Evolving Macroeconomic dynamics in a small open economy: An estimated Markov Switching DSGE model for the UK

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1 Evolving Macroeconomic dynamics in a small open economy: An estimated Markov Switching DSGE model for the UK Philip Liu Haroon Mumtaz April 8, Abstract This paper investigates the possibility of shifts in the UK economy using a Markov switching open economy DSGE model. We find overwhelming evidence to reject the hypothesis that the deep structural parameters of the underlying structural model had stayed constant throughout the sample period and there is significant changes to the volatility of the structural shocks. Counterfactual experiments based on the model with the best empirical fit indicate that the change in the policy rule as well as changes to the volatility of the structural shocks over the sample period are crucial features in explaining UK s macroeconomic performance. Key Words: Monetary policy, DSGE Model, Markov Switching and Bayesian estimation JEL codes: E5; F3; C3 Introduction The United Kingdom (UK) has experienced major structural and economic changes over the last three decades. A large empirical literature has argued that these changes have manifested themselves as shifts in the dynamics of macroeconomic variables. For example The authors thank the editor, Paul Evans, and an anonymous referee for their comments that have helped improve the paper. We also would like to thank Francesco Bianchi for his advice on model solution and participants at the Bank of England and the Reserve Bank of New Zealand seminars for useful comments. The paper does not reflect the views of the Bank of England or the International Monetary Fund. Economist, Strategy, Policy, and Review Department, International Monetary Fund, pliu@imf.org. Advisor, Center for Central Banking Studies, Bank of England, Haroon.mumtaz@bankofengland.co.uk.

2 Benati (4), Mumtaz and Surico (6) and Benati (8) show that the 97s and the 98s were characterised by volatile inflation and output growth. In addition, the persistence of inflation was estimated to be high during this period. In contrast, the period after the introduction of inflation targeting in 99 was associated with low inflation and output volatility and low inflation persistence. A related strand of this research has focussed on establishing links between changes in inflation and output dynamics and the change in the operation of monetary policy in the UK. Using a time-varying structural vector autoregression (VAR) model, Benati (8) argues that a fall in the volatility of demand and supply shocks can explain most of the recent stability in the UK s output and inflation with monetary policy playing a negligible role. On the other hand Nelson () found that prior to the adoption of inflation targeting in 99, UK interest rates rose less than one-for-one with increases in inflation. Nelson and Nikolov (4) argue that inflation outcomes in the 97s resulted from a combination of a weak response of monetary authorities to inflation and mis-measurement of the degree of excess demand. In a recent contribution Castelnuovo and Surico (5) show that the impact of (contractionary) monetary policy shocks on inflation was substantially different in the pre and post-inflation targeting period. The inflation response was large and positive in the earlier sub-sample, but smaller and negative after 99. This paper revisits this debate using an open economy structural dynamic stochastic general equilibrium (DSGE) model. VAR-based studies on this issue are often subject to a number of criticisms. First, these empirical studies are typically formulated in a closed economy setting. This is surprising given the fact that the UK is a small open economy (SOE) and international developments have become increasingly important especially during the recent financial crisis. Second, although VAR-based studies have the distinct advantage of simplicity and flexibility, identification of shocks is not uncontroversial. Benati and Surico (9) show that this problem may be especially important when the VAR model is used to uncover possible changes (across time) in the role of monetary policy and/or a change in the transmission mechanism. The approach in this paper mitigates these criticisms. In particular, we examine the evolving structure of the UK economy using an estimated open economy DSGE model in which the parameters of key structural equations are assumed to be subject to regime shifts, i.e. evolve as a Markov switching process. As in Davig and Leeper (7) and Farmer, Waggoner, and Zha (8), the model is solved under rational Two VAR-based exceptions are Mumtaz and Sunder-Plassmann (9) and Liu and Mumtaz (9)).

3 expectations and counterfactual experiments conducted in this framework have model consistent expectation. We estimate different versions of the model using Bayesian methods and examine the dynamics of the UK economy using the version that provides the best fit to the data. This analysis contributes to the literature on the UK transmission mechanism along two important dimensions. First, this is the first application of a Markov Switching DSGE model to UK data. Previous work examining changing UK macroeconomic dynamics has been largely based on time-varying VARs (Benati (8)) and or single-equation models (Nelson ()). In contrast, our approach allows one to gauge the sources of structural change in a systematic manner and link it to possible changes in deep parameters. Second, this is the first attempt (to our knowledge) to estimate an open economy DSGE model with Markov Switching. This extends the split-sample analysis by Lubik and Schorfheide (7) to a framework where agents have full knowledge of the possibility of regime shifts and takes this into account when forming expectations. We estimate four versions of the Markov switching DSGE model: () a version that allows a regime shift in shock volatilities, () a version allowing for (independent) shifts in shock volatility and parameters of the domestic Phillips curve, (3) allowing for (independent) shifts in shock volatility and parameters of the process for import price inflation and (4) allowing for (independent) shifts in shock volatility and parameters of the monetary policy rule. These possible sources of structural change have been highlighted in previous work on the UK economy. This paper is one of the first to consider them in a unified structural framework. We find that all of these models are preferred to the model with fixed parameters. Furthermore, the model with shifts in shock volatility and Taylor rule parameters provides the best data fit. Estimates from this model suggest that the mid 97s were characterised by a low reaction to inflation by the monetary authorities. In contrast, the central bank reacted more to output fluctuations and the change in the nominal exchange rate over this period. We find that this change in the policy rule had important consequences for the dynamics of macroeconomic variables such as output and inflation: Output, inflation and the real exchange rate responded more to monetary policy shocks during the mid-97s regime. Similarly, the response of inflation to cost-push and technology shocks was significantly larger during this regime. Counterfactual experiments which impose higher reaction to inflation over the entire 3

