Do Central Banks Respond to Exchange Rate Movements? Some New Evidence from Structural Estimation

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1 Do Central Banks Respond to Exchange Rate Movements? Some New Evidence from Structural Estimation Wei Dong International Department Bank of Canada January 4, 8 Abstract This paper investigates whether and how exchange rate movements were taken into account in formulating monetary policy in Australia, Canada, New Zealand and the United Kingdom. We develop 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 local currency pricing firms, and distribution services. Various forms of monetary policy rule and real exchange rate specifications are considered. Generally, with the real exchange rate specified endogenously and consistent with the structural model, the estimations lead to much higher marginal likelihood values than when the real exchange rate is specified exogenously. The estimation results of this paper lead us to favor the view that the Reserve Bank of Australia, the Bank of Canada and the Bank of England paid close attention to real exchange rate movements in the past, while the Reserve Bank of New Zealand did not seem to include exchange rate movements in their policy rule. On the one hand, the central bank of New Zealand seems to be less concerned about future inflation pressure induced by current exchange rate movements. On the other hand, the different structure of shocks in accounting for inflation and output variations in New Zealand, compared to the other three countries, suggests that it may be sufficient for the Reserve Bank of New Zealand to only respond to exchange rate movements indirectly through stabilizing inflation and output. Whats more, since exchange rate volatility might be emphasized when the expenditure-switching effect is small, if this effect were taken into account, the UK might benefit from higher exchange rate volatility. JEL Classification: F3, F4 Bank Classification: Exchange Rates; Monetary Policy Framework; International Topics This paper has benefited from discussions with Charles Engel and Ehsan Choudhri. I thank Larry Schembri, Don Coletti, Robert Lafrance, Eric Santor, Ali Dib, Carlos De Resende, Philipp Maier, René Lalonde, Michael Francis, Michael King and numerous seminar participants for helpful comments. Contact: wdong@bank-banque-canada.ca.

2 1 Introduction For a country not permanently fixing its exchange rates, the flexible exchange rate is an essential part of its monetary policy. As Taylor (1) referred to as a trinity, the monetary policy regime that can work well in the long term should be based on a flexible exchange rate, an inflation target and a monetary policy rule. However, this does not imply that movements in exchange rates have no implications on the economy that deserve central banks attention. In fact, exchange rate movements may cause adjustment of relative prices, and further of demands for domestic goods. Monetary policy, in addition, works in part through its effect on the exchange rate. The important question here is then to what extent central banks 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 banks would benefit from responding to exchange rate movements. There is no consensus on the conclusion yet. Ball (1999) argues that exchange rate movements affect domestic inflation through its effect on import prices, and thus central banks should optimally react to exchange rate movements. Svensson () examines inflation targeting in a small open economy also with a particular emphasis on exchange rates. 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 the forward-looking behavior essential to monetary policy. Furthermore, foreign disturbances may also enter through exchange rate variations. On the other hand, some studies suggest that there should be no role for the exchange rate in the optimal monetary policy rule. In a theoretical model, Clarida et al (1) find that when there is perfect exchange rate pass-through, central banks should target domestic inflation and ignore exchange rate movements. In this model, the representative household welfare criterion depends only on domestic inflation and the output gap variances, because the real exchange rate is proportional to the output gap. As a result, the real exchange rate becomes irrelevant for monetary policy decisions. West (4) suggests that exchange rate stabilization may aggravate instability elsewhere. Under some standard assumptions, he finds that the interest rate can be adjusted to smooth real exchange rate movements at the possible price of increased volatility in some other variables. The paper does not consider the desirability of including exchange rates into the monetary policy rule, though. The second literature estimates policy reaction functions to study the actual role of exchange rates in the monetary policy framework. For developed economies, Clarida et al (1998) show that the monetary authorities in some European countries and Japan responded to exchange rate misalignments. Along the same line, Calvo and Reinhart () find that many emerging economies use interest rates as the means of smoothing exchange rate fluctuations. A free floating exchange rate increases foreign exchange volatility, which may cause problems to banking system and induce balance-sheet effect. For this reason, countries may face fear of floating. In this context, there is some controversy as to whether this response is optimal or not. Rather than estimating monetary policy functions in a univariate setup, Lubik and Schorfheide (7) adopt a multivariate approach of estimating the structural model, and apply Bayesian maximum likelihood estimation methodology to address the issue of open economy monetary policy rules. They 1

