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Nonlinearities in exchange rate determination in a small open economy: Some evidence for Canada
North American Journal of Economics and Finance 24 (2013) 268–278
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North American Journal of Economics and Finance
Nonlinearities in exchange rate determination in a small open economy: Some evidence for Canada Bernd Kempa a,∗, Jana Riedel b a b
Department of Economics, University of Muenster, Universitätsstr. 14-16, 48143 Muenster, Germany Department of Economics, University of Muenster, Germany
a r t i c l e
i n f o
Article history: Received 17 November 2011 Received in revised form 16 November 2012 Accepted 19 November 2012 JEL classification: C11 C24 E42 F31 Keywords: Exchange rate models Taylor rule Bayesian econometrics Markov switching
a b s t r a c t We analyze bilateral Canadian-US dollar exchange rate movements within a Markov switching framework with two states, one in which the exchange rate is determined by the monetary model, and the other in which its behavior follows the predictions of a Taylor rule exchange rate model. There are a number of regime switches throughout the estimation period 1991:2–2008:12 which we can each relate to particular changes in Canadian monetary policy. These results imply that an active monetary policy stance may account for nonlinearities in the exchange rate-fundamentals nexus. The strong evidence of nonlinearities also confirms the notion that exchange rate movements cannot be explained exclusively in terms of any one particular exchange rate model. © 2012 Elsevier Inc. All rights reserved.
1. Introduction Standard monetary models of exchange rate determination possess rather weak explanatory power, as forcefully documented by Meese and Rogoff (1983) and Flood and Rose (1995). It has long been suspected that nonlinearities between exchange rates and their underlying fundamental determinants may account for the disappointing performance of these models (see e.g., Cheung, Chinn, & Pascual, 2005; Hsieh, 1989; McMillan, 2005).
∗ Corresponding author. Tel.: +49 251 8328661; fax: +49 251 8328666. E-mail addresses: [email protected] (B. Kempa), [email protected] (J. Riedel). 1062-9408/$ – see front matter © 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.najef.2012.11.001
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A growing body of literature employs the Markov-switching framework pioneered by Hamilton (1989) to model such nonlinearities. That literature usually finds significant time variation in the exchange rate-fundamentals nexus (Sarno, Valente, & Wohar, 2004), which may itself be due to timevarying transitional dynamics (Yuan, 2011), or to different sets of macroeconomic fundamentals acting as driving forces of the exchange rate during different time periods (Altavilla & De Grauwe, 2010). Focusing specifically on the empirical performance of the monetary exchange rate model, Frömmel, MacDonald, and Menkhoff (2005) confirm the presence of nonlinearities for a number of bilateral US dollar exchange rates. They also identify sub-periods in which the monetary model appears to be a suitable framework for explaining exchange rate movements. A recent strand of literature identifies as one of the major shortcomings of the monetary model its lack of attention to the market’s expectations of future values of the macroeconomic fundamentals (Engel & West, 2004, 2005). Such expectations may be captured by taking account of the endogeneity of monetary policy. For example, central banks following a Taylor rule base their monetary policy decisions on the expected future realizations of inflation and the output gap. A new class of monetary exchange rate models therefore incorporates a Taylor rule interest rate reaction function into an otherwise standard exchange rate model (Engel, Mark, & West, 2008; Engel & West, 2006). These models display exchange rate behavior quite different from the baseline monetary model. In particular, whereas in the monetary model an increase in the current inflation rate causes the exchange rate to depreciate, in Taylor rule models the exchange rate appreciates because higher inflation induces expectations of tighter future monetary policy (Clarida & Waldman, 2008).1 The aim of the present paper is twofold. First, we demonstrate that the monetary and Taylor rule exchange rate models yield a common estimating equation which differs only in terms of the signs of the expected coefficients. For this purpose we consider a variant of the two-country Taylor rule model introduced by Engel and West (2006). Beside expected inflation and the output gap, their model stipulates that the Taylor rule of one of the two countries also contains the exchange rate as an argument.2 Second, we analyze monthly bilateral Canadian-US dollar exchange rate movements for the estimation period 1991:2–2008:12. To this end we incorporate the common estimating equation into a Markov switching framework that takes account of nonlinearities in the relationship between exchange rates and their fundamentals. In the model we allow for two states, one in which the exchange rate is determined by the monetary model, and the other in which its behavior follows the predictions of the Taylor rule exchange rate model. We focus on the Canadian-US dollar exchange rate because it meets the assumptions of the Taylor rule model by Engel and West (2006). The Bank of Canada (BoC) adheres to an inflation target since the early 1990s, and has also traditionally engaged in exchange market management, with the bilateral Canadian-US dollar rate as the primary target of these intervention activities (Weymark, 1995, 1997).3 Moreover, in comparison to other bilateral exchange rates, the Canadian-US dollar rate fares particularly poorly in terms of explanations using standard monetary fundamentals (Cushman, 2000; Faust, Rogers, & Wright, 2003; Mark, 1995; Rapach & Wohar, 2002). Our results can briefly be summarized as follows. We find that the Canadian-US bilateral exchange rate is characterized by strong nonlinearities with respect to its fundamental determinants. In particular, the Markov switching model reveals a number of regime switches which can historically be linked to particular changes in Canadian monetary policy. This result implies both that an active monetary policy stance may account for the observed exchange rate nonlinearities, and that exchange rate movements cannot be explained exclusively in terms of any one particular exchange rate model. The remainder of the paper is structured as follows: Section 2 provides a characterization of the monetary and Taylor rule exchange rate models, and derives a common estimating equation for the
1 The growing literature on the empirical performance of Taylor rule exchange rate models is quite encouraging. Representative studies are Mark (2009) or Molodtsova and Papell (2009). 2 This feature is frequently, although not exclusively, associated with inflation targeting strategies in small open economies (Ball, 1999; Taylor, 2001). 3 This evidence has recently been confirmed by Lubik and Schorfheide (2007), who find that the BoC adjusts its policy interest rate in response to exchange rate movements.
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two models. Section 3 describes the data and the technical details of our estimation strategy, Section 4 reports on the estimation results, and a concluding section summarizes our findings. 2. Monetary and Taylor rule exchange rate models The monetary exchange rate model is based on standard logarithmic money market equilibrium conditions of the form mt − pt = yt − it , m∗t
− p∗t
=
yt∗
(1)
− it∗ ,
(2)
in which m, p, y and i denote the money supply, price level, national income and the nominal interest rate, respectively. Variables pertaining to the foreign country are denoted by asterisks. As usual, income and interest semi-elasticities of money demand are assumed to be identical for the home and the foreign economy. The foreign exchange market is described by a version of the uncovered interest parity (UIP) condition,4 e e∗ it − it∗ = (st − st ) + t+1 − t+1 .
