do central banks respond to exchange rate movements…economics.ca/2008/papers/0089.pdf · do...

Do Central Banks Respond to Exchange Rate Movements? Some New

Evidence from Structural Estimation

Wei Dong∗

International Department

Bank of Canada

January 24, 2008

Abstract

This paper investigates whether and how exchange rate movements were taken into account informulating monetary policy in Australia, Canada, New Zealand and the United Kingdom. We de-velop and estimate a structural general equilibrium two-sector model with sticky prices and wages,partial indexation on lagged inflation, a combination of both producer currency pricing and localcurrency pricing firms, and distribution services. Various forms of monetary policy rule and realexchange rate specifications are considered. Generally, with the real exchange rate specified en-dogenously and consistent with the structural model, the estimations lead to much higher marginallikelihood values than when the real exchange rate is specified exogenously. The estimation resultsof this paper lead us to favor the view that the Reserve Bank of Australia, the Bank of Canadaand the Bank of England paid close attention to real exchange rate movements in the past, whilethe Reserve Bank of New Zealand did not seem to include exchange rate movements in their policyrule. On the one hand, the central bank of New Zealand seems to be less concerned about futureinflation pressure induced by current exchange rate movements. On the other hand, the differentstructure of shocks in accounting for inflation and output variations in New Zealand, compared tothe other three countries, suggests that it may be sufficient for the Reserve Bank of New Zealand toonly respond to exchange rate movements indirectly through stabilizing inflation and output. Whatsmore, since exchange rate volatility might be emphasized when the expenditure-switching effect issmall, if this effect were taken into account, the UK might benefit from higher exchange rate volatility.

JEL Classification: F3, F4Bank Classification: Exchange Rates; Monetary Policy Framework; International Topics

∗This paper has benefited from discussions with Charles Engel and Ehsan Choudhri. I thank Larry Schembri, DonColetti, Robert Lafrance, Eric Santor, Ali Dib, Carlos De Resende, Philipp Maier, Rene Lalonde, Michael Francis, MichaelKing and numerous seminar participants for helpful comments. Contact: [email protected].

1 Introduction

For a country not permanently fixing its exchange rates, the flexible exchange rate is an essential part ofits monetary policy. As Taylor (2001) referred to as a trinity, the monetary policy regime that can workwell in the long term should be based on a flexible exchange rate, an inflation target and a monetarypolicy rule. However, this does not imply that movements in exchange rates have no implications on theeconomy that deserve central banks’ attention. In fact, exchange rate movements may cause adjustmentof relative prices, and further of demands for domestic goods. Monetary policy, in addition, works inpart through its effect on the exchange rate. The important question here is then to what extent centralbanks take into account of exchange rate movements in formulating monetary policy.

There are two strands of literature on this issue. The first literature studies whether central bankswould benefit from responding to exchange rate movements. There is no consensus on the conclusionyet. Ball (1999) argues that exchange rate movements affect domestic inflation through its effect onimport prices, and thus central banks should optimally react to exchange rate movements. Svensson(2000) examines inflation targeting in a small open economy also with a particular emphasis on exchangerates. He argues that exchange rates allow additional channels for the transmission of monetary policy,and that exchange rates being a forward-looking variable contributes to taking into account of theforward-looking behavior essential to monetary policy. Furthermore, foreign disturbances may alsoenter through exchange rate variations. On the other hand, some studies suggest that there shouldbe no role for the exchange rate in the optimal monetary policy rule. In a theoretical model, Claridaet al (2001) find that when there is perfect exchange rate pass-through, central banks should targetdomestic inflation and ignore exchange rate movements. In this model, the representative householdwelfare criterion depends only on domestic inflation and the output gap variances, because the realexchange rate is proportional to the output gap. As a result, the real exchange rate becomes irrelevantfor monetary policy decisions. West (2004) suggests that exchange rate stabilization may aggravateinstability elsewhere. Under some standard assumptions, he finds that the interest rate can be adjustedto smooth real exchange rate movements at the possible price of increased volatility in some othervariables. The paper does not consider the desirability of including exchange rates into the monetarypolicy rule, though.

The second literature estimates policy reaction functions to study the actual role of exchangerates in the monetary policy framework. For developed economies, Clarida et al (1998) show that themonetary authorities in some European countries and Japan responded to exchange rate misalignments.Along the same line, Calvo and Reinhart (2002) find that many emerging economies use interest ratesas the means of smoothing exchange rate fluctuations. A free floating exchange rate increases foreignexchange volatility, which may cause problems to banking system and induce balance-sheet effect. Forthis reason, countries may face “fear of floating”. In this context, there is some controversy as towhether this response is optimal or not.

Rather than estimating monetary policy functions in a univariate setup, Lubik and Schorfheide(2007) adopt a multivariate approach of estimating the structural model, and apply Bayesian maximumlikelihood estimation methodology to address the issue of open economy monetary policy rules. They

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develop a small-scale structural open economy model with four equations: the open-economy IS curve,the Phillips curve, the PPP equation, and the monetary policy rule. Five shocks are introduced tothe model. They are foreign output shock, foreign inflation shock, technology shock, monetary shockand terms-of-trade shock. In their model, the real exchange rate is assumed to be exogenously spec-ified following an autoregressive process, because with the terms of trade specified endogenously, theoptimization routines had difficulties finding the maximum of the posterior density and whenever theoptimization did converge, implausible parameter values were obtained. They apply their estimation tofour small open economies: Australia, Canada, New Zealand and the United Kingdom, and find thatthe central banks of Australia and New Zealand did not explicitly respond to nominal exchange ratesin the past two decades, while the Bank of Canada and the Bank of England did.

In this paper, we follow the second literature to directly estimate a dynamic stochastic generalequilibrium model to examine the role of exchange rates in monetary policy rules. We find somenew evidences from our estimation. First of all, in our estimation, endogenous real exchange ratespecification leads to much higher marginal likelihood values for all four countries, than exogenous realexchange rate specifications. In our view, the reason that the estimation of the fully structural modelis problematic in Lubik and Schorfheide (2007)’s work is that if the terms of trade is not taken asexogenously given in their model, there will be four shocks for five endogenous observable variables —the model would be stochastically singular. What’s more, it might be hard to fit such a small-scaleDSGE model well to the data.1 While in order to be able to exploit cross-equation restrictions and thelinks of the monetary policy rule with the rest of the economy, it is essential to start with a model thathas reasonably good fit.

We develop a much richer small open economy two-sector model in this paper. We assume theprices and wages are sticky following Calvo (1983), with partial indexation of prices and wages on laggedinflation. Besides producing non-tradable goods for consumption and investment, the non-tradablesector also provides distribution services to import foreign-produced tradable goods. We consider,in this paper, a combination of both producer currency pricing (PCP) and local currency pricing(LCP) firms in the tradable sector. This is because there is a potential tradeoff between the desiredexchange rate volatility and the magnitude of the expenditure-switching effect, which is determinedby the currency of invoicing, among other things. Our model is estimated via Bayesian maximumlikelihood estimation approach for various specifications of the monetary policy rule. The estimationresults lead us to favor the view that the Reserve Bank of Australia, the Bank of Canada and the Bankof England responded to real exchange rate movements in the past, while the Reserve Bank of NewZealand did not seem to include exchange rate movements in their policy rule.

On the one hand, since the degree of partial price indexation is estimated to be much larger forNew Zealand, which suggests that for New Zealand, current inflation may reflect less future inflationpressure. Therefore, when the Reserve Bank of New Zealand responds to current inflation, it is lessconcerned about future inflation pressure caused by current real exchange rate movements. On theother hand, the variance decomposition results suggest that the structure of shocks in accounting forinflation and output variations is different for New Zealand than for the other three countries. For the

1In Lubik and Schorfheide (2007) paper, no model assessment results were provided.

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central banks of Australia, Canada and the UK, it may not be sufficient to respond to real exchangerate variations only indirectly through targeting inflation rate and stabilizing output levels.

The remainder of this paper is organized as follows. Section 2 presents the theoretical model.Section 3 describes the data and the empirical methodology to be employed. Section 4 states heempirical results. Section 5 concludes the paper.