3 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 to the model. They are foreign output shock, foreign inflation shock, technology shock, monetary shock and terms-of-trade shock. In their model, the real exchange rate is assumed to be exogenously specified following an autoregressive process, because with the terms of trade specified endogenously, the optimization routines had difficulties finding the maximum of the posterior density and whenever the optimization did converge, implausible parameter values were obtained. They apply their estimation to four small open economies: Australia, Canada, New Zealand and the United Kingdom, and find that the central banks of Australia and New Zealand did not explicitly respond to nominal exchange rates in 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 general equilibrium model to examine the role of exchange rates in monetary policy rules. We find some new evidences from our estimation. First of all, in our estimation, endogenous real exchange rate specification leads to much higher marginal likelihood values for all four countries, than exogenous real exchange rate specifications. In our view, the reason that the estimation of the fully structural model is problematic in Lubik and Schorfheide (7) s work is that if the terms of trade is not taken as exogenously 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-scale DSGE model well to the data. 1 While in order to be able to exploit cross-equation restrictions and the links of the monetary policy rule with the rest of the economy, it is essential to start with a model that has reasonably good fit. We develop a much richer small open economy two-sector model in this paper. We assume the prices and wages are sticky following Calvo (1983), with partial indexation of prices and wages on lagged inflation. Besides producing non-tradable goods for consumption and investment, the non-tradable sector 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 desired exchange rate volatility and the magnitude of the expenditure-switching effect, which is determined by the currency of invoicing, among other things. Our model is estimated via Bayesian maximum likelihood estimation approach for various specifications of the monetary policy rule. The estimation results lead us to favor the view that the Reserve Bank of Australia, the Bank of Canada and the Bank of England responded to real exchange rate movements in the past, while the Reserve Bank of New Zealand 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 for New Zealand, which suggests that for New Zealand, current inflation may reflect less future inflation pressure. Therefore, when the Reserve Bank of New Zealand responds to current inflation, it is less concerned about future inflation pressure caused by current real exchange rate movements. On the other hand, the variance decomposition results suggest that the structure of shocks in accounting for inflation and output variations is different for New Zealand than for the other three countries. For the 1 In Lubik and Schorfheide (7) paper, no model assessment results were provided.

4 central banks of Australia, Canada and the UK, it may not be sufficient to respond to real exchange rate variations only indirectly through targeting inflation rate and stabilizing output levels. The remainder of this paper is organized as follows. Section presents the theoretical model. Section 3 describes the data and the empirical methodology to be employed. Section 4 states he empirical results. Section 5 concludes the paper. The Model Our model in this paper is similar to Dong (7). We consider a small open economy, where the foreign output, 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 composites of both domestic- and foreign-produced differentiated intermediate tradable goods to produce final goods for consumption and investment. In addition, we assume that distribution services are needed to bring foreign-produced tradable intermediate inputs to the domestic market. Several frictions are introduced including Calvo type sticky prices and wages with partial indexation on lagged inflation, a combination of both PCP and LCP firms, cost of adjustment in capital accumulation and consumption habit formation. For details on the model setup, we refer to Dong (7). In what follows, we simply discuss the solutions of the model. Our estimation is based on the first order conditions characterizing the households utility and firms profit maximization problems. Households derive utility from the consumption of tradable and non-tradable goods, as well as leisure. The optimal consumption path is given by: (C t hc t 1 ) ρ S t R t rp t = βe t (C t+1 hc t ) ρ S t+1 π t+1 (.1) ( ) ς PT,t C T,t = α T C t (.) C N,t = (1 α T ) P t ( PN,t P t ) ς C t. (.3) Here, ρ is the coefficient of relative risk aversion of households, β is the subjective discount factor, h is the habit formation coefficient, and ς is the elasticity of substitution between tradable and non-tradable consumption goods. Households provide labour services, L N,t, to non-tradable good producers, and L T,t to intermediate tradable good producers, at the wage rate W i t. They also own capital and rent it to producers at the rate rt,t k, rk N,t for tradable sector and non-tradable sectors respectively. The optimal wage setting and capital accumulation entails: W t = {ψ w [ W t 1 ( Pt 1 P t ) τw ] 1 γ + (1 ψ w )ϖ 1 γ t } 1 1 γ (.4) 3

5 [ ] [ ] χ(kt,t K T,t 1 ) χ(k T,t+1 KT,t) + 1 = Λ t,t+1 K T,t 1 KT,t + 1 δ + rt,t+1 k [ ] [ ] χ(kn,t K N,t 1 ) χ(k N,t+1 KN,t) + 1 = Λ t,t+1 K N,t 1 KN,t + 1 δ + rn,t+1 k (.5) (.6) Λ t,t+1 βe t(c t+1 hc t ) ρ (C t hc t 1 ) ρ, (.7) where ψ w captures the extent of wage stickiness, τ w is the degree of wage indexation, γ is the elasticity of substitution among different types of labor services, and ϖ i t is the optimal wage rate for labour service of type i at time t if household i is selected to reoptimize in that period. Finally, δ is the depreciation rate and χ represents size of adjustment cost. Households can hold domestic currency bond B t, 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 rp t. [ ( ) ] Et S t+1 rp t = exp ϕ n ξ t ϕ s 1 + ˆϕ t S t 1 ξ t S t B t /P t Y t. A modified UIP condition can be derived from the model: R t R t rp t = E t S t+1 S t. (.8) Or, alternatively, we can simply assume the real exchange rate to follow an autoregressive process as in Lubik and Schorfheide (7). We test the endogenous versus exogenous specifications of real exchange rates 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 elasticity of substitution between them σ. ( ) σ PH,t Y H,t = α H Y T,t (.9) Y F,t = (1 α H ) P T,t ( PF,t P T,t ) σ Y T,t. (.1) Intermediate tradable good producers use capital and labor as inputs, and act as monopolistic competitors for price setting. In this paper, I assume φ proportion of intermediate firms use LCP for their export pricing, while (1 φ) of them use PCP. Since the fraction of firms employing LCP versus It is used as a stationarity-inducing technique to ensure the existence of a unique steady state for the small open economy. For other ways of inducing stationarity of the equilibrium dynamics for small open economy models, see Schmitt-Grohé and Uribe (3). 4

