Does McCallum’s rule outperform Taylor’s rule during the financial crisis?

G Model

ARTICLE IN PRESS

QUAECO-1083; No. of Pages 13

The Quarterly Review of Economics and Finance xxx (2017) xxx–xxx

Contents lists available at ScienceDirect

The Quarterly Review of Economics and Finance journal homepage: www.elsevier.com/locate/qref

Does McCallum’s rule outperform Taylor’s rule during the financial crisis?夽 Alexander Jung Sonnemannstr. 20, 60314, Frankfurt, European Central Bank, Germany

a r t i c l e

i n f o

Article history: Received 21 November 2016 Received in revised form 7 November 2017 Accepted 12 November 2017 Available online xxx JEL Classification: E43 E52 E58

a b s t r a c t This paper makes an empirical comparison of two simple monetary policy rules, the McCallum rule and the Taylor rule and uses them to assess the monetary policy stance of the ECB during the financial crisis. After the Taylor rule, the McCallum rule ranks among the most widely analysed nominal feedback rules used for policy simulations. The retrospective evidence for the euro area suggests that these simple rules might have provided useful information about the policy stance of the ECB. While we find that for most of that period both rules were fairly close to actual policy, we find no support for McCallum (2000)’s claim on the superiority of his rule over the Taylor rule especially in an environment of very low interest rates. © 2017 Board of Trustees of the University of Illinois. Published by Elsevier Inc. All rights reserved.

Keywords: McCallum rule Taylor rule Monetary base Shadow rate Euro area

1. Introduction Friedman (1968) made a famous contribution to the literature suggesting that a central bank should increase the money supply by a constant percentage rate every year in order to meet its objective of price stability. Ever since, the notion that inflation is ultimately a monetary phenomenon has become a central principle of monetary economics. Because growth in the money supply is erratic due to structural change in an economy or its monetary sector, it is complicated for a central bank to gain control over the money supply. Against this background, money growth rules have received increasingly less attention by policy-makers (Orphanides, 2007), and the Taylor (1993) rule, which uses the policy rate as an instrument, has played a dominant role in the monetary policy assessments of central banks (Asso, Kahn, & Leeson, 2010). McCallum (1988) proposed a policy rule for the monetary base as an instrument. In relation to the Taylor rule, a potential advan-

夽 The author thanks, C. Tille, W. Lemke, M. El-Shagi and A. Belke for comments and discussion. An earlier version of the paper was presented at the 90th annual WEAI conference in Honolulu. The views expressed by the author are his own and do not necessarily reflect those of the Eurosystem. The author remains responsible for any errors or omissions. E-mail address: [email protected]

tage of that rule is that it does not include unobservable variables such as the real interest rate and the output gap. For quite some time, researchers have recognized the difficulties associated with the measurement of the output gap (McCallum, 2001; Orphanides, Porter, Reifschneider, Tetlow, & Finan, 2000). A money base rule could dominate the Taylor rule, if it is difficult to assess the state of the economy in real time (Razzak, 2003). Based on a counterfactual comparison of the Taylor rule and the McCallum rule for three major economies, McCallum (2000) finds that from an ex post perspective money base rules tend to outperform interest rate rules, especially for Japan. Since May 1999, in its publication “Monetary Trends”, the Federal Reserve Bank of St. Louis has regularly reported indications from a McCallum rule for the United States using alternative target inflation rates. Moreover, studies for Russia, China and India (Esanov, Merkl, & de Souza, 2005; Patra and Kapur, 2012; Sun, Gan, & Hu, 2012) find that a McCallum rule could be a suitable benchmark to assess the central banks’ policy decisions. The financial crisis had a strong impact on the global economy and on the transmission of monetary policy. Several major economies faced prolonged periods of low interest rates and even tested the zero lower bound. The zero lower bound on nominal interest rates has led most major central banks in the world to adopt non-standard measures implying a strong expansion of their balance sheets and thus an increased role for the monetary base

https://doi.org/10.1016/j.qref.2017.11.005 1062-9769/© 2017 Board of Trustees of the University of Illinois. Published by Elsevier Inc. All rights reserved.

