Does the RBNZ respond to exchange rate fluctuations?

Abstract

This note re-visits the evidence on whether the Reserve Bank of New Zealand targets exchange rates in its Taylor rule. Estimating a standard small-open-economy DSGE model of the New Zealand economy using Bayesian methods, we find that the DSGE model with exchange rate in the Taylor rule generates a statistically significant better fit compared to the model without the exchange rate. This supports the view that while inflation has the highest weight in the Taylor rule, the RBNZ targets the exchange rate when making interest rate decisions. We also find a large weight on the smoothing parameter. The weight on the exchange rate is statistically significant but is smaller compared to the parameter attached to output. We use a large time span (1975–2018) for New Zealand standards for the full sample, and we also perform various subsample analyses and find time-variation in the Taylor rule parameters.

KEYWORDS:

• Bayesian estimation
• Exchange rate
• Monetary policy

JEL Codes:

• C32
• E52
• F41

1. Introduction

In this note, we study whether the Reserve Bank of New Zealand (RBNZ, for short) targets the exchange rate when making monetary policy decisions. More precisely, we study whether the Taylor rule followed by the RBNZ includes a term on the exchange rate and whether this augmented Taylor rule generates a better fit compared to the standard Taylor rule.

Taylor’s (1993) seminal work is a simple description of the Federal Reserve’s reaction function. Taylor assumes that there is a systematic and stable relationship between (short-term) interest rates and economic conditions that increases predictability. While the ‘true' rule describing monetary policy is likely to be a non-linear, asymmetric, time-varying, multivariate function on a large information set about past, current, and future (expected) economic conditions, the Taylor rule has been shown to be a reasonable approximation of this ‘true' and complex policy process.

A key line of research considers augmented Taylor rule including other variables than inflation and output. Most prominently, asset prices have been added to an otherwise standard Taylor rule. Cecchetti, Genberg, and Wadhwani (2002) and Mishkin (2007) advocate the inclusion of measures for asset prices stressing that monetary policy is then able to effectively respond to asset price bubbles and achieve a higher degree of macroeconomic and financial stability. A different stream in the literature focuses on exchange rate movements. Clarida, Galí, and Gertler (1998) show that monetary policy did respond to exchange rate movements, but this reaction was of small quantitative importance. Further, Lubik and Schorfheide (2007) find that some countries (Australia, New Zealand, and the U. K.) do not respond to exchange rate movements, while others (Canada, for example) do.¹

Most recently, research has focused on time-variability in Taylor rule parameters. An early contribution is Judd and Rudebusch (1998) using OLS to estimate Taylor-rules over different time periods. More recently, VAR models and maximum likelihood estimations have been applied to this issue. Studies include Cogley and Sargent (2001, 2005), Lubik and Schorfheide (2004), Boivin (2006), Kim and Nelson (2006), and Sims and Zha (2006).

Those papers do not include expectation effects created by past policy switches. Davig and Leeper (2007) show that the presence of policy switches have crucial implication for determinacy. They show that a general Taylor principle applies, where the Taylor principle is satisfied in the long-run but not necessarily in the short-run. While all of the papers cited so far assume that switches are exogenous, Davig and Leeper (2008) build a model featuring endogenous switches. In this model, the parameters in the Taylor rule are themselves functions of endogenous variables. Switches are triggered, once some endogenous variables reach certain thresholds. They find significant expectation effects and asymmetric effects of symmetric shocks.

We contribute to the literature by studying whether the central bank of a small-open-economy targets the exchange rate in its monetary policy decision making process. For this purpose, we use the Lubik and Schorfheide (2007) model which builds upon the seminal open-economy DSGE model by Galí and Monacelli (2005). We estimate this model using data for the New Zealand economy from 1975 to 2018 using Bayesian methods.