(3)
The home-to-foreign interest rate differential on the left-hand side of Eq. (3) is a function of the current exchange rate misalignment, st − st , with st and st as the current and equilibrium exchange rates, respectively, both defined as the home currency price of foreign exchange. The parameter measures the degree of price flexibility in the economy, which governs the speed with which exchange rate misalignments are eliminated. If st is above st , agents expect the current exchange rate to depreciate, and require a relatively higher home interest rate as compensation for the expected loss of holding e home currency assets. By the same token, if the expected home inflation rate t+1 exceeds the expected e∗ foreign rate t+1 , agents likewise demand a compensation in terms of a relatively higher home interest rate for the expected loss in purchasing power of the home currency. Solving Eq. (3) for the current exchange rate yields st = st −
1 1 e e∗ (it − it∗ ) + (t+1 − t+1 ).
(4)
The equilibrium exchange rate is determined by assuming purchasing power parity (PPP) to hold in long-run equilibrium st = pt − p∗t .
(5) p∗t
Solving Eqs. (1) and (2) for pt and respectively, substituting into Eq. (5), and noting that in a long e e∗ , yields − t+1 run equilibrium, st = st , and hence it − it∗ = t+1 e e∗ − t+1 ). st = mt − m∗t − (yt − yt∗ ) + (t+1
(6)
Finally, substituting Eq. (6) into Eq. (4) results in e e∗ st = mt − m∗t − (yt − yt∗ ) + (t+1 − t+1 )+
1 e e∗ − t+1 ) − (it − it∗ )]. [(t+1
(7)
The general structure of Eq. (7) is originally due to Frankel (1979), and comprises both the flexible and the sticky-price variants of the monetary exchange rate model. Letting the parameter go to infinity yields the standard flex-price monetary model, as outlined by Frenkel (1976) and Bilson (1978). In this scenario, the exchange rate is a function of the home and foreign money supplies, output levels, and inflation expectations, where the latter is identical to the home-to-foreign interest rate differential by virtue of Eq. (3).
4 It is well known that the UIP assumption has little support in the data (see Diez de los Rios & Sentana, 2011). In the estimation stage we partially account for deviations from UIP by allowing for a regime switching constant.
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Allowing for finite realizations of the parameter introduces price stickiness into the model, resulting in the famous Dornbusch (1976) variant of the monetary model. In this environment, interest rates rather than price levels adjust to instantaneously clear the money market. Such liquidity effects open up the possibility of short-run exchange rate misalignments, and expected inflation may become detached from the interest rate differential. Hence both the expected inflation and the home-to-foreign interest rate differential serve as explanatory variables for the exchange rate in Eq. (7). Whereas the monetary model treats the money supply as an exogenous variable, central banks targeting a short-run interest rate allow the money supply to adjust endogenously to the liquidity needs in the economy. A formal treatment of interest rate targeting is the Taylor rule, which can easily be incorporated into the monetary model. Define the Taylor rules of a small (home) economy and a large (foreign) economy as e it = (t+1 − t ) + y (yt − yt ) + s st ,
(8)
e∗ it∗ = (t+1 − t ) + y (yt∗ − yt ),
(9)
in which and y denote the interest rate reaction parameters of the home and foreign central banks in response to deviations of expected inflation from a target rate, t , as well as deviations of output from trend, yt . Whereas these parameters are assumed to be identical for both countries, the central bank of the small home economy is assumed to also adjust the interest rate in response to changes in the exchange rate. We follow Engel and West (2006) in constructing a composite Taylor rule reaction function by subtracting Eq. (9) from Eq. (8), resulting in e e∗ it − it∗ = (t+1 − t+1 ) + y (yt − yt∗ ) + s st .
(10)
Inserting the UIP condition of Eq. (3) on the left-hand side of Eq. (10) and rearranging yields st =
1 e e∗ [(1 − )(t+1 st + − t+1 ) − y (yt − yt∗ )]. s + s +
(11)
To pin down the equilibrium exchange rate, set st = st in Eq. (11) to obtain st =
1 e e∗ [(1 − )(t+1 − t+1 ) − y (yt − yt∗ )]. s
(12)
Finally, substitution of Eq. (12) into Eq. (11) gives the solution of the exchange rate as a counterpart to the monetary model of Eq. (7) st =
1 e e∗ [(1 − )(t+1 − t+1 ) − y (yt − yt∗ )]. s
(13)
It turns out that the right-hand sides of the expressions in Eqs. (12) and (13) are identical, implying that the exchange rate is in permanent equilibrium in the Taylor rule model. This result immediately follows from the fact that with a Taylor rule, the central bank endogenously adjusts the money supply to clear the money market, regardless of whether prices are sticky or flexible. Note that as long as > 1, the exchange rate is lowered, i.e., the home currency appreciates, whenever the expected inflation differential rises. Realizations of > 1 are associated with the Taylor principle, according to which an increase in inflation expectations by 1% should prompt the central bank to raise the nominal interest rate by more than 1%, such that the real interest rate rises as well. Comparing the monetary model of Eq. (7) with the Taylor rule model of Eq. (13), their similarities and differences can be summarized as follows: • The exchange rate rises with positive expected inflation differentials in the monetary model. In contrast, the Taylor rule model predicts a negative association between the exchange rate and expected inflation as long as the Taylor principle is satisfied. • The flex-price as well as the sticky-price variants of the monetary model predict that positive innovations in the relative money supplies lead to a depreciation of the exchange rate from the
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viewpoint of the home economy (a rise in s). In contrast, money supplies play no role for exchange rate determination in the Taylor rule model. • Both the monetary and Taylor rule models identify a negative association between relative output and the exchange rate. • Only in the sticky-price version of the monetary model does the interest rate differential have a direct and negative impact on the exchange rate. This impact is associated with an exchange rate misalignment due to the presence of a liquidity effect. The monetary and Taylor rule models of Eqs. (7) and (13) can both be represented by the following estimation equation with Markov switching parameters and variances e e∗ − t+1 ) + ıSt (mt − m∗t ) + St (yt − yt∗ ) + St (it − it∗ ) + εt,St , st = St + ˇSt (t+1
t = 1, . . . , T.
