Do Central Banks respond to exchange rate movements? A Markov-Switching structural investigation

Do Central Banks respond to exchange rate movements? A Markov-Switching structural investigation Ragna Alstadheim Hilde C. Bjørnland Junior Maih February 16, 213 PRELIMINARY VERSION Abstract Do Central Banks Respond to Exchange Rate Movements? Yes, some do, according to Lubik and Schorfheide (27) who estimate structural general equilibrium models with monetary policy rules. However, their analysis is based on a sample with multiple regime changes, which may bias the results. We revisit their original question using a Markov switching set up which explicitly allows for parameter changes. Fitting the data from four small open economies to the model, we find that the size of policy responses, and the volatility of structural shocks, have not stayed constant during the sample period (1982-211). In particular, central banks in Canada and Sweden switched from a high response to the exchange rate in the 198s and early 199s, to a low response shortly after inflation targeting was implemented. Such decline in exchange rate response over time has not been observed in Norway, where the central bank has responded strongly to the exchange rate prior and post the inflation targeting implementation. In the UK, on the other hand, we observe little exchange rate response throughout the sample. Furthermore, we find that terms of trade shocks exacerbate the effects on output and inflation on countries that respond strongly to the exchange rate. Finally, our model suggests a similar changing pattern in all countries of high volatility in the 198s and during the financial crisis, and low volatility during the the 199s (the period of great moderation). The authors would like to thank Sandra Eickmeier and participants at the Monetary Policy and Commodity Prices Workshop at the ECB for comments. The views expressed in this paper are those of the authors and do not necessarily reflect the views of the IMF or the Norges Bank. Ragna Alstadheim, Norges Bank. Email: Ragna.Alstadheim@norges-bank.no Corresponding author: Hilde C. Bjørnland, BI Norwegian Business School and Norges Bank. Email: hilde.c.bjornland@bi.no Junior Maih, The International Monetary Fund. Email: jmaih@imf.org 1

1 Introduction Do Central Banks Respond to Exchange Rate Movements? Yes, some do, according to Lubik and Schorfheide (27) who estimate structural general equilibrium models with interest rate rules for monetary policy in small open economies. In particular, they find that the interest rate rules in Canada and the UK include responses to the nominal exchange rate, in addition to direct responses to the output gap and the inflation rate. Corroborate findings have been documented for Canada, New Zealand, Norway and Sweden in Bjørnland (29) and Bjørnland and Halvorsen (212) using instead structural vector autoregression (SVAR) models that allow for simultaneous responses between monetary policy and exchange rate changes. During the period that Lubik and Schorfheide (27) are analysing (1983-22), many countries went from having a formal exchange rate target to inflation targeting, either directly or via a period of informal exchange rate stabilisation (inside a band). Their analysis may therefore be based on samples with multiple regime changes. Furthermore, different policy responses may also imply changes to volatility. In particular, one would expect that domestic business cycle fluctuations in open economies (in particular those that are rich in natural resources) are likely to have a substantial international relative price component. Some inflation targeting central banks may therefore in periods have a specific interest in explicitly reacting to and smoothing exchange rate movements as a predictor of domestic volatility. Hence, assuming a time-invariant parameter reaction function as well as constant volatility during the sample period might bias the results. Against this background we analyse the importance of regime changes in the monetary policy responses and the shocks that hit small open economies. Our main focus is to explore whether inflation targeting central banks put the same weight on stabilizing the exchange rate throughout the period, independently of the known regime changes and the volatility of shocks. Furthermore, given that we observe a regime change, we analyse how this may have impacted the responses of output and inflation to structural shocks, and how the unconditional variances of endogenous variables have changed. A strong or weak response to the exchange rate, may imply larger or smaller volatility of endogenous variables, depending on the cocktail of disturbance hitting the economy. To answer these questions, we estimate a small open economy DSGE model like the one put forward in Lubik and Schorfheide (27), using Bayesian methods, but allowing for independent Markov switching in the shocks that hit the economy and in the monetary policy responses. 1 The analysis is applied to four small-open-economy countries: Canada, Norway, Sweden and the UK, that all have adopted inflation targeting during the period analysed (1982-211). Of these, Canada and the UK were included in the analysis in Lubik and Schorfheide (27), while Norway and Sweden are new. We contribute to the literature in the following ways. First, and to the best of our knowledge, this is the first paper addressing the specific question of regime shifts in the monetary policy responses and volatility in small open economies. While Liu and 1 The DSGE model put forward in Lubik and Schorfheide (27) is a simplified version of Galí and Monacelli (25). 2