2 The Model

Our model in this paper is similar to Dong (2007). We consider a small open economy, where the foreignoutput, prices and interest rate are taken as exogenous. There are two sectors in the domestic economy:tradable sector and non-tradable sector. Competitive final tradable good producers use compositesof both domestic- and foreign-produced differentiated intermediate tradable goods to produce finalgoods for consumption and investment. In addition, we assume that distribution services are neededto bring foreign-produced tradable intermediate inputs to the domestic market. Several frictions areintroduced including Calvo type sticky prices and wages with partial indexation on lagged inflation, acombination of both PCP and LCP firms, cost of adjustment in capital accumulation and consumptionhabit formation. For details on the model setup, we refer to Dong (2007). In what follows, we simplydiscuss the solutions of the model.

Our estimation is based on the first order conditions characterizing the households’ utility andfirms’ profit maximization problems. Households derive utility from the consumption of tradable andnon-tradable goods, as well as leisure. The optimal consumption path is given by:

(Ct − hCt−1)−ρSt

R∗t rpt

= βEt(Ct+1 − hCt)−ρSt+1

πt+1(2.1)

CT,t = αT

(PT,t

Pt

)−ς

Ct (2.2)

CN,t = (1− αT )(

PN,t

Pt

)−ς

Ct. (2.3)

Here, ρ is the coefficient of relative risk aversion of households, β is the subjective discount factor, h isthe habit formation coefficient, and ς is the elasticity of substitution between tradable and non-tradableconsumption goods.

Households provide labour services, LN,t, to non-tradable good producers, and LT,t to intermediatetradable good producers, at the wage rate W i

t . They also own capital and rent it to producers at therate rk

T,t, rkN,t for tradable sector and non-tradable sectors respectively. The optimal wage setting and

capital accumulation entails:

Wt =

{ψw

[Wt−1

(Pt−1

Pt−2

)τw]1−γ

+ (1− ψw)$1−γt

} 11−γ

(2.4)

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[χ(KT,t −KT,t−1)

KT,t−1+ 1

]= Λt,t+1

[χ(K2

T,t+1 −K2T,t)

2K2T,t

+ 1− δ + rkT,t+1

](2.5)

[χ(KN,t −KN,t−1)

KN,t−1+ 1

]= Λt,t+1

[χ(K2

N,t+1 −K2N,t)

2K2N,t

+ 1− δ + rkN,t+1

](2.6)

Λt,t+1 ≡ βEt(Ct+1 − hCt)−ρ

(Ct − hCt−1)−ρ , (2.7)

where ψw captures the extent of wage stickiness, τw is the degree of wage indexation, γ is the elasticity ofsubstitution among different types of labor services, and $i

t is the optimal wage rate for labour serviceof type i at time t if household i is selected to reoptimize in that period. Finally, δ is the depreciationrate and χ represents size of adjustment cost.

Households can hold domestic currency bond Bt, and foreign currency bond — B∗t . The foreign

interest rate R∗t is assumed to be exogenously given, and subject to a debt-elastic interest rate premium

rpt.2

rpt = exp[−ϕnξt − ϕs

(EtSt+1

St−1− 1

)+ ϕt

]

ξt ≡ StB∗t /PtYt.

A modified UIP condition can be derived from the model:

Rt

R∗t rpt

= EtSt+1

St. (2.8)

Or, alternatively, we can simply assume the real exchange rate to follow an autoregressive process as inLubik and Schorfheide (2007). We test the endogenous versus exogenous specifications of real exchangerates with the structural estimation.

Final tradable goods are produced as CES aggregates of domestic intermediate inputs and imports.The demands for each type of intermediate goods thus depend on their relative prices and the elasticityof substitution between them — σ.

YH,t = αH

(PH,t

PT,t

)−σ

YT,t (2.9)

YF,t = (1− αH)(

PF,t

PT,t

)−σ

YT,t. (2.10)

Intermediate tradable good producers use capital and labor as inputs, and act as monopolisticcompetitors for price setting. In this paper, I assume φ proportion of intermediate firms use LCP fortheir export pricing, while (1− φ) of them use PCP. Since the fraction of firms employing LCP versus

2It is used as a stationarity-inducing technique to ensure the existence of a unique steady state for the small openeconomy. For other ways of inducing stationarity of the equilibrium dynamics for small open economy models, seeSchmitt-Grohe and Uribe (2003).

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PCP will have an impact on the pass-through of exchange rates to domestic prices, central banks mayframe their policy in a way to take this into account. Let XH,t(s) denote the optimal price set for thehome market, and X l

H,t(s), XpH,t(s) denote the prices set for the foreign market respectively by an LCP

firm and a PCP firm. The price index for intermediate goods sold domestically, PH,t, and the exportprice index, P ∗

H,t, can then be expressed as:

PH,t =

{ψd

[PH,t−1

(Pt−1

Pt−2

)τd]1−ε

+ (1− ψd)X1−εH,t

} 11−ε

(2.11)

P ∗H,t =

ψd

[P ∗

H,t−1

(P ∗

t−1

P ∗t−2

)τd]1−ε

+ (1− ψd)

φ(X l

H,t)1−ε + (1− φ)

(Xp

H,t

St

)1−ε

11−ε

. (2.12)

where ε represents the elasticity of substitution among varieties produced within one country. Theforeign demand for exports from the small open economy is assumed to be exogenously given by:

Y ∗H,t = αf

(P ∗

H,t

P ∗t

)−σf

Y ∗t . (2.13)

Similarly, non-tradable goods are also produced with capital and labor. Non-tradable goods areused for consumption, investment, as well as distribution services to import foreign-produced interme-diate goods. The price index for non-tradable goods is given by:

PN,t =

{ψd

[PN,t−1

(Pt−1

Pt−2

)τd]1−ν

+ (1− ψd)X1−νN,t

} 11−ν

. (2.14)

We assume that to bring one unit of the tradable intermediate good to the domestic market, λ units ofa basket of the differentiated non-tradable goods are needed. Thus, the price index for foreign-producedintermediate goods in the home market, PF,t, and the trade balance value are given by:

PF,t(s) = StP∗t (s) + λPN,t (2.15)

TBt = PF,tYF,t − StP∗H,tY

∗H,t. (2.16)

The government balances its budget constraint. The aggregate government spending is assumedto be an exogenous process, with the shares on tradables and non-tradables depending on their relativeprices.

PtGt + Ptτt + Bt−1 =Bt

Rt

GT,t = αT

(PT,t

Pt

)−ς

Gt

GN,t = (1− αT )(

PN,t

Pt

)−ς

Gt.

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The monetary policy reaction function is described as a Taylor rule following Taylor (1993). Centralbanks take the domestic interest rate as the policy instrument to respond to the inflation rate as wellas to the output gap.

ln(Rt/R) = ρr ln(Rt−1/R) + (1− ρr)[απ ln(πt/π) + αy ln(Yt/Y )] + εrt. (i)

ρr is a parameter that captures interest-rate smoothing, and εrt is a temporary monetary policy shock.We are interested in investigating the role of exchange rates in the monetary policy rule, so we wantto test the hypothesis of rule (i) where central banks do not respond to any exchange rate movements,against the following possible rules:

ln(Rt/R) = ρr ln(Rt−1/R) + (1− ρr)[απ ln(πt/π) + αy ln(Yt/Y ) + αx ln(St/St−1)] + εrt (ii)

ln(Rt/R) = ρr ln(Rt−1/R) + (1− ρr)[απ ln(πt/π) + αy ln(Yt/Y ) + αx ln(qt/qt−1)] + εrt (iii)

ln(Rt/R) = ρr ln(Rt−1/R) + (1− ρr)[απ ln(πt/π) + αy ln(Yt/Y ) + αx ln(rpt/rpt−1)] + εrt. (iv)

In rule (ii), in addition to reacting to inflation and output gap, central banks also include nominalexchange rate movements in the policy rule, so to reduce nominal exchange rate volatility. In rule (iii),responding to real exchange rate movements is assumed instead of nominal exchange rate movements.Considering that all the four countries examined in this paper are fairly open economies, the centralbanks may want to respond to real exchange rate movements in order to smooth international relativeprice fluctuations that could affect their international competitiveness and have an effect on aggregatedemand for domestic goods. Finally in rule (iv), to maintain financial stability, central banks canpossibly react to risk premium shifts, which reflects changes in the expectations of risks in the financialmarket. We test these monetary policy rule candidates within the structural framework by estimatingvariants of the base model and evaluating marginal likelihood values and posterior odds.