εt,St ∼N(0, S2t ), (14)
Eq. (14) includes a time-varying constant, St , to account for the possibility of different levels in trend output and inflation targets between the two countries. The model allows for two regimes, St = L with probability Pr [St = L] = pL and St = H with probability Pr [St = H] = pH .5 We make the common assumption that the states St follow a first-order Markov chain. The underlying process can be described by the following transition probabilities governing the switches between the two states: Pr(St = L|St−1 = L) = pLL , Pr(St = H|St−1 = H) = pHH ,
Pr(St = H|St−1 = L) = 1 − pLL , Pr(St = L|St−1 = H) = 1 − pHH ,
such that the probability of being in a particular state at time t depends only on the state the system has been in at time t − 1. The system may thus prevail in any of the two states for a random period of time, and is replaced by the other state when switching takes place. 3. Data and estimation procedure To estimate the model we use monthly data from 1991:2 to 2008:12. Survey data on inflation expectations are taken from Consensus Economics.6 As monetary aggregate we use seasonally unadjusted M2 from the OECD Main Economic Indicators database. The remaining data are obtained from the IMF International Financial Statistics. Output is measured using a seasonally unadjusted industrial production index, and the short-term interest rate differential is obtained from using a three-month Treasury bill rate for Canada and the Federal funds rate for the United States. We use the Markov chain Monte Carlo (MCMC) algorithm to estimate the reduced form equation (14). For our purposes, MCMC offers two advantages over maximum likelihood estimation. First, as we are only interested in a comparison of the different model implications, Bayesian methods allow us to disregard possible nonstationarity in the data (Sims & Uhlig, 1991; Uhlig, 1994). Second, MCMC also allows us to utilize prior knowledge from theory as well as from other empirical studies. Estimation is divided into two parts. In the first part, we sample from the conditional posterior density of the states given the transition probabilities, the parameter vector and the data. To do so, we apply the forward-filtering backward-sampling (FFBS) algorithm. After initializing the probabilities of
5 Note that a small s denotes the natural logarithm of the exchange rate. We follow the common notation in the literature and indicate the vector of regimes by a capital S. 6 Using survey data instead of realized inflation rates obviates the need for explicitly specifying the expectations formation process of economic agents. However, one of the major drawbacks of using survey data is their perceived lack of reliability, which may itself be due to possibly biased responses of survey participants. The Consensus Economics poll is less subject to this critique as survey participants work with the private sector and are thus more likely to report a true notion of the expected economic development (Bleich, Fendel, & Rülke, 2012). For further discussion on the advantages and disadvantages of survey data see also Cunningham, Desroches, and Santor (2010).
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Table 1 Prior distributions for the coefficients in the Markov switching model, Eq. (14). Parameter
j ˇj ıj j j
Prior distribution j = L (monetary regime)
j = H (Taylor rule regime)
N(0, 10) N(30, 100) N(1, 10) N(− 1, 10) N(0, 100)
N(0, 10) N(0, 100) N(0, 100) N(− 1/0.14, 100) N(0, 100)
j ∼ IG(0.01/2, 0.15/2), j = L, H pjj ∼ Beta(1, 1), j = L, H
being either in state L or H in period t = 1, the state vector (S2 , . . ., ST ) is filtered by means of a prediction step and an update step. In the prediction step we obtain the predicted probability of being in a certain state in period t given the data up to t − 1, and in the update step we iterate forward to obtain the conditional probability of being in a certain state in T given the data for t = 1, . . ., T. Then we sample the states backwards and obtain a conditional probability distribution for the state vector (for details see e.g., Kim & Nelson, 1999). In the second part of the estimation procedure, we obtain the parameter vector and the error variances using the Gibbs sampler. We draw iteratively from the conditional distributions of the parameters given the variance, (prm| 2 ), and the variances given the parameters, ( 2 |prm), both conditional on the given data and states obtained from FFBS, until the sampler converges and we finally draw from the joint distribution of the parameters and the variances. The number of iterations is set to R + N. The first R = 1000 draws are cut off before the posterior densities and average parameter estimates are computed. The results presented below are based on using N = 40, 000 repetitions. We use rather uninformative prior distributions (see Table 1). The choice of the prior means of the parameters is mainly based on economic intuition and on the results of Lubik and Schorfheide (2007). In order to assign the prior distributions to the two Markov switching regimes, regime L is arbitrarily chosen to correspond to the monetary model, whereas regime H relates to the Taylor rule exchange rate model. The parameters are all drawn from normal distributions. The constant is expected to play no role in the monetary regime, but may be significant in the Taylor rule regime. For our analysis the inflation coefficient is most important for identifying the two regimes. For the monetary model considered in Eq. (7), the empirical literature suggests estimates of the interest semi-elasticity of money demand in the range of 30–60 (see Engel & West, 2005, p. 497, with further references therein). We set the prior mean for ˇL to 30, thus sticking to the conservative end of the empirically relevant range, but use a flat prior to account for the large variation of the empirical estimates. In contrast, the Taylor regime inflation coefficient should be negative. Since we cannot be sure a priori of whether the Taylor principle is satisfied, we choose a flat prior and impose a zero mean. The coefficient of the monetary aggregate is assumed to take on a positive value in the monetary model. We set the prior mean for ıL to unity, thus corresponding to the one-to-one mapping of the monetary aggregate to the exchange rate in the monetary model. According to Eq. (13), money is not linked to the exchange rate in the Taylor rule regime, and we therefore choose a zero mean. The output coefficients in the monetary and Taylor rule models, j , j = L, H, should be negative. In the monetary regime we simply use L ∼ N(− 1, 100), but in the Taylor regime we have to take into account the scaling coefficient s of Eq. (13). Lubik and Schorfheide (2007) find a mean coefficient of 0.14. We follow these authors and set a prior of −1/0.14 for H . Again, we do not impose a tight prior in the Taylor model regime and set the variance to 100. Finally the prior distribution of the interest rate coefficient is imposed to be flat around zero for both regimes. As a robustness check we allow for different prior distributions. We use several sets of parameter mean and variance priors. It turns out that results are fairly robust to changes in the prior means within economically plausible intervals. The chosen prior parameter variances are set in a range of
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Table 2 Estimation results for the Markov switching model, Eq. (14). Parameter
j ˇj ıj j j j pjj
Average coefficient estimates j=L
j=H
0.124 (−0.568, 0.821) 23.068 (20.209, 25.973) −0.124 (−0.477, 0.230) −1.548 (−1.802, −1.290) −0.012 (−0.029, 0.004) 0.006 (0.005, 0.008) 0.977 (0.958, 0.993)
2.456 (2.010, 2.903) −2.510 (−4.066, −0.909) 1.218 (0.984, 1.454) 0.180 (−0.286, 0.597) −0.008 (−0.013, −0.003) 0.003 (0.003, 0.004) 0.969 (0.946, 0.989)
Note: The numbers in parentheses denote the 0.10 and 0.90 quantiles of the posterior distribution.