Mumtaz (211) also analyse regime shifts in the UK using a Markov Switching open economy DSGE model, their focus is more general, analysing shifts in parameters and shocks to the whole DSGE model. Second, we use new solution algorithms, see Maih (212). The algorithms rely on Newton methods developed in Maih (212) and which extend Farmer et al. (211). Third, in contrast to Lubik and Schorfheide (27) who treat foreign output and inflation as unobservable (latent) variables, we include foreign (global) output and inflation as observables in the model in order to better identify the effects of foreign shocks. This help tie the dynamics of the small open economies model more explicitly to the global shocks. In the current version, we identify global output and inflation from GDP and inflation in the US, but we will also experience with constructing factors of global activity and inflation from different countries using principal components methods. Finally, unlike Lubik and Schorfheide (27), we do not detrend the data prior to the analysis. 2 We believe that non-filtered data are important in order to let the Markov-Switching framework inform about medium-term changes in the dynamics of the data, that detrending effectively eliminates. Our maintained hypothesis is that the variables can be stationary but from different distributions reflected by different regimes. We have three main findings. First, we find strong evidence that deep structural parameters and the volatility of structural shocks have not stayed constant through the sample period in any of the four countries. Second, our results give a more nuanced picture of the weight that central banks give to stabilizing the nominal exchange rate. In particular, we find that Sweden and the UK put less weight on stabilizing the exchange rate, as measured by the response to the nominal effective exchange rate, when inflation targeting was adopted in the early 199s. Canada also switched to a low For Norway, which adopted inflation targeting as late as in 21, we do not observe a systematic change in the response to the nominal effective exchange rate. Instead we find that there has been a high response to the exchange rate over the whole period, with the exception of the brief period in 22/23 and under the financial crisis. For the UK, on the other hand, there has been little exchange rate responses overall. Finally, we find that in countries that respond strongly to the exchange rate, the effects of terms of trade shocks on output and inflation are exacerbated. However, despite the difference in responses, our model suggests a similar changing pattern in all countries of high volatility in the 198s and during the financial crisis, and low volatility during the the 199s (the period of great moderation). The remainder of the paper is structured as follows: Section 2 describes the New Keynesian model for SOE, while the algorithms and the estimation procedure are described in Section 3. Data and priors are presented in section 4, while in section 5 we report the results. Section 6 discusses robustness while Section 7 concludes. 2 Lubik and Schorfheide (27) detrend the data using the Hodrick- Prescott (HP) filter. 3

2 A structural small open economy model Our model is a simplified version of Galí and Monacelli (25) which is adapted from Lubik and Schorfheide (27). The model consist of a forward-looking (open economy) IS equation, a Phillips curve, an exchange rate equation and a monetary policy (interest rate) rule. Following Lubik and Schorfheide (27), we rewrite the (consumption) Euler equation as an open economy IS-curve: y t = E t y t+1 (τ + λ)(r t E t π t+1 ) ρ z z t α(τ + λ)e t q t+1 + λ τ E t y t+1, (1) where < α < 1 is the import share (that measures the degree of openness), τ is the intertemporal substitution elasticity and we define λ = α(2 α)(1 τ). Note that the equation reduces to its closed economy variant when α =. The endogenous variables are output y t, the CPI inflation rate π t and the nominal interest rate r t. q t is the terms of trade, yt is world output, while z t is the growth rate of an underlying non-stationary world technology process A t. In order to obtain stationarity of the model, domestic and foreign output are both expressed in terms of percentage deviations from A t. 3 We will assume that yt and z t are exogenous variables that evolve as AR processes with autoregressive coefficients ρ y and ρ z respectively. Optimal price setting of domestic firms, together with an assumption of perfect risksharing across countries that links domestic potential output to foreign output, leads to the open economy Phillips curve π t = βe t π t+1 + αβe t q t+1 α q t + κ (τ + λ) (y t ȳ t ), (2) where ȳ t = α(2 α)(1 τ)/τyt is domestic potential output in the absence of nominal rigidities. Again this reduces to the closed economy variant with α =. In a standard New-Keynesian model, κ is the slope coefficient. It is related to the price stickiness, the degree of competition and the representative firm s cost function parameters. Like Lubik and Schorfheide (27), we treat κ itself as structural, but we do not model the underlying structure of the production side of the economy. 4 We introduce the nominal exchange rate (e t ) via the definition of consumer prices. Assume that relative Purchasing Power Parity (PPP) holds, we have: 3 This implies that observed domestic and foreign output growth correspond to respectively y t and y t adjusted by productivity growth z t. 4 Note that since we express the output gap as a function of foreign output, via the perfect risk-sharing assumption, κ embed both shocks to foreign output and domestic productivity (that by implicit assumption are proportional to shocks to the domestic output gap and marginal costs). This is in contrast to e.g. Smets and Wouters (27), where marginal cost enters the price setting equation directly, and hence the coefficient corresponding to our κ reflects the relationship between labor productivity and the real wage on the one hand, and inflation on the other hand. 4