4 sample period lead to lower and less volatile inflation during the mid-97s. This provides evidence that systematic monetary policy played an important part in determining inflation outcomes in the mid-97s. A similar result is obtained by imposing the low variance regime on the entire sample, indicate the importance of shocks (as well as systematic policy) for the UK s macroeconomy over the sample period. This result represents an important contrast to VAR-based analyses (see Benati (8)), where the role of policy was found to be negligible. The paper is arranged as follows: Section describes the linearised DSGE model, the solution method for forward looking Markov switching models and the algorithm to estimate the parameters of the model. Section 3 presents the parameter estimates for the various Markov switching models we consider. In section 4, we consider which of the estimated models provides the best fit and present impulse responses, historical decomposition and counterfactual experiments based on the selected model. Finally, section 5 concludes the main findings. Estimation of the Markov Switching DSGE Model. A small open economy DSGE model The model that we analyse is taken from Justiniano and Preston (9) and is a generalisation of the models developed in Gali and Monacelli (5) and Monacelli (5). In particular, Justiniano and Preston (9) introduce incomplete asset markets, habit formation and indexation of prices to past inflation. We refer the reader to Justiniano and Preston (9) for a detailed derivation of the model. Here, we provide a brief description of the key equations of the log linearised model, and Table () provides a complete list of the linearised model equations. Solving the households intertemporal utility maximisation problem gives the following log-linearised Euler equation ( + h)c t = hc t + E t c t+ h σ (i t E t π t+ ) + h σ (ɛ g,t ρ g ɛ g,t ) () where the log of current consumption c t depends on past, future consumption and the real rate of interest i t E t π t+. h denotes the degree of habit persistence, σ denotes the inverse elasticities of intertemporal substitution and ɛ g,t is a preference shock. The Phillips curve 4

5 for domestic price inflation is defined as ( + βδ H )π H,t = δ H π H,t + βe t π H,t+ + ( θ H)( θ H β) θ H mc t () and the marginal cost mc t is given by mc t = ϕy t ( + ϕ)ɛ a,t + αs t + σ h (c t hc t ) (3) where π H,t is domestic price inflation, y t denotes domestic output, s t denotes terms of trade, ɛ a,t is an exogenous technology shock, ϕ is the inverse elasticity of labour supply and α is the import share. Equation () states that domestic inflation is related to expected future inflation via the discount factor β, inflation lagged one period through the degree of indexation δ H and to marginal cost via γ = (θ H)(θ H β) θ H, where θ H is the fraction of firms that can not optimally adjust their price every period. In the small open economy setting, domestic price inflation depends on several sources of foreign disturbances through the marginal cost term in equation (3). In particular, there is a direct effect from the terms of trade and a indirect effect that operates through the goods market clearing condition y t = ( α)c t + α[η(s t + q t ) + y t ] (4) where y t denotes foreign output and q t denotes the real exchange rate. Equation (4) shows that domestic production is the sum of domestic consumption plus exports to the rest of the world. As in Monacelli (5), import retailers are assumed to be monopolistic competitors and this is a feature that introduces deviations from the law of one price for imported goods. Solving the retailers optimisation problem gives the following Phillips curve for import price inflation ( + βδ F )π F,t = δ F π F,t + βe t π F,t+ + ( θ F )( θ F β) θ F ψ F,t + ɛ cp,t (5) where π F,t denotes domestic currency import price inflation, ψ F,t = q t ( α)s t denotes deviations from the law of one price and ɛ cp,t is the exogenous cost-push shock. Equation (5) states that import price inflation depends on its lag via the indexation parameter δ F, expected future inflation and marginal cost captured by the law of one price (LOP) gap. As the fraction of importing firms that can not optimally adjust price (θ F ) tends to, the 5