6 PCP will have an impact on the pass-through of exchange rates to domestic prices, central banks may frame their policy in a way to take this into account. Let X H,t (s) denote the optimal price set for the home market, and XH,t l (s), Xp H,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, P H,t, and the export price index, PH,t, can then be expressed as: [ ( ) τd ] 1 ε Pt 1 P H,t = {ψ d P H,t 1 + (1 ψ d )X 1 ε H,t P t P t } 1 1 ε [ ( P PH,t = ψ d PH,t 1 ) τd ] ( ) 1 ε t 1 X p 1 ε + (1 ψ d ) φ(x H,t) l 1 ε H,t + (1 φ) S t 1 1 ε (.11). (.1) where ε represents the elasticity of substitution among varieties produced within one country. foreign demand for exports from the small open economy is assumed to be exogenously given by: The ( P ) σf YH,t H,t = α f Pt Yt. (.13) Similarly, non-tradable goods are also produced with capital and labor. Non-tradable goods are used for consumption, investment, as well as distribution services to import foreign-produced intermediate goods. The price index for non-tradable goods is given by: P N,t = {ψ d [ P N,t 1 ( Pt 1 P t ) τd ] 1 ν + (1 ψ d )X 1 ν N,t } 1 1 ν. (.14) We assume that to bring one unit of the tradable intermediate good to the domestic market, λ units of a basket of the differentiated non-tradable goods are needed. Thus, the price index for foreign-produced intermediate goods in the home market, P F,t, and the trade balance value are given by: P F,t (s) = S t Pt (s) + λp N,t (.15) T B t = P F,t Y F,t S t P H,tY H,t. (.16) The government balances its budget constraint. The aggregate government spending is assumed to be an exogenous process, with the shares on tradables and non-tradables depending on their relative prices. P t G t + P t τ t + B t 1 = B t R t ( ) ς PT,t G T,t = α T G t G N,t = (1 α T ) P t ( PN,t P t ) ς G t. 5

7 The monetary policy reaction function is described as a Taylor rule following Taylor (1993). Central banks take the domestic interest rate as the policy instrument to respond to the inflation rate as well as to the output gap. ln(r t /R) = ρ r ln(r t 1 /R) + (1 ρ r )[α π ln(π t /π) + α y ln(y t /Y )] + ɛ rt. (i) ρ r is a parameter that captures interest-rate smoothing, and ɛ rt is a temporary monetary policy shock. We are interested in investigating the role of exchange rates in the monetary policy rule, so we want to test the hypothesis of rule (i) where central banks do not respond to any exchange rate movements, against the following possible rules: ln(r t /R) = ρ r ln(r t 1 /R) + (1 ρ r )[α π ln(π t /π) + α y ln(y t /Y ) + α x ln(s t /S t 1 )] + ɛ rt (ii) ln(r t /R) = ρ r ln(r t 1 /R) + (1 ρ r )[α π ln(π t /π) + α y ln(y t /Y ) + α x ln(q t /q t 1 )] + ɛ rt (iii) ln(r t /R) = ρ r ln(r t 1 /R) + (1 ρ r )[α π ln(π t /π) + α y ln(y t /Y ) + α x ln(rp t /rp t 1 )] + ɛ rt. (iv) In rule (ii), in addition to reacting to inflation and output gap, central banks also include nominal exchange 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 central banks may want to respond to real exchange rate movements in order to smooth international relative price fluctuations that could affect their international competitiveness and have an effect on aggregate demand for domestic goods. Finally in rule (iv), to maintain financial stability, central banks can possibly react to risk premium shifts, which reflects changes in the expectations of risks in the financial market. We test these monetary policy rule candidates within the structural framework by estimating variants 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 for the small open economy, all foreign variables are taken as exogenously determined. ln R t = (1 ρ R ) ln R + ρ R ln R t 1 + ɛ R t ln A T,t = (1 ρ AT ) ln A T + ρ AT ln A T,t 1 + ɛ AT t ln A N,t = (1 ρ AN ) ln A N + ρ AN ln A N,t 1 + ɛ ANt ln Y t = (1 ρ y ) ln Y + ρ y ln Y t 1 + ɛ y t ln P t = φ (ln(p l,t /S t)) + (1 φ ) ln P p,t ln(p l,t /P l,t 1 ) = (1 ρ p ) ln(π l ) + ρ p ln(p l,t 1 /P l,t ) + ɛ p t 6

