, Robert H. “OnTechnical Analysis.” Review of FinancialStudies, 1989, 2(4), pp. 527–51.

Brunnermeier, Markus K. Asset pricing underasymmetric information: Bubbles, crashes,technical analysis, and herding. Oxford: Ox-ford University Press, 2001.

Cheung, Yin-Wong; Chinn, Menzie D. and Pas-cual, Antonio G. “Empirical Exchange RateModels of the Nineties: Are Any Fit to Sur-vive?” Journal of International Money andFinance (forthcoming).

Chinn, Menzie D. and Meese, Richard A. “Bank-ing on Currency Forecasts: How PredictableIs Change in Money?” Journal of Interna-tional Economics, 1995, 38(1–2), pp. 161–78.

Chionis, Dionysios and MacDonald, Ronald. “Ag-gregate and Disaggregate Measures of theForeign Exchange Risk Premium.” Interna-tional Review of Economics and Finance,2002, 11(1), pp. 57–84.

DeMarzo, Peter and Skiadas, Costis. “Aggrega-tion, Determinacy, and Informational Effi-ciency for a Class of Economies withAsymmetric Information.” Journal of Eco-nomic Theory, 1998, 80(1), pp. 123–52.

Devereux, Michael B. and Engel, Charles. “Ex-change Rate Pass-through, Exchange RateVolatility, and Exchange Rate Disconnect.”Journal of Monetary Economics, 2002, 49(5),pp. 913–40.

Dow, James and Gorton, Gary. “Profitable In-formed Trading in a Simple General Equilib-rium Model of Asset Pricing.” Journal ofEconomic Theory, 1995, 67(2), pp. 327–69.

Elliot, Graham and Ito, Takatoshi. “Heteroge-neous Expectations and Tests of Efficiency inthe Yen/Dollar Forward Exchange Rate Mar-ket.” Journal of Monetary Economics, 1999,43(2), pp. 435–56.

Engel, Charles and West, Kenneth D. “ExchangeRates and Fundamentals.” Journal of Politi-cal Economy, 2005, 113(3), pp. 485–517.

Evans, Martin D. D. and Lyons, Richard K. “In-formational Integration and FX Trading.”Journal of International Money and Finance,2002a, 21(6), pp. 807–31.

Evans, Martin D. D. and Lyons, Richard K. “Or-der Flow and Exchange Rate Dynamics.”Journal of Political Economy, 2002b, 110(1),pp. 170–80.

Evans, Martin D. D. and Lyons, Richard K. “ANew Micro Model of Exchange Rate Dynam-ics.” National Bureau of Economic Research,Inc., NBER Working Papers: No. 10379,2004.

Foster, F. Douglas and Viswanathan, S. “StrategicTrading When Agents Forecast the Forecastsof Others.” Journal of Finance, 1996, 51(4),pp. 1437–78.

Froot, Kenneth A. and Ramadorai, Tarun. “Cur-rency Returns, Institutional Investor Flows,and Exchange Rate Fundamentals.” Journalof Finance, 2005, 60(3), pp. 1535–66.

Gennotte, Gerard and Leland, Hayne. “MarketLiquidity, Hedging, and Crashes.” AmericanEconomic Review, 1990, 80(5), pp. 999–1021.

Gourinchas, Pierre-Olivier and Rey, Helene. “In-ternational Financial Adjustment.” NationalBureau of Economic Research, Inc., NBERWorking Papers: No. 11155, 2005.

Gourinchas, Pierre-Olivier and Tornell, Aaron.“Exchange Rate Puzzles and Distorted Be-liefs.” Journal of International Economics,2004, 64(2), pp. 303–33.

Grossman, Sanford J. “On the Efficiency ofCompetitive Stock Markets Where TradersHave Diverse Information.” Journal of Fi-nance, 1976, 31(2), pp. 573–85.

Grundy, Bruce D. and McNichols, Maureen.“Trade and the Revelation of Informationthrough Prices and Direct Disclosure.” Re-view of Financial Studies, 1989, 2(4), pp.495–526.

Hamilton, James D. Time series analysis. Prince-ton: Princeton University Press, 1994.

Hau, Harald. “Competitive Entry and Endoge-nous Risk in the Foreign Exchange Market.”


Review of Financial Studies, 1998, 11(4), pp.757–87.

Hau, Harald; Killeen, William P. and Moore, Mi-chael. “How Has the Euro Changed the For-eign Exchange Market?” Economic Policy,2002, 17(34), pp. 149–91.

He, Hua and Wang, Jiang. “Differential Informa-tion and Dynamic Behavior of Stock TradingVolume.” Review of Financial Studies, 1995,8(4), pp. 919–72.

Hussman, John P. “Market Efficiency and Inef-ficiency in Rational Expectations Equilibria:Dynamic Effects of Heterogeneous Informa-tion and Noise.” Journal of Economic Dy-namics and Control, 1992, 16(3–4), pp. 655–80.

Ito, Takatoshi. “Foreign Exchange Rate Expec-tations: Micro Survey Data.” American Eco-nomic Review, 1990, 80(3), pp. 434–49.

Jeanne, Olivier and Rose, Andrew K. “NoiseTrading and Exchange Rate Regimes.” Quar-terly Journal of Economics, 2002, 117(2), pp.537–69.

Kasa, Kenneth. “Forecasting the Forecasts ofOthers in the Frequency Domain.” Review ofEconomic Dynamics, 2000, 3(4), pp. 726–56.