6 deviations from LOP becomes smaller. Justiniano and Preston (9) introduce incomplete asset substitution between domestic and foreign bonds gives the following uncovered interest rate parity condition E t q t+ q t = (i t π t+ ) (i t π t+) + χa t + ɛ φ,t (6) where a t denotes the level of foreign assets position, χ is the debt elasticity with respect to the interest rate premium and ɛ φ,t is the risk premium shock. The foreign assets budget constraint is simply defined as c t + a t = a β t α(q + αs t ) + y t. The model is closed by assuming the behaviour of the monetary authority is described by the following Taylor-type interest rate rule: i t = ρ i i t + ( ρ i ) [λ π t + λ y t + λ 3 e t + σ m η m,t ] (7) where e t is the change in the nominal exchange rate, η m,t is the interest rate shock, ρ t is the degree of interest rate smoothing, λ, λ and λ 3 are the reaction coefficients to inflation, output and the change in the nominal exchange rate. The model consists of model variables X t (including 4 expectation terms) and 8 exogenous processes Z t. These 8 exogenous processes constitute the structural shocks included by Justiniano and Preston (9) : () preference shock ɛ g,t () technology shock ɛ a,t (3) import cost-push shock ɛ φ,t (4) risk premium shock ɛ φ,t (5) monetary policy shock η m,t (6) foreign output shock ɛ Y,t (7) foreign inflation shock ɛ π,t (8) foreign interest rate shock ɛ I,t. The model can be rewritten in matrix form as Γ X t+ = Γ X t + ΨZ t + Πη t (8) Under rational expectation and no regime shifts, the model in equation (8) can be solved using a standard rational expectation algorithm such as the Gensys solution method proposed in Sims (). This returns the solution in the form of X t = G (Φ) X t + AZ t (9) where Φ denotes the structural parameters of the model. Equation (9) can be combined with an observation equation of the form Y t = HX t () 6

7 where Y t represents the observed data and H is the loading matrix. The Kalman filter algorithm can then be used to evaluate the likelihood function and estimate the underlying parameters.. Solution and estimation of the Markov switching model We consider the possibility of structural change in the UK economy by allowing key equations in Table () to be subject to regime shifts. In particular, we estimate three versions of the model that allow for: (i) Markov switching in the policy rule (equation (7)), (ii) Markov switching in the domestic price inflation Phillips curve (equation ()), and (iii) Markov switching process for import price inflation (equation (5)). In each case, we allow for independent regime switching in the volatility of the eight structural shocks. We compare these estimated models with restricted specifications that either only allow a regime switch in the volatility or rules out regime shifts all together. Cases i, ii and iii are of particular interest as they represent the key dimensions along which the structure of the UK economy may have changed and have been highlighted in previous work on the UK economy. For example, a large (mostly reduced form or single-equation) literature has argued that the parameters of the UK monetary policy rule changed after the introduction of inflation targeting in 99 (e.g. Nelson ()). Similarly, several studies focus on possible changes in inflation persistence (e.g. Benati (4)) and the possibility of a change in exchange rate pass-through (Mumtaz, Oomen, and Wang (6)). Our specification allows us to approach these issues within an unified structural framework and to consider the relative importance of each scenario. To specify the Markov switching DSGE model, we partition the parameter vector Φ into three blocks Φ = {Φ S ; Σ s ; Φ} where Φ S denotes the parameters that are subject to regime shifts, Σ s denotes the variance of the regime switching volatilities, while Φ are the remaining time-invariant parameters. The superscript S denotes the unobserved regime associated with the deep parameters and is assumed to take on the discrete values S =,. The superscript s =, denotes the unobserved regime associated with the volatilities and evolves independently of S. The two state variables S and s are assumed to follow a first order Markov chain with the following 7

8 transition probability matrices respectively: P = P P P P and Q = Q Q Q Q where P ij = p (S t = j S t = i) and Q ij = p (s t = j s t = i). Note that an alternative approach is to model time-variation by allowing for drift in the structural parameters within a non-linear DSGE model as in Fernandez-Villaverde and Rubio-Ramirez (7). However, the computational burden inherent in this approach implies that time-variation can only be introduced one parameter at a time. This constraint is quite limiting in our context where the interest lies in possible shifts in structural equations. While it may be interesting to consider one parameter shift at a time for the Phillips curve or the policy rule, our aim is to gauge the macroeconomic impact of shifts in the (entire) policy rule or equations governing domestic and import price dynamics. Therefore, the Markov switching approach is preferred for our application. The regime switching DSGE model for regime S can re-written as Γ ΓS, Γ, X t+ = Γ ΓS, Γ, X t + Ψ ΨS Π Z t + η t () Π We follow the method described in Farmer, Waggoner, and Zha (8) to solve the model in (). The technical appendix provides a more detail description of the solution method. Farmer, Waggoner, and Zha (8) proceed by re-writing the Markov Switching DSGE model as a fixed parameter model in an expanded state vector: Γ Xt+ = Γ Xt + Ῡu t + Πη t () where the parameter matrices Γ, Γ, Ῡ and Π are functions of structural parameters and the transition probabilities. Farmer, Waggoner, and Zha (8) define a minimum state variable (MSV) solution to the system () and provide a method to check for existence and uniqueness of the solution. Moreover, they prove that the MSV solution to the expanded system () is an MSV solution to the original model in (). If a unique solution exists then this can be written as a Markov Switching VAR X t = G S X t + A S Z t (3) 8