The exogenous shocks in this model are assumed to evolve according to AR(1) processes. As forthe small open economy, all foreign variables are taken as exogenously determined.

ln R∗t = (1− ρR∗) ln R∗ + ρR∗ lnR∗

t−1 + εR∗t

ln AT,t = (1− ρAT ) lnAT + ρAT ln AT,t−1 + εATt

ln AN,t = (1− ρAN ) ln AN + ρAN lnAN,t−1 + εANt

ln Y ∗t = (1− ρy∗) ln Y ∗ + ρy∗ ln Y ∗

t−1 + εy∗t

lnP ∗t = φ∗(ln(P ∗

l,t/St)) + (1− φ∗) ln P ∗p,t

ln(P ∗l,t/P ∗

l,t−1) = (1− ρp∗) ln(π∗l ) + ρp∗ ln(P ∗l,t−1/P ∗

l,t−2) + εp∗t

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ln(P ∗p,t/P ∗

p,t−1) = ln(P ∗l,t/P ∗

l,t−1)

ln Gt = (1− ρg) lnG + ρg ln Gt−1 + εgt

ln ϕt = (1− ρϕ) ln ϕ + ρϕ ln ϕt−1 + εϕt.

In this model, real variables are assumed to be stationary. The structural model is log-linearized arounda deterministic steady state for estimation. For details on the log-linearized equations, we refer to theappendix in Dong (2007).

3 Empirical Approach

The structural model is estimated using Bayesian maximum likelihood method. We use data on fivemacroeconomic series for the estimation. They are real wage rate, output, real exchange rate, short terminterest rate, and trade balance value over steady state exports. The foreign variables for the domesticsmall open economy are constructed as geometric weighted averages of the G-7 countries, excluding thedomestic country under consideration. The time-varying weights are based on each country’s share oftotal real GDP.

The model is taken to the data for four countries: Australia, Canada, New Zealand and the UnitedKingdom. The data are seasonally adjusted quarterly series. The period covered for our estimation isdifferent across countries due to their specific histories. For Australia, our dataset starts at 1984:1. Thispoint is chosen because the Australian dollar was floated in December 1983. Most exchange controlswere abolished then, and major steps of deregulation of the financial system took place. Our dataset forCanada covers the period 1970:1 to 2006:4, in light of its floating exchange rate since 1970. The startingpoint for the Reserve Bank of New Zealand is 1985:2. In March 1985, the fixed exchange rate of NewZealand dollar with respect to a trade-weighted basket of currencies was terminated. Major financialsector policy reforms were also carried out through the year of 1984. The case of the United Kingdomis a bit more complicated, because over the 1990s, the Bank of England has evolving commitment tothe ERM. What’s more, between October 1990 and September 1992, the United Kingdom belonged tothe “hard” ERM and the exchange rate was fixed. The dataset might be too short to deliver reliableestimation results if we restricted ourselves to the starting point of 1992:4. So in the benchmark case,we selected 1979:3 as the starting point. Thatcher assumed power then and fighting inflation becamea clear policy objective. Next, for the sensitivity analysis, we re-estimate the model for the UK over1992:4 to 2006:4 to see if the results stay robust.

We employ Bayesian maximum likelihood estimation approach in this paper to estimate the struc-tural model. Priors on the parameters are assigned first based on results from past studies and infor-mation outside the data set, to measure the ex ante plausibility of parameter values. The time seriesdata are then brought in to revise the parameter values based on information from the data series to get

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posterior estimates.3 The Bayesian approach also provides a framework to compare and choose modelson the basis of the marginal likelihood values. The marginal likelihood of a model M is defined as:

L =∫

θp(θ|M)p(Y |θ, M)dθ,

where θ represents the parameter vector and Y denotes the observable data series. p(θ|M) is the priordensity of the parameters, and p(Y |θ, M) is the likelihood function. The marginal density indicatesthe likelihood of the model given the data. As a Bayesian alternative to hypothesis testing, the Bayesfactor between model i and j can be computed as:

Bi,j =Li

Lj.

Let pi denote the prior probability assigned to model i, the posterior probability that model i islikely is then given by:

ppi =piLi

ΣjpjLj.

The posterior odds is defined as the ratio of the posterior probability that model i is plausible over theprobability that it is not:

POi =ppi

1− ppi.

The Bayes factor and the posterior odds are used to compare models in this paper, in order to testwhich specification is more plausible in terms of central banks responding to exchange rate movements.

Probability statements about the parameters are made before observing the data. In this paper,since the estimation algorithm is computationally very intensive, some parameters are fixed by calibra-tion because: (i) they are not major parameters of interest in this paper; (ii) they no longer appearin the log-linearized model, but only affect the steady state values; or (iii) there is a consensus in theliterature about their values.

The subjective discount factor β is given a standard value of 0.99 for quarterly data. The relativerisk aversion parameter ρ is set to equal 4. The inverse of labor supply elasticity µ is set equal to 2.The weight of tradable goods in the consumption basket, αT , takes a value of 0.5. The elasticity ofsubstitution between tradables and non-tradables — ς, is given a value of 0.6. The elasticity of substi-tution among different types of labor services γ is assumed to be 6. The quarterly capital depreciationrate, δ, is set to 0.025. For Canada, the share of capital in tradable good production, η, is set to 0.37,the share of capital in non-tradable good production, θ, is set to 0.28. These calibrated values arebased on the estimation results of a two-sector small open economy model for Canada by Ortega andRebei (2006). For Australia, New Zealand and the United Kingdom, the corresponding values are set

3In this paper, the model is estimated using a numerical optimization procedure provided by Dynare. Dynare is acollection of MATLAB routines which study the transitory dynamics of non-linear models. More information can befound at: http://www.cepremap.cnrs.fr/dynare/.

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to η = 0.36, θ = 0.32, following usual simulation practices. The average fraction of labor effort in thetradable good sector is inferred from the data on the distribution of civilian employment by economicsector for several industrialized countries.4 This share is on average approximately 0.27 for Australia,0.29 for Canada, 0.30 for New Zealand and 0.31 for the United Kingdom during their own estimationperiods.

The priors we choose for the structural parameters to be estimated are displayed in Tables 1-4 foreach of the four countries. For most of them, fairly loose priors are used, with means centered at valuescommonly regarded as reasonable. Particularly, with respect to the priors for the fraction of firmsemploying LCP versus PCP for their exports, inferences are drawn from International Merchandise

Trade: Featured Article published by the Australian Bureau of Statistics, survey results for Canadafrom Murray, Powell, and Lafleur (2003), as well as publications by ECU Institute. Based on informationfrom these sources, the prior means for φ and φ∗ are set at 0.73 and 0.31 for Australia, 0.76 and 0.3 forCanada, 0.7 and 0.3 for New Zealand, and respectively 0.3, 0.4 for the UK.5

Priors on the policy coefficients are chosen to match values generally associated with the Taylorrule. The prior mean for the coefficient on lagged interest rate term ρr is set at 0.8, with a standarddeviation of 0.1. The coefficient on the inflation rate απ is given a prior mean of 1.6. The prior meanfor the coefficient on the output gap is set at 0.5. A large standard deviation of 0.2 is given, since theempirical evidence on the value of this parameter is diverse. With respect to the coefficient on exchangerates or risk premium movements, whenever it is applicable, a prior mean of 0.25 is specified. For theparameters of the shocks, little guidance is provided by the literature, so loose priors, which are notvery informative, are specified.

