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The contribution of economic fundamentals to movements in exchange rates☆

Nathan S. Balke a,b,⁎, Jun Ma c,1, Mark E. Wohar d,2

a Department of Economics, Southern Methodist University, Dallas, TX 75275, United Statesb Research Department, Federal Reserve Bank of Dallas, United Statesc Department of Economics, Finance, and Legal Studies, Culverhouse College of Commerce & Business Administration, University of Alabama, Tuscaloosa, AL 35487-0224, United Statesd Department of Economics, Mammel Hall 332S, University of Nebraska at Omaha, Omaha, NE 68182-0286, United States

a b s t r a c ta r t i c l e i n f o

Article history:Received 1 November 2011Received in revised form 17 October 2012Accepted 19 October 2012Available online 26 October 2012

JEL Classification:F31C32C12

Keywords:Bayesian analysisExchange rate decompositionMonetary modelState-space model

Starting from the asset pricing approach of Engel and West, we examine the degree to which fundamentalscan explain exchange rate fluctuations. We show that it is not possible to obtain sharp inferences aboutthe relative contribution of fundamentals using only data on observed monetary fundamentals—moneyminus output differentials across countries—and exchange rates. We use additional data on interest rateand price differentials along with the implications of the monetary model of exchange rates to decomposeexchange rate fluctuations. In general, we find that money demand shifts, along with observed monetary fun-damentals, are an important contributor to exchange rate fluctuations.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

The well-known paper by Meese and Rogoff (1983) showed that asimple random walk model for exchange rates can beat various timeseries and structural models in terms of out-of-sample forecastingperformance. Although some of the subsequent literature on ex-change rate predictability find evidence in favor of beating the ran-dom walk benchmark, most of those results do not hold up toscrutiny. The extant literature has found the linkage between thenominal exchange rate and fundamentals to be weak (Cheung et al.,2005; Sarno, 2005). This weak linkage has become known as the “ex-change rate disconnect puzzle”.

Engel and West (2005) took a new line of attack in this analysisand demonstrate that this so-called disconnect between fundamen-tals and nominal exchange rates can be reconciled within a rational

expectations model. The Engel and West (2005) model implies thatthe exchange rate is the present discounted value of expected eco-nomic fundamentals. Specifically,

st ¼ f t þ EtX∞j¼1

ψj⋅Δf tþj

24

35þ Rt ; ð1:1Þ

where st is the spot exchange rate, ft is the current value of observedfundamentals (for example money growth and output growth differ-entials), and ψ is the discount factor. The term Rt includes current andexpected future values of unobserved fundamentals (risk premia,money demand shocks, etc.) as well as perhaps “nonfundamental”determinants of exchange rate movements.

The “exchange rate disconnect puzzle” reflects the fact that fluctua-tions in st− ft can be “large” and persistent, while the promise of thepresent value approach is that this disconnect can be explained by theexpectations of future fundamentals. The potential empirical successof the Engel and West model hinges on two major assumptions. First,fundamentals are non-stationary. Second, the factor used to discountfuture fundamentals is “large” (between 0.9 and unity). Nonstationaryfundamentals impart nonstationarity to exchange rates while a largediscount factor gives greater weight to expectations of future funda-mentals relative to current fundamentals. As a result, current funda-mentals are only weakly related to exchange rates as exchange ratesappear to follow an approximate random walk. The first assumption

Journal of International Economics 90 (2013) 1–16

☆ The authors would like to thank Philip Brock, Craig Burnside, Charles Engel, BruceHansen, Chang-Jin Kim, Chris Murray, James Nason, Charles Nelson, Hashem Pesaran,Jeremy Piger, Tatsuma Wada, Kenneth West, two anonymous referees, and seminarparticipants at numerous institutions and conferences for their helpful comments.The views expressed in this paper are those solely of the authors and not of the FederalReserve Bank of Dallas or the Federal Reserve System.⁎ Corresponding author at: Department of Economics, SouthernMethodist University,

Dallas, TX 75275, United States. Tel.: +1 214 768 2693(Office).E-mail addresses: [email protected] (N.S. Balke), [email protected] (J. Ma),

[email protected] (M.E. Wohar).1 Tel.: +1 205 348 8985.2 Tel.: +1 402 554 3712.

0022-1996/$ – see front matter © 2012 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.jinteco.2012.10.003

Contents lists available at SciVerse ScienceDirect

Journal of International Economics

j ourna l homepage: www.e lsev ie r .com/ locate / j i e


of nonstationary fundamentals has been supported by empirical work(Engel and West, 2005; Engel et al., 2007), however, only recently hasthere been direct evidence in support for the second assumption of alarge discount factor (Sarno and Sojli, 2009).

The key research question that still remains is to what extent canexpectations of future fundamentals explain exchange rate move-ments? The challenge in evaluating the present value model is thatnot only the expected future fundamentals are not observed butother economic fundamentals, i.e. the Rt in Eq. (1.1), are also not ob-served. Indeed, Engel and West (2005) acknowledge that the kind ofdecompositions based on forecasting observed fundamentals such asthose applied to stock prices (see Campbell and Shiller, 1988) is madedifficult by the presence of unobserved fundamentals.3

In this paper, we use a simple monetary model of exchange ratesto specify explicitly the relationship between economic fundamentalsand exchange rates. To sharpen our focus on expectations about fu-ture fundamentals, we use a state-space model to convenientlymodel the relationship between observed fundamentals and theunobserved predictable components of fundamentals. We integratethe state-space model into the present value model of the exchangerate to show the links between the predictable component of funda-mentals and exchange rate fluctuations. We use annual data on thepound to the dollar exchange rate, money, output, prices, and interestrates for the UK and US from 1880 to 2010. The directly observed fun-damental in our model is money supply differentials between the UKand US minus output differentials between the UK and the US. Thisvariable has been the primary focus of the literature's examinationof fundamentals' contribution to exchange rate movements. For ex-ample, Mark (1995) evaluates the ability of this variable to forecastthe future exchange rate movements for a set of countries includingthe United States, Canada, Germany, Japan, and Switzerland sincethe end of the BrettonWoods regime. Rapach andWohar (2002) con-struct this variable for 14 industrial countries covering a period ofmore than a century and study the cointegration relationship be-tween the exchange rates and the fundamentals. Mark and Sul(2001) further demonstrate that the panel data techniques are ableto find more evidence of predictability of this variable to the futureexchange rate movements. More recently, Cerra and Saxena (2010)conduct a comprehensive study of a very large dataset consisting of98 countries and find more evidence that this fundamental variablehelps to forecast the future exchange rate movements.