8 ln(p p,t/p p,t 1) = ln(p l,t /P l,t 1 ) ln G t = (1 ρ g ) ln G + ρ g ln G t 1 + ɛ gt ln ˆϕ t = (1 ρ ϕ ) ln ˆϕ + ρ ϕ ln ˆϕ t 1 + ɛ ϕt. In this model, real variables are assumed to be stationary. The structural model is log-linearized around a deterministic steady state for estimation. For details on the log-linearized equations, we refer to the appendix in Dong (7). 3 Empirical Approach The structural model is estimated using Bayesian maximum likelihood method. We use data on five macroeconomic series for the estimation. They are real wage rate, output, real exchange rate, short term interest rate, and trade balance value over steady state exports. The foreign variables for the domestic small open economy are constructed as geometric weighted averages of the G-7 countries, excluding the domestic country under consideration. The time-varying weights are based on each country s share of total real GDP. The model is taken to the data for four countries: Australia, Canada, New Zealand and the United Kingdom. The data are seasonally adjusted quarterly series. The period covered for our estimation is different across countries due to their specific histories. For Australia, our dataset starts at 1984:1. This point is chosen because the Australian dollar was floated in December Most exchange controls were abolished then, and major steps of deregulation of the financial system took place. Our dataset for Canada covers the period 197:1 to 6:4, in light of its floating exchange rate since 197. The starting point for the Reserve Bank of New Zealand is 1985:. In March 1985, the fixed exchange rate of New Zealand dollar with respect to a trade-weighted basket of currencies was terminated. Major financial sector policy reforms were also carried out through the year of The case of the United Kingdom is a bit more complicated, because over the 199s, the Bank of England has evolving commitment to the ERM. What s more, between October 199 and September 199, the United Kingdom belonged to the hard ERM and the exchange rate was fixed. The dataset might be too short to deliver reliable estimation results if we restricted ourselves to the starting point of 199:4. So in the benchmark case, we selected 1979:3 as the starting point. Thatcher assumed power then and fighting inflation became a clear policy objective. Next, for the sensitivity analysis, we re-estimate the model for the UK over 199:4 to 6:4 to see if the results stay robust. We employ Bayesian maximum likelihood estimation approach in this paper to estimate the structural model. Priors on the parameters are assigned first based on results from past studies and information outside the data set, to measure the ex ante plausibility of parameter values. The time series data are then brought in to revise the parameter values based on information from the data series to get 7

9 posterior estimates. 3 The Bayesian approach also provides a framework to compare and choose models on the basis of the marginal likelihood values. The marginal likelihood of a model M is defined as: L = p(θ M)p(Y θ, M)dθ, θ where θ represents the parameter vector and Y denotes the observable data series. p(θ M) is the prior density of the parameters, and p(y θ, M) is the likelihood function. The marginal density indicates the likelihood of the model given the data. As a Bayesian alternative to hypothesis testing, the Bayes factor between model i and j can be computed as: B i,j = L i L j. Let p i denote the prior probability assigned to model i, the posterior probability that model i is likely is then given by: pp i = p il i Σ j p j L j. The posterior odds is defined as the ratio of the posterior probability that model i is plausible over the probability that it is not: P O i = pp i 1 pp i. The Bayes factor and the posterior odds are used to compare models in this paper, in order to test which 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 calibration because: (i) they are not major parameters of interest in this paper; (ii) they no longer appear in the log-linearized model, but only affect the steady state values; or (iii) there is a consensus in the literature about their values. The subjective discount factor β is given a standard value of.99 for quarterly data. The relative risk aversion parameter ρ is set to equal 4. The inverse of labor supply elasticity µ is set equal to. The weight of tradable goods in the consumption basket, α T, takes a value of.5. The elasticity of substitution between tradables and non-tradables ς, is given a value of.6. The elasticity of substitution among different types of labor services γ is assumed to be 6. The quarterly capital depreciation rate, δ, is set to.5. For Canada, the share of capital in tradable good production, η, is set to.37, the share of capital in non-tradable good production, θ, is set to.8. These calibrated values are based on the estimation results of a two-sector small open economy model for Canada by Ortega and Rebei (6). For Australia, New Zealand and the United Kingdom, the corresponding values are set 3 In this paper, the model is estimated using a numerical optimization procedure provided by Dynare. Dynare is a collection of MATLAB routines which study the transitory dynamics of non-linear models. More information can be found at: 8