e t = π t (1 α) q t π t, (3) where π t is world inflation, which is exogenous and is assumed to evolve as an AR process. The policy rule allows for the possibility of including nominal exchange rate depreciation: r t = ρ r r t 1 + (1 ρ r )(γ π π t + γ y y t + γ e e t ) + ɛ r,t, (4) We assume that the policy coefficients γ π, γ y and γ e. We also allow for a smoothing term in the rule, with < ρ r < 1. ɛ r,t is the exogenous monetary policy shock, which can be interpreted as the unsystematic component of monetary policy (deviation from rule). Finally, instead of solving endogenously for terms of trade, we follow Lubik and Schorfheide (27) and add a law of motion for their growth rate to the system: q t = ρ q q t 1 + ɛ q,t 3 The Markov-Switching DSGE model In this section, we describe a general framework for the Markov switching DSGE or rational expectations model. Then we briefly discuss the solution method and the estimation approach. All the algorithms used for the computations in this paper are done using RISE, an object-oriented Matlab toolbox for solving and estimating Markov switching rational expectations (MSRE) models 5. 3.1 The general framework For a linear model like the one considered in this paper, the general Markov-switching rational expectations model can be written as 6 : E t { A + st+1 x t+1 (, s t ) + A s t x t (s t, s t 1 ) + A s t x t 1 (s t 1, s t 2 ) + B st ε t } = (5) x t is a n 1 vector including all the endogenous (predetermined and non-predetermined) variables; ε t N (, I), is the vector of structural shocks. The regime index s t, which could be a composite of states from different Markov chains, switches between a finite number of possibilities with cardinality h. And so, s t = 1, 2,..., h. (s t, s t 1 ) denotes the state today s t and the state in the previous period s t 1. 5 RISE is the acronym for Rationality In Switching Environments. It is available free of charge at https://github.com/jmaih/rise_toolbox and is being developed by Junior Maih 6 See Maih(212) for the general nonlinear case. 5

The Markov transition probabilities are summarized by a matrix Q = [p st,s t+1 ], where p st,s t+1 = prob(s t+1 s t ), with s t+1 = 1, 2,..., h. In other words, p st,s t+1 denotes the probability of going from state s t in the current period to state s t+1 next period. This allows us to define the expectation h E t A st+1 x t+1 (, s t ) p st,st+1 A st+1 E t x t+1 (s t+1, s t ) (6) s t+1 =1 3.2 Solution and stability Solving the type of systems above is not straightforward and the traditional solution methods for constant-parameter DSGE models cannot be used. As can be seen from the problem, the solution in each state will be a function of the solution in all other states and vice-versa. To solve the system we rely on Newton methods developed in Maih (212) and which extend Farmer et al. (211). The Newton method in Maih (212) concentrates on minimum state variable (MSV) solutions of the form: x t (s t, s t 1 ) = T st x t 1 (s t 1, s t 2 ) + R st ε t (7) The traditional stability concepts for constant-parameter linear rational expectations models do not extend to the markov switching case. Following the lead of Svensson and Williams (25) and Farmer et al. (211), we characterize stable solutions using the concept of Mean Square Stability (MSS), borrowed from the engineering literature. See for instance, Gupta et al. (23) or Costa et al. (25). Consider the MSRE system whose solution is given by equation (7) and with transition probability matrix Q. This system is MSS if for any initial condition x, there exist a vector µ and a matrix Σ independent of x such that lim t Ex t µ = and lim t Ex t x t Σ =. A necessary and sufficient condition for MSS is that matrix Υ, has all its eigenvalues inside the unit circle. T 1 T 1 Υ (Q I n 2 n 2)... T h T h 3.3 Estimation In order to estimate the model, the likelihood has to be computed. Because of the presence of unobserved variables and unobserved states of the Markov chains, the likelihood has to be computed using a filtering procedure. The standard Kalman filter is not appropriate in this case because the information up to time t includes all the history of the states of the Markov chains. The most accurate filtering procedure should take into account 6

all possible paths, which are multiplied by a factor of h (the number of states) at each iteration. This is infeasible. Kim and Nelson (1999) propose an approximation that makes filtering possible. Their strategy is to limit the number of states that are carried forward at each iteration of the Kalman filter. This is done through an operation called collapse, which, essentially, averages across states. Even when carrying forward only a few states, this filtering procedure is still expensive. Waggoner and Zha (28) 7 exploit Kim and Nelson s idea and propose a variant in which the collapse occurs right after the prediction step of the Kalman filter, rather than right after the updating step as in Kim and Nelson (1999). The two approaches lead to numerically similar results and the Waggoner-Zha approach, which we follow, achieves those results with substantial computational savings. In both cases, the calculation of the probabilities is done using the Hamilton (1994) filter. For the smoothing step, we adapt the Durbin and Koopman (21) smoother for constantparameter models. Our adaptation has the advantage of giving the same results as the Kim and Nelson (1999) smoothing procedure and also allowing smoothing based on the Waggoner-Zha filtering procedure. The paper uses a Bayesian approach for estimating the models. In particular, we combine the likelihood, described above, with the prior density of the parameters, thereby forming the posterior kernel which we maximize to get the mode of the posterior distribution. While the estimate of the mode represents the most likely value, it also serves as a starting point for initializing the Markov chain Monte Carlo (MCMC) procedure aimed at constructing the full posterior distribution and computing the marginal data density (MDD). Even for simple models as the one considered here, finding the mode is computationally challenging given that the posterior kernel has many peaks. Our optimization strategy is to use a stochastic grid search algorithm, which is derivative-free, to locate areas of the parameter space in which the global peak may lie and then use a Newton-based optimization procedure to climb to that peak. 4 Empirical implementation We proceed with a discussion on the data, the construction of the factors of global output and inflation, the choice of prior distribution for the Bayesian analysis and a description of the choice of parameters that are allowed to switch. We also discuss briefly the timing of policy changes that has actually taken place in history, such as when the central banks adopted inflation targeting. 7 See Zha (211) for reference 7