Please cite this article in press as: Jung, A. Does McCallum’s rule outperform Taylor’s rule during the financial crisis? The Quarterly Review of Economics and Finance (2017), https://doi.org/10.1016/j.qref.2017.11.005

G Model QUAECO-1083; No. of Pages 13 2

ARTICLE IN PRESS A. Jung / The Quarterly Review of Economics and Finance xxx (2017) xxx–xxx

as policy instrument. In an economic environment where the zero lower bound on interest rates becomes binding, it may be difficult for a central bank to implement the required negative interest rates. Moreover, the natural rate of interest, which normally is subject to some time-variation, has fallen considerably. Thus, the indications from an interest rate rule could become difficult to interpret for policy-makers. Despite this criticism, Taylor (2012) considers his rule to be “sound” also in those circumstances, since a central bank could still pursue other measures in order to further ease its monetary policy stance in the presence of the zero lower bound. This view is also supported by the observation that several major central banks have implemented negative rates (Jackson, 2015), thereby overcoming the zero lower bound constraint. A knowledge gap exists as to whether base money rules, in which the natural rate of interest does not enter, would have been superior to the Taylor rule in a financial crisis. The aim of the paper is to address this question by examining the implications of the McCallum rule and the Taylor rule for the monetary policy stance of the ECB during the financial crisis. In an environment characterised by massive output losses, high unemployment and low interest rates, the policy rate may no longer be the sole indicator of the monetary policy stance. Since the monetary base can still be influenced by the central bank’s actions, the central bank can switch to a monetary base rule. A theoretical rationale for such an approach was given in Christiano and Rostagno (2001), who suggest that a central bank could monitor the money growth rate in parallel to the Taylor rule and commit to abandoning the Taylor rule in favour of a money growth rule under a clearly specified escape clause. Moreover, in addressing shortcomings of the New Keynesian model, other researchers (Beck and Wieland, 2007; Lucas, 2007) have argued that monetary information should continue to be used as a cross-check of the economic information in the monetary policy process. The paper is organised as follows. Section 2 introduces the McCallum rule and the Taylor rule. Section 3 specifies a McCallum rule for the euro area. Section 4 assesses the McCallum rule for the euro area and compares it with the Taylor rule during the financial crisis. Section 5 concludes.

2. The McCallum rule and the Taylor rule 2.1. Simple rules and monetary policy strategies A monetary policy strategy is the general approach used by central banks to achieve their primary objective − in the case of the ECB this goal is price stability. It provides both a framework for the internal deliberations among policy-makers and for explaining monetary policy decisions to the public in a clear and transparent manner. This makes it easier for the general public to understand the response pattern of monetary policy to economic developments, and thus to anticipate the broad direction of monetary policy over the policy horizon. It also helps to stabilise private sector expectations and to reduce fluctuations on the financial markets. While many central banks today pursue an inflation targeting strategy, the ECB prefers a two-pillar monetary policy strategy, which rests on an economic and a monetary analysis (for details see Issing, 2006). A monetary policy strategy may lack sufficient institutional discipline to assure the achievement of the central bank’s goal(s) and there may be trade-offs between goals such as those between price stability and financial stability. The debate on rules versus discretion has illustrated that simple rules may not qualify as an optimal monetary policy strategy for a central bank. Though, a broad consensus exists among academic macroeconomists that policymakers’ choices should closely track pre-determined rules.

For example, Taylor (1993) demonstrated that the Federal Reserve’s monetary policy choices could, in fact, be well-approximated by a simple feedback rule. At the current juncture, however, it appears that central banks are unlikely to give up their discretionary powers to a nominal feedback rule. In that sense, a more promising avenue for a simple rule would be its use as an indicator of the monetary policy stance. Rather than stating that monetary policy should follow a specific fixed rule, simple rules could also be used as reference guides. In the literature, policy rules are understood as a positive and normative description how a policy instrument (e.g., short-term interest rate, monetary base, exchange rate) responds to changes in the macroeconomic environment (Blattner & Margaritov, 2010). As emphasized by Bernanke and Boivin (2003), central bankers routinely monitor a large number of economic variables, whereas simple policy rules typically only focus on a subset of these data. In empirical work, policy rules are often linked to macro models or are presented as single equation reduced forms. Their estimation is linked to a wide range of assumptions, e.g., concerning expectation formation, data and model uncertainty, and the monetary policy instrument. Monetary policy has to be forward-looking, since policy actions affect inflation only with a lag. Simple rules can incorporate this element by replacing inflation and output variables with their corresponding forecasts at the policy horizon. However, simple rules only include a subset of the information available about the likely future path of inflation and output. As a matter of fact, an obvious limitation of the rules as guides to policy is that they ignore useful information about macroeconomic variables from other forwardlooking indicators. Optimal rules, which are derived from a first order condition of the central bank’s objective function, are typically model dependent (McCallum & Nelson, 2005). Compared to an assessment of all relevant monetary, financial and economic indicators, which seems to be supported by optimal monetary policy considerations (Dieppe, Küster, & McAdam, 2005), the advantage of a simple rule is that it has low information requirements. Nevertheless, in a realtime policy context, the application of these policy rules can be sensitive to the estimate of the natural interest rate, the value of the inflation target, the approach applied to estimate potential output and the quality of inflation and output forecasts. In addition, lags in the publication of statistical data on GDP and frequent revisions thereafter can hamper the application of a simple rule in assessing the monetary policy stance. An argument against the validity of simulations performed with nominal feedback rules is that they could suffer from the Lucas critique. Lucas (1976) argues that the parameters of traditional macroeconometric models depend implicitly on agents’ expectations of the policy process and are unlikely to remain stable as policymakers change. In the present example, this argument means that the parameters used to simulate the data generating process for economic variables are calibrated from data absent nominal feedback rules, and they would presumably change if a nominal feedback rule were put into place. While at a theoretical level, the Lucas critique is uncontested – reduced-form models are not invariant to policy-induced structural changes –, its empirical relevance in the case of nominal feedback rules is less clear (Rudebusch, 2005). Against this background, the following four criteria should be applied, when evaluating the usefulness of a monetary policy rule for practical purposes (McCallum, 1988): first, a policy rule should be robust in different models of the economy; second, the policy rule should help to reduce cyclical fluctuations in output and contribute to maintaining price stability; third, a policy rule should be specified in terms of an instrument variable that the monetary authority can control directly and/or accurately; and fourth, the rule should not rely upon the absence of regulatory change and