10 to η =.36, θ =.3, following usual simulation practices. The average fraction of labor effort in the tradable good sector is inferred from the data on the distribution of civilian employment by economic sector for several industrialized countries. 4 This share is on average approximately.7 for Australia,.9 for Canada,.3 for New Zealand and.31 for the United Kingdom during their own estimation periods. The priors we choose for the structural parameters to be estimated are displayed in Tables 1-4 for each of the four countries. For most of them, fairly loose priors are used, with means centered at values commonly regarded as reasonable. Particularly, with respect to the priors for the fraction of firms employing 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 Canada from Murray, Powell, and Lafleur (3), as well as publications by ECU Institute. Based on information from these sources, the prior means for φ and φ are set at.73 and.31 for Australia,.76 and.3 for Canada,.7 and.3 for New Zealand, and respectively.3,.4 for the UK. 5 Priors on the policy coefficients are chosen to match values generally associated with the Taylor rule. The prior mean for the coefficient on lagged interest rate term ρ r is set at.8, with a standard deviation of.1. The coefficient on the inflation rate α π is given a prior mean of 1.6. The prior mean for the coefficient on the output gap is set at.5. A large standard deviation of. is given, since the empirical evidence on the value of this parameter is diverse. With respect to the coefficient on exchange rates or risk premium movements, whenever it is applicable, a prior mean of.5 is specified. For the parameters of the shocks, little guidance is provided by the literature, so loose priors, which are not very 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 specifications. 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 endogenously determined 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 other cases are not reported, but the log marginal likelihood values are shown in Table 5. As we can see from 4 The time series data covering is from the Bureau of Labor Statistics website. 5 Recent 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 invoiced in the the domestic currency may change slightly. However, as the International Merchandise trade article pointed out, in Australia s case, this was largely caused by changes in exports or imports of a small number of commodities invoiced mainly in Australian dollars. In other words, the modest movements of the invoice currency fractions are due to adjustments in export or import structure, rather than the invoice currency switching by firms. Overall, it seems reasonable to assume that the fractions φ and φ of firms adopting LCP are constant. 9

11 this table, in all cases, the endogenous real exchange rate specification leads to much larger marginal likelihood values than the exogenous real exchange rate specification, though the difference is not as dramatic for Canada as for other three countries. 6 In Lubik and Schorfheide (7) paper, the real exchange rate is assumed to be exogenously given, because they had difficulty of finding maximum in the neighborhood of reasonable parameter values if 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 of four equations and five exogenous shocks. It is taken to the data for estimation with five observable data 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 five observable variables. As emphasized by Ingram, Kocherlakota and Savin (1994), the number of shocks being less than the number of endogenous observable variables might make the model stochastically singular. In that case, if the model implies that certain combinations of the endogenous variables are deterministic, while in the data these exact linear relationships do not hold, the estimation would lead to implausible results. In addition, Lubik and Schorfheide (7) adopt a small scale structural model and 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 links between monetary policy reaction function with the rest of the economy. While the major advantage of adopting structural estimation rather than simply estimating one policy reaction function is that the former approach allows us to capture these links which may have important implications on policy decision. Now that endogenous q t 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 rate determined endogenously. As stated in Section, we consider four forms of central banks responses. They can potentially respond to nominal exchange rates fluctuations, real exchange rates movements, or risk premium shifts, in addition to the inflation rate and output gap. We also estimate the model under the restriction α x =, in which case central banks are assumed not to respond to any exchange rate movement. The marginal likelihood values are displayed in Table 5. The Bayes factors and posterior odds are computed and presented in Table 6. For Australia, the log marginal data density associated with the α x = case is larger than that of central banks responding to s t or rp t case. But the marginal data density of the benchmark model is 4.99 larger on a log-scale than the α x = model. The values of Bayes factor and posterior odds clearly show that the benchmark model is the preferred model compared to others. This leads us to favor the view that the Reserve Bank of Australia responded to real exchange rate movements in the past two decades. For Canada, the marginal likelihood value of responding to s t model is quite close to that of the α x = model. The log marginal density of the benchmark model though is still the largest among all of them, which seems to suggest that the Bank of Canada also paid close attention to real exchange rate movements in the past. The UK s case is very similar to Canada s case. The log marginal 6 It is worth noticing that the numbers in Table 5 are log marginal likelihood values, so the difference between any two marginal likelihood values is actually in the scale of the log difference to the power of e. 1