4.1 Data We use quarterly data for the period 1982:2-211:4. 8 For each country, there are seven observable variables: domestic real GDP, inflation, nominal effective exchange rate, terms of trade and short term interest rate, as well as foreign output and inflation. In this respect, we differ from Lubik and Schorfheide (27), which do not use foreign observables in their estimations. All data except the nominal interest rate and the exchange rate are seasonally adjusted. Output growth rates are computed as log differences of GDP and multiplied by 1 to convert them into quarter to quarter percentages. Inflation rates are defined as log differences of the consumer price indices and multiplied by 4 to get annualized percentage rates. We use the log differences (multiplied by 1) of the trade-weighted nominal effective exchange rate to obtain depreciation rates 9. Percentage changes in the terms of trade are computed as log differences and multiplied by 1 while the nominal interest rate is measured in levels. All series are demeaned prior to analysis. For further details on data and the sources, see Appendix A. 4.2 Choice of priors and Markov switches The choice of prior distribution for the structural parameters are presented in Table 1 along with the estimated posterior mode for a model with constant regime as a benchmark. With the exception of the parameter α, we allow for loose priors to entertain the idea that there has been multiple regime changes in the sample. α, which is the import share, is tightly centered around.2, as in Lubik and Schorfheide (27). Note also that we allow the prior on the autoregressive coefficient on terms of trade, ρ q, to take negative values, as data suggests a negative autoregressive coefficient for terms of trade in some of the countries. For each country, we will allow for four competing Markov switching models; Time invariant (constant) regime, markov switch in volatilities only, switch in parameters in the policy rule only, and (independent) markov switch in volatility and parameters in the monetary policy rule. With four countries this implies that we will estimate a total of 16 models. In the model that allows for regime switching in the open economy interest rate rule, we allow the parameters ρ r, γ π, γ y and γ e to follow an independent two-state Markov process, where we denote the low response regime as (coef, 1) and the high response regime as (coef, 2). To compare systematically across countries, we normalize the high response regime (coef, 2) to be the regime where the central bank responds strongly to the exchange rate, i.e. γ e (coef, 1) < γ e (coef, 2). In the model that allows for regime switching in the shocks, we let volatility of all structural and foreign shocks σ r, σ z, σ y, σ π and σ q to follow an independent two-state Markov process, where we denote the low volatility regime as (vol, 1) and the high volatility 8 The start date reflects data availability for the interest rate series in Sweden. 9 Note that in order to make an increase correspond to a depreciation rate, we invert the exchange rate. 8

regime as (vol, 2). Again, to compare systematically across countries, we normalize the high volatility regime (vol, 2) to be the regime where the volatility (in productivity) is highest, i.e. σ z (vol, 1) < σ z (vol, 2) 4.3 Known policy changes - Inflation targeting Before estimating the model, it is useful to acknowledge the periods of known policy changes that has taken place, such as when the central banks switched from a regime of exchange rate targeting to to inflation targeting. Canada adopted inflation target in February 1991, but has changed the explicit target and range several times since then. However, since the end of 1995, the target for the annual rate of total consumer price inflation has been the 2 percent midpoint of a 1 to 3 per cent range. Sweden and the UK switched to inflation targeting in the early 199s after currency crises and the collapse of their fixed exchange rate regimes (to the ECU in 1992). In Norway, the fixed exchange rate regime was abandoned in December 1992, and thereafter became more flexible. However, monetary policy was still oriented towards maintaining a stable exchange rate in relation to European currencies, although without defining a central exchange rate with fluctuation margins. Eventually in early 21, a formal inflation targeting framework was adopted. 5 Results We start by comparing the parameter estimates in time invariant model for Canada with the results in Lubik and Schorfheide (27) before turning to our preferred multiple regime switching model. 5.1 Parameter estimates - Time invariant Rational Expectation Model The estimation result for the posterior mode, along with the prior mode and distribution for Canada using a time invariant (constant) model is reported in Table 1. The results for the other countries can be obtained at request. 9