4 Empirical Results

4.1 Estimation Results

Marginal Likelihood Values

We estimate the model under various exchange rate and monetary policy reaction function specifica-tions. In Table 1-4, the estimation results for the benchmark case are reported for Australia, Canada,New Zealand and the United Kingdom, where the real exchange rate is assumed to be endogenouslydetermined and the central bank includes real exchange rate movements in the monetary policy rule,in addition to inflation rate and output gap. To be brief, the parameter estimation results for othercases are not reported, but the log marginal likelihood values are shown in Table 5. As we can see from

4The time series data covering 1960-2006 is from the Bureau of Labor Statistics website.5Recent studies have debated whether exchange rate pass-through into import prices may have declined in recent years

in industrialized countries. The evidences are still mixed so far. Over time, the proportion of exports and imports invoicedin the the domestic currency may change slightly. However, as the International Merchandise trade article pointed out, inAustralia’s case, this was largely caused by changes in exports or imports of a small number of commodities invoiced mainlyin Australian dollars. In other words, the modest movements of the invoice currency fractions are due to adjustments inexport or import structure, rather than the invoice currency switching by firms. Overall, it seems reasonable to assumethat the fractions φ and φ∗ of firms adopting LCP are constant.

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this table, in all cases, the endogenous real exchange rate specification leads to much larger marginallikelihood values than the exogenous real exchange rate specification, though the difference is not asdramatic for Canada as for other three countries.6

In Lubik and Schorfheide (2007) paper, the real exchange rate is assumed to be exogenously given,because they had difficulty of finding maximum in the neighborhood of reasonable parameter valuesif they let the real exchange rate to be determined endogenously as the structural model suggests.However, this problem may be due to stochastic singularity of the model. Their model consists offour equations and five exogenous shocks. It is taken to the data for estimation with five observabledata series: interest rate, inflation rate, output growth, depreciation rate and terms of trade changes.If the terms of trade is not taken as an exogenous shock, then there would be four shocks for fiveobservable variables. As emphasized by Ingram, Kocherlakota and Savin (1994), the number of shocksbeing less than the number of endogenous observable variables might make the model stochasticallysingular. In that case, if the model implies that certain combinations of the endogenous variables aredeterministic, while in the data these exact linear relationships do not hold, the estimation would leadto implausible results. In addition, Lubik and Schorfheide (2007) adopt a small scale structural modeland base their estimation on the equation system of the open-economy IS curve, the Phillips curve,the PPP equation, and the monetary policy rule. It might not be rich enough to capture the linksbetween monetary policy reaction function with the rest of the economy. While the major advantageof adopting structural estimation rather than simply estimating one policy reaction function is thatthe former approach allows us to capture these links which may have important implications on policydecision.

Now that endogenous qt specification leads to much higher marginal likelihood values in all cases,we now turn to the comparison of different forms of monetary policy rules with the real exchange ratedetermined endogenously. As stated in Section 2, we consider four forms of central banks’ responses.They can potentially respond to nominal exchange rates fluctuations, real exchange rates movements, orrisk premium shifts, in addition to the inflation rate and output gap. We also estimate the model underthe restriction αx = 0, in which case central banks are assumed not to respond to any exchange ratemovement. The marginal likelihood values are displayed in Table 5. The Bayes factors and posteriorodds are computed and presented in Table 6.

For Australia, the log marginal data density associated with the αx = 0 case is larger than that ofcentral banks responding to ∆st or ∆rpt case. But the marginal data density of the benchmark modelis 4.9292 larger on a log-scale than the αx = 0 model. The values of Bayes factor and posterior oddsclearly show that the benchmark model is the preferred model compared to others. This leads us tofavor the view that the Reserve Bank of Australia responded to real exchange rate movements in thepast two decades. For Canada, the marginal likelihood value of responding to ∆st model is quite closeto that of the αx = 0 model. The log marginal density of the benchmark model though is still the largestamong all of them, which seems to suggest that the Bank of Canada also paid close attention to realexchange rate movements in the past. The UK’s case is very similar to Canada’s case. The log marginal

6It is worth noticing that the numbers in Table 5 are log marginal likelihood values, so the difference between any twomarginal likelihood values is actually in the scale of the log difference to the power of e.

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likelihood of the benchmark model is 9.8307 larger on a log-scale than the absence of exchange rateresponse model. The benchmark model is strongly preferred than other models. The Bayes factor is atmost 0.0071 for other models compared to the benchmark, and the posterior odds of the benchmark isaround 139.64. Therefore, our estimation results suggest that the Bank of England responded to realexchange rate movements over the sample period. The case for New Zealand, however, is different. Themarginal data density is the largest for the absence of exchange rate response case. The Bayes factorfor αx = 0 model is 18.514 against the benchmark. The Reserve Bank of New Zealand did not seem toinclude exchange rate variations in their policy rule in the past twenty years.

Central banks may want to respond to real exchange rate movements in order to smooth inter-national relative price fluctuations that may affect international competitiveness and have an effect onaggregate demand for domestic goods. Foreign impacts that a small open economy usually cannot affordto ignore may enter through exchange rate movements. Real exchange rate movements may also reflectpotential future inflation pressure, which central banks would want to deal with now. Then how comeNew Zealand is an exception in the past? The answer to this question would depend fundamentallyon the link between exchange rates and the rest of the economy. We address this issue in what followsbased on the structural parameter estimation results.

Model Assessment

Before we analyze the estimation results of the parameters, first we assess the conformity of themodel to the data, because convincing references can only be drawn from a reasonable model. For thispurpose, unconditional second moments are computed and reported in Table 7-10 for the four countriesin benchmark case. The first block reports the statistics of the data, and the second block presentsthe corresponding estimates implied by the model, which are computed from 1,000 random draws inthe posterior distributions of the structural parameters. The median from the simulated distributionof moments are reported, together with the 10th and 90th percentiles. For Australia, Canada and theUnited Kingdom, the benchmark model is the preferred model. While for New Zealand it is not. Theparameter estimation results though are almost the same for the benchmark model and for the preferredmodel with the absence of exchange rate response.

As shown in the tables, in all cases, we see that the standard deviations and autocorrelations ofthe observable series are very well matched with their counterparts derived from simulations of themodel. The data moments fall within the corresponding model confidence intervals. Particularly, forall countries, the persistence and excess volatility of real exchange rates and trade balances are wellcaptured by the simulated model. The model also provides generally good characterizations of thecross correlation properties. In most cases, the data values lie within the error bands implied by themodel. The confidence intervals, however, are usually large. This implies that there is a large degreeof uncertainty about the model-based correlations, due to short data series. Overall, the model doesa reasonably good job of matching properties of the data, though there certainly may be room forimprovements in the future.

Parameter Estimates

11

The estimation results for the four countries in the benchmark case are reported in Table 1-4. Theparameter estimates for the αx = 0 model for New Zealand are also reported in Table 11. The firstthree columns in each table give an overview of the prior distributions specified for the parameters.The next two columns present the estimated posterior mode from directly maximizing the log of theposterior distributions given the priors and the likelihood based on the data, and the correspondingstandard errors computed from the inverse Hessian. The last three columns report the mean and the90% confidence interval of the posterior distributions obtained by using the Monte Carlo MetropolisHastings algorithm. It is subject to 1,000,000 draws, and the first 500,000 draws are dropped.

The Calvo stickiness parameters ψd for domestic producer prices and ψw for wage rates are esti-mated to be around 0.68 to 0.74 for all countries, which implies that, on average, prices and wages arere-optimized approximately once every three to four quarters. These estimated lengths of price andwage contracts are in line with the macro literature. Lubik and Schorfheide (2006) report estimates ofthe price stickiness parameter ranging from 0.74 to 0.78 in their two-country structural model. Ambler,Dib, and Rebei (2003) estimate the Calvo adjustment parameter to be 0.68 for Canada with a smallopen economy model. Microeconomic evidences, however, tend to suggest less sticky prices. For allcountries, prices are estimated to be less sticky than wage rates.7 When firms and households are notallowed to adjust prices and wage rates, they index the current levels by past inflation. Parameters τd

and τw captures the degree of this indexation. They are estimated to be 0.27 and 0.33 for Australiain the benchmark case, 0.28 and 0.24 for Canada in the benchmark case, 0.25 and 0.15 for the UK inthe benchmark case, as well as 0.47 and 0.30 for New Zealand in the absence of exchange rate responsecase. The estimated degree of price indexation for Australia, Canada and the UK being close to 0.25corresponds to the weight on lagged inflation in the New Keynesian Phillips Curve to be about 0.2,and the weight on future inflation term to be about 0.8. While in New Zealand’s case, the estimateddegree of price indexation is 0.47, which implies a weight of 0.32 on the lagged inflation rate and 0.68on the future inflation rate in the Phillips Curve. Since in the model, central banks are assumed torespond directly to current inflation, that the current inflation depends less on future inflation in NewZealand may provide a case for the Reserve Bank of New Zealand to be less concerned about the futureinflation pressure induced by exchange rate movements.