Please cite this article in press as: Jung, A. Does McCallum’s rule outperform Taylor’s rule during the financial crisis? The Quarterly Review of Economics and Finance (2017), https://doi.org/10.1016/j.qref.2017.11.005

G Model

ARTICLE IN PRESS

QUAECO-1083; No. of Pages 13

A. Jung / The Quarterly Review of Economics and Finance xxx (2017) xxx–xxx

technical innovation in the payments system and financial industries. 2.2. The McCallum rule Based on econometric research using several decades of data for the United States (US), McCallum (1988) argued that nominal income targeting should be considered as a monetary policy strategy for the US Federal Reserve (Fed) and for other central banks. His research suggested that the Fed could have stabilised nominal GDP growth in the US close to a smooth non-inflationary target path over decades, if it had followed that rule, especially during the 1930s and 1970s, and despite severe regulatory and financial turmoil. In its initial formulation the McCallum rule was designed as a (simple) instrument rule for the monetary base using a nominal spending target. Although the ECB does not control the growth of the monetary base, it could do so if it chose to. We use this growth rate as an indicator of monetary policy ease or restrictiveness, even if the ECB is not operating so as to ensure control of this rate. The path implied by the McCallum rule provides a benchmark for the monetary expansion of the monetary base. The McCallum rule could be interpreted as a dynamic monitoring range for base money (Stuart, 1996). Despite the fact that its derivation is made under the assumption that the underlying trend measures for output and velocity are fairly stable, the rule captures the possibility of changes in trend velocity. The McCallum rule can be written as follows (McCallum, 1988): bt = x∗ − ¯vt + (x∗ − xt−1 )

(1)

where bt denotes the log of the monetary base, vt is the average rate of growth of base velocity (over n periods, typically four years), xt is the log of nominal output, ␭ a response parameter (with a positive value, initially set to 0.5), “*” denotes a target variable and  refers to the period-by-period change. In this context, the nominal GDP target can be either set at a fixed value or be approximated by a ten-year average. With a view to the fact that most central banks in the world focus on some form of an inflation target (Hammond, 2012), an alternative version of the rule was provided by McCallum (2000) using a decomposition of the nominal spending target into an inflation target and an estimate of (real) potential output growth.1 Based on (1), the nominal GDP target can be decomposed into an inflation target ␲* and the long-run average rate of growth of real GDP yr* (which is not affected by monetary policy): bt = ∗ + yr ∗ − ¯vt − (t − ∗ ) − ˜yt

(2a)

bt = ∗ + yr ∗ − ¯vt − (t − ∗ ) − (yrt − yr ∗ )

(2b)

bt = ∗ + yr ∗ − ¯vt − (t − ∗ )

(2c)

where ␲t denotes the inflation rate, yr real GDP (in logs), y˜ t the (real) output gap (and the notations as above). The inflation target can be set at different values, while typically a value of 2% is used for the ECB. We provide three variants of the McCallum rule. In this context, (2c) does not immediately follow from (1), since it removes the output gap, which is not an observable variable and there are measurement problems. Moreover, as a robustness check, further variants of (2a), (2b), (2c) can be computed, which have a forward(backward-) looking term for the inflation gap and the output (growth) gap. Because the steady state is characterised by a closed

1 In applying the rule in practice, instead of using a medium-term assumption for nominal GDP the Federal Reserve Bank of St. Louis decomposed it into an inflation target and an estimate of real potential output growth (Stark and Croushore, 1998).