Table 1: Canada: Constant model - Prior and posterior mode Param Prior distr Prior prob low high mode mode std τ Beta.9.17.83.4 1.416e-8 k Gamma.9.12.87.58 7.179e-9 α Beta.9.12.28.3 9.81e-9 ρ q Uniform.9 -.7.7.35.8415 ρ y Beta.9.35.75.97.144 ρ π Beta.9.5.948.48.4318 ρ z Beta.9.35.75.36.3823 ρ r Beta.9.5.948.78 8.151e-9 γ π Gamma.9.9 3.58 6.824e-9 γ y Gamma.9.5 3.43 7.179e-9 γ e Gamma.9.5 3.41 8.151e-9 σ r InvGam.9.5 2.99 1.1.4329 σ q InvGam.9.5 2.99 1.7.4386 σ z InvGam.9.5 2.99.48.7259 σ y InvGam.9.5 2.99.17.2616 σ π InvGam.9.5 2.99 1.9.4537 The table suggests structural parameters that are broadly in line with the model parameters reported in Lubik and Schorfheide (27), with the exception of the parameter α that is estimated to be very low and the parameters on the policy reaction function, that suggests a higher weight on exchange rates and output relative to inflation. However, given that we allow for loose priors and use a longer sample (9 years of extra data at the end) this is not very surprising. In fact, we would argue that if the data is generated by different distributions reflected by different regimes, forcing a time invariant distribution to the data should potentially give different results depending on the sample analysed. 5.2 Parameter estimates - Switching policy rule and volatility Table 2 displays for all countries the posterior mode of the estimated parameters in a model with both switching volatility and policy responses. We find that the size of policy responses, and the volatility of structural shocks, have not stayed constant during the sample period (1982-211). For all countries, there is a substantial difference between the high and low volatility regimes and between the high and low policy response regimes. We start by investigating the coefficients on the policy reaction function; ρ r, γ π, γ y and γ e. There is clear evidence that the central bank has responded strongly to the exchange rate in regime (coef, 2), while the response to inflation is highest in regime (coef, 1). Interest rate smoothing is also more pronounced in regime 1. The response to output varies between the different countries, with Canada and the UK responding more strongly to output also in regime (coef, 1), while Norway and Sweden responding more strongly to output in regime 2. Hence, regime (coef, 1) can be characterized by an interest rate rule with more focus in interest rate smoothing and high inflation response, while regime 1

(coef, 2) is characterized by high exchange rate response. Among the countries, we find Norway to have the strongest interest rate response to the exchange rate, followed by Canada, Sweden and the UK. The probability of moving from a low exchange rate response to a high response regime, is also highest in Norway. Table 2: Regime switches - Posterior mode Param Names Prior distr Prior prob low high Canada Norway Sweden UK τ beta.9.17.83.9259.4752.78.5825 k gamma.9.12.87.5741 1.97.1441.458 α beta.9.12.28.1531.4633.182.163 ρ q beta.9.1.8.2462.966.576.45 ρ y beta.9.4.8.9493.9711.9557.9611 ρ π beta.9.1.8.4777.3554.5793.2446 ρ z beta.9.4.8.52.7879.633.4378 ρ r(coef, 1) beta.9.5.948.9265.711.9462.9395 ρ r(coef, 2) beta.9.5.948.7554.9778.11.678 γ π(coef, 1) gamma.9.5 3.5666.8464.1279.3645 γ π(coef, 2) gamma.9.5 3.4785.5134.1161.364 γ y(coef, 1) gamma.9.1 3 3.414 2.19 1.965 3.685 γ y(coef, 2) gamma.9.1 3 1.99 2.943 3.15.7688 γ e(coef, 1) gamma.9.5 3.139.1.1.1 γ e(coef, 2) gamma.9.25 3.141 4.69.67.82 σ r(vol, 1) InvGam.9.5 1.16.26.9.8 σ r(vol, 2) InvGam.9.5 1.34.84.24.32 σ q(vol, 1) InvGam.9.5 1.121.639.14.86 σ q(vol, 2) InvGam.9.5 1.353.393.189.186 σ z(vol, 1) InvGam.9.5 1.42.29.28.26 σ z(vol, 2) InvGam.9.5 1.73.11.88.95 σ y (vol, 1) InvGam.9.5 1.36.29.4.42 σ y (vol, 2) InvGam.9.5 1.176.151.115.1 σ φ (vol, 1) InvGam.9.5 1.171.9.13.18 σ φ (vol, 2) InvGam.9.5 1.331.634.343.481 σ y(vol, 1) InvGam.9.5 1.17.66.17.18 σ y(vol, 2) InvGam.9.5 1.39.93.65.39 σ φ(vol, 1) InvGam.9.5 1.14.188.15.19 σ φ(vol, 2) InvGam.9.5 1.34.8.386.198 coef tp 1 2 beta.9.1.3.5.111.5.5 coef tp 2 1 beta.9.1.3.14.96.175.172 vol tp 1 2 beta.9.1.3.268.53.265.55 vol tp 2 1 beta.9.1.3.1641.115.165.2527 Regarding the Markov state processes for volatility, we find that all shocks display highest volatility in regime (vol, 2) in all countries. In all countries, the probability of moving from a high volatility regime to low volatility regime is high. 11