9 Alternative solution methods are described in Davig and Leeper (7) and Svensson and Williams (7). However, as discussed in Farmer, Waggoner, and Zha (8), these methods do not provide a diagnostic to check for uniqueness of the solution. We find that the Farmer, Waggoner, and Zha (8) solution method works well even in our relatively large-scale model with the iterative procedure converging rapidly in most cases. Combining equation (3) with the observation equation in () gives the following state space model with Markov switching: X t = G S X t + A S Z t, where Z t N(, Q s ) Y t = HX t (4) where the Markov states S and s evolve independently with transition probability matrices P and Q respectively. The presence of the unobserved DSGE states X t and the unobserved Markov states implies that the standard Kalman filter can no longer be used to provide inference on X t and to calculate the value of the likelihood. Inference using the standard Kalman filter is only based on information up to time t. However, with the presence of the unobserved Markov states, inference has to be conditioned on both current and past values of S and s. As noted by Kim and Nelson (999), each iteration of the filter implies an M fold increase in the number of cases to consider (where M denotes the number of regimes) making the computation problem intractable fairly rapidly. Kim and Nelson (999) propose an approximation which makes this filter operational. The key feature of this approximation is that a limited number of states are carried forward in the Kalman filter iterations each period, these are then collapsed at the end of each iteration. To apply this algorithm in our setting, we start by defining a new state variable St which indexes both S t and s t and has a four state transition matrix given by P = P Q. Following Kim and Nelson (999) and Davig and Doh (8), we track St, St and St, which implies we account for 4 3 = 64 possible paths for the state variables at every point in time. Intuitively, Kim and Nelson (999) s algorithm (detailed in the technical appendix) involves running the Kalman filter for each of the paths and then taking a weighted average using the weights given by the probability assigned to each path from the filter proposed in Hamilton (989). We adopt a Bayesian approach to model estimation. In particular, we combine the approximate likelihood function (obtained via the procedure described above) with prior distributions We have assumed no measurement errors. 9

10 for the parameters and use a random walk Metropolis Hastings algorithm with, replications to approximate the posterior. Details on implementation and convergence are provided in the technical appendix to the paper. We estimate the baseline rational expectations with no regime switching and four versions of the Markov switching DSGE model, and section (4) compares the relative fit of these models against the data: Model : Rational expectations with no regime switching. Model : Rational expectations with -state Markov switching in the volatility of the structural shocks (this does not require any adjustments to the standard rational expectation solution algorithm because certainty equivalence holds in our linear framework). Model : In addition to the switching in the volatility of the shocks, we also allow for the parameters of the domestic price inflation Phillips curve (θ H and δ H in equation ) to follow an independent -state Markov process. This is useful to assess whether the domestic structural Phillips curve has changed over time. Model 3: Similar to model, the third case allows for regime switching in the import price inflation equation (θ F and δ F in equation 5). This can be used to assess whether exchange rate pass-through have changed over time. Model 4: The fourth version of the estimated model considers regime switching in the open economy Taylor rule (ρ i, λ, λ, and λ 3 in equation 7) to assess changes to the monetary policy reaction function. Model 5: The final version of the model allows two regimes for all structural parameters in the model but assumes that agents do not form expectations about the possibility of a regime shift. Instead, the model is solved in each regime independently (using Gensys). This proxies a sample split or breakpoint type approach to modeling structural change... Priors specifications The prior distributions along with the lower and upper bounds for the model parameters are summarised in Table (). These are based on the prior distributions in Justiniano and

11 Preston (9) and Lubik and Schorfheide (7). We calibrate the degree of openness parameter α to be.85 which is equal to the average shares for imports and exports share in the UK. We assume the degree of risk aversion (inverse of the intertemporal elasticity) σ follows a Gamma distribution with a mean of and a standard deviation of., and this is in line with the values suggested by Rotemberg and Woodford (999). Similarly, the inverse Frisch elasticity of labour supply ϕ and elasticity of substitution between domestic and foreign goods η are both assumed to have a mean of.5 and a quite large standard deviation of.75 because of wide range of these estimates in the literature. The degree of habit persistence h follows a Beta distribution with a mean of.8 and a standard deviation of.. Both of the Calvo pricing parameters θ H and θ F are assumed to follow a Beta distribution centered around.5 and a standard deviation of.. indexation parameters are found to be crucial in fitting the dynamics of inflation, here we adopt a fairly agnostic view by specifying very loose priors for δ H and δ F The (mean centered around.5 and standard deviation of.5). The debt elasticity with respect to the interest rate premium χ is assumed to follow a Gamma distribution with a mean of. and a standard deviation of.. We follow Justiniano and Preston (9) in setting the priors for the parameters of the Taylor rule. The prior for the interest rate smoothing coefficient is assumed follow Beta distribution with a mean of.5 and a standard deviation of.5. For the reaction coefficients, they are assumed to follow a Gamma distribution with means of.5,.5 and.5 for inflation, output and exchange rate changes (the standard deviations are.5,.3 and.3 respectively). The autoregressive parameter for the exogenous stochastic disturbances (risk premium, technology, preference, import cost-push, foreign inflation, foreign output and foreign interest rate shocks) are all assumed to follow a Beta distribution with a mean of.5 and a standard deviation of.5. The priors for the standard deviation of these shocks follow an inverse Gamma distribution with very wide variance (mean of.5 and a standard deviation of ). Finally, we follow Sims and Zha (6a) in specifying a Dirichlet prior for the transition probabilities, with the scale matrix chosen to reflect the belief that regimes are persistent. The parameters for the Dirichlet distribution is assumed to be α = 8 and α =, this gives the probability of staying in the same regime to be We also assume the priors on the model s structural parameters are symmetric across the different regimes. 3 Let α = α + α, the mean of the Dirichlet(α + α ) distribution is E (x i ) = αi α.