3

inflation (and output) gap, in the long run the implied benchmark paths for base money growth in (1) and (2a), (2b), (2c) only depend on the inflation target, the (estimate of) potential real GDP growth and average velocity. Moreover, if potential real GDP growth, the inflation target and velocity are constant, the “steady-state path” of the McCallum rule corresponds to Friedman’s constant money growth rule. 2.3. The Taylor rule Taylor (1993) proposed a rule because there was a growing consensus that interest rate rules that respond positively to deviations of inflation and output from their respective targets work well in a large variety of models and circumstances. In principle, this path should be consistent with price stability over the medium to longer term, since the Taylor rule includes the inflation target in addition to the (equilibrium) real interest rate. It is specified in terms of an interest rate as instrument and allows for the inclusion of an inflation target. The classic Taylor rule (3), which could be written in many different ways (and with alternative parameters), is derived under the assumption that the interest rate channel is not impaired:2 rt = r ∗ + t + 0.5 · (t − ∗ ) + 0.5 · y˜ t

(3)

where rt denotes the policy rate (short-term nominal interest rate) at time t, r* is the natural real interest rate (as measured by the long-run average real rate of interest), ␲* is the inflation target, ␲t is the inflation rate and y˜ t the (real) output gap (as measured by the deviation of current real GDP from potential or natural-rate value). We use output gap series from the IMF, which are normally computed using an HP filter applying a smoothing parameter. For the Fed, Taylor (1993) has argued that for an assessment of monetary policy using the Taylor rule a response factor of 0.5 for the inflation and the output gap should be used.3 Although, this specification of the rule can accommodate different values for the inflation target of the central bank, for economies such as the United States and the euro area typically a value of 2% is used in empirical research. As shown by Woodford (2001) and subject to two caveats, the Taylor rule incorporates several features of an optimal monetary policy which are desirable for stabilising inflation around an inflation target (e.g., 2% per annum). One point of criticism is that from a welfare-theoretic perspective that minimises relative-price distortions associated with imperfect synchronisation of price changes, the target inflation rate in this rule should be actually zero. A second point is that when measuring the output gap this should refer to the gap between actual output and a “natural rate” of output rather than a deterministic trend. A simple (forward-looking) policy rule, which takes into account the above mentioned criticism of the output gap can be written as follows (Orphanides, 2003): r t = r t−1 + ˇ · (t+n − ∗) +  · (yr t+n − yr∗)

(4)

with the notations as above, and ␲t+n is the inflation forecast and yrt+n is the real output forecast (both n steps ahead), and yr* is potential output growth, ␤ and ␥ are response factors with positive values. Orphanides (2003) refers to the rule (4) as “natural-growth targeting rule” to highlight that it relies on estimates of the economy’s natural growth rate and responds to perceived imbalances

2 There also exist other versions of the Taylor rule, which allow for interest rate smoothing. See e.g., Sack and Wieland (2000). In addition, the literature has favoured the use of forward-looking Taylor rules, as opposed to the classic rule, which uses a contemporaneous inflation gap and output gap. See Orphanides (2003). 3 Note Bernanke and Boivin (2003) have shown that the use of estimated factors can improve the fit when estimating the policy reaction function.

Please cite this article in press as: Jung, A. Does McCallum’s rule outperform Taylor’s rule during the financial crisis? The Quarterly Review of Economics and Finance (2017), https://doi.org/10.1016/j.qref.2017.11.005

G Model QUAECO-1083; No. of Pages 13 4

ARTICLE IN PRESS A. Jung / The Quarterly Review of Economics and Finance xxx (2017) xxx–xxx