Our key results can be summarized as follows. First, we compare two DSGE models one with the exchange rate in the Taylor rule and one without it (i.e. the baseline model). We find that the model with the exchange rate generates a statistically significantly better fit compared to the baselined model. The estimated Taylor rule shows a high degree of smoothness and a high weight on the inflation rate. The weight on the exchange rate is statistically significant and positive. Hence, the nominal interest rate increases, ceteris paribus, when the exchange rate depreciates. Second, we find that these results hold in three subsamples. We select three events to run our Bayesian regression on the sample before and after the event. These three events are: (i) fixed to floating exchange rate regime (1984: Q4), (ii) inflation targeting introduced (1989: Q4; still in place), and (iii) the Global Financial Crisis (2006: Q4). Our results hold for all subsamples. Third, this subsample analysis also documents instability of parameters over time. Put differently, the weights in the Taylor rule and the smoothing parameter vary sizably over the subsamples. This could indicate time-variability in these policy parameters.

2. The model

In this section, we want to review the model used by Lubik and Schorfheide (2007), which is based upon the seminal open-economy DSGE model by Galí and Monacelli (2005). The model consists of (i) an open-economy IS equation, (ii) an open-economy New Keynesian Phillips curve, and (iii) a Taylor-type interest rate rule describing monetary policy. Since the model is standard, we refer the reader to the technical appendix and these two papers for the full derivation of the model.² In the following, foreign variables are denoted by an asterisk.

The world economy is a continuum of small-open economies represented by the unit interval. Since each country is infinitesimal small with respect to the world, its policy decisions have no impact on the rest of the world. While shocks are idiosyncratic amongst countries, preferences, technology and market structure are identical. Firms set prices according to Calvo (1983) staggering using labor as the only input. At any time t, the labor market is assumed to be in the Walrasian equilibrium.

Households in the model generate utility from consuming, $C_t$, and from enjoying leisure, $1-N_t$. They consume a composite consumption index, which consist of home, $C_{H,t}$, and foreign (imported), $C_{F,t}$, consumption goods. These home (and foreign) goods, $C_{H,t}$, are sub-indices of consumption of imperfectly substitutable home (and foreign) goods. Similarly, the consumer price index, $P_t$, is an aggregate index of home and foreign (imported) goods prices.

The consumption Euler equation can then be written as an open-economy IS equation $\begin{array}{rl}{y}_t& =E_t[y_{t+1}]-[\tau +\alpha (2-\alpha )(1-\tau )][R_t-E_t({\pi }_{t+1})]-{\rho }_z{z}_t\\ & -\alpha [\tau +\alpha (2-\alpha )(1-\tau )]E_t[\mathrm{\Delta }{q}_{t+1}]+\alpha (2-\alpha )\frac{1-\tau }{\tau }{E}_t[\mathrm{\Delta }{y}_{t+1}^{\ast }],\end{array}$where $y_t$ denotes aggregate output and ${\pi }_t$ denotes the CPI inflation rate. Further, $\mathrm{\Delta }{q}_t$ denotes the change in the terms of trade and $1>\alpha >0$ is the openness of the home economy (or the import share). Terms of trade are defined as relative price of exports in terms of imports.

The first shock in the model is a non-stationary technology shock, $A_t$, where $z_t$ is the growth rate of this shock. As a consequence of the non-stationary technology shock, all variables are expressed as percentage deviations from $A_t$. Further, the second shock is driving the world output, $y_t^{\ast }$.

Firms in the model home country use labor as only input and produce along the linear production function, $Y_t=A_t{N}_t$. Firms set prices according to the discrete time version of Calvo's (1983) model, i.e. only a fraction of firms is allowed to reset prices. This optimal price setting problem gives rise to an open-economy New Keynesian Phillips Curve ${\pi }_t=\beta E_t[{\pi }_{t+1}]+\mathrm{\alpha \beta }{E}_t[\mathrm{\Delta }{q}_{t+1}]-\alpha \mathrm{\Delta }{q}_t+\frac{\phi }{\tau +\alpha (2-\alpha )(1-\tau )}[y_t-{\overline{y}}_t],$where potential output (i.e. flexible price output level) is given by ${\overline{y}}_t=-\alpha (2-\alpha )(1-\tau )/\tau y_t^{\ast }$ and $\phi >0$ is a structural parameter driven by the labor supply elasticity, price stickiness (Calvo probability), and the demand elasticity.