12 .. Data description UK data from 97Q to 9Q is used for the estimation of the model. Quarterly observations on UK GDP (y t ), real effective exchange rate (q t ), import price deflator (P F,t ), quarterly nominal interest rate (i t ), overall CPI (P t ) are taken from the Office for National Statistics and Bank of England databases. US quarterly nominal interest rate (i t ), overall CPI (P t ) and GDP (y t ) are taken from the St Louis Fed FRED database. We take logs of all the series apart from the nominal interest rates. The first difference of the import price deflator, UK CPI and US CPI series is used to approximate import price inflation, domestic inflation and foreign inflation. To compute the domestic and foreign output deviations from the model steady state, we detrend the UK and U.S. GDP data separately using a HP filter. Lastly, all variables are rescaled to have a zero mean over the sample. 3 Parameter Estimates 3. Time-invariant rational expectation model Table (3) presents the mean of the posterior parameter estimates across the five models we consider and the 95% probability intervals are shown in parenthesis. The first column presents the baseline time-invariant rational expectation model. The estimated value for the intertemporal elasticity of substitution σ is.8, which is slightly higher than the value reported in Lubik and Schorfheide (7) for the UK and smaller than Justiniano and Preston (9) found for other SOEs. 4 The posterior estimate for the inverse elasticity of labour supply ϕ is higher than the range of estimates reported in Justiniano and Preston (9). This may reflect our sample coverage of periods where the labour markets in the UK were more rigid. The mean estimate for the elasticity of substitution between foreign and domestic goods η is.9, which reflects UK s small open economy position and the estimate is consistent with other SOE. The estimated value of the Calvo parameters θ H and θ F suggest home goods prices are optimised around every quarters and import prices adjust less frequently at around 7 quarters. In contrast to other studies for the UK, such as DiCecio and Nelson (7), we find consumption habits and inflation indexation play a limited role in the model. This finding is consistent with the results reported in Justiniano and Preston (9) where 4 The results for the UK reported by Lubik and Schorfheide (7) are in the working paper version of their paper.

13 the authors argue that this is because of the set of autoregressive shocks chosen for the model. The interest rate smoothing coefficient in the policy rule is estimated to be.8. The inflation reaction coefficient is estimated to be.5, this is in line with the results reported in DiCecio and Nelson (7) over a similar sample period. However, the coefficient on output is found to be relatively small, around.. In contrast to the result reported by Lubik and Schorfheide (7), we find the coefficient on the exchange rate to also be quite small, around.. This may reflect the wider coverage of our data sample, which includes the 97s and the most recent inflation targeting experience. The results are consistent with the findings by Justiniano and Preston (9). One noticeable aspect of the baseline estimation is the very high degree of persistence for the domestic shocks. The autoregressive coefficients for preference (ρ g ) and risk premium shocks (ρ φ ) are very close to unit root, this partly explains the low degree of intrinsic persistence the model captures. On the other hand, the persistence of the foreign shocks is similar to the ones reported in Justiniano and Preston (9). 3. The model with switching variances The second and third column of Table (3) present the estimated parameters of our first Markov switching specification M, i.e., the model that only allows the volatility of shocks to switch across the two regimes. Although this specification is fairly restrictive in a sense that it does not allow the structure of the economy to change, it is instructive to consider the parameter estimates from this model as a comparison to the more flexible specifications presented below. Consider the time-invariant parameter estimates. These estimates are similar to those obtained in the fixed parameter specification above. There are a few noticeable differences. In particular, the estimated elasticity of substitution between domestic and foreign goods is significantly smaller at.7, while the reaction to inflation in the policy rule is somewhat larger at.7. Moreover, the estimated autocorrelation of structural shocks is generally smaller than the fixed parameter specification. The bottom panels of the table present the estimates of the variance of shocks in the two regimes and the associated transition matrix Q. The estimates of Q indicate that both regimes are fairly persistent, on average, lasting for about four years. Regime is the high-volatility state, with the posterior estimate of the shock variances substantially larger. The difference across regimes is largest 3