We show that a state-space model using only two observables—money supplyminus output differential and the exchange rate—has dif-ficulty inferring the relative importance of expected future fundamen-tals. Using Bayesian model averaging across different specifications ofthe state-space model, we show that the posterior distribution of thecontribution of observed fundamentals to the variance of exchangerates is bimodal, with roughly equal weight placed on close to a zerocontribution and on close to a 100% contribution. The reason for thisgreat uncertainty about the relative contributions of observed funda-mentals is that in the data the predictable component of changes in ob-served fundamentals is relatively small compared to the unpredictablecomponent—most of the information about future fundamentals iscontained in exchange rates rather than observable fundamentals.This makes identification of the separate contribution of expectationsof future observed fundamentals problematic.

To solve this identification problem,we bring additional informationto bear on the analysis which helps to move us away from the polarcases of 0% and 100% variance decomposition. First we incorporate

data on interest rate and price differentials by including two additionalobservation equations in our state-space model—one corresponding toa relative money demand equation and the other to deviations fromcovered interest parity. These additional observation equations provideinformation about previously unobserved fundamentals—money de-mand shifters and uncovered interest parity risk premium. Anothersource of information is prior information about key parameters in thestate-space model. Specifically, prior information about the half-life ofdeviations from purchasing power parity help to identify expected fu-ture deviations from purchasing power parity while prior informationabout the interest semi-elasticity of money demand helps determinesthe value of the discount factor. These additional sources of informationcan result in sharper inference about the relative contribution of thevarious fundamentals. Specifically, we find that monetary fundamen-tals, especially money demand shifters, explain the bulk of exchangerate movements. Fluctuations in the risk premium play a lesser role.

Our findings have important implications for exchange rate modelsthat relate the exchange rate fluctuations to the economic fundamentalssuch as the output and monetary factors. Our results indicate that theseeconomic fundamentals, either directly observed or indirectly inferred,contribute to exchange ratemovements in a substantialway. The large lit-erature that finds it difficult for economic models to produce a betterout-of-sample forecast for the exchange rate than a random walk maysimply be due to the predictable component of fundamentals beingsmall relative to the unpredictable component. That is, a simple regres-sion cannot detect the small signals buried under the volatile noise.

The rest of the paper is organized as follows. In Section 2, we out-line the simple monetary model of exchange rates used by Engel andWest (2005) to show how the spot exchange rate can be written as afunction of expectations of future fundamentals, some of which areobserved and some of which are unobserved. In Section 3, we developa state-space model to describe the dynamics of the predictable com-ponent of observed fundamentals and embed it in the simple rationalexpectations monetary model of exchange rates. In Section 4, wedemonstrate using Bayesian model averaging that there is substantialuncertainty about the quantitative contribution of observed funda-mentals to exchange rate movements. In Section 5, we use additionalinformation to obtain tighter inferences about relative contributionsof observed and unobserved fundamentals. Section 6 conducts a sen-sitivity analysis to alternative model specifications and choice ofpriors. In Section 7, we provide additional evidence that the factorthat is a major contributor to exchange rate movements is truly asso-ciated with money demand shifters. Section 8 concludes.

2. The monetary exchange rate model

We start with the classical monetary model as below (all variablesare in logarithm except for the interest rates, and asterisk denotes for-eign variable):

mt−pt ¼ ϕyt−λit þ vmdt ð2:1Þ

m�t−p�t ¼ ϕy�t−λi�t þ v�md

t ð2:2Þ

The variable definitions used in our model are the natural log ofmoney supply (m), natural log of price level (p), and nominal interestrate (i). Variables with asterisk represent the foreign country.4 Theterms vt

md and vt⁎md represent unobserved variables that shift moneydemand.

We integrate into themodel a generalized Uncovered Interest Parity(UIP) condition that allows for a time-varying risk premium, rtuip, since

3 An active literature has developed based on the insights in the Engel and West(2005). Several papers try to infer the importance of unobserved fundamentals in highfrequency data by using on information order flows (Evans, 2010; Rime et al., 2010).Nason and Rogers (2008) generalize the Engel andWest present value model of the ex-change rate to a dynamic stochastic general equilibrium model and estimate aresulting unobserved components model using quarterly US and Canada data.

4 We treat UK as the home country. The exchange rate is quoted as pounds perdollar.

2 N.S. Balke et al. / Journal of International Economics 90 (2013) 1–16


in general UIP fails and the equilibriummodelwould imply a non-trivialrisk premium (see Engel, 1996):

it−i�t ¼ Etstþ1−st þ ruipt ; ð2:3Þ

where st is the natural log of the exchange rate. To complete model, weadd the Purchasing Power Parity (PPP) relationship:

st ¼ pt−p�t þ rpppt : ð2:4Þ

Since the PPP in general only holds in the long run (Rogoff, 1996), thevariable rt

ppp picks up these deviations from PPP.Combining Eqs. (2.1) through (2.4), one can derive a stochastic

difference equation that describes how the exchange rate woulddepend on observed monetary fundamentals and an unobservedremainder. The algebra can be manipulated so as to express the ex-change change rate in terms of its deviation from observed funda-mentals, similar to the stock price decomposition by Campbell andShiller (1988):

st−f t ¼ ψ⋅Et stþ1−f tþ1� �þ ψ⋅Et Δf tþ1

� �þ Rt ; ð2:5Þ

where, ft≡(mt−mt⁎)−ϕ(yt−yt⁎) is the observed monetary funda-

mental, and ψ ¼ λ1þλ is the so-called discount factor.5 In the following

estimation exercise, we set ϕ=1 as in Rapach andWohar (2002) andMark (1995). As we have data on money and output, ft is typically ob-servable. The unobserved term, Rt, consists of the unobserved moneydemand shifter as well as deviations from both uncovered interestrate parity and purchasing power parity: Rt=ψrtuip+(1−ψ)rtppp−(1−ψ)rtmd where rt

md=vtmd−vt⁎md. Engel and West (2005, 2006)

show that this asset price formulation for the exchange rates is verygeneral and can be derived from a variety of monetary policy modelsincluding the Taylor rule and may include more fundamental infor-mation under that type of monetary policy rule.

We can iterate Eq. (2.5) forward. Under the assumption of no ex-plosive solution, the model can be solved as below:

st−f t ¼ EtX∞j¼1

ψj⋅Δf tþj

24

35þ Et

X∞j¼0

ψj⋅Rtþj

24

35; ð2:6Þ

where, st− ft is the deviation of the current exchange rate from itscurrent observed monetary fundamental. Eq. (2.6) is similar to thepresent discounted value formula for the exchange rate derived inEngel and West (2005, 2006), and this equation states that any devi-ation of current exchange rate from its observed fundamentals shouldreflect the variation of the present discounted value of agent'sexpected future economic fundamentals.

3. Decomposing the contribution of observed fundamentals andunobserved shocks

One obstacle in evaluating the above exchange rate model is thatwhat matters in explaining current deviation of exchange rate fromits fundamentals are agent's expectations of future fundamentalsbut these expectations are not directly observable. The state-spacemodel offers a convenient framework in which we can model the ex-pectations as latent factors and allow them to have flexible dynamics.In doing this, we can extract agent's expectations using the Kalmanfilter and decompose the current deviation of exchange rate from itsfundamentals into the contributions of expectations of future ob-served fundamentals and current and future unobserved remainder.Furthermore, instead of assuming that the discount factor is close to

unity as in Engel and West (2005, 2006), we can directly estimatethe discount factor and provide further statistical evidence for theEngel and West model.