12 likelihood of the benchmark model is larger on a log-scale than the absence of exchange rate response model. The benchmark model is strongly preferred than other models. The Bayes factor is at most.71 for other models compared to the benchmark, and the posterior odds of the benchmark is around Therefore, our estimation results suggest that the Bank of England responded to real exchange rate movements over the sample period. The case for New Zealand, however, is different. The marginal data density is the largest for the absence of exchange rate response case. The Bayes factor for α x = model is against the benchmark. The Reserve Bank of New Zealand did not seem to include 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 international relative price fluctuations that may affect international competitiveness and have an effect on aggregate demand for domestic goods. Foreign impacts that a small open economy usually cannot afford to ignore may enter through exchange rate movements. Real exchange rate movements may also reflect potential future inflation pressure, which central banks would want to deal with now. Then how come New Zealand is an exception in the past? The answer to this question would depend fundamentally on the link between exchange rates and the rest of the economy. We address this issue in what follows based on the structural parameter estimation results. Model Assessment Before we analyze the estimation results of the parameters, first we assess the conformity of the model to the data, because convincing references can only be drawn from a reasonable model. For this purpose, unconditional second moments are computed and reported in Table 7-1 for the four countries in benchmark case. The first block reports the statistics of the data, and the second block presents the corresponding estimates implied by the model, which are computed from 1, random draws in the posterior distributions of the structural parameters. The median from the simulated distribution of moments are reported, together with the 1th and 9th percentiles. For Australia, Canada and the United Kingdom, the benchmark model is the preferred model. While for New Zealand it is not. The parameter estimation results though are almost the same for the benchmark model and for the preferred model with the absence of exchange rate response. As shown in the tables, in all cases, we see that the standard deviations and autocorrelations of the observable series are very well matched with their counterparts derived from simulations of the model. The data moments fall within the corresponding model confidence intervals. Particularly, for all countries, the persistence and excess volatility of real exchange rates and trade balances are well captured by the simulated model. The model also provides generally good characterizations of the cross correlation properties. In most cases, the data values lie within the error bands implied by the model. The confidence intervals, however, are usually large. This implies that there is a large degree of uncertainty about the model-based correlations, due to short data series. Overall, the model does a reasonably good job of matching properties of the data, though there certainly may be room for improvements in the future. Parameter Estimates 11

13 The estimation results for the four countries in the benchmark case are reported in Table 1-4. The parameter estimates for the α x = model for New Zealand are also reported in Table 11. The first three 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 the posterior distributions given the priors and the likelihood based on the data, and the corresponding standard errors computed from the inverse Hessian. The last three columns report the mean and the 9% confidence interval of the posterior distributions obtained by using the Monte Carlo Metropolis Hastings algorithm. It is subject to 1,, draws, and the first 5, draws are dropped. The Calvo stickiness parameters ψ d for domestic producer prices and ψ w for wage rates are estimated to be around.68 to.74 for all countries, which implies that, on average, prices and wages are re-optimized approximately once every three to four quarters. These estimated lengths of price and wage contracts are in line with the macro literature. Lubik and Schorfheide (6) report estimates of the price stickiness parameter ranging from.74 to.78 in their two-country structural model. Ambler, Dib, and Rebei (3) estimate the Calvo adjustment parameter to be.68 for Canada with a small open economy model. Microeconomic evidences, however, tend to suggest less sticky prices. For all countries, prices are estimated to be less sticky than wage rates. 7 When firms and households are not allowed to adjust prices and wage rates, they index the current levels by past inflation. Parameters τ d and τ w captures the degree of this indexation. They are estimated to be.7 and.33 for Australia in the benchmark case,.8 and.4 for Canada in the benchmark case,.5 and.15 for the UK in the benchmark case, as well as.47 and.3 for New Zealand in the absence of exchange rate response case. The estimated degree of price indexation for Australia, Canada and the UK being close to.5 corresponds to the weight on lagged inflation in the New Keynesian Phillips Curve to be about., and the weight on future inflation term to be about.8. While in New Zealand s case, the estimated degree of price indexation is.47, which implies a weight of.3 on the lagged inflation rate and.68 on the future inflation rate in the Phillips Curve. Since in the model, central banks are assumed to respond directly to current inflation, that the current inflation depends less on future inflation in New Zealand may provide a case for the Reserve Bank of New Zealand to be less concerned about the future inflation pressure induced by exchange rate movements. The proportions of domestic and foreign firms using LCP to set export prices, φ and φ, are estimated to be.78 and.9 for Australia,.81 and.5 for Canada,.74 and.4 for New Zealand, and.34 and.4 for the United Kingdom. For the first three countries, LCP is dominant for its own exports, 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 domestic and foreign varieties in the domestic market and in the foreign market, σ and σ f, are estimated to be around 1.4 to., which are in the upper half of the range of macro estimates. The distribution margin ϱ is estimated to be.7 for Australia,.56 for Canada,.59 for New Zealand, and much larger at.8 for the UK. The distribution margin measures the fraction of the import price accounted for by distribution costs. A slightly larger fraction of firms exporting to Australia, Canada or New Zealand price their products in the local market currency, compared to the UK. This may suggest a bit larger expenditure-switching effect in the UK when prices are sticky in the short run. However, as 7 Sticky wages play an important role in allowing the model to generate reasonable price stickiness. 1