14 for domestic shocks where all estimates show a significant change in volatility with no overlap across regimes in the 95% confidence bands. Consistent with VAR-based studies, the variance of the monetary policy shock σ M displays a large change across the sample, with the regime estimates less than half of that in regime. The top left panel of figure () plots the posterior mean of the filter probabilities associated with the high-variance regime. The figure shows that the high-volatility state, regime was dominant during the 97s and the early 98s. The mid-98s saw a brief switch to regime, but the probability of the high-volatility state increased again towards the end of the 98s and beginning of the 99s. The inflation targeting period was largely associated with the low-volatility state. However, the recent financial crisis was clearly associated with the high-volatility state. Note that this pattern of volatility shifts is very similar to those reported by time-varying VAR-based studies (see Benati (8) and Groen and Mumtaz (8)). 3.3 The model with the switching domestic Phillips curve The second Markov switching specification that we investigate allows regime shifts along two dimensions. First, as in the specification described in section 3., the variance of the structural shocks is regime dependent. Secondly, we allow the parameters of the Phillips curve (equation ) to follow an independent Markov process. The fourth and fifth columns in table (3) summarise the posterior parameter estimates for this model denoted as M. The time-invariant estimates are very similar to those obtained for M and M. In particular, the estimated parameters for the policy rule and the parameters of the import price inflation equations are virtually identical to that of M. The estimated parameters for the equation for import price inflation (equation 5) are also very similar to the variances-only model. The regime dependent estimate of the indexation parameter δ H indicates a slightly higher value of indexation in regime. However, the relatively large error bands in both regimes indicate that evidence for a systematic shift in this parameter is weak. In contrast, there is a significant shift in the Calvo parameter θ H with regime coefficient almost twice as large as that in regime. Note that the 95% error bands are quite tight in both regimes with no overlap across regimes, which indicates strong evidence for a systematic shift in this parameter. The coefficients imply domestic prices are re-optimised every 3.5 quarters in the first regime and around quarters in second. The second row right panel of figure () shows the filter probability of the second regime associated with the switching domestic Phillips curve 4

15 parameters Pr (S t = Y t ), which can be interpreted as the low price stickiness regime. This probability was high in the mid 97s, the early and the mid-98s, the early 99s and finally during the recent recession in 8/9. In figure (), we plot this probability along with the output and CPI inflation for the UK. It is interesting to note that regime is clearly associated with periods of low GDP growth. Similarly, the fluctuations in CPI inflation are higher in this regime. That is, this regime is associated with the great inflation of the mid and the late 97s, the inflationary episodes during the mid-98s and the early 99s and fluctuations in inflation seen during the last year. These results suggest that the degree of price stickiness is lower during periods characterised by recession and/or large changes in inflation. This pattern of change in the degree of price stickiness matches the predictions of the literature on time-dependent pricing (see for example Dotsey, King, and Wolman (999)). With time-dependent pricing, firms face menu costs in adjusting prices. However, the cost associated with keeping prices fixed becomes larger in periods associated with higher inflation variability resulting in a decrease in price stickiness during these periods. Our results are therefore more in line with the time-dependent pricing specification than Calvo pricing that underpins the model presented in section. 5 The bottom panels of table (3) present the estimated regime switching shock variances. As before, regime is the high-volatility state with both foreign and domestic shocks are substantially more volatile. The second row (left panel) of figure () indicates the timing of the volatility regimes are closely matched with that of model. 3.4 The model with switching import price dynamics Next, we allow for regime switching in the Phillips curve for import price inflation (equation 5), the posterior estimates are shown in sixth and seventh column of Table (3). The estimate of θ F is higher in regime suggesting that this regime is associated with higher degree of import price stickiness. Note, however, that the error bands around the estimates of this parameter in both regimes are large with little evidence that there is a statistically significant shift in this parameter. Similarly, while the point estimate of δ F is substantially higher in regime, the large error bands do not support a systematic shift in this parameter. Similar conclusion can be drawn from the third row right panel of figure () which shows the estimated filter probability of regime associated with the structural parameters. The sample is dominated by regime with Pr (S t = Y t ) close to zero over most of the sample 5 Similar results were reported by Fernandez-Villaverde and Rubio-Ramirez (7) for the US. 5

16 period. Although many reduced form VAR-based studies have documented a decline in import price pass-through for the UK (see Liu and Mumtaz (9)), we find only weak evidence of a systematic switch in the structural parameters of the import price Phillips curve. In contrast, the left panel of the third row of figure shows clear evidence of shift in the shock variances. Note that for this model, Pr (s t = Y t ) corresponds to the low-volatility regime. The figure shows that the timing of the volatility regimes are consistent with with the previous two estimated models. 3.5 The model with the switching Taylor Rule We investigate possible changes in the monetary policy rule by allowing all the coefficients of equation (7) to be regime dependent (along with shock variances as above). The eight and ninth column of table (3) present both the estimated regime dependent and time-invariant parameters. The estimated value of P suggests that the first regime is highly persistent. This regime is characterised by a strong reaction to inflation with the posterior mean of λ estimated at.8. In contrast, the mean estimate of λ in regime is slightly lower at.5. Note that the second regime is also characterised by significantly higher interest rate smoothing. The point estimates of λ and λ 3 suggest that regime was associated with a stronger reaction to the output and exchange rate changes. However, the difference across regimes does not appear to be significant with the confidence intervals over-lapping. In figure (3) we explore the differences across regimes in the estimated coefficients further. The left panels of the figure plot the estimated posterior distribution of λ, λ and λ 3 across the two regimes. Consider the top left panel. The panel clearly shows that the mass of the estimated regime distribution of λ lies to the right of the regime distribution. Note that while the Taylor principle does not apply directly in this open economy Markov switching setting, it is interesting to note that the regime distribution of λ includes values below in its lower tail pointing to the fact that this regime was associated with a weaker reaction of the central bank to inflation. Note that as there is a significant shift in the degree of interest rate smoothing across regimes, it is also useful to compare the distribution of the impact coefficient on inflation in the policy rule λ ( ρ). The top right panels of figure (3) plot the posterior distribution of λ ( ρ) in both regimes. It is immediately clear that once interest rate smoothing is accounted for, regime is clearly associated with a significantly higher reaction to inflation by the monetary authority. 6