Given Eq. (2.6), the exchange rate relative to current observedfundamentals, st− ft, depends on expectations of Δft+ i and expecta-tions of rtþi ¼ Rtþi

ψ . Denote the expectations by Et[Δft+1]=gt and Et[rt+1]=μt. The realized variables are just the sum of their conditionalexpectation and a realized unforecastable shock:

Δf t ¼ gt−1 þ εft ; ð3:1Þ

rt ¼ μ t−1 þ εrt : ð3:2Þ

The realized shocks (or forecast errors) εtf and εtr are white noise.At the same time, the predictable components of Δft and rt followautoregressive processes:

1−ϕg Lð ÞL� �

gt ¼ εgt ; ð3:3Þ

1−ϕμ Lð ÞL� �

μ t ¼ εμt ; ð3:4Þ

where εtg and ε1μ are expectation (or “news”) shocks and lag polyno-

mialsϕg Lð Þ ¼Xki¼1

ϕg;iLi−1 andϕμ Lð Þ ¼

Xki¼1

ϕμ;iLi−1 describe the dynam-

ics of the predictable components. The four shocks [εtg εtμ εtf εtr]′ areallowed to be contemporaneously correlated but they are seriallyuncorrelated. Note the implied univariate time series models for Δftand rt are just ARMA(k,max(1,k)) models, where k is the number ofautoregressive terms in ϕg(L) and ϕμ(L). Recall that while economicagents know the values of gt and μt, the econometrician does notand must infer them from observable variables.

Using Eq. (2.6) and evaluating expectations, we can write the ex-change rate relative to observed current monetary fundamental as:

st−f t ¼ B1 Lð Þgt þ B2 Lð Þμ t þ ψμt−1 þ ψεrt ; ð3:5Þ

where EtX∞j¼1

ψj⋅Δf tþj

24

35 ¼ B1 Lð Þgt ; Et

X∞j¼1

ψjþ1⋅rtþj

24

35 ¼ B2 Lð Þμ t , and

ψrt=ψμt−1+ψεtr. The contribution of expectations of observed fun-

damentals, EtX∞j¼1

ψj⋅Δf tþj

24

35, will in fact depend on current (and pos-

sibly lagged) values of the unobserved component gt. The coefficientsof the lag polynomials, B1(L) and B2(L), depend on the values of ψ,ϕg(L), and ϕμ(L). In general, the larger the value of ψ and the morepersistent is gt, the larger are the coefficients of B1(L).

Given the observed monetary fundamentals, Δft, we can write themodel in a state-space form with the measurement equation:

Δf tst−f t

� �¼ L 0 1 0

B1 Lð Þ B2 Lð Þ þ ψL 0 ψ

� � gtμ t

εftεrt

2664

3775; ð3:6Þ

and the transition equation:

gtμ t

εftεrt

2664

3775 ¼

ϕg Lð Þ 0 0 00 ϕg Lð Þ 0 00 0 0 00 0 0 0

2664

3775

gt−1μ t−1

εft−1εrt−1

2664

3775þ

εgtεμtεftεrt

2664

3775: ð3:7Þ

Given the parameters of the state-space model, we can determinethe relative contribution of monetary fundamentals through the ef-fect of gt on st− ft in Eq. (3.6).

5 Note here that it is the UIP equation that links interest rate differentials to the ex-change rate change and hence gives the result that the discount factor is a function ofthe interest semi-elasticity of money demand.

3N.S. Balke et al. / Journal of International Economics 90 (2013) 1–16


As none of the state variables is directly observed and must be in-ferred from the two observed time series, identification of thestate-space model will depend on the dynamics of the observedtime series and its variance/covariance matrix.6 Balke and Wohar(2002) and Ma and Wohar (2012) show that inference about the rel-ative contribution of the unobserved components may be very weakif the observed fundamental does not provide a lot of direct informa-tion about the relative size of the predictable component of funda-mentals. For example, if the variance of innovations to thepredictable components, σg

2, is small relative to the variance of theunpredictable component, σf

2, then observations of Δft provide verylittle information about gt, leaving only st− ft to infer both gt and μt.7

One can see this by rewriting the state-space model as a VARMA:

1−ϕg Lð ÞL 0

0 1−ϕg Lð ÞL� �

1−ϕμ Lð ÞL� � !

Δf tst−f t

� �¼

L 0 1−ϕg Lð ÞL� �

0

B1 Lð Þ 1−ϕμ Lð ÞL� �

B2 Lð Þ þ ψð Þ 1−ϕg Lð ÞL� �

0 1−ϕg Lð ÞL� �

1−ϕμ Lð ÞL� �

0@

1A

εgtεμtεftεrt

0BB@

1CCA

ð3:8Þ

If σ2g=σ

2f is “small”, then observations of Δft are not sufficient to

identify ϕg(L)—this polynomial is nearly canceled out in the Δft equa-tion. As there could be numerous combinations of ϕg(L) and ϕμ(L)that would yield the same autoregressive dynamics for st− ft, wheth-er there is sufficient information to identify ϕg(L) and ϕμ(L) would de-pend on the moving average dynamics of st− ft.

Taking annual observations of the nominal exchange rate, relativemoney supply, and relative real GDP between the US and UK and UKand US interest rates from 1880 to 2010 (see Supplementary Appendixfor details of data construction), the top panel of Fig. 1 plots the log UK–US exchange rate, st, and the log level of the observed monetary funda-mental, ft, while the lower panel of Fig. 1 plots the realized fundamentalsgrowth (Δft) along with the deviation of current exchange rate from theobserved monetary fundamentals (st− ft). In the data, st− ft is quite per-sistent and volatile while the realized fundamentals growth is much lesspersistent and less volatile. Fig. 1 suggests that the persistent componentgt is likely to be “small” relative toΔftwhich in turn implies that it may bedifficult to separately identify gt and μt from data on st− ft alone.

4. Implications of weak identification for exchangerate decompositions

As suggested above, most of the information about the predictablecomponent of the observedmonetary fundamentals might actually bein the exchange rate, st− ft, rather than in observed monetary funda-mentals growth itself, Δft. This suggests that the model is weaklyidentified as essentially a single data series (st− ft) is used to identifytwo components (gt and μt). To demonstrate the extent to which thisidentification problem holds in practice, we consider five alternative,non-nested models. Each of these five models gives rise to anARMA(4,4) model for st− ft but will imply very different exchangerate decompositions. Specifically, we consider the following AR spec-ifications for ϕg(L)L and ϕμ(L)L respectively: (i) AR(2) and AR(2),(ii) AR(4) and AR(0), (iii) AR(3) and AR(1), (iv) AR(1) and AR(3),(v) AR(0) and AR(4). For all five models, we assume that the innova-tions in the four components [εtg εtμ εtf εtr]′ are correlated with oneanother.