Since we are interested in whether the RBNZ targeted the exchange rate in conducting monetary policy, we introduce the nominal exchange rate, $e_t$, via the CPI and assuming that relative purchasing power parity holds. Then, it follows ${\pi }_t=\mathrm{\Delta }{e}_t+(1-\alpha )\mathrm{\Delta }{q}_t+{\pi }_t^{\ast },$where ${\pi }_t^{\ast }$ is the third shock in the model, a world inflation shock.

The process for the terms of trade is governed by the following law of motion $\mathrm{\Delta }{q}_t={\rho }_q\mathrm{\Delta }{q}_{t-1}+{\epsilon }_t^q,$where ${\epsilon }_t^q$ is the fourth shock in the model. The terms of trade are determined via an international goods market clearing condition $\mathrm{\Delta }{y}_t^{\ast }-\mathrm{\Delta }{y}_t=[\tau +\alpha (2-\alpha )(1-\tau )]\mathrm{\Delta }{q}_t.$

Intuitively, an increase in world output will lead to a higher demand for domestically produced goods. This, in turn, will lead to an improvement in the terms of trade.

Monetary policy in the model follows a Taylor-type interest rate rule with smoothing (Del Negro, Schorfheide, Smets, & Wouters, 2007; Liu, 2010; Lubik & Schorfheide, 2007; Smets & Wouters, 2007). In this rule, the RBNZ responds to inflation, output, and the nominal exchange rate. The rule is given by $R_t={\rho }_R{R}_{t-1}+(1-{\rho }_R)[{\vartheta }_{\pi }{\pi }_t+{\vartheta }_y{y}_t+{\vartheta }_e\mathrm{\Delta }{e}_t]+{\epsilon }_t^R,$where ${\vartheta }_i$ for all $i\in (\pi ,y,e)$ are the weights on inflation, output, the nominal exchange rate respectively. The fifth and final shock in the model is a monetary policy shock denoted by ${\epsilon }_t^R$.

3. Methodology and data

The model described in the previous section is estimated using Bayesian methods (see, for example, Del Negro et al., 2007; Smets & Wouters, 2007). We use five blocks of 200,000 draws each for our MCMC chains.

The model has five shocks and we use the following five time series: domestic output, domestic inflation, terms of trade, the domestic nominal interest rate (90-day), and world output. All time series bar the interest rate, in order to ensure stationarity, are first-differenced.

We use quarterly, seasonally adjusted observations and our sample spans the period from 1975:Q2 to 2018:Q1 (173 observations). Data is publicly available and is obtained from the Reserve Bank of New Zealand.

In our analysis, we will use the full sample (1975:Q2 to 2018:Q1), as well as three subsamples. The rationale for splitting the sample is that the underlying monetary policy response parameters might not be stable over time and might change due to significant policy changes. In addition, New Zealand experienced significant policy changes that could lead to structural breaks. For New Zealand, these include changes in exchange rate policy, the design of monetary policy (e.g. implementation of inflation targeting), or large imported shocks (Global Financial Crisis, GFC for short).

The first subsample (1975:Q2 to 1984:Q4 to 2018:Q1) splits the sample into the time with a fixed vs. a floating exchange rate. The second sample (1975:Q2 to 1989:Q4 to 2018:Q1) splits the sample into pre- and post-inflation targeting. Finally, the third subsample (1975:Q2 to 2006:Q4 to 2018:Q1) splits the sample into pre- and post-GFC.