17 The second and third panels of the figure show the estimated posterior for λ and λ 3, respectively. The regime estimates of these parameters are relatively imprecise with a wide posterior distributions. Once, fluctuation in interest rate smoothing is accounted for, the impact coefficients on the output and the exchange rate are similar across regimes (see the right panels of figure 3). There are a number of different ways of interpreting the result that regime is associated with higher interest rate smoothing. First, following conventional wisdom that the high estimate of ρ may reflect the fact that this regime saw a more gradual adjustment of interest rates by the monetary authority. Alternatively, as suggested by Rudebusch (), higher smoothing may reflect more persistent shocks during this period. Finally, the high estimate of ρ could also reflect that the true policy rule over this period may contain other variables beyond output, inflation and the exchange rate that is examined here. The fourth row and right panel of figure () shows the estimated filter probability of the coefficient regimes. The sample is dominated by regime with regime concentrated in the mid 97s. In particular, Pr (S t = ) >.5 over the period 975Q to 978Q, suggests that these three years were associated with a weaker reaction by monetary authorities to inflation. In contrast, the onset of the premiership of Margaret Thatcher was associated with a larger response to inflation fluctuations. DiCecio and Nelson (9) present narrative evidence that suggests that the 97s were characterised by policy makers with unorthodox views on the causes of inflation, believing for example that monetary restraint was not sufficient for controlling inflation in the long run. Our estimates of the switching Taylor rule are consistent with DiCecio and Nelson s 9 evidence in the period. The left panel of the fourth row of figure shows that the high-variance regime (regime ) dominated the pre-inflation targeting period, with high-volatility again returning in the last few quarters. While these results highlight changes in the reaction of the UK monetary authority to inflation, they also suggest that the reaction to the exchange rate has not changed significantly over time. This is somewhat surprising given UK s membership in the Exchange Rate Mechanism (ERM) over part of the sample. 6 One explanation is that our framework treats the US as the foreign country while the Pound was linked to the German Deutschmark over this period. However, Clarida, Gali, and Gertler (998) demonstrate that even if the Sterling/Deutschmark rate was directly included in the policy rule, this only yields a very small coefficient. In contrast, they find that the German short-term interest 6 UK was a member of the ERM from 99 to 99. 7

18 rate was the most important variable. This suggests a different policy rule maybe required to describe the ERM period and it is left as future work. To check the sensitivity of these results to the prior distribution chosen for the policy rule parameters, we re-estimate the model using a larger prior variance for the inflation coefficient. In particular, we double the prior variance to.5 to see if this would yield a lower inflation reaction coefficient for regime. 7 Our initial results are robust to this alternative prior specification. Using a simple closedeconomy DSGE model, Davig and Doh (8) also found similar results for the US where the estimated inflation coefficients across both regimes exceeded. This is in contrast to Clarida, Gali, and Gertler (998) and Lubik and Schorfheide s (4) who found indeterminacy, such that the monetary policy authority does not raise nominal interest rate aggressively enough in response to inflation, was a pervasive feature in the US economy before 979. Davig and Doh (8) and our results demonstrate that once we allow for changes in the volatility of the structural shocks, the weak response to inflation developments becomes less apparent. By comparing the estimates between model M and M (discussed earlier) also reveal similar conclusion. 4 Model selection and time-varying dynamics of the UK economy The results in the above sections highlight key structural changes in the UK economy. In order to establish the empirical relevance of these structural shifts, we compare the relative fit of the estimated models. version of the estimated DSGE model discussed above. In particular, we estimate the marginal likelihood for each The model associated with the largest marginal likelihood is then used to characterise the time-varying dynamics of the UK economy. The marginal likelihood is estimated via the modified harmonic mean method (see technical appendix). Table (4) presents the estimated value of the log marginal likelihood for each version of the model that we consider. It is clear from the table that the time-invariant DSGE model, with the lowest marginal likelihood, is strongly rejected by the data. Within, the Markov 7 Note that the fact that we find a lower coefficient on inflation during the mid-97s is consistent with Nelson (). Nelson (), however, also allows for several additional breaks in the sample while our model focuses on two unobserved regimes. We retain the assumption of two regimes, because the additional computational burden inherent in having more than two regimes makes estimation of several Markov switching DSGE models infeasible. 8