We take a Bayesian approach to account for uncertainty about thespecification of the underlying state-space model. To evaluate these

alternative models, we first estimate the posterior distribution of the pa-rameters for each of thefive competingmodels. The posterior distributionof the parameters given the data and a particularmodel,wewill denote asP[θm|YT,M=m], where m is the model and θm is the parameter vector ofmodelm. The posterior probability of modelm is then:

P mjY½ � ¼ B mð Þh mð Þ∑m∈M

B mð Þh mð Þ ; ð4:1Þ

where M is the set of models, h(m) is the prior probability of model m,B(m)=∫L(YT,θm)h(θm)dθm,L(YT,θm) is the likelihood, and h(θm) is theprior density of the parameters. As we are interested in determining therelative contribution of fundamentals to exchange rate decompositionwe calculate the variance decomposition, V(θm,m), implied by a givenmodel m and parameter vector, θm. Given the posterior distribution ofthe parameters, we can obtain the posterior distribution of the variancedecomposition for a givenmodel, P[V(θm,m)|m,YT]. Finally,we can employBayesianmodel averaging to account formodel uncertainty on the poste-rior distribution of the variance decomposition.

Given the nonlinear (in parameters) structure of the model, thereis no closed form solution for the posterior distribution given stan-dard priors; therefore, we use a Metropolis-Hastings Markov ChainMonte Carlo (MH-MCMC) to approximate the posterior distributionof the parameters given the model (see the Supplemental Appendixfor details). We can easily construct the posterior distribution of thevariance decomposition from the results of the MH-MCMC as wellthe posterior probabilities for the five models given the data. In thissection, we consider the case of very diffuse priors so that the likeli-hood function is the principal determinant of the posterior distribu-tion.8 The posterior distribution is based on 500,000 draws from theMH-MCMC after a burn-in period of 500,000 draws.

To save space we do not present all the histograms of the posteriordistribution of parameters (these are available upon request). Fig. 2 dis-plays for all fivemodels the posterior distribution of the contributions ofthe predictable component of the fundamentals, gt, to the variance ofdeviations of the exchange rate from observedmonetary fundamentals,st− ft. For the Model 1, the posterior distribution of the observedfundamental's contribution to exchange rate variance is concentratedaround 100% but does show a small secondary mode close to zero.Model 2, in which ϕg(L) is an AR(4) and ϕμ(L) is an AR(0), also impliesthat the observed fundamentals explains nearly all the variance of ex-change rates. Models 4 and 5, on the other hand, imply that observedmonetary fundamentals explain almost none of the variance of ex-change rates (ϕg(L) is an AR(1) and ϕμ(L) is an AR(3) for Model 4 andAR(0) and AR(4), respectively, for Model 5). Model 3 (ϕg(L) is anAR(3) and ϕμ(L) is an AR(1)), suggests a bimodal distribution withprobability mass concentrated on the extremes.

Which of the five models does the data prefer? From the MCMCposterior distribution, we can construct the posterior distribution ofthe log likelihoods, log(L(YT,θm)), for each model.9 While Model 1has the highest posterior probability, it is not substantially higherthan Model 5 and even Models 2 through 4 have non-negligible pos-terior probabilities. In fact, the cumulative distribution of the posteri-or distribution of log likelihoods for the five models (not shown to

6 See the Supplementary Appendix for a more detailed discussion of identification ofthe above state-space model.

7 Ma and Nelson (2012) show that for a large class of models that a small signal-to-noise ratio indicates that the model is weakly identified and , as a result, the uncertain-ty about the parameter estimates will be large.

8 Formally, for each of the models the individual autoregressive parameters have aprior distribution of joint truncated normal N(0,100), the prior distribution ψ isU(0,1), the variances of innovations in Eq. (3.7) are distributed U(0,1000) while theco-variances of innovations in Eq. (3.7) are distributed U(−1000,1000). Draws inautoregressive parameters that imply nonstationarity are rejected as are draws wherethe variance-covariance of matrix of innovations in Eq. (3.7) is not positive definite.These prior distributions ensure that for this model and data, the acceptance in theMetropolis-Hastings sampler depends only on the likelihoods; thus, when comparingmodels the likelihoods are going to be decisive.

9 The posterior probabilities of the five models are 0.38, 0.09, 0.11, 0.15, and 0.27,respectively.



conserve space) are quite close to one another and benchmark modeldoes not stochastically dominate all the other models.10

In the lower right panel of Fig. 2 we plot the histogram for the ob-servedmonetary fundamental's variance decomposition of st− ft oncewe account for model uncertainty. Here the variance decompositionfor eachmodel is weighted by its posterior probability. Taking into ac-count of model uncertainty suggests a bimodal distribution for thecontribution of observed monetary fundamentals on the variance ofst− ft, with the probability mass concentrated on either a zero contri-bution or 100% contribution. Using data on exchange rates and ob-served monetary fundamentals alone is not sufficient to determineto what extent exchange rates are driven by monetary fundamentals.

5. Incorporating additional information to the analysis

As we demonstrated above, the basic model that only includes theexchange rate and the observed monetary fundamentals as observ-ables does not generate sharp inferences about the relative contribu-tion of observed fundamentals to exchange rate fluctuations. In otherwords, the two data series st− ft and Δft do not have sufficient infor-mation to pin down the relative contribution of the fundamentals. Inprinciple, to resolve this issue one has to providemore information. Inthis section, we use a combination of additional data, the insights im-plied by the simple monetary model, and prior information about keyparameters to sharpen inferences about the sources of exchange ratefluctuations. In particular, the information we bring to bear is aboutthe remainder term, Rt, rather than directly about Δft.

5.1. An expanded decomposition of exchange rates

The monetary model discussed in Section 2 suggests that the wecan break the remainder into its constituent parts: an unobservedmoney demand shifter where rt

md=vtmd−vt⁎md, deviations from un-

covered interest parity rtuip, and deviations from purchasing power

parity rtppp. The monetary model suggests that these along with

observed monetary fundamentals will in turn help determine ex-change rate movements. The monetary model also suggests thatprice differentials (pt−pt⁎) and interest rate differentials are relatedto rt

md, rtuip, and rtppp.