between the growth of aggregate demand and aggregate supply instead of an output gap. Despite the fact that the Taylor rule is one of the most popular benchmarks for the assessment of the monetary policy stance of central banks, the literature finds certain limitations for practical policy purposes and proposes enhancements. First, policy rates of most central banks have been subject to what some have called the “great deviation” (Hofmann & Bogdanova, 2012). It means that these rates typically have been below the levels implied by the Taylor rule since the early 2000s. Moreover, deviations of policy interest rates from the levels implied by the Taylor rule increased especially after the turn of the century. During the financial crisis two factors contributed to a widening of the deviation. One was the unprecedented increase in uncertainty, which made it difficult for central banks to produce high-quality inflation and output forecasts. Another was the zero-lower bound, which prevented the central banks to quickly lower policy rates beyond zero. In fact, the rule could destabilise the economy in an environment with a binding zero lower bound (Benhabib, Schmitt-Grohé, & Uribe, 2001). As a remedy some studies find that the Taylor rule specification can be improved by the inclusion of international spillovers, by modelling non-linear dynamics (Beckmann, Belke, & Dreger, 2017) and by using a specification of the Taylor rule that targets the real rate instead of the nominal rate (Belke and Klose, 2013). Other studies based on Taylor rule reaction functions model explicitly the monetary policy interdependence between the ECB and the Fed and consider a leader–follower relationship between the ECB and the Fed with the latter behaving as the Stackelberg leader (e.g., Belke and Cui, 2010). Second, an issue is whether final or real-time data is used in the analysis. Real-time data have the advantage that they fully capture uncertainties, which are present, when policy-makers take their monetary policy decisions. Using Taylor’s rule as an example, Orphanides (2001) demonstrates that real-time policy recommendations differ considerably from those obtained with ex post revised data. Moreover, the Taylor rule may not be robust to different vintages of the data and to other concepts of estimating the output gap (Bernanke, 2010; Orphanides, 2003). In addition, as shown by Belke and Klose (2011) for the example of the euro area, using real-time data instead of final data may lead to higher coefficients for the inflation and output gap. Third, the natural interest rate may be time-varying as opposed to a constant, as assumed in the rule specification. It has been shown that the natural rate in the United States fell to close to zero during the financial crisis and has remained there (Holston, Laubach, & Williams, 2017). The authors also find that large declines in natural rates of interest have occurred over the past 25 years in four major economies. There appears to be a substantial amount of comovement over time, suggesting an important role for global factors in shaping natural rates of interest. Recent estimates of mediumterm equilibrium real rates for the euro area are near zero percent (Beyer and Wieland, 2017), i.e. considerably below Taylor’s long run equilibrium real rate of 2%. Despite these points, John Taylor suggested in his interventions at the ECB watcher conferences in 2014 and 2017 that a more ruleoriented monetary policy would be preferable, since it would even strengthen the independence of a central bank and it would help to create a needed rules-based international monetary system. To this end, he argued that his classic rule (Taylor, 1993) should be used as relevant benchmark for policy analysis (with e.g. an inflation target of 2% and a 2% real policy interest rate) and, when interest rates go below zero, to look at money growth and to use forward guidance as policy rule. Against this background, we use the specification (3) as main benchmark for comparison with McCallum’s rule and use forward-looking rules as check for robustness.

Fig. 1. Balance sheet expansions of major central banks. (Index January 2007 = 100) Notes: Weekly data. Indices are based on quarterly averages of assets in national currencies. Data refer to the simplified balance sheet (methodology focusing on the monetary policy elements of the balance sheet). Sources: Bank of England, Bank of Japan, Federal Reserve Board and ECB.

3. A McCallum rule for the Euro area The monetary policy of the ECB provides an interesting case study, since it has regularly monitored money and credit developments (e.g., Beyer and Reichlin, 2006) and the money and banking statistics are of high quality. For the euro area, the literature has demonstrated that a monetary policy assessment aimed at price stability can benefit from the valuable information contained in monetary aggregates (e.g., Masuch, Nicoletti-Altimari, Rostagno, & Pill, 2003). Moreover, there is evidence for the euro area that, prior to the financial crisis, policy rules including money growth variables may have outperformed conventional Taylor rules (Beck and Wieland, 2008; Scharnagl, Gerberding, & Seitz, 2010). Despite massive changes in the monetary policy transmission mechanism, information contained in monetary aggregates seems to have remained useful for policy-makers in real-time, when assessing future trends in the real economy (Papademos and Stark, 2010). Moreover, during the financial crisis the ECB adopted (large-scale) asset purchase programmes, marking a change from a conventional interest rate policy to an active management of the euro area balance sheet and hence its monetary base. As a result, banks’ excess reserves, which were low prior to the adoption of the measures, increased to unprecedented high volumes. As illustrated in Fig. 1, with the start of the financial crisis other main central banks adopted non-standard monetary policies, which were also aimed at actively influencing the evolution of their balance sheets.4 A comparison of the actual outcomes and a monetary policy rule may give a different message when using a (forward-looking) rule with real-time forecasts of inflation and output instead of final values (Jung, 2013; Orphanides, 2007). Whether final or real-time data should be used depends on the purpose of the analysis. Final data should be used whenever the research interest is to assess the setting of the monetary policy stance with the benefit of hindsight. Real-time data should be used when assessing the performance of the monetary policy given its genuine constraints (data and

4 For a comparison of different Quantitative Easing programmes see Fawley and Neely (2013).

Please cite this article in press as: Jung, A. Does McCallum’s rule outperform Taylor’s rule during the financial crisis? The Quarterly Review of Economics and Finance (2017), https://doi.org/10.1016/j.qref.2017.11.005

G Model QUAECO-1083; No. of Pages 13

ARTICLE IN PRESS A. Jung / The Quarterly Review of Economics and Finance xxx (2017) xxx–xxx