Turning to the other structural parameters (that are not switching), two features should be pointed out. First, the parameter α that measures the degree of openness, is estimated to be largest in Norway, followed by Sweden, UK and Canada. 1. Second, the parameter κ that measures the slope coefficient in the Phillips curve is estimated to be below one in all countries but Norway, where it is just above one. A high value for κ may relate to the fact that the output gap is also linked to foreign output, via the perfect risk-sharing assumption, implying that κ in our model reflects shocks to foreign output in addition to domestic productivity. Given that Norway is the most open of these countries (measured by α), a high κ may also be reasonable. Figures 1,2, 3 and 4 display the smoothed probabilities in Canada, Norway, Sweden and the UK respectively. Each figure displays in the upper row the smoothed probabilities of being in a low or high policy response regime ((coef, 1) and (coef, 2) respectively) and in the bottom row, the probability of being in a low or high volatility regime ((vol, 1) and (vol, 2) respectively). Figure 1: Smoothed probabilities - Canada 1 high response.8.6.4.2 Q2 82 Q3 89 Q1 97 Q2 4 Q4 11 1 high volatility.8.6.4.2 Q2 82 Q3 89 Q1 97 Q2 4 Q4 11 The figures emphasize that the central banks in Sweden and the UK switched from primarily responding to the exchange rate in the 198s, to responding more to inflation 1 The parameter value for Canada is now well within the band that Lubik and Schorfheide (27) reported 12

Figure 2: Smoothed probabilities - Norway high response 1.8.6.4.2 Q2 82 Q3 89 Q1 97 Q2 4 Q4 11 1 high volatility.8.6.4.2 Q2 82 Q3 89 Q1 97 Q2 4 Q4 11 and output shortly after inflation targeting was implemented in the early 199s. For Canada, the switch from high response to low response occurred a few years later, in 1997/1998. Such decline in the exchange rate response over time has not been observed in Norway, where the cental bank has responded strongly to the exchange rate both prior and post implementing inflation targeting, with the exception of the brief period in 1993/1993 when Norway formally abandoned a fixed exchange rate regime. Although the weight put on the variables in the interest rate rule vary from country to country, there is a striking similarity in the timing of the probabilities of being in a regime of high or low volatility. In particular, independent of the interest rate responsiveness to the exchange rate in the different countries, the probability of staying in a regime of low volatility is high in the 199s and until 24/25 in all countries (see the bottom row in the Figures). In all countries, there is also a high probability of staying in a high volatility regime in in the period of the financial crisis. However, only for Sweden and the UK, is there a high probability of staying in a regime of high volatility in the 198s. Interestingly, these are also the two countries that first switched into a regime of low exchange rate response. 13

Figure 3: Smoothed probabilities - Sweden high response 1.8.6.4.2 Q2 82 Q3 89 Q1 97 Q2 4 Q4 11 1 high volatility.8.6.4.2 Q2 82 Q3 89 Q1 97 Q2 4 Q4 11 Finally, we calculate duration times, that is the time spent in each state, see Table 3. As already suggested in the figure above, Norway has the highest duration in the regime where there is a high response to the exchange rate, followed by Sweden, Canada and the UK. Regarding volatility, all countries spend substantial more time in a regime of low volatility than in high volatility. How does our result compare to previous studies analysing monetary policy responses in a time invariant (constant) regime? Lubik and Schorfheide (27), estimating a DSGE model with time invariant parameters, find that the interest rate increases systematically in all countries following an exchange rate depreciation. However, the response is modest, but varies somewhat between the different countries (Canada and the UK responding the most). Using a structural VAR model, identified with long run neutrality restrictions so that monetary policy and the exchange rate can respond instantaneously to news, Bjørnland (29) also finds evidence of exchange rate responses in all countries, with the possible exception of the UK. When we allow the model to be characterised by multiple regimes, we find that only in Norway, does the central bank respond strongly to the exchange rate prior and post 14

Figure 4: Smoothed probabilities - UK high response 1.8.6.4.2 Q2 82 Q3 89 Q1 97 Q2 4 Q4 11 1 high volatility.8.6.4.2 Q2 82 Q3 89 Q1 97 Q2 4 Q4 11 implementing inflation targeting. Although Canada, Sweden and the UK have responded to the exchange rate, the response was clearly more persistent prior to adopting inflation targeting. The response in the UK is however the weakest, which is consistent with the findings in Bjørnland (29). Table 3: Duration time CA NO SW UK const state 1 Inf Inf Inf Inf Policy response low 9.47 1.713 8.657 3.246 high 1.712 3.33 2.579 1.384 Volatility low 11.58 1.19 11.68 11.94 high 1.367 2.9 2.262 1.869 15