The model is linked to the observed time series via the following measurement equation $Y_t=\left[\begin{array}{c}d{y}_t\\ d{\pi }_t\\ \begin{array}{c}d{q}_t\\ \begin{array}{c}d{y}_t^{\ast }\\ R_t\end{array}\end{array}\end{array}\right]=\left[\begin{array}{c}{y}_t-y_{t-1}\\ {\pi }_t-{\pi }_{t-1}\\ \begin{array}{c}{q}_t-q_{t-1}\\ \begin{array}{c}{y}_t^{\ast }-y_{t-1}^{\ast }\\ R_t\end{array}\end{array}\end{array}\right].$We estimate the three structural parameters of the model, $\alpha ,\tau ,\phi$, and only calibrate the discount factor, $\beta$, to 0.9937. This implies a steady state interest rate of about 2.5 percent. We select the following priors for the estimated parameters. Following Lubik and Schorfheide (2007), we assume that $\alpha$ belongs to the Beta family with mean 0.2 and standard deviation 0.05. The intertemporal substitution elasticity, $\tau$, is Beta distributed with mean 0.5 and standard deviation 0.2. The third and final structural parameter, $\phi$, belongs to the Gamma family with mean 0.5 and standard deviation 0.25. For all shock processes, we assume that the autocorrelation parameters are Beta distributed with mean 0.5 and standard deviation 0.2. For the standard errors of the shocks, we assume they are Inverse Gamma distributed with mean 0.1 and standard deviation 2. These values are taken from Smets and Wouters (2007).

Finally, for the Taylor rule parameters, we follow the strategy by Lubik and Schorfheide (2007). The smoothing parameter follows a Beta distribution with mean 0.5 and standard deviation 0.2. The weight on inflation is Gamma distributed with mean 1.5 and standard deviation 0.5. The weight on output and the exchange rate both follow a Gamma distribution with mean 0.25 and standard deviation 0.13.

4. Estimation results

We estimate the model using Bayesian methods with and without the exchange rate in the Taylor rule and evaluate the model fit across specifications. Results are presented in Table 1.

Table 1. Log-likelihood (LLN) and Bayes factor.

		Sample 1		Sample 2		Sample 3
	Full sample	Before	After	Before	After	Before	After
LLN without FX	508.53	38.97	411.53	60.84	503.73	299.63	171.31
LLN with FX	697.55	98.22	562.96	148.54	707.30	412.79	272.60
Bayes factor	378.04	118.48	302.86	175.40	407.14	246.32	202.59

Notes: Log-likelihood values and the Bayes factor (2*log(B)) are reported. The classification from Kass and Raftery (1995): 2*log(B) > 10 is ‘very strong evidence' in favor of the model with exchange rate targeting. Cut-off points are 1984:Q4 for sample 1, 1989:Q4 for sample 2, and 2006:Q4 for sample 3. Before and after refer to the time period before, after this cut-off point, respectively.

We find that the model with the exchange rate in the Taylor rule has a statistically better fit compare to the model without the exchange rate in the rule. This holds for the full sample and every subsample. In the table, we denoted the sample before the cut-off point as the ‘before' and the sample after the cut-off as ‘after'.

Having established that the model with the exchange rate in the Taylor rule is preferred by the data, we can discuss the parameter estimates. Results are presented in Table 2. First, we notice that the posterior estimates are tightly estimated and are shifted away from their priors indicating that the data is informative.

Table 2. Estimation results.