The proportions of domestic and foreign firms using LCP to set export prices, φ and φ∗, areestimated to be 0.78 and 0.29 for Australia, 0.81 and 0.25 for Canada, 0.74 and 0.24 for New Zealand,and 0.34 and 0.24 for the United Kingdom. For the first three countries, LCP is dominant for its ownexports, but PCP is dominant for other countries’ exports to them. While for the UK, in either case,invoicing in the producers’ currency is more frequent. The elasticity of substitution between domesticand foreign varieties in the domestic market and in the foreign market, σ and σf , are estimated tobe around 1.4 to 2.0, which are in the upper half of the range of macro estimates. The distributionmargin % is estimated to be 0.72 for Australia, 0.56 for Canada, 0.59 for New Zealand, and muchlarger at 0.82 for the UK. The distribution margin measures the fraction of the import price accountedfor by distribution costs. A slightly larger fraction of firms exporting to Australia, Canada or NewZealand price their products in the local market currency, compared to the UK. This may suggest abit larger expenditure-switching effect in the UK when prices are sticky in the short run. However, as

7Sticky wages play an important role in allowing the model to generate reasonable price stickiness.

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emphasized by Dong (2007), the higher % is, the smaller the effect of exchange rate movements on therelative quantities. Since distribution costs account for a very large share in import prices in the UK,expenditure switching over tradable goods would be much more insignificant there. Krugman (1989)pointed out that exchange rate volatility might be emphasized if the expenditure-switching effect issmall. Therefore, based on this reasoning, if the expenditure-switching effect were taken into account,the Bank of England might benefit from higher exchange rate volatility.

Turning to the estimates of the coefficients in monetary policy reaction functions, we find theinterest rate to be quite persistent for all the countries. The coefficient for the inflation rate is greaterthan 1. The Taylor principle is satisfied. All four countries respond quite aggressively to the outputgap. For Australia, Canada and the United Kingdom, the estimated coefficients on real exchange ratemovements are significantly different from zero. The estimates of the risk premium coefficients, the ARparameters and standard deviations for the unobserved shocks are also reported. It’s worth noticingthat the estimated exogenous processes for these shocks differ significantly, though the same priors aregiven at the beginning.

Impulse Responses

To further understand the dynamics of the model, impulse responses for the country of Canada inthe benchmark case are presented in Figure 1-2. In the figures, the impulse responses of four variablesof interest to eight exogenous shocks are displayed. The four variables are output, real exchange rate,inflation rate and interest rate. The impulse responses show the consequences of a one-unit increase inthe exogenous shock for the value of variables. The responses are calculated from a random selection of1,000 parameters out of the 500,000 draws from the posterior distributions. Together with the medianresponse, the 10% and 90% percentiles are also shown.

A technology shock in the non-tradable sector increases imports through the effect on distributionservices, therefore drives up domestic output. As a result, the domestic currency depreciates. Thefinal tradable good producers then switch expenditure from imports to domestically-produced goods.Positive technology shock lowers inflation. Relaxing monetary policy then helps to appreciate domesticcurrency. Similarly, a technology shock in the tradable sector also induces a drop in inflation and interestrate. But since a technology shock in the tradable sector actually increases the amount of domestic-produced intermediate goods, thus reduces imports, the demand for foreign currency decreases and thedomestic currency appreciates. Central bank loosening policy contributes to the expansionary effect onoutput.

A risk premium shock drives up the demand for foreign currency. The demand for domestic cur-rency then reduces, and the domestic currency depreciates. Monetary policy is tightened at first tocope with inflation, relaxed then to stimulate production. A positive monetary policy shock impliestightening in the monetary policy which makes production drop. Domestic bonds become more at-tractive compared to foreign bonds, so domestic currency appreciates and the real exchange rate falls.Domestic production is driven up in response to a government spending shock. This then increases thedemand for domestic money, which causes inflation as well as puts upward pressure on the domesticinterest rate. As a result, the domestic currency appreciates.

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An increase in the foreign prices leads to expenditure switching from foreign-produced goods todomestic-produced goods. But since the majority of domestic firms use local currency pricing fortheir exports, this in fact implies an increasing demand of foreign currency. Foreign currency thenappreciates. Foreign inflation is passed through to the domestic economy. In response, the interest rateincreases. From quarter 2 to quarter 7 after the shock, the inflation rate is actually falling, but themonetary policy is still tightening up, because there is real depreciation going on. The effects of theforeign interest rate shock on the variables are not surprisingly in line with those of the risk premiumshock. The two shocks are identified in the model through the observed foreign interest rate series. Inother words, the risk premium shock captures whatever is left unaccounted for by the observed foreigninterest rate shock. Finally a foreign output shock increases the demand for domestic exports, furtherdomestic output. The rising of domestic exports together with increasing demand for foreign importslead to higher demand for foreign currency. The foreign output shock suggests an ease on domesticinflation, thus a loosening up in the monetary policy.

Variance Decomposition

The variance decomposition results for various horizons are presented in Table 12-15 for the fourcountries of their preferred models, in order to infer the role of various structural shocks in driving themovements of output, real exchange rate, inflation and interest rate.

Not surprisingly we find that the foreign price shock plays an important role in accounting forthe forecast error variances of the domestic variables, since all the four economies considered here aresmall open economies. The technology shock in the tradable sector is generally also very importantin generating variations of inflation and interest rate, as well as output and the real exchange rate inaddition to the foreign price shock. When we compare the variance decomposition results for NewZealand with the results for the other three countries, however, we find the pattern is very different.Particularly, the major shocks explaining for forecast error variances of output and inflation for NewZealand are different from those for Australia, Canada and the United Kingdom. Even if central banksfollow a policy rule without explicitly responding to exchange rate movements, the indirect effect ofexchange rates on interest rates still exist due to the effects of exchange rates on inflation rate andoutput gap. The variance decompositions of inflation and output therefore help to explain why theReserve Bank of New Zealand does not include exchange rate movements into their policy reactionfunction.

With respect to the inflation rate, besides the foreign price shock, it is the technology shocks inboth tradable and non-tradable sectors that account for significant percentages of πt variations forAustralia, Canada and the United Kingdom. While for New Zealand, only the technology shock in thetradable sector explains a big part of the forecast error variances of πt, while the role of the technologyshock in the non-tradable sector is not important at all. As we can see from the impulse responsefigures and the earlier analysis, a positive technology shock in the tradable sector induces a drop inthe real exchange rate; while a positive technology shock in the non-tradable sector drives up the realexchange rate initially. In this paper, the technology shocks in the tradable and non-tradable sectorsare assumed to be independent. In other words, we can think of the two shocks in this model asorthogonal decompositions of real world productivity shocks. Since in reality every tradable sector has

14

non-tradable components and vice versa, we would expect to see same signs for these two shocks eventhough they are taken as orthogonal in the model. Now that their implications for real exchange ratemovements are different, for the central banks of Australia, Canada and the UK, it is not sufficient torespond to real exchange rate variations indirectly through targeting inflation rate. The Reserve Bankof New Zealand, on the other hand, faces a simpler problem, since non-tradable technology shock isinsignificant in accounting for its inflation variances.