5.3 Terms of trade Given the focus on openness in this paper, we study the response to a terms of trade shock (that increases export prices relative to import prices) in all countries. Figure?? shows the impulse responses following a terms of trade shock in the four different regimes identified in Canada (the results for the other countries are displayed in the appendix). 11 Figure 6 displays the generalized impulse responses (over all the regimes) to the terms of trade shock in Canada, Sweden, Norway and the UK. Figure 5: Impulse responses terms of trade - Canada 1 x 1 4 Output gap 1 x 1 3 PHI 8 6 1 4 2 2 3 4 2 3 6 9 12 5 3 6 9 12.5.1.15.2.25.3.35.4 Exchange rate x Interest rate (demeaned) 1 3.2.4.6.8 1.45 3 6 9 12 1.2 3 6 9 12 regime 1 (coef 1,vol 1 ) regime 2 (coef 1,vol 2 ) regime 3 (coef 2,vol 1 ) regime 4 (coef 2,vol 2 ) The impulse responses plotted in Figure?? emphasize that responding strongly to the exchange rate will exacerbate the effects of a terms of trade shock on both output and domestic inflation. In particular, the Figure emphasizes that a favorable terms of trade shock appreciates the exchange rate and increases output and inflation on impact. Since both the terms of trade and the real interest rate enters the model through expectation terms, the effect on output (and inflation) will depend on the expected interest rate response. If the central bank is in a policy regime of high interest rate response to the exchange rate (coef, 2), the exchange rate will appreciate by much less, as the interest rate will also take into account the fact that the exchange rate has appreciated. This will reverse the initial exchange rate response and push up output and inflation relative to a regime of no interest rate response. Hence, the exchange rate response reinforces the effect on output and inflation. On the other hand, if the central bank is in a regime of low response to the exchange rate, it will 11 Impulse responses to all shocks can be obtained at request. 16

ignore the exchange rate and instead increase the interest to curve the effect on output and inflation (see in particular the results for Norway in Appendix B). Figure 6 that gives the generalized impulse responses emphasizes this further. For an oil exporting country like Norway that is hit recurrently by positive terms of trade shocks (that increases output), a strong reduction in the interest rate to prevent the exchange rate from appreciating, stimulates aggregate output and inflation further (again, see Appendix B for details on the responses in the various regimes.) Figure 6: Generalized impulse responses to Terms of trade shocks - All 8 x Output gap 1 3 6 4 CA NO SW UK.3.25.2 PHI 2.15.1.5 2 4 3 6 9 12.5 3 6 9 12.1.5.5.1.15.2.25 Exchange rate x Interest rate (demeaned) 1 3 1 2 3 4 5.3 3 6 9 12 6 3 6 9 12 6 Robustness [To be completed] TO DO Global activity factor (using principal components) rather than US GDP and inflation as proxy for foreign variables. 17

Taylor rule specifications - lags Refinements to the model. Currently perfect pass through. Large response to the output gap (via foreign output). Could enforce imperfect pass through and local currency pricing. 7 Conclusion We analyze whether central banks in small open economies respond to the exchange rate. Using a Markov switching DSGE model explicitly allowing for parameter changes, we find that the size of policy responses, and the volatility of structural shocks, have not stayed constant during the sample period (1982-211). In particular, central banks in Sweden and the UK switched from primarily responding to the exchange rate (and output) in the 198s, to inflation shortly after inflation targeting was implemented in the early 199s, while Canada switched later, in 1997/1998. Such decline in exchange rate response over time has not been observed in Norway, where the central bank responds strongly to the exchange rate prior and post implementing inflation targeting (but with different intensity). Finally, we find that terms of trade shocks exacerbates the effects on output and inflation on countries that respond strongly to the exchange rate. 18