1 and 1000 and only in rare cases does this influence the results. Indeed, estimation results change significantly only if the variance is increased up to more than 1000 or decreased below unity.7 4. Results Table 2 and Fig. 1 present the average coefficient estimates and their distributional properties for the Markov switching model of Eq. (14). As the coefficient for expected inflation is significantly positive in regime L, but significantly negative in regime H, we can associate regime L with the monetary model, and regime H with the Taylor rule exchange rate model. Relative money supplies are insignificant in regime L, but exert a significantly positive effect in regime H. This coefficient thus does not conform to the expected sign in the Taylor rule model. As predicted by theory, the coefficient for relative output is significantly negative in regime L, but turns out to be insignificantly different from zero in regime H. 8 Finally, the coefficient on the interest rate differential is negative but insignificant, implying that our model does not provide any clear evidence of exchange rate overshooting phenomena across the sample period under consideration. Fig. 2 visualizes the regime switches along the time axis. The results indicate that the Markov switching model identifies the individual regimes with a very high level of precision as the estimated probabilities of being in the Taylor rule regime are mostly close to either zero or one. We can relate the observed regime switches to particular changes in Canadian monetary policy.9 The Markov switching model identifies the Taylor rule model right at the start of the sample in 1991, at which the BoC adopted its formal inflation targeting strategy. Except for a small blip in 1993, the regime is stable throughout the early and mid-1990s, before it switches into the monetary regime in 1998. Until that point in time, the BoC intervened systematically in the foreign exchange market to resist significant upward or downward pressure on the Canadian dollar. Due to the perceived ineffectiveness of that strategy, starting in 1998, the BoC changed its policy by intervening in foreign exchange markets on a discretionary basis, rather than systematically, and only in exceptional circumstances (Bank of Canada, 2011). The Markov switching model picks up this de-emphasizing of the exchange rate target by indicating a switch into the monetary regime.
7
Detailed results of the robustness checks are available from the authors on request. We also estimated the model in Eq. (14) by restricting the coefficients for the interest rate and money supply differentials to zero in the Taylor rule model. This way we account for the fact that these variables should not affect the exchange rate in the Taylor rule regime. The results are fairly robust, with the output differential coefficient becoming significantly negative. We interpret these results as additional support for our model. 9 Dodge (2002) provides a brief history of monetary policy in Canada before and after the adoption of formal inflation targets. 8
−5
0
0.6
5
1
2
3
25
−6
30
0.5
1.0
−1.5
−0.5 0.0
0.5
1.0
1.5
60 100 −0.020
−0.010
0.000
0
300
700
interest rate coeff., j=H posterior density
400 200
0.008
2.5
20
posterior density
15 25
posterior density posterior density
0
variance, j=L
2.0
output coeff., j=H
0.00 0.02 0.04
0.004
1.5
0.8
−0.5
interest rate coeff., j=L
0.000
1.0
0.2
posterior density
posterior density
1.5
−1.0
5
−0.04
4
2.0 0.5
output coeff., j=L
−0.08
2
money coeff., j=H
0.5
−1.5
0
1.0
1.5
money coeff., j=L
−2.0
−2
0.0
posterior density
1.4 0.8
0.0
−4
inflation coeff., j=H
0.2
posterior density
inflation coeff., j=L
−1.5 −1.0 −0.5
5
0.05 0.20
posterior density
0.15
20
4
constant, j=H
0.05
posterior density
constant, j=L
15
275
0.0
posterior density
0.6 0.3 0.0
posterior density
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0.000
0.002
0.004
variance, j=H
Fig. 1. Posterior distributions for the estimated parameters in Eq. (14).
0.010
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1.0
0.8
0.6
0.4
0.2
0.0 1995:01
2000:01
2005:01
Fig. 2. Probabilities of being in regime H (Taylor rule regime) for the estimated model in Eq. (14).
During 2003 and 2004, the Canadian dollar appreciated sharply against the US dollar, and the BoC reacted to this development by means of a substantial loosening of its monetary policy stance (Ragan, 2005). This policy change towards a renewed focus on the exchange rate shows up in our model by a switch back into the Taylor rule exchange rate regime in 2005. Only towards the end of the sample period does the identification become less clear-cut, as the system starts to alternate between the two regimes. This instability of the regime identification may be associated with the onset of the financial and economic crisis beginning in mid-2007. To evaluate the goodness-of-fit, we compare the root mean squared errors (RMSE) of our regime-switching model with a linear model specification. The results clearly indicate that the nonlinear model outperforms the linear alternative in terms of model fit, even when accounting for the estimated number of parameters. Indeed, the RMSE of our baseline model is 0.055 compared to 0.101 in the linear model using the Gibbs sampler. This result is robust to the chosen estimation method for the linear model. Interestingly, even the restricted Markov switching model discussed in Footnote 8 has a lower RMSE (0.060) than the linear model. 5. Conclusion This paper analyzes exchange rate movements in terms of two different exchange rate models within a Markov switching framework. In contrast to much of the previous literature on nonlinearities between exchange rates and their fundamental determinants, our setup explicitly allows for switches between two regimes, one in which the exchange rate is determined primarily by the monetary model, and the other in which the exchange rate follows the predictions of the Taylor rule model. We utilize a variant of the Taylor rule exchange rate model introduced by Engel and West (2006), which we show to yield an estimating equation analogous to the monetary model. Since the model by Engel and West is primarily designed for a small open economy targeting the exchange rate in its Taylor rule, we focus on the Canadian-US dollar exchange rate after the Bank of Canada adopted formal inflation targeting in February 1991. The results of our empirical analysis indicate that the Markov switching model identifies the individual regimes with a very high level of precision. We detect a number of regime switches across the estimation period 1991:2–2008:12, which we can each relate to particular changes in Canadian monetary policy. These results imply that an active monetary policy stance may account for nonlinearities in the exchange rate-fundamentals nexus. The strong evidence of nonlinearities also confirms the notion that exchange rate movements cannot be explained exclusively in terms of any one particular exchange rate model.