Kasa, Kenneth; Walker, Todd B. and Whiteman,Charles H. “Asset Pricing with Heteroge-neous Beliefs: A Frequency-Domain Ap-proach.” Unpublished Paper, 2004.

King, Robert G. “Monetary Policy and the In-formation Content of Prices.” Journal of Po-litical Economy, 1982, 90(2), pp. 247–79.

Kollman, Robert. “Monetary Policy Rules in theOpen Economy: Effects on Welfare andBusiness Cycles.” Journal of Monetary Eco-nomics, 2002, 49(5), pp. 989–1015.

Lucas, Robert E., Jr. “Expectations and the Neu-trality of Money.” Journal of Economic The-ory, 1972, 4(2), pp. 103–24.

Lyons, Richard K. The microstructure approachto exchange rates. Cambridge, MA: MITPress, 2001.

MacDonald, Ronald and Marsh, Ian W. “Cur-rency Forecasters Are Heterogeneous: Con-firmation and Consequences.” Journal ofInternational Money and Finance, 1996,15(5), pp. 665–85.

MacDonald, Ronald and Taylor, Mark P. “TheMonetary Approach to the Exchange Rate:Rational Expectations, Long-Run Equilibrium,and Forecasting.” International Monetary FundStaff Papers, 1993, 40(1), pp. 89–107.

Mankiw, N. Gregory and Reis, Ricardo. “StickyInformation versus Sticky Prices: A Proposalto Replace the New Keynesian PhillipsCurve.” Quarterly Journal of Economics,2002, 117(4), pp. 1295–1328.

Mark, Nelson C. “Exchange Rates and Funda-mentals: Evidence on Long-Horizon Predict-ability.” American Economic Review, 1995,85(1), pp. 201–18.

Mark, Nelson C. and Sul, Donggyu. “NominalExchange Rates and Monetary Fundamen-tals: Evidence from a Small Post–BrettonWoods Panel.” Journal of International Eco-nomics, 2001, 53(1), pp. 29–52.

Mark, Nelson C. and Wu, Yangru. “RethinkingDeviations from Uncovered Interest Parity:The Role of Covariance Risk and Noise.”Economic Journal, 1998, 108(451), pp.1686–1706.

McCafferty, Stephen and Driskill, Robert.“Problems of Existence and Uniqueness inNonlinear Rational Expectations Models.”Econometrica, 1980, 48(5), pp. 1313–17.

Meese, Richard A. and Rogoff, Kenneth. “Empir-ical Exchange Rate Models of the Seventies:Do They Fit out of Sample?” Journal ofInternational Economics, 1983, 14(1–2), pp.3–24.

Morris, Stephen and Shin, Hyun Song. “SocialValue of Public Information.” American Eco-nomic Review, 2002, 92(5), pp. 1521–34.

Mussa, Michael. “The Exchange Rate, the Bal-ance of Payments and Monetary and FiscalPolicy under a Regime of Controlled Float-ing.” Scandinavian Journal of Economics,1976, 78(2), pp. 229–48.

Obstfeld, Maurice and Rogoff, Kenneth. “The SixMajor Puzzles in International Macroeco-nomics: Is There a Common Cause?” in BenS. Bernanke and Kenneth Rogoff, eds.,NBER macroeconomics annual 2000. Cam-bridge, MA: MIT Press, 2001, pp. 339–90.

Osler, Carol L. “Stop-Loss Orders and PriceCascades in Currency Markets.” Journal ofInternational Money and Finance, 2005,24(2), pp. 219–41.

Pearlman, Joseph G. and Sargent, Thomas J.“Knowing the Forecasts of Others.” Reviewof Economic Dynamics, 2005, 8(2), pp. 480–97.

Romer, David. “Rational Asset-Price Move-ments without News.” American EconomicReview, 1993, 83(5), pp. 1112–30.


Sargent, Thomas J. “Equilibrium with SignalExtraction from Endogenous Variables.”Journal of Economic Dynamics and Control,1991, 15(2), pp. 245–73.

Singleton, Kenneth J. “Asset Prices in a Time-Series Model with Disparately Informed, Com-petitive Traders,” in William A. Barnett andKenneth J. Singleton, eds., New approaches tomonetary economics: Proceedings of the Sec-ond International Symposium in EconomicTheory and Econometrics. Cambridge: Cam-bridge University Press, 1987, pp. 249–72.

Spiegel, Matthew and Subrahmanyam, Avanidhar.“Informed Speculation and Hedging in a Non-competitive Securities Market.” Review of Fi-nancial Studies, 1992, 5(2), pp. 307–29.

Townsend, Robert M. “Forecasting the Forecastsof Others.” Journal of Political Economy,1983, 91(4), pp. 546–88.

Vives, Xavier. “Short-Term Investment and theInformational Efficiency of the Market.” Re-view of Financial Studies, 1995, 8(1), pp.125–60.

Wang, Jiang. “A Model of Intertemporal AssetPrices under Asymmetric Information.” Re-view of Economic Studies, 1993, 60(2), pp.249–82.

Wang, Jiang. “A Model of Competitive StockTrading Volume.” Journal of Political Econ-omy, 1994, 120(1), pp. 127–68.

Woodford, Michael. “Imperfect CommonKnowledge and the Effects of Monetary Pol-icy,” in Philippe Aghion, Roman Frydam,Joseph Stiglitz, and Michael Woodford, eds.,Knowledge, information and expectations inmodern macroeconomics: In honor of Ed-mund S. Phelps. Princeton, Princeton Univer-sity Press, 2003, pp. 25–58.


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