		Sample 1		Sample 2		Sample 3
	Full sample	Before	After	Before	After	Before	After
Inflation	2.92	6.15	2.55	6.12	3.60	2.28	6.33
	[2.88,2.97]	[5.26,7.07]	[2.52,2.59]	[5.60,6.69]	[3.33,3.81]	[2.25,2.31]	[5.50,7.11]
Output	0.56	0.28	0.40	0.25	0.79	0.31	0.34
	[0.53,0.59]	[0.07,0.45]	[0.38,0.42]	[0.22,0.28]	[0.76,0.83]	[0.31,0.31]	[0.07,0.59]
Exch. Rate	0.45	0.66	0.39	0.45	0.11	0.41	0.47
	[0.43,0.47]	[0.33,1.06]	[0.37,0.41]	[0.41,0.48]	[0.09,0.13]	[0.41,0.42]	[0.07,0.59]
Smoothing	0.85	0.76	0.85	0.71	0.93	0.83	0.84
	[0.83,0.85]	[0.67,0.84]	[0.83,0.86]	[0.69,0.73]	[0.91,0.94]	[0.82,0.83]	[0.80,0.88]

Notes: The point estimates for the weights in the Taylor-rule and 90% confidence interval. Cut-off points are 1984:Q4 for sample 1, 1989:Q4 for sample 2, and 2006:Q4 for sample 3. Before and after refer to the time period before, after this cut-off point respectively.

In the full sample, we find that the weight on inflation is 2.92, which clearly satisfies the Taylor principle (${\vartheta }_{\pi }\ge 1$). While other studies in the literature use different models and different time samples, we still want to put this value in perspective. Lubik and Schorfheide (2007) find a value of 1.69, Liu (2010) reports 1.25, Funke, Kirkby, and Mihaylovksi (2018) find the so far highest value of 1.9. Hence, our value is by far the largest value found. This could be driven by the choice of modeling and the specification of the Taylor rule.³ For the weight on output, we find a value of 0.56 which is similar to the value in Liu (2010) of 0.50 and Medina, Munro, and Soto (2007) of 0.39 and larger compared to the values by Lubik and Schorfheide (2007) of 0.25 and Funke et al. (2018) of 0.03. The smoothing parameter is estimated to be 0.85, which is smaller compared to Medina et al. (2007) with 0.90, but larger compared to Liu (2010) with 0.78 and Funke et al. (2018) with 0.74. In any case, it implies a large amount of persistence in the interest rate.

Most interestingly, we find that the RBNZ put a significant weight on the nominal exchange rate and target it with a weight of 0.45. While Lubik and Schorfheide (2007) find a statistically insignificant value of 0.04. In contrast to this previous finding, our results indicate that the RBNZ did target the nominal exchange rate. However, the weight is smaller compared to the weight on inflation and output. This finding implies an increase in the nominal interest rate in response to an exchange rate depreciation.

Compared to the related literature, our results show a larger weight on inflation and output, a large persistence of the interest rate, and a significant targeting of the nominal exchange rate by the RBNZ. The differences we find to other papers in the literature are likely due to a combination of factors: modeling choices, Taylor rule specifications, as well as different data sets used (incl. time span and detrending choices).

Overall, our results indicate that monetary policy in New Zealand puts a high weight on inflation, consistent with the goal to stabilize inflation, and targets output and the exchange rate. This can be interpreted as focusing on domestic (output) and foreign (exchange rate) or imported business cycle drivers.

5. Subsample results

In the first subsample (1975:Q2 to 1984:Q4 to 2018:Q1), we split the sample into before and after New Zealand switched from a fixed to a floating exchange rate regime. Our results from the full sample largely hold (see Table 2). The weight on the exchange rate is still statistically significant for the before and the after cut-off sample. It indicates, however, that the RBNZ puts a much lower weight on the exchange rate after the floating exchange rate regime was implemented. The weight in the Taylor rule decreases from 0.66 to 0.39.

The weight on inflation dramatically decreases from 6.15 to 2.55 at the time the floating exchange rate regime is put in place. At the same time, the weight on output increases from 0.28 to 0.4. Further, the smoothing parameter also increases (0.76 to 0.85), indicating a more gradual adjustment path of monetary policy. This could have been beneficial either because the uncertainty about the economy is high (i.e. noisy data) or to steer the economy using only small interest rate adjustments mainly via affecting expectations (Kendall & Ng, 2013).