Using notation similar to that in Section 3, we assume each of thefour components of exchange rates consists of a predictable andunpredictable component:

Δf t ¼ gt−1 þ εft 1−ϕg Lð ÞL� �

gt ¼ εgt ð5:1Þ

rpppt ¼ μpppt−1 þ εpppt 1−ϕppp Lð ÞL

� �μpppt ¼ εμ;pppt ð5:2Þ

ruipt ¼ μuipt−1 þ εuipt 1−ϕuip Lð ÞL

� �μuipt ¼ εμ;uipt ð5:3Þ

rmdt ¼ μmd

t−1 þ εmdt 1−ϕmd Lð ÞLð Þμmd

t ¼ εμ;mdt

ð5:4Þ

We specify ϕg(L)L, ϕppp(L)L, ϕuip(L)L, ϕmd(L)L to be AR(1)'s to keepthe model parsimonious and also to keep a similar ARMA(4,4) struc-ture for the reduced form for st− ft that was present in the simplemodel of Section 3. The state vector is: St=[gt gt−1 μtuip μt−1

uip μtppp

μt−1ppp μtmd μt−1

md εtf εtuip εtppp εtmd]′ and the transition equation is

St ¼ FSt−1 þ Vt ð5:5Þ

where Vt=[εtg 0 εtμ,uip 0 εtμ,ppp 0 εtμ,md 0 εtf εtuip εtppp εtmd]′. We denote thevariance–covariance matrix of Vt by Q. The Supplemental Appendixdescribes the F matrix in the state equation in detail.

We use data on interest rate and price level differentials to con-struct two additional observation equations. Our observation vectornow consists of four variables: relative velocities or relative moneydemand in the two countries (mt−yt−pt−(mt

⁎−yt⁎−pt⁎)= ft−(pt−pt⁎)), interest rate differentials (it− it⁎), along with the growthrate in observed monetary fundamentals (Δft), and the exchangerate relative to current observed monetary fundamental (st− ft).

10 The figure that plots all five cumulative distributions of the posterior distribution isavailable upon request.

Fig. 1. UK–US exchange rate and observed monetary fundamentals log exchange rate (s) and observed level of monetary fundamentals (f).



Using the simple monetary model in Section 2, the relative moneydemand equation is given by:

f t− pt−p�t� ¼ − ψ

1−ψit−i�t� þ rmd

t : ð5:6ÞThe uncovered interest rate condition implies:

it−i�t ¼ Et stþ1−f tþ1� þ EtΔf tþ1− st−f tð Þ þ ruipt : ð5:7Þ

Recall that the growth rate of observed monetary fundamentals is

Δf t ¼ gt−1 þ εft ; ð5:8Þ

and the exchange rate equation is given by

st−f t ¼ EtX∞j¼1

ψj⋅Δf tþj

24

35þ Et

X∞j¼0

ψjþ1⋅rtþj

24

35; ð5:9Þ

where ψ rt=ψrtuip+(1−ψ)rtppp−(1−ψ)rtmd. We do not include devi-ations from PPP in the observation vector as it is just a linear

combination of two of the other observation variables: ft−(pt−pt⁎)and st− ft.

Taking expectations and writing Eqs. (5.6)–(5.9) in terms of thestate variables, St, yields the following measurement equation:

f t− pt−p�tð Þit−i�tΔf tst−f t

2664

3775 ¼

− ψ1−ψ Hsf þ HΔf

� �F−Hsf þ Huip

� �þ Hmd

Hsf þ HΔf

� �F−Hsf þ Huip

HΔfHsf

266664

377775St ;

ð5:10Þ

where the loading matrices H's are described in detail in the Supple-mental Appendix. Eqs. (5.5) and (5.10) describe the state-spacemodel which includes observations on relative money demand, inter-est rate differentials, growth rate of observed monetary fundamen-tals, and the exchange rate minus fundamentals.

We also can bring prior information to bear on the estimation ofsome of the key model parameters. While we do not use observations

Fig. 2. Histograms of posterior distribution of variance decomposition of st− ft for various models.



on PPP deviations, there is, however, a large literature on PPP devia-tions that we can draw upon to provide information about μtppp. Weassume a prior distribution for ϕppp (see Eq. (5.2)) so that thehalf-life for PPP deviations is similar to that found in the literature(see Rogoff, 1996). Specifically, we assume a Beta(10,2) distributionfor the prior distribution of ϕppp.

One of the other key parameters in the model is the discount factor:ψ ¼ λ

1þλ where λ is the interest semi-elasticity of money demand. Asthere is a large literature on the estimation of money demand, we usethis literature to help determine a prior distribution for λ. Specifically,we set the prior distribution of λ to be a Gamma with mode equal to10 and standard deviation of 8.66.11We chose this prior based on stud-ies of long-run money demand that typically estimate thesemi-elasticity of money to be in the range from around 5 to 20.12

Bilson (1978) estimates λ to be 15 in the monetary model, whereasFrankel (1979) finds λ to be equal to 7.25 while Stock and Watson(1993, 802, table 2, panel I) give a value of λ around 10. A more recentstudy by Haug and Tam (2007) suggest values ranging from around 10to 20.13

5.2. Estimation results

Fig. 3 displays posterior distributions of λ and ψ and contrasts themwith their prior distributions. As before we use a Metropolis-HastingsMCMC to draw 500,000 draws from the posterior distribution (with aburn-in sample of 500,000 draws). The posterior distribution for λ sug-gests a semi-elasticity of around 17, somewhat higher than themode ofthe prior distribution, but the posterior distribution is substantiallytighter than the prior distribution. The posterior distribution for the

discount factor, ψ, suggests a value around .95 not far from the modeof the prior, but again substantially tighter. Fig. 3 also displays posteriordistributions of autoregressive parameters for the four predictable com-ponents: gt, μtppp, μtppp, and μtmd. The posterior distribution of theautoregressive parameters suggests that all the unobserved predictablecomponents are fairly persistent.14

Fig. 4 displays the posterior distribution of variance decomposi-tion of (st− ft).15 We can see that the contributions of the risk premi-um (rtuip) and of deviations from PPP (rtppp) are small. The greatestcontribution comes from the predictable component of the moneydemand shifter, μtmd, while the contribution of predictable componentof directly observed monetary fundamentals, gt, is more modest. Notethat the contribution of the covariance between gt and μtmd tends to benegative. However, the posterior distribution for the joint contribu-tion of the predictable components of monetary fundamentals, gtand μtmd, is very large and centered closely around 100%. Thus, the ex-change rate disconnect in our context appears to be due to fluctua-tions in money demand that are typically not accounted for in theso-called fundamentals.

Fig. 5 displays historical decompositions of st− ft. The historicaldecompositions display the contribution of each of the states overthe entire sample. The historical decompositions reported in Fig. 5are based on the 5th, 95th, and 50th percentiles of the posterior dis-tribution. Note because the Q matrix (variance–covariance matrix inthe transition equation) in the state-space model is not diagonal,the states are in general correlated with one another and the histori-cal decomposition are, in general, not orthogonal.

The top left panel displays the historical decomposition of st− ftdue to the monetary fundamentals, both the predictable componentof Δft and unobserved money demand shifters, rtmd. The individualcontributions of deviations from uncovered interest rate parity, rtuip,

11 Formally, we set prior distribution for λ to be a Gamma(3,5).12 All of the variables are scaled up by 100 so that the appropriate scale for λ is aroundten. See the discussion in Engel and West (2005).13 Prior distributions on the other autoregressive parameters are fairly diffuse:N(0.5,(1.5)2), truncated at −1 and 1. The variances in Q are distributed U(0,1000)while the co-variances in Q are distributed U(−1000,1000). Draws for which the Qmatrix is not positive definite are rejected.