19 switching DSGE models, Model M has the lowest marginal likelihood which suggests that it is not simply the volatility of structural shocks that has changed over time but also the structure of the economy. Model M and Model M 3 are fairly similar in terms of the estimated marginal likelihood. However, Model M 4 which allows the policy rule to switch is clearly preferred. This suggests that for the UK economy, a change in the policy rule as well as a change in shock variances is a crucial feature of the data. A remaining question of interest is whether a fit similar to model M 4 can be achieved by splitting the sample (apriori or by incorporating switching in the DSGE model) at appropriate dates and ignoring the possibility that agents form expectations about the change in regime. Model M 5 is an attempt to proxy this approach to modelling time-variation. This model allows all parameters to switch but the possibility of switching is not reflected in the model solution. In other words, agents do not form expectations about the possibility of regime shifts. Instead, the solution of the model is solved separately in each regime using the standard rational expectations algorithm rather than the solution method outlined in section (.). The estimation of this model, therefore, proxies a sample split or structural break approach to investigating shifts in structural parameters adopted in a number of recent papers. The last two columns of Table (3) show that the estimates from this model and suggest two interesting observations. First, a large change in the policy rule, with regime (prevalent in the mid-97s see last row of figure ()) associated with a smaller reaction to inflation. Second, a large change in the volatility of structural shocks. However, the marginal likelihood of this model is lower than that of model M 4. This suggests agent s expectation of regime switches is an important feature of the observed data for the UK. Finally, we consider the role played by the open economy feature of our model. We re-estimate model M4, but suppress the role of the exchange rate and the influence from the rest of the world by setting the import share (α) and the Taylor rule coefficient on the exchange rate (λ ) to zero. 8 This restricted model displays a substantially diminished fit with an estimated marginal likelihood of indicating that the open economy dimension of the model is an important feature for the UK. Furthermore, in the absence of the exchange rate channel, the model attributes a higher interest rate response with respect to output fluctuations. 8 Detailed estimation results for this version of the model are available from the authors. 9

20 4. Evolving dynamics of the UK economy In this section, we use the preferred model based on the marginal likelihood (Model M 4 ) to examine changes in UK macroeconomic dynamics. First, we look at the impulse response functions of the estimated model to key structural shocks across the two regimes. In addition, we compute the historical decomposition to evaluate the role of different shocks in driving the key macroeconomic variables. Finally, we present a series of counterfactual experiments to examine the role of (systematic) monetary policy in bringing about changes in the dynamics of the UK economy. 4.. The evolving impact of structural shocks Figure (4) presents the impulse response to a monetary policy, cost-push and productivity shock in each regime for domestic output, real exchange rate, interest rate and inflation. 9 The first two columns present the impulse responses in regime (high/active inflation reaction) and regime respectively. The third column presents the difference in the estimated impulse response functions across the two regimes. For the monetary policy shock, there are interesting differences across the two regimes. The response of output, inflation and the real exchange rate under the passive inflation regime is significantly larger than the estimate in the active regime. This suggests for a given monetary policy shock, the policy rule in the mid-97s would have resulted in a larger fluctuations in the macro-economy compared with the rest of the sample. This is in contrast to most of the VAR-based evidence that has tried to characterise changes in the impact of monetary policy in the UK. For example, Benati (8) reports little change in the response of inflation and output to a monetary policy shock using a time-varying structural VAR model. As argued in Benati and Surico (9), this difference between structural VAR and DSGE based impulse responses may reflect the inability of VARs to accurately distinguish between changing (underlying) shock volatility and coefficient shifts. The role of changing monetary policy is also evident from the response of inflation to a cost-push shock. The regime response of inflation is three times larger (on impact) than 9 As in Sims and Zha (6a), the impulse response functions are estimated for each regime separately. We do not, for example, take into account the possibility of a regime switch once a shock occurs. We also estimate a Markov switching VAR model based on our UK dataset, and the results are available upon request. The results indicate that while the estimated VAR identifies strong shifts in the shock volatility, there is little evidence to suggests shifts in the VAR parameters.

21 the regime response. On the other hand, the nominal interest rate response is slightly larger in regime and results in larger contraction in output. While the inflation response within regime is smaller, this comes at a cost of larger output fluctuations. Similarly for the productivity shock, the inflation response in regime is also larger while the output response is somewhat smaller. In general, the estimated impulse response functions point to significant changes in the dynamics of inflation. With a more active monetary policy response from the central bank, inflation variations are generally lower in the face of structural shocks to the economy. However, the lower inflation variability comes at the cost of higher output variability in general. Therefore, the lower output variability observed in the second part of the sample can be largely attributed to factors other than changes in the monetary policy rule. 4.. Historical shock decomposition To investigate the role of key structural shocks in driving the UK s macroeconomic performance, we compute the historical decomposition using the median parameter estimates of model M 4. To do this, we first apply the approximate smoothing algorithm described in Kim and Nelson (999) to the state-space presentation of the model in equation (4) to estimate the smoothed structural shocks. Given the set of historical shocks, we then compute the contribution of these shocks to the model s observed variables from 97Q to 9Q. Figure (5) shows the results for detrended output and the demeaned quarterly inflation rate. For easier comparison, we group the eight structural shocks into four categories: foreign shocks include risk premium, foreign inflation, interest rate and output shocks; supply shocks include cost-push and productivity shocks; demand is preference shock and policy is the monetary policy shock. The decompositions also demonstrate that the high inflation period in the mid-97s and early 98s was largely attributed to monetary policy shocks The decomposition shows supply-side shocks, in particular technology shocks, are crucial during periods large output fluctuations. For example, the past four recessions (including the recent financial crisis) over the sample period was associated with large and persistent negative contributions from supply-side shocks. On the other hand, its role on inflation has been limited. It is clear from figure (5) that monetary policy shocks were the biggest contributor to the high inflation during the mid-97s and the early 98s. This observation is Results for other structural shocks are also available upon request to the authors. The results for other variables are also available upon request.