References Bjørnland, H. C. (29). Monetary policy and exchange rate overshooting: Dornbusch was right after all. Journal of International Economics 79 (1), 64 77. Bjørnland, H. C. and J. I. Halvorsen (212). How does monetary policy respond to exchange rate movements? new international evidence. Oxford Bulletin of Economics and Statistics, Forthcoming. Costa, O., M. Fragoso, and R. Marques (25). Discrete-time Markov jump linear systems. Springer. Durbin, J. and S. Koopman (21). Time Series Analysis by State Space Methods. Farmer, R., D. Waggoner, and T. Zha (211). Minimal state variable solutions to markovswitching rational expectations models. Journal of Economic Dynamics and Control 35 (12), 215 2166. Galí, J. and T. Monacelli (25). Monetary policy and exchange rate volatility in a small open economy. Review of Economic Studies 72, 77 734. Gupta, V., R. Murray, and B. Hassibi (23). On the control of jump linear markov systems with markov state estimation. In American Control Conference, 23. Proceedings of the 23, Volume 4, pp. 2893 2898. IEEE. Hamilton, J. (1994). The Time Series Analysis. Princeton Univers. Press. Kim, C.-J. and C. R. Nelson (1999, November). Has the u.s. economy become more stable? a bayesian approach based on a markov-switching model of the business cycle. The Review of Economics and Statistics 81 (4), 68 616. Liu, P. and H. Mumtaz (211). Evolving macroeconomic dynamics in a small open economy: An estimated markov switching dsge model for the uk. Journal of Money, Credit and Banking 43 (7), 1443 1474. Lubik, T. A. and F. Schorfheide (27). Do central banks respond to exchange rate movements? a structural investigation. Journal of Monetary Economics 54, 169 187. Maih, J. (212). New solutions to first-order perturbed markov switching rational expectations models. Mimeo, International Monetary Fund. Smets, F. and R. Wouters (27). Shocks and frictions in us business cycles: A bayesian dsge approach. American Economic Review 97 (3), 586 66. Svensson, L. and N. Williams (25). Monetary policy with model uncertainty: distribution forecast targeting. Technical report, National Bureau of Economic Research. Zha, T. (211). Nonlinearity in markov-switching structural models. Presentation at 1 september 211 european central bank workshop on the role of non-linear methods in empirical macroeconomics and forecasting. 19

Appendices Appendix A Data and sources We use the trade-weighted nominal effective exchange rate, NEER, from the IMFs IFS database for all countries. Note that in order to make an increase correspond to a depreciation rate, we invert the NEER. For the other series, we use the following: Canada: Terms of trade data are from the OECD Economic Outlook. The short term interest rate is the average 3-Month Treasury Bill Yield from the Bank of Canada. The CPI is from OECD MEI. We have seasonally adjusted it. Real GDP is from Statistics Canada, SA. Norway Terms of trade data are from Statistics Norway, SA. The interest rate is three month NIBOR interest rate, Norges Bank. CPI is from Statistics Norway, SA. Real GDP data is from Statistics Norway, SA. Sweden Terms of trade data are from Statistics Sweden, SA. The short term rate is average quarterly short term rate from the Swedish Riksbank from 1982. The CPI data is from Statistics Sweden, SA. Real GDP is from OECD MEI, we have seasonally adjusted it. United Kingdom Terms of trade data are from the Office for National Statistics, SA The interest rate is the three month interbank rate taken from OECD MEI [OECD MEI GBR.IR3TIB1. The CPI is from OECD MEI [GBR.CPALTT1.IXOB.Q]. We have seasonally adjusted it. Real GDP data is from the Office for National Statistics, SA 2

Foreign GDP and Inflation for the foreign variables, we use US data. Real GDP is U.S.: Gross Domestic Product (SAAR, Bil.Chn.25$), from the Bureau of Economic Analysis, S.A. The CPI is from the Bureau of Labor Statistics, SA. 21

Appendix B Extra figures Figure 7: Impulse responses terms of trade - Norway 2 x Output gap 1 3 1 1 2 3 4 5 6.3.25.2.15.1.5 PHI 7 3 6 9 12 3 6 9 12 Exchange rate Interest rate (demeaned).5.2.1.4.15.6.2.8.25.1.3.12.35 3 6 9 12.14 3 6 9 12 regime 1 (coef 1,vol 1 ) regime 2 (coef 1,vol 2 ) regime 3 (coef 2,vol 1 ) regime 4 (coef 2,vol 2 ) 22

Figure 8: Impulse responses terms of trade - Sweden 2.5 2 1.5 1.5.5 1 3 x 1 4 Output gap 1.5 3 6 9 12.5 x 1 3 PHI.5 1 1.5 2 2.5 3 3.5 3 6 9 12.5.1.15 Exchange rate 1 x Interest rate (demeaned) 1 4 1 2 3 4 5 6.2 3 6 9 12 7 3 6 9 12 regime 1 (coef 1,vol 1 ) regime 2 (coef 1,vol 2 ) regime 3 (coef 2,vol 1 ) regime 4 (coef 2,vol 2 ) Figure 9: Impulse responses terms of trade - UK 1 x 1 4 Output gap 8 6 4 2 2 3 6 9 12.5 x 1 3 PHI.5 1 1.5 2 2.5 3 3.5 3 6 9 12.5.1.15 Exchange rate 1 x Interest rate (demeaned) 1 4 1 2 3 4 5 6.2 3 6 9 12 7 3 6 9 12 regime 1 (coef 1,vol 1 ) regime 2 (coef 1,vol 2 ) regime 3 (coef 2,vol 1 ) regime 4 (coef 2,vol 2 ) 23