Fig. 3. Prior and posterior distributions for the interest semi-elasticity of money demand, the discount factor, and the autoregressive parameters for the benchmark model.

14 Mark andWu (1998) also find that the expected risk premium is persistent using aVAR to calculate expectations.15 These values can be above 100% due to the fact that some of the covariances arenegative.



and deviations from PPP, rtppp, are also presented in Fig. 5. From Fig. 5,one observes that most of movement in the UK/US exchange rate, es-pecially in the later part of the sample, appear to be due to monetaryfundamentals, and in particular to money demand shifters, rtmd. Therisk premium, rtuip, and deviations from PPP, rtppp, while not as impor-tant as rtmd also contribute to exchange rate fluctuations. In particular,the results suggest that monetary factors (ft and rt

md) explain the longswings in the exchange rate while deviations from parity conditionsappear to explain some of the short-run movements in exchangerates. The lower right graph in Fig. 5 shows the total contribution ofall the factors to movements of st− ft. This graph is a check to seethat the contributions of the factors add up to the exchange rate it-self.16

In summary, an expanded four-observation variable state-spacemodel where we model each of the components in the remainderterm, rt, suggests that the unobservable money demand shifters(rtmd) explain a large fraction of the exchange rate fluctuations, withthe contribution of Δft being much smaller. This is, in fact, consistent

with the previous literature that concludes that the connection be-tween the observed monetary fundamentals, here ft, and exchangerate is weak. Our interpretation is that it is actually unobserved fun-damentals, specifically relative money demand shifters, rmd, that areresponsible for a large fraction of exchange rate fluctuations.17

6. Sensitivity analysis

To examine whether the inferences derived in the previous sec-tion hold up to alternative choices about model specification andprior distributions, in this section we consider several changes inthe benchmark model of Section 5. This includes: changing the vectorof observable variables, allowing diffuse priors for the discount factor,modeling money demand shifters as nonstationary, allowing the pa-rameters in the state-space model to differ across fixed and flexibleexchange rate regimes, and including an idiosyncratic factor in theexchange rate equation to capture the possibility of exchange ratefluctuations unrelated to fundamentals.

16 In the Supplementary Appendix to this paper, we present additional historical de-compositions for the level of exchange rate (st) and for Δft. Factors underlying ft and rt

md

explain nearly all of the low frequency movements in the exchange rate. On the otherhand, the predictable component, gt, explain only a small fraction of the fluctuations inΔft. This is consistent with the results in Section 4, where the predictable component ofΔft was small relative to the unpredictable component.

17 These results are reminiscent of West (1987) who shows that the volatility ofdeutschemark-dollar exchange rates can be reconciled with the volatility of fundamen-tals if one allows for shocks to money demand and deviations to PPP. Here we actuallyinclude observable information about money demand to help identify the magnitudeof money demand shocks.

Fig. 4. Posterior distribution of the variance decomposition of st− ft for the benchmark model.



6.1. Changing the vector of observables.

In the benchmark model we presented and estimated inSections 5.1 and 5.2, we included st− ft and ft−(pt−pt⁎) as observ-ables along with it− it⁎ and Δft. To be sure that the results are not driv-en by which variables are included as observables, we drop ft−(pt−pt⁎) from the observation vector and include deviations from PPP (st−(pt−pt⁎)) as an observable.18

We find that the results from this specification are qualitativelysimilar to the results from the benchmark model. The posterior distri-butions of the underlying parameters are similar and more impor-tantly the variance decompositions for st− ft are similar acrossmodels (see Supplementary Appendix). Fig. 6 presents the posteriordistributions of the variance decomposition for the case where we re-place ft−(pt−pt⁎) with PPP deviations. Like the benchmark model,the variance in relative money demand are the single most importantcontributor to the variance of st− ft while the posterior distribution ofthe joint contribution of Δft and rt

md is also highly concentratedaround 100%. Compared to the benchmark model, fluctuations inthe UIP risk premium are more important here, typically contributing

more than the variance in the predictable component of Δft. In sum-mary, using direct observations of deviations from PPP instead of ob-servations on ft−(pt−pt⁎) does not change the conclusion thatfluctuations in money demand shifter is the single most importantcontributor to fluctuations in of st− ft.19

6.2. Diffuse priors

To see if the resultswere sensitive to our priors aboutmoney demand,we consider the alternative prior where the prior distribution of the dis-count factor, ψ, is substantially more diffuse than the benchmark case.20

Note that a diffuse prior for ψ actually implies a tight prior for λ.Fig. 7 displays the prior and posterior distributions of λ, ψ, and the

autoregressive parameters whenwe assume a diffuse prior for ψ. Despitetheflat prior forψ, the posterior distribution for the discount factor is sub-stantially more concentrated than the prior and is centered on the valueof 0.9. The posterior distribution of λ is slightly shifted to the left relativeto the benchmark model and centered around the value of ten. The

18 See the Supplemental Appendix for derivation of the state-space model that in-cludes deviations from PPP as an observable.

19 We also considered the case where we include ft−(pt−pt⁎) and st−(pt−pt⁎) as ob-servables but do not include st− ft as an observable. For this case, the results were alsoqualitatively similar to the benchmark model with relative money demand shocks be-ing the most important contributor to the variance of st− ft (see SupplementalAppendix).20 In particular, we set the prior distribution for ψ to be U(0,1).

Fig. 5. Historical decompositon of st− ft for the benchmark model. Median, 5th, and 95th percentiles of the posterior distribution.



Fig. 6. Posterior distribution of variance decompositions of st− ft for model that drops ft−(pt−pt⁎) and includes PPP deviations and st− ft as observables.

Fig. 7. Smoothed posterior distributions for key parameters for the model with diffuse priors for the discount factor.



posterior distributions of the autoregressive parameters are similar tothose of the benchmarkmodel. The slightly lower values for the discountfactor notwithstanding, the variance decomposition for the diffuse priorcase is very similar to the benchmark model (see Supplementary Appen-dix Fig. S-5). Once again, most of the variance of st− ft is explained by thevariance of the predictable component of rtmd.

We also considered a model where the prior distribution forsemi-elasticity of money demand with respect to the interest ratewas diffuse (see Supplementary Appendix for the figures).21 Onceagain, despite the prior distribution being quite different from bench-mark model, the posterior distribution is qualitatively similar. Like-wise, the variance decompositions for the model with diffuse priorsfor λ are similar to those in the benchmark model (see Supplementa-ry Appendix Fig. S-7). It appears that diffuse priors on either λ or on ψyield results that are not qualitatively different from those in thebenchmark model.