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Do central banks respond to exchange rate movements? A structural investigation. Journal of Monetary Economics, 54, 3–24. Mark, N. C. (1995). Exchange rates and fundamentals: Evidence on long-horizon predictability. American Economic Review, 85, 201–218. Mark, N. C. (2009). Changing monetary policy rules, learning, and real exchange rate dynamics. Journal of Money, Credit, and Banking, 41, 1047–1070. McMillan, D. G. (2005). Smooth-transition error-correction in exchange rates. The North American Journal of Economics and Finance, 16, 217–232. Meese, R. A., & Rogoff, K. (1983). Empirical exchange rate models of the seventies: Do they fit out of sample? Journal of International Economics, 14, 3–24. Molodtsova, T., & Papell, D. H. (2009). Out-of-sample exchange rate predictability with Taylor rule fundamentals. Journal of International Economics, 77, 167–180. Ragan, C. (2005). The exchange rate and Canadian inflation targeting. Working paper 2005-34. Bank of Canada. Rapach, D. E., & Wohar, M. E. (2002). Testing the monetary model of exchange rate determination: New evidence from a century of data. Journal of International Economics, 58, 359–385. Sarno, L., Valente, G., & Wohar, M. E. (2004). Monetary fundamentals and exchange rate dynamics under different nominal regimes. Economic Inquiry, 42, 179–193.
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Contents lists available at SciVerse ScienceDirect
North American Journal of Economics and Finance
Nonlinearities in exchange rate determination in a small open economy: Some evidence for Canada Bernd Kempa a,∗, Jana Riedel b a b
Department of Economics, University of Muenster, Universitätsstr. 14-16, 48143 Muenster, Germany Department of Economics, University of Muenster, Germany
a r t i c l e
i n f o
Article history: Received 17 November 2011 Received in revised form 16 November 2012 Accepted 19 November 2012 JEL classification: C11 C24 E42 F31 Keywords: Exchange rate models Taylor rule Bayesian econometrics Markov switching
a b s t r a c t We analyze bilateral Canadian-US dollar exchange rate movements within a Markov switching framework with two states, one in which the exchange rate is determined by the monetary model, and the other in which its behavior follows the predictions of a Taylor rule exchange rate model. There are a number of regime switches throughout the estimation period 1991:2–2008:12 which we can each relate to particular changes in Canadian monetary policy. These results imply that an active monetary policy stance may account for nonlinearities in the exchange rate-fundamentals nexus. The strong evidence of nonlinearities also confirms the notion that exchange rate movements cannot be explained exclusively in terms of any one particular exchange rate model. © 2012 Elsevier Inc. All rights reserved.
1. Introduction Standard monetary models of exchange rate determination possess rather weak explanatory power, as forcefully documented by Meese and Rogoff (1983) and Flood and Rose (1995). It has long been suspected that nonlinearities between exchange rates and their underlying fundamental determinants may account for the disappointing performance of these models (see e.g., Cheung, Chinn, & Pascual, 2005; Hsieh, 1989; McMillan, 2005).
∗ Corresponding author. Tel.: +49 251 8328661; fax: +49 251 8328666. E-mail addresses: [email protected] (B. Kempa), [email protected] (J. Riedel). 1062-9408/$ – see front matter © 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.najef.2012.11.001
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A growing body of literature employs the Markov-switching framework pioneered by Hamilton (1989) to model such nonlinearities. That literature usually finds significant time variation in the exchange rate-fundamentals nexus (Sarno, Valente, & Wohar, 2004), which may itself be due to timevarying transitional dynamics (Yuan, 2011), or to different sets of macroeconomic fundamentals acting as driving forces of the exchange rate during different time periods (Altavilla & De Grauwe, 2010). Focusing specifically on the empirical performance of the monetary exchange rate model, Frömmel, MacDonald, and Menkhoff (2005) confirm the presence of nonlinearities for a number of bilateral US dollar exchange rates. They also identify sub-periods in which the monetary model appears to be a suitable framework for explaining exchange rate movements. A recent strand of literature identifies as one of the major shortcomings of the monetary model its lack of attention to the market’s expectations of future values of the macroeconomic fundamentals (Engel & West, 2004, 2005). Such expectations may be captured by taking account of the endogeneity of monetary policy. For example, central banks following a Taylor rule base their monetary policy decisions on the expected future realizations of inflation and the output gap. A new class of monetary exchange rate models therefore incorporates a Taylor rule interest rate reaction function into an otherwise standard exchange rate model (Engel, Mark, & West, 2008; Engel & West, 2006). These models display exchange rate behavior quite different from the baseline monetary model. In particular, whereas in the monetary model an increase in the current inflation rate causes the exchange rate to depreciate, in Taylor rule models the exchange rate appreciates because higher inflation induces expectations of tighter future monetary policy (Clarida & Waldman, 2008).1 The aim of the present paper is twofold. First, we demonstrate that the monetary and Taylor rule exchange rate models yield a common estimating equation which differs only in terms of the signs of the expected coefficients. For this purpose we consider a variant of the two-country Taylor rule model introduced by Engel and West (2006). Beside expected inflation and the output gap, their model stipulates that the Taylor rule of one of the two countries also contains the exchange rate as an argument.2 Second, we analyze monthly bilateral Canadian-US dollar exchange rate movements for the estimation period 1991:2–2008:12. To this end we incorporate the common estimating equation into a Markov switching framework that takes account of nonlinearities in the relationship between exchange rates and their fundamentals. In the model we allow for two states, one in which the exchange rate is determined by the monetary model, and the other in which its behavior follows the predictions of the Taylor rule exchange rate model. We focus on the Canadian-US dollar exchange rate because it meets the assumptions of the Taylor rule model by Engel and West (2006). The Bank of Canada (BoC) adheres to an inflation target since the early 1990s, and has also traditionally engaged in exchange market management, with the bilateral Canadian-US dollar rate as the primary target of these intervention activities (Weymark, 1995, 1997).3 Moreover, in comparison to other bilateral exchange rates, the Canadian-US dollar rate fares particularly poorly in terms of explanations using standard monetary fundamentals (Cushman, 2000; Faust, Rogers, & Wright, 2003; Mark, 1995; Rapach & Wohar, 2002). Our results can briefly be summarized as follows. We find that the Canadian-US bilateral exchange rate is characterized by strong nonlinearities with respect to its fundamental determinants. In particular, the Markov switching model reveals a number of regime switches which can historically be linked to particular changes in Canadian monetary policy. This result implies both that an active monetary policy stance may account for the observed exchange rate nonlinearities, and that exchange rate movements cannot be explained exclusively in terms of any one particular exchange rate model. The remainder of the paper is structured as follows: Section 2 provides a characterization of the monetary and Taylor rule exchange rate models, and derives a common estimating equation for the
1 The growing literature on the empirical performance of Taylor rule exchange rate models is quite encouraging. Representative studies are Mark (2009) or Molodtsova and Papell (2009). 2 This feature is frequently, although not exclusively, associated with inflation targeting strategies in small open economies (Ball, 1999; Taylor, 2001). 3 This evidence has recently been confirmed by Lubik and Schorfheide (2007), who find that the BoC adjusts its policy interest rate in response to exchange rate movements.