We notice that 99% of the forecast error variances of output are explained by the tradable sectortechnology shock and the foreign price shock in New Zealand. While for the other three countries, therisk premium shock plays an as important role as the technology shock in the tradable sector, if notmore. The implications of the risk premium shock, temporary monetary policy shock as well as theforeign interest rate shock are quite different from those of other shocks. They have no direct effect onthe demands of domestic-produced goods, rather they only work through their effects on exchange ratesto lead to expenditure switching. In comparison, other shocks have direct impacts on the demands ofdomestic goods; expenditure switching is then induced through exchange rate movements and it worksin the opposite direction of the direct effect. For example, as a “demand” shock, the governmentspending shock drives up domestic production. A positive government expenditure shock increases thedemand for domestic money. This puts upward pressure on the domestic interest rate, and appreciatesthe domestic currency. Domestic final good producers then tend to substitute foreign for domesticvarieties.

Now in response to a positive risk premium shock, the domestic currency depreciates. Domestic fi-nal good producers tend to substitute domestic-produced for foreign-produced goods, and imports drop.Aggregate output falls as a result, since decreasing imports not only have impacts on the tradable finalgood production, but also reduce non-tradable good production due to lower demand for distributionservices. In this case, if central banks respond to the output drop by loosening up monetary policy, lowerdomestic interest rate would further depreciate domestic currency. Therefore, for Australia, Canadaand the United Kingdom, where the risk premium shock plays a role in driving output variations, itmakes sense for the central banks to respond to real exchange rate movements directly, because theindirect response through reacting to output gap works in the wrong direction. While for New Zealand,this is much less a concern.

4.2 Sensitivity analysis

In this section, we assess the sensitivity of the estimation results to alternative data samples,8 andexpected inflation targeting rules. Generally, we find that alternative data sample for the UK does notchange the major empirical results. Models with expected inflation targeting rule, however, are inferiorto models with current inflation targeting rule, as they lead to lower log marginal likelihood values.

Alternative Sample for the UK

As mentioned in Section 3, for the main estimation, we choose a starting point for the UK data8This is only relevant for the UK’s case.

15

series at 1979:3. However, over the 1990s, the Bank of England has evolving commitment to the ERM,between October 1990 and September 1992, the UK even belonged to the “hard” ERM. The exchangerate movements during this period might be much milder than it would have been otherwise. Sincethis might have impacts on the estimation of the monetary policy reaction function, in this section,we use the post-ERM data for the United Kingdom, starting from 1992:4 to 2006:4 to re-estimate themodels. The parameter estimation results are presented in Table 16, and the log marginal likelihoodvalues corresponding to various specifications of the real exchange rate and monetary policy rule areshown in Table 17.

All the major results stay the same in this sensitivity analysis. Endogenous real exchange ratespecifications lead to much higher log marginal likelihood values than exogenous real exchange ratespecifications in all cases. The marginal data density of the model where central banks directly respondto real exchange rate variations is the largest, which suggests that this is the preferred model. Theparameter estimation results also stays similar to the original estimates based on longer data series.One exception is that the estimate of the degree of price indexation, τd, now is much larger than itsoriginal estimate of 0.25. The current estimate is about 0.47. This in principle would imply that during1992:4 to 2006:4, the current inflation level depends less on future inflation rate and more on laggedinflation in the UK. However, the estimation results still suggest that the Bank of England includedcurrent real exchange rate movements in its monetary policy rule. As we analyzed in Section 4.1, theimportance of various structural shocks in accounting for inflation and output variances have influencesfor this.

Targeting Expected Inflation

Our second robustness check is with respect to the possibility of expected inflation targeting inmonetary policy rules. Current real exchange rate movements may have implications for future inflationlevels. But would it be possible that central banks directly respond to the future inflation pressure? Toanswer this question, we re-estimate the various versions of the model under endogenous real exchangerate specification. Particularly, in this exercise, we assume central banks target future inflation ratherthan current inflation. The new monetary policy rules can then be specified as:

ln(Rt/R) = ρr ln(Rt−1/R) + (1− ρr)[απ ln(πt+1/π) + αy ln(Yt/Y )] + εrt (i)

ln(Rt/R) = ρr ln(Rt−1/R) + (1− ρr)[απ ln(πt+1/π) + αy ln(Yt/Y ) + αx ln(St/St−1)] + εrt (ii)

ln(Rt/R) = ρr ln(Rt−1/R) + (1− ρr)[απ ln(πt+1/π) + αy ln(Yt/Y ) + αx ln(qt/qt−1)] + εrt (iii)

ln(Rt/R) = ρr ln(Rt−1/R) + (1− ρr)[απ ln(πt+1/π) + αy ln(Yt/Y ) + αx ln(rpt/rpt−1)] + εrt. (iv)

The log marginal densities from these estimations are displayed in Table 18 for Canada. Comparingthese values to the baseline case, we see that expected inflation targeting assumption leads to lowermarginal likelihood values in all cases. Central banks responding to ∆qt model is still the preferred

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model among these four models, but it seems that central banks are more likely to react to currentinflation, rather than expected inflation.

5 Conclusion

In this paper, we develop and estimate a small open economy structural model for Australia, Canada,New Zealand and the United Kingdom, to study whether and how exchange rate movements wereformulated in their monetary policy. Our Bayesian estimation results suggest that the Reserve Bank ofAustralia, the Bank of Canada and the Bank of England responded to real exchange rate movementsin the past, while the Reserve Bank of New Zealand did not. For New Zealand, current inflation seemsto reflect less future inflation pressure and contains more information on past inflation. So the centralbank of New Zealand might be less concerned about future inflation pressure caused by current realexchange rate movements. In addition, the structure of shocks in accounting for inflation and outputvariations is different for New Zealand than for the other three countries, which indicates that it maynot be sufficient for the central banks of Australia, Canada and the UK to respond to real exchangerate variations only indirectly through stabilizing inflation and output levels.

The empirical results are tested for sensitivity to alternative data length and expected inflationtargeting. The main results stay robust. More robustness check can be carried out with respect to thespecification of output’s role in the monetary policy rule, and alternative prior specifications for theBayesian estimation. We expect to report results from these analysis in the next draft of the paper.

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Reference:

Ambler, S., A. Dib, and N. Rebei. 2003. “Nominal Rigidities and Exchange Rate Pass-Through in aStructural Model of a Small Open Economy.” Bank of Canada Working Paper No. 2003-29.

Ball, L. 1999. “Policy Rules for Open Economies.” In Monetary Policy Rules, 127-44, Chicago: Uni-versity of Chicago Press.

Calvo, G. A. 1983. “Staggered Prices in a Utility Maximization Framework.” Journal of MonetaryEconomics 12(3): 383–98.

Calvo, G. and C. Reinhart. 2002. “Fear of Floating.” Quarterly Journal of Economics, 177: 379–408.

Clarida, R., J. Gali, and M. Gertler. 1998. “Monetary Policy Rules in Practice: Some InternationalEvidence.” European Economic Review, 42: 1033–67.

Clarida, R., J. Gali, and M. Gertler. 2001. “Open versus Closed Economies an Integrated Approach”American Economic Review, 91(2): 248–52.

Dong, W. 2007. “Expenditure-Switching Effect and the Choice of Exchange Rate Regime.” Bank ofCanada Working Paper No. 2007-54.

ECU Institute. 1995. International Currency Competition and the Future Role of the Single EuropeanCurrency. Final report of the “European Monetary Union — international monetary system”working group. London: Kluwer Law International.

Engel, C. 2003. “Expenditure Switching and Exchange-Rate Policy.” In NBER Macroeconomics Annual2002, 231–72, edited by B. S. Bernanke and K. S. Rogoff.

Ingram, B. F., N. R. Kocherlakota and N. E. Savin. 1994. “Explaining Business Cycles: A Multiple-shock Approach.” Journal of Monetary Economics, 34(3): 415–28.

Krugman, P. 1989. Exchange Rate Instability. Cambridge: MIT Press.

Lubik, T. and F. Schorfheide. 2006. “A Bayesian Look at New Open Economy Macroeconomics.”NBER Macroeconomics Annual 2005, 313–66, edited by D. Acemoglu, K. Rogoff and M. Woodford.

——. 2007. “Do Central Banks Respond to Exchange Rate Movements? A Structural Investigation.”Journal of Monetary Economics, 54(4): 1069–87.