6.3. Nonstationary money demand shifter.

The previous models suggest that there is substantial persistence inthe relative money demand variable, ft−(pt−pt⁎). The benchmarkmodel assumed that rtmd is stationary. To determinewhether the resultshold up when rt

md is nonstationary, wemodify the above model by pos-iting that: Δrtmd=μt−1

md +εtmd with (1−ϕmdL)μtmd=εtμ,md, where μtmd isstationary. We can rewrite the exchange rate equation as:

st−f t ¼ −rmdt þ Et

X∞j¼1

ψj⋅ Δf tþj−Δrmdtþj

� �24

35þ Et

X∞j¼0

ψj⋅ ψruiptþj þ 1−ψð Þrppptþj

� �24

35:

ð6:1Þ

This equation has a nice interpretation. One can think of st− ft+rtmd

as the deviation of the exchange rate from its current monetary funda-mentals, where the monetary fundamentals include relative moneysupplies (mt−mt

⁎) less relative money demands (yt−yt⁎+rtmd). The

bracket terms in Eq. (6.1) are just expectations of future growth ratesof monetary fundamentals and current and expected values of devia-tions from PPP and UIP.2221 For the diffuse λ case, we set the prior distribution of λ to a Gamma(1.1,100). Recall

that ψ=λ/1+λ. A diffuse distribution for λ implies a relatively tight prior for ψ close toone. 22 See the Supplementary Appendix for the state-space representation of this model.

Fig. 8. Historical decomposition of st− ft for model with nonstationary rmd. Median, 5th, and 95th percentile of posterior distribution.



Because rtmd is nonstationary, we cannot do the standard variance

decomposition exercise, so instead we present the historical decom-position of the exchange rate in Fig. 8.23 From Fig. 8, it is clear thatthe most of the long-run movements in the exchange rate are dueto the monetary fundamentals. Note, in fact, that the vast majorityof long-run swings in st− ft can be captured by current value of rtmd.Expectations of future Δft as well as the uncovered interest parity fac-tor play only a modest role in changes in st− ft while expectations offuture Δrtmd contribute to some of the higher frequency movements inst− ft.

6.4. Fixed versus flexible exchange rate regimes.

As the benchmark model combines periods of fixed and floating ex-change rate regimes, it might be important to account for different ex-change rates regimes. In particular we want to see if the distinctionbetween fixed and flexible exchange rate regimes is important empiri-cally, as Engel and Kim (1999) point out. To investigate this issue we es-timated amodel inwhich the interest semi-elasticity ofmoney demand,the autoregressive parameters in the state-space model, and the overall

scale of the variance/covariancematrix differ across fixed versus flexibleregimes.24 We estimate the model with nonstationary money demandas there are apparent trends in both observations of ft−(pt−pt⁎) andst− ft during the recent floating exchange rate period.

Comparing fixed versus flexible exchange rate periods, the poste-rior distributions of the semi-elasticity of money and the discount fac-tor are lower under fixed exchange rates than under flexibleexchange rates (see Figs. S-9 and S-10 in the Supplementary Appen-dix). The posterior distributions for the semi-elasticity of money aswell as the discount factors in both fixed and flexible exchange rateregimes are substantially lower than in the benchmark model withthe fixed exchange rate regime parameters being, in turn, substantial-ly smaller than the flexible exchange rate parameters. All of the vari-ances are substantially smaller in fixed exchange rate periodcompared with flexible exchange rate periods.25 This finding is

23 The distribution for the semi-elasticity and the discount factor are similar to theprevious models. The mode (and mean) of the posterior distribution ϕmd is smallerthan in the previous models, as ϕmd reflects the persistence of Δrtmd rather than rt

md.

24 Given the large number of covariances in the Q matrix (36 parameters) and thelimited number of observations in both the fixed and flexible exchange rate period,we restricted the variance/covariance matrix Q to change across regimes by settingQi=P Li P’ where P is a lower triangular matrix with ones on the diagonal and is con-stant across regimes while Li is a diagonal matrix whose elements can vary across re-gimes. This allows the Q matrix to change across regimes but limits the number ofvariance parameters that vary across regimes to eight.25 For some of the variances, the posterior distribution for flexible exchange periodsis very diffuse suggesting that the limited number of observations prevents the modelfrom estimating these variances with precision.

Fig. 9. Historical decomposition of st− ft for model that allows for changes across fixed and floating exchange rate regimes. Median, 5th and 95th percentiles of the posteriordistribution.



largely consistent with Engel and Kim (1999) who also report that thevolatile regime of the exchange rate between U.S. and U.K. appears tocorrespond to the floating periods.

Fig. 9 displays the historical decomposition of st− ft for the modelin which we allow the parameters to change across fixed and flexibleexchange rate regimes. Like the previous results, most of the variationin st− ft is due to fluctuations in rt

md. Interestingly, deviations fromPPP play a more important role in this model than they typicallyplayed in the previous models. This appears to be especially thecase during periods of fixed exchange rates where expectationsabout future changes in ft and rt

md were estimated to have verysmall effects on fluctuations in exchanges.

6.5. Idiosyncratic factor in the exchange rate observation equation

Thus far, we have modeled the remainder term in Eq. (2.6) asreflecting unobserved fundamentals. However, this remainder mightalso reflect nonfundamental fluctuations in st− ft. To evaluate wheth-er nonfundamental factors have played a role in fluctuations in st− ft,we include an idiosyncratic factor in the observation equation for st−ft. We assume the idiosyncratic factor affects only st− ft and isuncorrelated with the other state variables in the model. We considerboth the case where this idiosyncratic factor is stationary and the casewhere it is nonstationary (see Supplementary Appendix for details)and estimate both models by Bayesian methods. For both of these

models, the other factors are assumed to be stationary (similar tothe benchmark model). Fig. 10 displays posterior distribution of thehistorical decompositions for the model with a nonstationary idio-syncratic component in st− ft.26 From Fig. 10, it is clear that this idio-syncratic factor contributes little to fluctuations in st− ft; lendingsupport for our interpretation of the remainder term as reflectingunobserved fundamentals.

7. Discussion and interpretation

The above results suggest thatwithin the context of the simplemon-etarymodel, relativemoney demand shocks can account for a large por-tion of exchange rate fluctuations and that taken as whole monetaryfundamentals (ft−rt

md=mt−mt⁎−(yt−yt⁎)−rt

md) account for a vastmajority of exchange rate fluctuations. Two questions naturally arise.First, does themoney demand factor estimated above, rtmd, reflect actualmoney demand or is a “remainder” that is used to fit st− ft and as suchhas no real economic interpretation? Second, what role does the assetpricing approach play in the apparent reconciliation of exchange ratesto monetary fundamentals (both observed and unobserved)?

Fig. 10. Historical decomposition of st− ft for model that includes a nonstationary idiosyncratic component in the st− ft observation equation. Median, 5th and 95th percentiles ofthe posterior distribution.