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two models. Section 3 describes the data and the technical details of our estimation strategy, Section 4 reports on the estimation results, and a concluding section summarizes our findings. 2. Monetary and Taylor rule exchange rate models The monetary exchange rate model is based on standard logarithmic money market equilibrium conditions of the form mt − pt = yt − it , m∗t
− p∗t
=
yt∗
(1)
− it∗ ,
(2)
in which m, p, y and i denote the money supply, price level, national income and the nominal interest rate, respectively. Variables pertaining to the foreign country are denoted by asterisks. As usual, income and interest semi-elasticities of money demand are assumed to be identical for the home and the foreign economy. The foreign exchange market is described by a version of the uncovered interest parity (UIP) condition,4 e e∗ it − it∗ = (st − st ) + t+1 − t+1 .
(3)
The home-to-foreign interest rate differential on the left-hand side of Eq. (3) is a function of the current exchange rate misalignment, st − st , with st and st as the current and equilibrium exchange rates, respectively, both defined as the home currency price of foreign exchange. The parameter measures the degree of price flexibility in the economy, which governs the speed with which exchange rate misalignments are eliminated. If st is above st , agents expect the current exchange rate to depreciate, and require a relatively higher home interest rate as compensation for the expected loss of holding e home currency assets. By the same token, if the expected home inflation rate t+1 exceeds the expected e∗ foreign rate t+1 , agents likewise demand a compensation in terms of a relatively higher home interest rate for the expected loss in purchasing power of the home currency. Solving Eq. (3) for the current exchange rate yields st = st −
1 1 e e∗ (it − it∗ ) + (t+1 − t+1 ).
(4)
The equilibrium exchange rate is determined by assuming purchasing power parity (PPP) to hold in long-run equilibrium st = pt − p∗t .
(5) p∗t
Solving Eqs. (1) and (2) for pt and respectively, substituting into Eq. (5), and noting that in a long e e∗ , yields − t+1 run equilibrium, st = st , and hence it − it∗ = t+1 e e∗ − t+1 ). st = mt − m∗t − (yt − yt∗ ) + (t+1
(6)
Finally, substituting Eq. (6) into Eq. (4) results in e e∗ st = mt − m∗t − (yt − yt∗ ) + (t+1 − t+1 )+
1 e e∗ − t+1 ) − (it − it∗ )]. [(t+1
(7)
The general structure of Eq. (7) is originally due to Frankel (1979), and comprises both the flexible and the sticky-price variants of the monetary exchange rate model. Letting the parameter go to infinity yields the standard flex-price monetary model, as outlined by Frenkel (1976) and Bilson (1978). In this scenario, the exchange rate is a function of the home and foreign money supplies, output levels, and inflation expectations, where the latter is identical to the home-to-foreign interest rate differential by virtue of Eq. (3).
4 It is well known that the UIP assumption has little support in the data (see Diez de los Rios & Sentana, 2011). In the estimation stage we partially account for deviations from UIP by allowing for a regime switching constant.
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Allowing for finite realizations of the parameter introduces price stickiness into the model, resulting in the famous Dornbusch (1976) variant of the monetary model. In this environment, interest rates rather than price levels adjust to instantaneously clear the money market. Such liquidity effects open up the possibility of short-run exchange rate misalignments, and expected inflation may become detached from the interest rate differential. Hence both the expected inflation and the home-to-foreign interest rate differential serve as explanatory variables for the exchange rate in Eq. (7). Whereas the monetary model treats the money supply as an exogenous variable, central banks targeting a short-run interest rate allow the money supply to adjust endogenously to the liquidity needs in the economy. A formal treatment of interest rate targeting is the Taylor rule, which can easily be incorporated into the monetary model. Define the Taylor rules of a small (home) economy and a large (foreign) economy as e it = (t+1 − t ) + y (yt − yt ) + s st ,
(8)
e∗ it∗ = (t+1 − t ) + y (yt∗ − yt ),
(9)
in which and y denote the interest rate reaction parameters of the home and foreign central banks in response to deviations of expected inflation from a target rate, t , as well as deviations of output from trend, yt . Whereas these parameters are assumed to be identical for both countries, the central bank of the small home economy is assumed to also adjust the interest rate in response to changes in the exchange rate. We follow Engel and West (2006) in constructing a composite Taylor rule reaction function by subtracting Eq. (9) from Eq. (8), resulting in e e∗ it − it∗ = (t+1 − t+1 ) + y (yt − yt∗ ) + s st .
(10)
Inserting the UIP condition of Eq. (3) on the left-hand side of Eq. (10) and rearranging yields st =
1 e e∗ [(1 − )(t+1 st + − t+1 ) − y (yt − yt∗ )]. s + s +
(11)
To pin down the equilibrium exchange rate, set st = st in Eq. (11) to obtain st =
1 e e∗ [(1 − )(t+1 − t+1 ) − y (yt − yt∗ )]. s
(12)
Finally, substitution of Eq. (12) into Eq. (11) gives the solution of the exchange rate as a counterpart to the monetary model of Eq. (7) st =
1 e e∗ [(1 − )(t+1 − t+1 ) − y (yt − yt∗ )]. s
(13)
It turns out that the right-hand sides of the expressions in Eqs. (12) and (13) are identical, implying that the exchange rate is in permanent equilibrium in the Taylor rule model. This result immediately follows from the fact that with a Taylor rule, the central bank endogenously adjusts the money supply to clear the money market, regardless of whether prices are sticky or flexible. Note that as long as > 1, the exchange rate is lowered, i.e., the home currency appreciates, whenever the expected inflation differential rises. Realizations of > 1 are associated with the Taylor principle, according to which an increase in inflation expectations by 1% should prompt the central bank to raise the nominal interest rate by more than 1%, such that the real interest rate rises as well. Comparing the monetary model of Eq. (7) with the Taylor rule model of Eq. (13), their similarities and differences can be summarized as follows: • The exchange rate rises with positive expected inflation differentials in the monetary model. In contrast, the Taylor rule model predicts a negative association between the exchange rate and expected inflation as long as the Taylor principle is satisfied. • The flex-price as well as the sticky-price variants of the monetary model predict that positive innovations in the relative money supplies lead to a depreciation of the exchange rate from the
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viewpoint of the home economy (a rise in s). In contrast, money supplies play no role for exchange rate determination in the Taylor rule model. • Both the monetary and Taylor rule models identify a negative association between relative output and the exchange rate. • Only in the sticky-price version of the monetary model does the interest rate differential have a direct and negative impact on the exchange rate. This impact is associated with an exchange rate misalignment due to the presence of a liquidity effect. The monetary and Taylor rule models of Eqs. (7) and (13) can both be represented by the following estimation equation with Markov switching parameters and variances e e∗ − t+1 ) + ıSt (mt − m∗t ) + St (yt − yt∗ ) + St (it − it∗ ) + εt,St , st = St + ˇSt (t+1
t = 1, . . . , T.