5

model uncertainty). For those rules, which include contemporaneous gaps, we use final data, whereas for the forward-looking rules, we include real-time data from the ECB staff macroeconomic projections. In this section, we derive alternative benchmark paths for the euro area monetary base from the McCallum rule (for data sources, see Table A1 in the Appendix A). First, we discuss issues related to the use of the euro area monetary base. Second, we explain the calibration of the McCallum rule for the euro area and provide a comparison of outcomes with the path implied by calibrated and estimated base money rules. Third, we estimate the parameter of the base money rules and compare the parameterisations of these rules with those from the calibrated rule. 3.1. The euro area monetary base In general, the monetary base is defined as the sum of currency in circulation and reserve balances. In the euro area, base money consists of currency in circulation, the deposits that credit institutions are required to maintain with the Eurosystem in order to cover the minimum reserve requirements (required central bank reserves) and credit institutions’ holdings of highly liquid deposits with the Eurosystem over and beyond the level of required central bank reserves (excess central bank reserves and recourse to the deposit facility). The ECB has chosen the following operational definition of its monetary base for the euro area:5 Monetarybase = banknotes in circulation + Euro area 



credit institutions current account + Eurosystem s deposit facility This measure, which only includes liabilities in the Eurosystem’s balance sheet and refers to period averages, applies to the euro area as a whole. Its currency in circulation component includes vault cash, but excludes coins (the demand for which can be assumed to be fairly stable in a given regime). In the euro area, a long historical time series of the monetary base is not available. This is because at the beginning of monetary union (in 1999), harmonisation of the time series across member countries, which was based on the ECB regulation on minimum reserves, took effect. Prior to it, the technical features of reserve requirements varied significantly across countries.6 In addition, the national systems foresaw different functions of the reserve requirements in their monetary policy frameworks and mirrored specific properties of national financial systems. Important cross-country differences concerned the liability base for which reserve requirements apply, the reserve ratios and the level of remuneration which is zero in some countries (for details see European Monetary Institute, 1995, p. 124n.). Furthermore, the currency in circulation component of the monetary base series contains a structural break related to the euro cash changeover, which took effect in January 2002. For this reason, a dummy (cashdum) is introduced, which is 1 from 2001Q2 to 2002Q2 and zero otherwise. Other breaks in the series owing to euro area enlargement have been addressed by using time series that take into account the changing composition of the euro area.

5

See Table 1.4.3 in the ‘Minimum reserve and liquidity statistics’ section of the ECB’s Economic Bulletin. Genuine data in accordance with this definition are available from February 1999, i.e., the date when Monetary and Financial Institutions (MFIs) in the euro area had to comply with the new minimum reserve system of the Eurosystem. 6 The relevant provisions are the Council Regulation (EC) No. 2531/98 of 23 November 1998 and ECB Regulation of 1 December 1998 on the application of minimum reserves (ECB/1998/15).

Fig. 2. M3 multiplier and base money in the euro area. (index, 1999 = 100; multiples of base money) Note: the M3 multiplier is the ratio of the stock of M3 and the stock of base money. Source: ECB.

In assessing the usefulness of the monetary base as a policy instrument, the question whether a (stable) money multiplier exists and more specifically whether there is a stable link from bank reserves to money and to bank lending, has attracted some attention in policy debates. When large shocks to the financial system impact on the transmission mechanism and interest rates approach the zero lower bound, as was the case during the financial crisis, a central bank may not have full control over its money supply. Moreover, instabilities in the demand for currency in circulation can translate into similar instabilities of the monetary base. In this case, Hafer, Haslag, & Hein (1996) suggest using total reserves, which are part of the monetary base, as relevant measure. For the United States, Anderson and Rasche (2001) find that over a period of 80 years including the Great Depression a stable money demand for the monetary base can be identified. This could provide support for the use of the monetary base as an instrument for monetary policy. By contrast, other researchers (Carpenter & Demiralp, 2010; Reis 2012; Williams, 2012) suggest that the linkage between the monetary base and the economy has broken during the crisis. Despite their analysis, the Fed embarked on three rounds of largescale expansion of its balance sheet, thereby signalling that it would believe in the effectiveness of the link between reserves and the real economy (Blinder, 2010; Taylor, 2009). For the euro area recent evidence suggests that the money multiplier has become less stable during the financial crisis (see Fig. 2). The reason is that since 2008 the annual growth rate of the broad monetary aggregate continued to be lower than that of base money, implying a (trend) decline in the money multiplier. 3.2. Calibrated base money rules The McCallum rule essentially comprises of three parts. First, it includes a constant term which is the nominal GDP growth target and can be decomposed into an inflation target and a long-run estimate of real GDP growth. In the calibrated version we set both the inflation target and the desired GDP growth to 2%, respectively. To this end, we consider that the ECB’s aim of inflation “below, but close to, 2%” is a focal point for medium- to long-term inflation (␲*). While potential output estimates are highly uncertain, esti-

Please cite this article in press as: Jung, A. Does McCallum’s rule outperform Taylor’s rule during the financial crisis? The Quarterly Review of Economics and Finance (2017), https://doi.org/10.1016/j.qref.2017.11.005