Murray, J., J. Powell, and L.-R. Lafleur. 2003. “Dollarization in Canada: An Update.” Bank of CanadaReview(Summer): 29–34.

Ortega, E. and N. Rebei. 2006. “The Welfare Implications of Inflation versus Price-Level Targeting ina Two-Sector, Small Open Economy.” Bank of Canada Working Paper No. 2006-12.

Schmitt-Grohe, S. and M. Uribe. 2003. “Closing Small Open Economy Models.” Journal of Interna-tional Economics 61(1): 163–85.

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Smets F. and R. Wouters. 2003. “An Estimated Dynamic Stochastic General Equilibrium Model ofthe Euro Area.” Journal of the European Economic Association 1(5): 1123–75.

Svensson, L. 2000. “Open-Economy Inflation Targeting.” Journal of International Economics, 50,155–83.

Taylor, J. B. 1993. “Discretion versus Policy Rules in Practice.” Carnegie-Rochester Conference Serieson Public Policy 39: 195–214.

Taylor, J. 2001. “The Role of the Exchange Rate in Monetary-Policy Rules.” American EconomicReview, 91(2): 263–67.

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Table 1: Parameter Estimates: Australia (Benchmark Case)

Australia

Prior Distribution Posterior Maximization Posterior DistributionParameters Distribution Mean Std Mode Std Error Mean 10% 90%

ψd Beta 0.70 0.10 0.6832 0.0399 0.6893 0.6261 0.7533ψw Beta 0.70 0.10 0.7361 0.0455 0.7361 0.6655 0.8092τd Beta 0.50 0.15 0.2730 0.0815 0.2936 0.1633 0.4236τw Beta 0.50 0.15 0.3270 0.0963 0.3333 0.1845 0.4829φ Beta 0.73 0.10 0.7755 0.0987 0.7482 0.5998 0.9044φ∗ Beta 0.31 0.10 0.2883 0.0978 0.2995 0.1489 0.4437σ Gamma 1.50 0.25 1.5082 0.2552 1.5745 1.1385 1.9942σf Gamma 1.50 0.25 2.0388 0.1849 2.0478 1.7416 2.3396ρr Beta 0.80 0.10 0.9270 0.0122 0.9274 0.9080 0.9472απ Gamma 1.60 0.10 1.3992 0.0911 1.4118 1.2596 1.5589αy Gamma 0.50 0.20 1.2094 0.2447 1.2678 0.8629 1.6764αx Gamma 0.25 0.10 0.3414 0.0844 0.3501 0.2067 0.4853ϕs Gamma 0.45 0.20 0.3322 0.0454 0.3409 0.2733 0.4115ϕn Gamma 0.01 0.005 0.0211 0.0047 0.0222 0.0146 0.0301χ Gamma 10.0 2.00 14.742 2.2565 15.134 11.352 18.637% Beta 0.40 0.10 0.7224 0.0525 0.7071 0.6252 0.7987ρp Beta 0.80 0.10 0.5386 0.0913 0.5517 0.4072 0.6899

ρAT Beta 0.85 0.05 0.9664 0.0120 0.9605 0.9401 0.9823ρAN Beta 0.80 0.10 0.2967 0.0660 0.2930 0.1882 0.3982ρϕ Beta 0.80 0.10 0.8110 0.0714 0.8007 0.6901 0.9172σp Inv Gamma 0.01 4.00 0.0836 0.0178 0.0848 0.0562 0.1110σr Inv Gamma 0.01 4.00 0.0027 0.0002 0.0027 0.0024 0.0031

σAT Inv Gamma 0.01 4.00 0.0225 0.0049 0.0256 0.0164 0.0344σAN Inv Gamma 0.01 4.00 0.0718 0.0204 0.0834 0.0456 0.1202σϕ Inv Gamma 0.01 4.00 0.0141 0.0032 0.0155 0.0100 0.0211

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Table 2: Parameter Estimates: Canada (Benchmark Case)

Canada





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Table 3: Parameter Estimates: New Zealand (Benchmark Case)

New Zealand





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Table 4: Parameter Estimates: United Kingdom (Benchmark Case)

United Kingdom





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Table 5: Log Marginal Likelihood Values

Country

Log Marginal Data Density Australia Canada United Kingdom New Zealand

Exogenous qt (αx ·∆qt) 1972.3148 2331.0128 2057.0877 1494.4706Exogenous qt (αx ·∆st) 1970.6426 2323.6941 2052.6940 1497.3074Exogenous qt (αx = 0) 1974.2266 2327.8959 2057.5062 1500.1402

Endogenous qt (αx ·∆qt) 2050.9687 2339.0076 2156.4702 1571.8088Endogenous qt (αx ·∆st) 2044.5143 2335.1464 2151.5262 1572.7490Endogenous qt (αx ·∆rpt) 2043.3401 2329.5963 2141.2144 1570.9025Endogenous qt (αx = 0) 2046.0395 2334.7595 2146.6395 1574.7373

Table 6: Bayes Factor and Posterior Odds

Country

Australia Canada United Kingdom New Zealand

Bayes Factor


Posterior Odds


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Table 7: Unconditional Second Moments: Australia (Benchmark Case)

Australia

Variables Std Deviation Autocorrelation Correlation Correlation Correlation

with yt with qt with tbt

Data

wt 0.0106 0.7156 -0.1416 0.0711 0.2066yt 0.0111 0.7852 1.0000 -0.1471 0.3462qt 0.0748 0.8349 -0.1471 1.0000 -0.3984rt 0.0041 0.8182 0.4692 -0.0561 0.1879

tbt 0.1216 0.7959 0.3462 -0.3984 1.0000

Model

wt 0.0264 0.9127 0.4577 -0.3936 0.1794(0.0179, 0.0405) (0.7731, 0.9865) (0.2156, 0.6572) (-0.6566, -0.0855) (-0.0957, 0.4401)

yt 0.0155 0.7386 1.0000 -0.3703 0.3039(0.0125, 0.0194) (0.6063, 0.8439) (-0.6088, -0.1152) (0.0461, 0.5366)

qt 0.0764 0.8667 -0.3703 1.0000 -0.4988(0.0601, 0.0984) (0.7628, 0.9334) (-0.6088, -0.1152) (-0.6945, -0.2153)

rt 0.0122 0.9523 -0.4760 0.4050 -0.0874(0.0075, 0.0193) (0.8111,1.0000) (-0.6574, -0.2793) (0.1078, 0.6440) (-0.3609, 0.1814)

tbt 0.1243 0.8242 0.3039 -0.4988 1.0000(0.0979, 0.1584) (0.7055, 0.9059) (0.0461, 0.5366) (-0.6945, -0.2153)

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Table 8: Unconditional Second Moments: Canada (Benchmark Case)

Canada



Data

wt 0.0109 0.7987 -0.3104 -0.0016 -0.0361yt 0.0142 0.8578 1.0000 0.2099 -0.0870qt 0.0314 0.8428 0.2099 1.0000 0.1868rt 0.0039 0.8131 0.5087 -0.0884 -0.1493

tbt 0.0442 0.5975 -0.0870 0.1868 1.0000

Model

wt 0.0169 0.8593 0.2732 -0.5547 0.0342(0.0116, 0.0267) (0.6462, 0.9916) (-0.1132, 0.6017) (-0.8106, -0.1396) (-0.3155, 0.3509)

yt 0.0136 0.7199 1.0000 -0.1143 0.1370(0.0105, 0.0172) (0.5219, 0.8653) (-0.4891, 0.2875) (-0.2156, 0.4474)

qt 0.0381 0.8657 -0.1143 1.0000 -0.0524(0.0268, 0.0553) (0.6650, 0.9843) (-0.4891, 0.2875) (-0.3822, 0.3003)

rt 0.0086 0.9008 -0.3287 0.5279 0.0200(0.0051, 0.0151) (0.6656, 1.0000) (-0.5991, 0.0280) (0.0507, 0.8234) (-0.3242, 0.3683)

tbt 0.0556 0.7219 0.1370 -0.0524 1.0000(0.0432, 0.0703) (0.5202, 0.8492) (-0.2156, 0.4474) (-0.3822, 0.3003)