εt,St ∼N(0, S2t ), (14)
Eq. (14) includes a time-varying constant, St , to account for the possibility of different levels in trend output and inflation targets between the two countries. The model allows for two regimes, St = L with probability Pr [St = L] = pL and St = H with probability Pr [St = H] = pH .5 We make the common assumption that the states St follow a first-order Markov chain. The underlying process can be described by the following transition probabilities governing the switches between the two states: Pr(St = L|St−1 = L) = pLL , Pr(St = H|St−1 = H) = pHH ,
Pr(St = H|St−1 = L) = 1 − pLL , Pr(St = L|St−1 = H) = 1 − pHH ,
such that the probability of being in a particular state at time t depends only on the state the system has been in at time t − 1. The system may thus prevail in any of the two states for a random period of time, and is replaced by the other state when switching takes place. 3. Data and estimation procedure To estimate the model we use monthly data from 1991:2 to 2008:12. Survey data on inflation expectations are taken from Consensus Economics.6 As monetary aggregate we use seasonally unadjusted M2 from the OECD Main Economic Indicators database. The remaining data are obtained from the IMF International Financial Statistics. Output is measured using a seasonally unadjusted industrial production index, and the short-term interest rate differential is obtained from using a three-month Treasury bill rate for Canada and the Federal funds rate for the United States. We use the Markov chain Monte Carlo (MCMC) algorithm to estimate the reduced form equation (14). For our purposes, MCMC offers two advantages over maximum likelihood estimation. First, as we are only interested in a comparison of the different model implications, Bayesian methods allow us to disregard possible nonstationarity in the data (Sims & Uhlig, 1991; Uhlig, 1994). Second, MCMC also allows us to utilize prior knowledge from theory as well as from other empirical studies. Estimation is divided into two parts. In the first part, we sample from the conditional posterior density of the states given the transition probabilities, the parameter vector and the data. To do so, we apply the forward-filtering backward-sampling (FFBS) algorithm. After initializing the probabilities of
5 Note that a small s denotes the natural logarithm of the exchange rate. We follow the common notation in the literature and indicate the vector of regimes by a capital S. 6 Using survey data instead of realized inflation rates obviates the need for explicitly specifying the expectations formation process of economic agents. However, one of the major drawbacks of using survey data is their perceived lack of reliability, which may itself be due to possibly biased responses of survey participants. The Consensus Economics poll is less subject to this critique as survey participants work with the private sector and are thus more likely to report a true notion of the expected economic development (Bleich, Fendel, & Rülke, 2012). For further discussion on the advantages and disadvantages of survey data see also Cunningham, Desroches, and Santor (2010).
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Table 1 Prior distributions for the coefficients in the Markov switching model, Eq. (14). Parameter
j ˇj ıj j j
Prior distribution j = L (monetary regime)
j = H (Taylor rule regime)
N(0, 10) N(30, 100) N(1, 10) N(− 1, 10) N(0, 100)
N(0, 10) N(0, 100) N(0, 100) N(− 1/0.14, 100) N(0, 100)
j ∼ IG(0.01/2, 0.15/2), j = L, H pjj ∼ Beta(1, 1), j = L, H
being either in state L or H in period t = 1, the state vector (S2 , . . ., ST ) is filtered by means of a prediction step and an update step. In the prediction step we obtain the predicted probability of being in a certain state in period t given the data up to t − 1, and in the update step we iterate forward to obtain the conditional probability of being in a certain state in T given the data for t = 1, . . ., T. Then we sample the states backwards and obtain a conditional probability distribution for the state vector (for details see e.g., Kim & Nelson, 1999). In the second part of the estimation procedure, we obtain the parameter vector and the error variances using the Gibbs sampler. We draw iteratively from the conditional distributions of the parameters given the variance, (prm| 2 ), and the variances given the parameters, ( 2 |prm), both conditional on the given data and states obtained from FFBS, until the sampler converges and we finally draw from the joint distribution of the parameters and the variances. The number of iterations is set to R + N. The first R = 1000 draws are cut off before the posterior densities and average parameter estimates are computed. The results presented below are based on using N = 40, 000 repetitions. We use rather uninformative prior distributions (see Table 1). The choice of the prior means of the parameters is mainly based on economic intuition and on the results of Lubik and Schorfheide (2007). In order to assign the prior distributions to the two Markov switching regimes, regime L is arbitrarily chosen to correspond to the monetary model, whereas regime H relates to the Taylor rule exchange rate model. The parameters are all drawn from normal distributions. The constant is expected to play no role in the monetary regime, but may be significant in the Taylor rule regime. For our analysis the inflation coefficient is most important for identifying the two regimes. For the monetary model considered in Eq. (7), the empirical literature suggests estimates of the interest semi-elasticity of money demand in the range of 30–60 (see Engel & West, 2005, p. 497, with further references therein). We set the prior mean for ˇL to 30, thus sticking to the conservative end of the empirically relevant range, but use a flat prior to account for the large variation of the empirical estimates. In contrast, the Taylor regime inflation coefficient should be negative. Since we cannot be sure a priori of whether the Taylor principle is satisfied, we choose a flat prior and impose a zero mean. The coefficient of the monetary aggregate is assumed to take on a positive value in the monetary model. We set the prior mean for ıL to unity, thus corresponding to the one-to-one mapping of the monetary aggregate to the exchange rate in the monetary model. According to Eq. (13), money is not linked to the exchange rate in the Taylor rule regime, and we therefore choose a zero mean. The output coefficients in the monetary and Taylor rule models, j , j = L, H, should be negative. In the monetary regime we simply use L ∼ N(− 1, 100), but in the Taylor regime we have to take into account the scaling coefficient s of Eq. (13). Lubik and Schorfheide (2007) find a mean coefficient of 0.14. We follow these authors and set a prior of −1/0.14 for H . Again, we do not impose a tight prior in the Taylor model regime and set the variance to 100. Finally the prior distribution of the interest rate coefficient is imposed to be flat around zero for both regimes. As a robustness check we allow for different prior distributions. We use several sets of parameter mean and variance priors. It turns out that results are fairly robust to changes in the prior means within economically plausible intervals. The chosen prior parameter variances are set in a range of
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Table 2 Estimation results for the Markov switching model, Eq. (14). Parameter
j ˇj ıj j j j pjj
Average coefficient estimates j=L
j=H
0.124 (−0.568, 0.821) 23.068 (20.209, 25.973) −0.124 (−0.477, 0.230) −1.548 (−1.802, −1.290) −0.012 (−0.029, 0.004) 0.006 (0.005, 0.008) 0.977 (0.958, 0.993)
2.456 (2.010, 2.903) −2.510 (−4.066, −0.909) 1.218 (0.984, 1.454) 0.180 (−0.286, 0.597) −0.008 (−0.013, −0.003) 0.003 (0.003, 0.004) 0.969 (0.946, 0.989)
Note: The numbers in parentheses denote the 0.10 and 0.90 quantiles of the posterior distribution.