In the second subsample (1975:Q2 to 1989:Q4 to 2018:Q1), we look into the time before and after inflation targeting was implemented; which was a significant break in the conduct of monetary policy in New Zealand. The Reserve Bank of New Zealand Act 1989 importantly established: (i) operational independence for the RBNZ, (ii) a single-decision maker (the RBNZ Governor), and (iii) specified that price stability is the single policy target.⁴

Our results show sizable changes in the monetary policy reaction function after the implementation of inflation targeting. First, the weight on inflation decreases from 6.12 to 3.60. The value of 3.60 is still higher than the full sample estimate and indicates a strong reaction to the inflation rate. Second, we find a large increase in the response to output (0.25 to 0.79) and in the amount of smoothing (0.71 to 0.93). Interestingly, the response to the exchange rate falls from 0.45 to 0.11, but is still statistically significant. Again, the change to inflation targeting showed a dramatic change in the weights in the Taylor rule. It appears that weight was shifted away from targeting the exchange rate to targeting output as well as increasing interest rate smoothing.

In the third subsample (1975:Q2 to 2006:Q4 to 2018:Q1), we split the sample into before and after the start of the Global Financial Crisis. The only noteworthy difference we find is a much larger weight on inflation (6.33 vs. 2.28) after the GFC. The other values remain stable.

Overall, the implementation of the floating exchange rate regime lead to changes in the conduct of monetary policy, in that the RBNZ reduced the weight on the exchange rate and increased the weight on output and the smoothing aspect of policy. More dramatic are the changes following the implementation of inflation targeting. Here, we find a larger response to output and a large shift towards smoothing. Further, the weight on the exchange rate has been reduced sizably. Finally, the subsample results presented in this section need to be interpreted with caution, given that we sometimes only have 10 years (40 observations) of data available.

6. Conclusion

The title of this paper asks the question: Does the RBNZ Respond to Exchange Rate Fluctuations? We estimate a small-open-economy DSGE model using Bayesian methods to answer this question. Using data from 1975 to 2018, we find that the DSGE model with exchange rate in the Taylor rule generates a statistically significant better fit compared to the model without the exchange rate. This supports the view that the RBNZ targets the exchange rate when making monetary policy decisions. The estimated Taylor rule shows a high degree of interest rate smoothing and a high parameter on targeting the inflation rate. In addition, the weight on the exchange rate is statistically significant but is smaller compared to the parameter attached to output.

A potential shortcoming of the analysis is the small-scale nature of the model. The exchange rate might be correlated with other variables which are not included. Future research should consider larger models, especially models with an emphasis on investment and labor market features, to assess the robustness of our results. Along this line, investigating how the dual mandate introduced to New Zealand in 2018 would have affected the business cycle.

In addition, we believe that it would be interesting to study the time-variability in the Taylor rule coefficients, potentially with a time-varying parameter VAR model. Finally, while our study was positive in nature, we are interested in studying optimal monetary policy and determining the optimal weight on the exchange rate for the New Zealand economy. We leave these questions to the future.

Acknowledgements

We would like to thank Özer Karagedikli for helping us with the data collection. The views and opinions in this paper are our own. All errors are our own.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Other papers using the Galí and Monacelli (2005) and Lubik and Schorfheide (2007) models include Justiniano and Preston (2010) for Australia, Canada, and New Zealand or Zhang, Martinez-Garcia, Wynne, and Grossman (2021) for Australia, Canada, South Korea, Sweden, Switzerland, and the UK.

2 For a full derivation of the Galí and Monacelli (2005) model, please see the technical appendix.

3 This is not driven by including the earlier observations. We started the estimation in 1991:Q1 and found an even larger weight on inflation.

4 See Buckle (2018) and McDermott and Williams (2018) for an overview of monetary policy in New Zealand.