G Model QUAECO-1083; No. of Pages 13

ARTICLE IN PRESS A. Jung / The Quarterly Review of Economics and Finance xxx (2017) xxx–xxx

6

Fig. 3. McCallum rule and actual base money expansion for the euro area. Note: The above McCallum rule shown refers to version (2b) assuming an inflation target of 2%, potential output growth of 2% and a response factor of 0.5. Source: ECB and own calculations.

mates of the potential output growth in the euro area, as measured by a 10 year moving average, show that the rate may have fallen during the financial crisis from around 2% to below 1%. Most longerterm estimates for (real) potential output in the euro area are in the range of 1%–1.5% (Anderton et al., 2014). Second, it includes an estimate of the trend decline of velocity, which is modelled as a moving average of 16 quarters (calculated recursively), as suggested by McCallum. This part captures structural changes in the demand for base money, such as those owing to financial innovations. Third, a variable term captures the response of the monetary base to changes in the real economy, i.e. an inflation and output (growth) gap. We report the calibrated McCallum rule based on (2b), which allows setting an inflation target.7 It explains the annual growth rate of base money (at a quarterly frequency). The monetary response factor ␭ is set to 0.5. This value ensures a stable response to changes in the real economy, since according to simulations by Stark and Croushore (1998) for the United States this property is satisfied for values of ␭ in the range [0.4–0.8].8

3.3. A comparison of the McCallum rule path with the outturn We assess actual money base growth rates relative to the path implied by the calibrated base money rule and identify episodes for which both rules agree or disagree. When assessing actual monetary base developments relative to the path implied a rule, annual growth rates have been used. Fig. 3 shows a comparison of the actual monetary base expansion with the calibrated (contemporaneous) version of the McCallum rule (using an inflation target and long-run output growth of 2% respectively).

7

We checked versions (1), (2a) and (2c) and found them to be close to (2b). A wider range of response parameters could be consistent with the optimality conditions of a simple policy rule. We refer to the parameterisation used in McCallum (2000). 8

In the years preceding the financial crisis the comparison suggests that the monetary base expansion was close to the benchmark. Though, when the financial crisis hit the euro area strongly, several departures between the McCallum rule path and actual outcomes can be observed. Four episodes stand out for which a closer assessment is warranted. At the end of 2010, the rule indicated that a stronger monetary base expansion would have been warranted. A similar observation can be made at the beginning of 2013. By contrast, at the end of 2011 and from the beginning of 2015, the rule suggested that the base money accelerated too fast. How do these indications from the base money rules square with the actual policy decisions of the ECB during the financial crisis? Indeed, several non-standard measures adopted by the ECB implied substantial changes for the path of the euro area monetary base. We find that the timing of several non-standard measures which the ECB adopted during the financial crisis was not always consistent with the indications of the McCallum rule. This could suggest that, given the difficulties to control base money, the ECB did not finetune its monetary policy so as to follow that rule. In the first episode (end of 2010), the rule indicated the need for a stronger expansion of the monetary base. In May 2011, the ECB adopted the Securities Markets Programme (SMP), which comprised outright purchases of certain types of sovereign bonds. Though, the volume of bank reserves (and thus the monetary base) remained broadly unchanged, since they were also fully sterilized through liquidity-absorbing operations, so as to not affect central bank liquidity conditions (Cour-Thimann & Winkler, 2012). In the second episode (end of 2011), the rule indicated that the money base expansion was becoming too rapid. In December 2011 and February 2012, the ECB introduced two longer-term refinancing operations (LTROs) with three-year maturity. However, these measures implied a stronger expansion in base money. In the third episode (at the beginning of 2012) money base growth significantly undershot the rule path. As of early 2013, VLTRO repayments by banks were allowed by the ECB. This had the effect that the money base was shrinking. It took until June 2014, when the ECB introduced the TLTROs, thus marking the start of credit easing, which

Please cite this article in press as: Jung, A. Does McCallum’s rule outperform Taylor’s rule during the financial crisis? The Quarterly Review of Economics and Finance (2017), https://doi.org/10.1016/j.qref.2017.11.005

G Model QUAECO-1083; No. of Pages 13

ARTICLE IN PRESS A. Jung / The Quarterly Review of Economics and Finance xxx (2017) xxx–xxx

was followed by a stronger expansion of the monetary base. In the fourth episode (beginning of 2015) the rule indicated that the expansion of the monetary base would need to moderate. In January 2015, the ECB adopted an expanded asset purchase programme (APP) including large-scale purchases of covered bonds, ABS and public sector bonds. As part of the APP, the ECB started to buy public sector bonds as of March 2015 and later (in December 2015 and March 2016) extended both size and duration of its large-scale public sector purchase programme (PSPP). This package of measures contributed to an acceleration of the euro area monetary base.