14 emphasized by Dong (7), the higher ϱ is, the smaller the effect of exchange rate movements on the relative 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 is small. 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 the interest rate to be quite persistent for all the countries. The coefficient for the inflation rate is greater than 1. The Taylor principle is satisfied. All four countries respond quite aggressively to the output gap. For Australia, Canada and the United Kingdom, the estimated coefficients on real exchange rate movements are significantly different from zero. The estimates of the risk premium coefficients, the AR parameters and standard deviations for the unobserved shocks are also reported. It s worth noticing that the estimated exogenous processes for these shocks differ significantly, though the same priors are given at the beginning. Impulse Responses To further understand the dynamics of the model, impulse responses for the country of Canada in the benchmark case are presented in Figure 1-. In the figures, the impulse responses of four variables of 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 in the exogenous shock for the value of variables. The responses are calculated from a random selection of 1, parameters out of the 5, draws from the posterior distributions. Together with the median response, the 1% and 9% percentiles are also shown. A technology shock in the non-tradable sector increases imports through the effect on distribution services, therefore drives up domestic output. As a result, the domestic currency depreciates. The final tradable good producers then switch expenditure from imports to domestically-produced goods. Positive technology shock lowers inflation. Relaxing monetary policy then helps to appreciate domestic currency. Similarly, a technology shock in the tradable sector also induces a drop in inflation and interest rate. But since a technology shock in the tradable sector actually increases the amount of domesticproduced intermediate goods, thus reduces imports, the demand for foreign currency decreases and the domestic currency appreciates. Central bank loosening policy contributes to the expansionary effect on output. A risk premium shock drives up the demand for foreign currency. The demand for domestic currency then reduces, and the domestic currency depreciates. Monetary policy is tightened at first to cope with inflation, relaxed then to stimulate production. A positive monetary policy shock implies tightening in the monetary policy which makes production drop. Domestic bonds become more attractive 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 the demand for domestic money, which causes inflation as well as puts upward pressure on the domestic interest rate. As a result, the domestic currency appreciates. 13

15 An increase in the foreign prices leads to expenditure switching from foreign-produced goods to domestic-produced goods. But since the majority of domestic firms use local currency pricing for their exports, this in fact implies an increasing demand of foreign currency. Foreign currency then appreciates. Foreign inflation is passed through to the domestic economy. In response, the interest rate increases. From quarter to quarter 7 after the shock, the inflation rate is actually falling, but the monetary policy is still tightening up, because there is real depreciation going on. The effects of the foreign interest rate shock on the variables are not surprisingly in line with those of the risk premium shock. The two shocks are identified in the model through the observed foreign interest rate series. In other words, the risk premium shock captures whatever is left unaccounted for by the observed foreign interest rate shock. Finally a foreign output shock increases the demand for domestic exports, further domestic output. The rising of domestic exports together with increasing demand for foreign imports lead to higher demand for foreign currency. The foreign output shock suggests an ease on domestic inflation, thus a loosening up in the monetary policy. Variance Decomposition The variance decomposition results for various horizons are presented in Table 1-15 for the four countries of their preferred models, in order to infer the role of various structural shocks in driving the movements of output, real exchange rate, inflation and interest rate. Not surprisingly we find that the foreign price shock plays an important role in accounting for the forecast error variances of the domestic variables, since all the four economies considered here are small open economies. The technology shock in the tradable sector is generally also very important in generating variations of inflation and interest rate, as well as output and the real exchange rate in addition to the foreign price shock. When we compare the variance decomposition results for New Zealand 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 New Zealand are different from those for Australia, Canada and the United Kingdom. Even if central banks follow a policy rule without explicitly responding to exchange rate movements, the indirect effect of exchange rates on interest rates still exist due to the effects of exchange rates on inflation rate and output gap. The variance decompositions of inflation and output therefore help to explain why the Reserve Bank of New Zealand does not include exchange rate movements into their policy reaction function. With respect to the inflation rate, besides the foreign price shock, it is the technology shocks in both tradable and non-tradable sectors that account for significant percentages of ˆπ t variations for Australia, Canada and the United Kingdom. While for New Zealand, only the technology shock in the tradable sector explains a big part of the forecast error variances of ˆπ t, while the role of the technology shock in the non-tradable sector is not important at all. As we can see from the impulse response figures and the earlier analysis, a positive technology shock in the tradable sector induces a drop in the real exchange rate; while a positive technology shock in the non-tradable sector drives up the real exchange rate initially. In this paper, the technology shocks in the tradable and non-tradable sectors are assumed to be independent. In other words, we can think of the two shocks in this model as orthogonal decompositions of real world productivity shocks. Since in reality every tradable sector has 14