26 The model with a stationary idiosyncratic component yields similar results.



7.1. Is rtmd really a money demand shifter?

Recall that what we call the relative demand factor, rtmd, is derivedfrom Eq. (5.6) reproduced for convenience below:

f t− pt−p�t� ¼ − ψ

1−ψit−i�t� þ rmd

t ð7:1Þ

where ψ1−ψ ¼ λ is the interest semi-elasticity of money demand. As

both ft−(pt−pt⁎) and (it− it⁎) are directly observed, if we knew thevalue of λ then we could back out rt

md completely independent ofany data on exchange rates. In this case, it would seem clear thatrtmd reflects relative money demand across the two countries. Howev-er, in our empirical analysis we estimate λ and, in fact, use our modelto also “fit” (it− it⁎), so it is conceptually possible that rtmd is used to“fit” exchange rates rather than relative money demand. To what ex-tent is rt

md actually being used to help capture movements in ft−(pt−pt⁎) as opposed to st− ft?

Fig. 11 displays the historical decomposition for ft−(pt−pt⁎) for themodel with nonstationary money demand and that allows for differ-ences between fixed and flexible exchange rate regimes—the othermodels yield very similar decompositions. From Fig. 11, rtmd explainsmost of the movements in ft−(pt−pt⁎). The other factors affect ft−(pt−pt⁎) indirectly through their effect on− ψ

1−ψ it−i�t�

but this indirecteffect is small compared to the direct effect of rtmd on ft−(pt−pt⁎). It is

clear that the model is using rtmd to “fit” ft−(pt−pt⁎) which does not in-clude any direct data on exchange rates.

As it turns out, rtmd is useful for “fitting” both ft−(pt−pt⁎) and st−ft. In the data, observed monetary fundamentals, ft, move so much rel-ative to the exchange rate and price differentials that ft−(pt−pt⁎)and st− ft are strongly negatively correlated. This is particularly truein the recent flexible exchange rate period. Here the relative moneysupply in the UK versus the US has risen dramatically relative to theexchange rate and price differentials. Fluctuations in rt

md are usefulin reconciling this strong negative correlation.

Why rtmd and not the other factors? Deviations from PPP and UIP

are small relative to movements in ft−(pt−pt⁎) and st− ft. Therefore,it is the presence of rtmd and not the other fundamental factors thatexplain the movements of both ft−(pt−pt⁎) and st− ft. That this sin-gle factor can explain so much of the movements in ft−(pt−pt⁎) andst− ft also explains why an idiosyncratic factor in the st− ft equation isestimated to contribute so little to the fluctuations in st− ft.

Thefluctuations in rtmdwe find are also linked to the instability of the

money demand that has been documented in the literature. Fig. 12breaks up rt

md into a money demand factor for the UK, rtmd,UK=mt−yt−pt+λit, and a money demand factor for the US, rtmd,US=mt

⁎−yt⁎−pt⁎+λit⁎. From Fig. 12, it is clear that most of the fluctuations in rt

md

have their source in the UK rather than the US. Nielsen (2007) studiesmoney demand in UK from 1873 to 2001 and documents a considerableamount of variation in themoney velocity. His finding of a large decline

Fig. 11. Historical decomposition of ft−(pt−pt⁎) for model that allows for changes across fixed and floating exchange rate regimes. Median, 5th and 95th percentiles of the posteriordistribution.



in money velocity in the UK, starting from the early 1980s is consistentwith large increases in rt

md,UK (and in rtmd) that we find in our analysis.

Apparently, a large portion of money in UK starting from early 1980scannot be accounted for by interest rates and nominal income levels.These unobserved monetary factors turns out to be important inexplaining the movements of both ft−(pt−pt⁎) and st− ft.

7.2. The importance of the asset pricing approach

The fact that monetary fundamentals, here ft−rtmd, can capture

the long swings in exchange rates (st−(ft−rtmd) is substantially less

volatile and persistent than st) might suggest that the asset pricingapproach to exchange rate determination is not really needed to ex-plain exchange rate movements. This would, however, be an incorrectinterpretation. In fact, the asset pricing approach is crucial for gettingthe monetary (both observed and unobserved) fundamentals to mat-ter so much. Recall that the asset pricing approach to exchange ratesimplies the following equation

st ¼X∞i¼0

ψi Et

1−ψð Þ f tþi−rmdtþi

� �þ ψruiptþi þ 1−ψð Þrppptþi

h ið7:2Þ

Note that when ft and rtmd are very persistent (i.e. have a near unit

root), we can write Eq. (7.2) as

st ¼ f t−rmdt þ

X∞i¼1

ψi Et

Δf tþi−Δrmdtþi

� �h iþX∞i¼0

ψi Et

ψruiptþi þ 1−ψð Þrppptþi

� �h ið7:3Þ

The direct effect of monetary fundamentals is (1−ψ)(ft−rtmd)

while effect of expectations of future monetary fundamentals is

ψ f t−rmdt

� þX∞i¼1

ψi Et

Δf tþi−Δrmdtþi

� � �. Note that because we estimate

ψ to be in the vicinity of .9, then nearly 90% of the effect of ft−rtmd

on st is due to expectations of future values of ft−rtmd. Thus, the

asset pricing approach allows ft−rtmd to have a large impact on st

that would otherwise be missed if one only considers the direct effectof monetary fundamentals.

8. Conclusion

In this paper, we use the asset pricing approach proposed by Engeland West (2005, 2006) to quantify the contribution of monetary fun-damentals to exchange rate movements within a monetary model ofexchange rate determination. Using a state-space framework to

model both the predictable and unpredictable components of funda-mentals, we derive the restrictions implied by a rational expectations,present value model of the exchange rate for the observation equa-tions in the state-space model. Employing annual data on the poundto the dollar exchange rate, money, output, prices, and interest ratesfor the UK and US from 1880 to 2010, we estimate various versionsof this state-space model by Bayesian methods.

We show that using information on just directly observed mone-tary fundamentals, mt−mt

⁎−(yt−yt⁎), and exchange rates is plaguedby weak identification of the expected future fundamentals. The pos-terior distribution of the contribution of observed fundamentals tothe variance of exchange rates is bimodal, with roughly equal weightplaced on close to a zero contribution and on close to a 100% contri-bution. We solve the identification problem by using i) additionaldata on interest rate and price differentials, and ii) prior informationabout key parameters in the model. We find that directly observedmonetary fundamentals and money demand shifters contributemost to movements in exchange rates and while deviations from un-covered interest parity and purchasing power parity contribute to alesser extent. The results suggest that monetary fundamentals, as de-fined in this paper, appear to explain long-run movements in ex-change rates (consistent with the monetary approach to exchangerate determination) while the risk premium associated with devia-tions from uncovered interest parity and deviations from purchasingpower parity explain only a fraction of the short-run movements inexchange rates.

Appendix A. Supplementary data

Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j.jinteco.2012.10.003.

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