1 and 1000 and only in rare cases does this influence the results. Indeed, estimation results change significantly only if the variance is increased up to more than 1000 or decreased below unity.7 4. Results Table 2 and Fig. 1 present the average coefficient estimates and their distributional properties for the Markov switching model of Eq. (14). As the coefficient for expected inflation is significantly positive in regime L, but significantly negative in regime H, we can associate regime L with the monetary model, and regime H with the Taylor rule exchange rate model. Relative money supplies are insignificant in regime L, but exert a significantly positive effect in regime H. This coefficient thus does not conform to the expected sign in the Taylor rule model. As predicted by theory, the coefficient for relative output is significantly negative in regime L, but turns out to be insignificantly different from zero in regime H. 8 Finally, the coefficient on the interest rate differential is negative but insignificant, implying that our model does not provide any clear evidence of exchange rate overshooting phenomena across the sample period under consideration. Fig. 2 visualizes the regime switches along the time axis. The results indicate that the Markov switching model identifies the individual regimes with a very high level of precision as the estimated probabilities of being in the Taylor rule regime are mostly close to either zero or one. We can relate the observed regime switches to particular changes in Canadian monetary policy.9 The Markov switching model identifies the Taylor rule model right at the start of the sample in 1991, at which the BoC adopted its formal inflation targeting strategy. Except for a small blip in 1993, the regime is stable throughout the early and mid-1990s, before it switches into the monetary regime in 1998. Until that point in time, the BoC intervened systematically in the foreign exchange market to resist significant upward or downward pressure on the Canadian dollar. Due to the perceived ineffectiveness of that strategy, starting in 1998, the BoC changed its policy by intervening in foreign exchange markets on a discretionary basis, rather than systematically, and only in exceptional circumstances (Bank of Canada, 2011). The Markov switching model picks up this de-emphasizing of the exchange rate target by indicating a switch into the monetary regime.
7
Detailed results of the robustness checks are available from the authors on request. We also estimated the model in Eq. (14) by restricting the coefficients for the interest rate and money supply differentials to zero in the Taylor rule model. This way we account for the fact that these variables should not affect the exchange rate in the Taylor rule regime. The results are fairly robust, with the output differential coefficient becoming significantly negative. We interpret these results as additional support for our model. 9 Dodge (2002) provides a brief history of monetary policy in Canada before and after the adoption of formal inflation targets. 8
−5
0
0.6
5
1
2
3
25
−6
30
0.5
1.0
−1.5
−0.5 0.0
0.5
1.0
1.5
60 100 −0.020
−0.010
0.000
0
300
700
interest rate coeff., j=H posterior density
400 200
0.008
2.5
20
posterior density
15 25
posterior density posterior density
0
variance, j=L
2.0
output coeff., j=H
0.00 0.02 0.04
0.004
1.5
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0.000
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posterior density
posterior density
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−0.04
4
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output coeff., j=L
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2
money coeff., j=H
0.5
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0
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−2
0.0
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−1.5 −1.0 −0.5
5
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posterior density
0.15
20
4
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0.05
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constant, j=L
15
275
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0.000
0.002
0.004
variance, j=H
Fig. 1. Posterior distributions for the estimated parameters in Eq. (14).
0.010
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1.0
0.8
0.6
0.4
0.2
0.0 1995:01
2000:01
2005:01
Fig. 2. Probabilities of being in regime H (Taylor rule regime) for the estimated model in Eq. (14).
During 2003 and 2004, the Canadian dollar appreciated sharply against the US dollar, and the BoC reacted to this development by means of a substantial loosening of its monetary policy stance (Ragan, 2005). This policy change towards a renewed focus on the exchange rate shows up in our model by a switch back into the Taylor rule exchange rate regime in 2005. Only towards the end of the sample period does the identification become less clear-cut, as the system starts to alternate between the two regimes. This instability of the regime identification may be associated with the onset of the financial and economic crisis beginning in mid-2007. To evaluate the goodness-of-fit, we compare the root mean squared errors (RMSE) of our regime-switching model with a linear model specification. The results clearly indicate that the nonlinear model outperforms the linear alternative in terms of model fit, even when accounting for the estimated number of parameters. Indeed, the RMSE of our baseline model is 0.055 compared to 0.101 in the linear model using the Gibbs sampler. This result is robust to the chosen estimation method for the linear model. Interestingly, even the restricted Markov switching model discussed in Footnote 8 has a lower RMSE (0.060) than the linear model. 5. Conclusion This paper analyzes exchange rate movements in terms of two different exchange rate models within a Markov switching framework. In contrast to much of the previous literature on nonlinearities between exchange rates and their fundamental determinants, our setup explicitly allows for switches between two regimes, one in which the exchange rate is determined primarily by the monetary model, and the other in which the exchange rate follows the predictions of the Taylor rule model. We utilize a variant of the Taylor rule exchange rate model introduced by Engel and West (2006), which we show to yield an estimating equation analogous to the monetary model. Since the model by Engel and West is primarily designed for a small open economy targeting the exchange rate in its Taylor rule, we focus on the Canadian-US dollar exchange rate after the Bank of Canada adopted formal inflation targeting in February 1991. The results of our empirical analysis indicate that the Markov switching model identifies the individual regimes with a very high level of precision. We detect a number of regime switches across the estimation period 1991:2–2008:12, which we can each relate to particular changes in Canadian monetary policy. These results imply that an active monetary policy stance may account for nonlinearities in the exchange rate-fundamentals nexus. The strong evidence of nonlinearities also confirms the notion that exchange rate movements cannot be explained exclusively in terms of any one particular exchange rate model.
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