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Table 9: Unconditional Second Moments: New Zealand (Benchmark Case)

New Zealand



Data

wt 0.0129 0.6948 0.0413 -0.1959 -0.0877yt 0.0169 0.8117 1.0000 -0.6145 0.0569qt 0.0893 0.8720 -0.6145 1.0000 -0.2713rt 0.0037 0.6647 0.2056 -0.3512 0.1140

tbt 0.0909 0.4679 0.0569 -0.2713 1.0000

Model

wt 0.0361 0.9336 0.5846 -0.5076 0.1794(0.0245, 0.0528) (0.8053, 0.9983) (0.3593, 0.7472) (-0.7299, -0.1946) (-0.0740, 0.3961)

yt 0.0238 0.7809 1.0000 -0.4857 0.2269(0.0191, 0.0297) (0.6586, 0.8765) (-0.6812, -0.1899) (-0.0349, 0.4678)

qt 0.0964 0.9060 -0.4857 1.0000 -0.2391(0.0725, 0.1275) (0.7955, 0.9703) (-0.6812, -0.1899) (-0.4742, 0.0420)

rt 0.0115 0.9387 -0.5612 0.2064 -0.0606(0.0079, 0.0175) (0.7990, 1.0000) (-0.7148, -0.3610) (-0.1682, 0.5370) (-0.2916, 0.1608)

tbt 0.1318 0.7055 0.2269 -0.2391 1.0000(0.1083, 0.1655) (0.5845, 0.8128) (-0.0349, 0.4678) (-0.4742, 0.0420)

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Table 10: Unconditional Second Moments: United Kingdom (Benchmark Case)

United Kingdom



Data

wt 0.0083 0.7545 0.1810 -0.1294 0.1466yt 0.0121 0.8672 1.0000 0.0172 0.4606qt 0.0706 0.8079 0.0172 1.0000 -0.0495rt 0.0032 0.8200 0.2384 -0.1496 0.1534

tbt 0.0395 0.6282 0.4606 -0.0495 1.0000

Model

wt 0.0310 0.9546 0.5088 -0.7108 0.0158(0.0209, 0.0474) (0.8320, 1.0000) (0.2311, 0.7200) (-0.8614, -0.4598) (-0.2243, 0.2453)

yt 0.0137 0.7841 1.0000 -0.3100 0.1555(0.0111, 0.0169) (0.6705, 0.8676) (-0.5855, -0.0389) (-0.0921, 0.3671)

qt 0.0928 0.8974 -0.3100 1.0000 -0.1024(0.0687, 0.1255) (0.7869, 0.9645) (-0.5855, -0.0389) (-0.3371, 0.1439)

rt 0.0104 0.9650 -0.4917 0.6971 -0.0048(0.0067, 0.0160) (0.8440, 1.0000) (-0.6924, -0.2687) (0.4179, 0.8592) (-0.2392, 0.2281)

tbt 0.0641 0.8166 0.1555 -0.1024 1.0000(0.0509, 0.0813) (0.7153, 0.8965) (-0.0921, 0.3671) (-0.3371, 0.1439)

28

Table 11: Parameter Estimates: New Zealand (αx = 0)

New Zealand


ψd Beta 0.70 0.10 0.6897 0.0424 0.7028 0.6367 0.7725ψw Beta 0.70 0.10 0.7372 0.0483 0.7458 0.6679 0.8222τd Beta 0.50 0.15 0.4699 0.0850 0.4788 0.3387 0.6111τw Beta 0.50 0.15 0.3017 0.1183 0.3482 0.1464 0.5485φ Beta 0.70 0.10 0.7414 0.1004 0.7218 0.5673 0.8742φ∗ Beta 0.30 0.10 0.2439 0.0909 0.2633 0.1237 0.4008σ Gamma 1.50 0.25 1.6280 0.2673 1.6930 1.2472 2.1366σf Gamma 1.50 0.25 1.9838 0.1712 1.9954 1.7283 2.2757ρr Beta 0.80 0.10 0.9285 0.0128 0.9274 0.9065 0.9480απ Gamma 1.60 0.10 1.4763 0.0952 1.4820 1.3261 1.6349αy Gamma 0.50 0.20 0.8231 0.1968 0.8418 0.5145 1.1542ϕs Gamma 0.45 0.20 0.4260 0.0394 0.4220 0.3702 0.4772ϕn Gamma 0.01 0.005 0.0264 0.0053 0.0271 0.0185 0.0357χ Gamma 10.0 2.00 15.067 2.1771 15.526 11.868 18.950% Beta 0.40 0.10 0.5926 0.0562 0.5878 0.4933 0.6804ρp Beta 0.80 0.10 0.7371 0.1093 0.7253 0.5813 0.8751



29

Table 12: Variance Decompositions: Australia (Benchmark Case)

Australia

qt yt πt rt

Tradable technology shock 1 22.467 3.1036 41.741 88.9444 9.6759 7.6476 44.695 84.3278 8.7875 8.4854 44.529 80.73112 8.7492 9.5310 44.380 78.138

Non-tradable technology shock 1 0.3787 0.1919 42.271 0.00314 0.2852 8.4524 31.617 0.46388 0.2515 9.4378 31.456 0.481812 0.2591 9.3024 30.444 0.6278

Risk premium shock 1 22.654 26.226 0.1197 5.21984 9.1217 32.672 6.4224 6.47238 8.2607 31.525 6.8485 7.566212 8.1530 31.338 7.7268 8.3027

Monetary policy shock 1 0.0935 1.4956 0.0108 2.45594 0.0402 1.0726 0.0323 2.29558 0.0283 1.0235 0.0390 2.153312 0.0262 1.0062 0.0391 2.0586

Government spending shock 1 0.0000 3.7558 0.0064 0.01504 0.0003 2.6604 0.0049 0.01398 0.0004 2.5367 0.0049 0.013112 0.0004 2.4938 0.0047 0.0125

Foreign price shock 1 54.149 65.210 15.850 3.24804 80.765 47.318 17.125 6.29208 82.570 46.816 17.012 8.915912 82.711 46.152 17.288 10.718

Foreign interest rate shock 1 0.2469 0.0076 0.0001 0.11374 0.1025 0.1704 0.1034 0.13418 0.0944 0.1689 0.1088 0.136112 0.0947 0.1701 0.1148 0.1401

Foreign output shock 1 0.0108 0.0096 0.0009 0.00024 0.0088 0.0069 0.0010 0.00168 0.0070 0.0067 0.0018 0.002312 0.0066 0.0066 0.0020 0.0025

30

Table 13: Variance Decompositions: Canada (Benchmark Case)

Canada

qt yt πt rt









31

Table 14: Variance Decompositions: New Zealand (αx = 0)

New Zealand

qt yt πt rt









32

Table 15: Variance Decompositions: United Kingdom (Benchmark Case)

United Kingdom

qt yt πt rt









33

Table 16: Parameter Estimates: United Kingdom, 1992Q4–2006Q4

United Kingdom





34

Table 17: Log Marginal Likelihood Values: UK 92:4–06:4

Log Marginal Data Density United Kingdom

Exogenous qt (αx ·∆qt) 904.7616Exogenous qt (αx ·∆st) 902.7681Exogenous qt (αx = 0) 907.4079

Endogenous qt (αx ·∆qt) 964.9776Endogenous qt (αx ·∆st) 958.4531Endogenous qt (αx ·∆rpt) 958.4522Endogenous qt (αx = 0) 961.4617

Table 18: Log ML: Targeting Expected Inflation

Log Marginal Data Density Canada

Endogenous qt (αx ·∆qt) 2326.7813Endogenous qt (αx ·∆st) 2325.0873Endogenous qt (αx ·∆rpt) 2311.5038Endogenous qt (αx = 0) 2316.3575

35

Figure 1: Impulse Responses: Canada

0 10 20 30 40−1

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Figure 2: Impulse Responses: Canada

0 10 20 30 40−5

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37

do central banks respond to exchange rate movements…economics.ca/2008/papers/0089.pdf · do...

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