16 non-tradable components and vice versa, we would expect to see same signs for these two shocks even though they are taken as orthogonal in the model. Now that their implications for real exchange rate movements are different, for the central banks of Australia, Canada and the UK, it is not sufficient to respond to real exchange rate variations indirectly through targeting inflation rate. The Reserve Bank of New Zealand, on the other hand, faces a simpler problem, since non-tradable technology shock is insignificant in accounting for its inflation variances. We notice that 99% of the forecast error variances of output are explained by the tradable sector technology shock and the foreign price shock in New Zealand. While for the other three countries, the risk premium shock plays an as important role as the technology shock in the tradable sector, if not more. The implications of the risk premium shock, temporary monetary policy shock as well as the foreign interest rate shock are quite different from those of other shocks. They have no direct effect on the demands of domestic-produced goods, rather they only work through their effects on exchange rates to lead to expenditure switching. In comparison, other shocks have direct impacts on the demands of domestic goods; expenditure switching is then induced through exchange rate movements and it works in the opposite direction of the direct effect. For example, as a demand shock, the government spending shock drives up domestic production. A positive government expenditure shock increases the demand for domestic money. This puts upward pressure on the domestic interest rate, and appreciates the domestic currency. Domestic final good producers then tend to substitute foreign for domestic varieties. Now in response to a positive risk premium shock, the domestic currency depreciates. Domestic final 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 final good production, but also reduce non-tradable good production due to lower demand for distribution services. In this case, if central banks respond to the output drop by loosening up monetary policy, lower domestic interest rate would further depreciate domestic currency. Therefore, for Australia, Canada and the United Kingdom, where the risk premium shock plays a role in driving output variations, it makes sense for the central banks to respond to real exchange rate movements directly, because the indirect response through reacting to output gap works in the wrong direction. While for New Zealand, this is much less a concern. 4. Sensitivity analysis In this section, we assess the sensitivity of the estimation results to alternative data samples, 8 and expected inflation targeting rules. Generally, we find that alternative data sample for the UK does not change the major empirical results. Models with expected inflation targeting rule, however, are inferior to 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 data 8 This is only relevant for the UK s case. 15

17 series at 1979:3. However, over the 199s, the Bank of England has evolving commitment to the ERM, between October 199 and September 199, the UK even belonged to the hard ERM. The exchange rate movements during this period might be much milder than it would have been otherwise. Since this 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 199:4 to 6:4 to re-estimate the models. The parameter estimation results are presented in Table 16, and the log marginal likelihood values corresponding to various specifications of the real exchange rate and monetary policy rule are shown in Table 17. All the major results stay the same in this sensitivity analysis. Endogenous real exchange rate specifications lead to much higher log marginal likelihood values than exogenous real exchange rate specifications in all cases. The marginal data density of the model where central banks directly respond to real exchange rate variations is the largest, which suggests that this is the preferred model. The parameter 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, τ d, now is much larger than its original estimate of.5. The current estimate is about.47. This in principle would imply that during 199:4 to 6:4, the current inflation level depends less on future inflation rate and more on lagged inflation in the UK. However, the estimation results still suggest that the Bank of England included current real exchange rate movements in its monetary policy rule. As we analyzed in Section 4.1, the importance of various structural shocks in accounting for inflation and output variances have influences for this. Targeting Expected Inflation Our second robustness check is with respect to the possibility of expected inflation targeting in monetary policy rules. Current real exchange rate movements may have implications for future inflation levels. But would it be possible that central banks directly respond to the future inflation pressure? To answer this question, we re-estimate the various versions of the model under endogenous real exchange rate specification. Particularly, in this exercise, we assume central banks target future inflation rather than current inflation. The new monetary policy rules can then be specified as: ln(r t /R) = ρ r ln(r t 1 /R) + (1 ρ r )[α π ln(π t+1 /π) + α y ln(y t /Y )] + ɛ rt (i) ln(r t /R) = ρ r ln(r t 1 /R) + (1 ρ r )[α π ln(π t+1 /π) + α y ln(y t /Y ) + α x ln(s t /S t 1 )] + ɛ rt (ii) ln(r t /R) = ρ r ln(r t 1 /R) + (1 ρ r )[α π ln(π t+1 /π) + α y ln(y t /Y ) + α x ln(q t /q t 1 )] + ɛ rt (iii) ln(r t /R) = ρ r ln(r t 1 /R) + (1 ρ r )[α π ln(π t+1 /π) + α y ln(y t /Y ) + α x ln(rp t /rp t 1 )] + ɛ rt. (iv) The log marginal densities from these estimations are displayed in Table 18 for Canada. Comparing these values to the baseline case, we see that expected inflation targeting assumption leads to lower marginal likelihood values in all cases. Central banks responding to q t model is still the preferred 16