Table 1 Johansen cointegration tests for the euro area monetary base. System

Rank r

Trace statistics

Critical values 95%

Result

mb, y

=0 ≤1 =0 ≤1 ≤2 =0 ≤1 =0 ≤1 ≤2

43.13** 7.98 75.75** 26.30 8.92 45.97** 19.16 84.47** 28.29 12.72

42.17 21.62 66.10 42.17 21.62 42.17 21.62 66.10 42.17 21.62

One cointegration vector

mb, y, lt

mb, v mb, v, y

4. Assessing the McCallum rule for the euro area Previous studies have examined how well monetary policy based on the rules would have performed using counterfactual simulations (McCallum, 2000; Stark and Croushore, 1998; Dueker and Fischer, 1998; Sun et al., 2012). However, our interest here is in assessing whether the rules would have provided useful information about the policy response in the episode of the global financial crisis. This is done by looking at whether past policy errors can be identified by observing the divergence of actual policy from the paths implied by the rules based on historical data rather than simulations. To this end, we assess whether the ECB’s reaction function can be described by a base money rule. We look into several specifications of estimated base money rules for the euro area. First, in order to examine the long-run drivers of the monetary base and to check whether there is a stable long-run relationship between them and the monetary base, we make Johansen cointegration tests. From the perspective of a stable long-run money demand function, longrun drivers are output and (long-term) interest rates (Anderson & Rasche, 2001). According to the quantity identity, long-run drivers of money are velocity and (nominal) output. Second, we test different specifications of the base money rules, in order to check which specification and parameterisation best fits euro area data. The purpose of this analysis is twofold. It is a check whether the calibrated and the estimated parameters of the base money rules for the euro area match. It gives clues on whether the ECB’s monetary policy response during the financial crisis has on average been in line with one of the above base money rules. 4.1. Estimated base money rules In a first step, we look into the integration properties of the variables. The results of the ADF-tests (not shown here for brevity of the analysis) on base money, real GDP (in logs), the (long-term) interest rate and, base money velocity indicate that these variables are all integrated of order one. In line with theoretical priors, further indicators used in the Taylor rule such as the inflation and output gap are found to be I(0). Second, we look into the cointegration properties of the variables considered applying the Johansen (1991) test, which has the advantage that it reports information about the number of cointegrating vectors (cointegration rank r). Another advantage of the Johansen cointegration test for applied analysis is that its indications can be used as a rough specification test. It is, however, somewhat sensitive to the lag structure and requires longer runs of data to provide robust results. In this context, it is necessary to take into account a possible break owing to the financial crisis. A further limitation is that in the euro area base money data have been distorted by the cash changeover in 2002Q1. Any structural break does affect the power of cointegration tests when the process generating the data does not have a common factor. Therefore, we follow the approach proposed by Johansen, Mosconi, & Nielsen (2000), who propose to conduct the tests in a cointegration model with piece-

7

One cointegration vector

One cointegration vector One cointegration vector

Notes: Johansen cointegration test for rank r with two lags; sample 1999.3 to 2016.2, ** denotes significance at the 5% level * at the 10% level (eigenvalue statistics provide similar indications), mb is base money (in logs), y is nominal GDP (in logs), lt denotes long-term interest rates on government bonds, v is base money velocity (in logs). These regressions include two break dummies: CASHDUM, which is one between 2001Q2 and 2002Q2 and zero otherwise, and FINDUM, which takes the value zero until 2008Q3 and 1 thereafter. Critical values by Giles & Godwin (2012) were used with one break: q = 3, v1 = 0.05 and v2 = 0.45.

wise linear trend and known break points, and use critical values as computed by Giles and Godwin (2012). These critical values capture whether one or more breaks are included in the cointegration regression. Table 1 shows the results of Johansen cointegration tests of the euro area monetary base and the drivers, which have been included in the above base money rules. We report the tests including a break dummy for the cash changeover (CASHDUM) around the start of 2002 and the financial crisis (FINDUM) in 2008Q3, when the collapse of Lehman Brothers marked the beginning of the crisis. These tests confirm the existence of one long-term relationship between the monetary base and (nominal) output and the (longterm) interest rate (at the 5% significance level), thereby indicating the presence of a stable (long-run) money demand function for base money. The validity of the quantity equation is supported at the 5% significance level for which cointegration between base money, velocity and (nominal) GDP is found. In a third step, we estimate the parameters of the McCallum rule (1) and (2) for the euro area. We address the criticism of the output gap, distinguishing between two alternative versions with and without reaction to the output gap. We include a dummy for potential breaks around the cash changeover (January 2002) and the start of the financial crisis (September 2008). We provide estimates with both contemporaneous and forward-looking measures of the inflation and output gap (Table 2). A methodological issue is whether base money is an exogenous or endogenous variable. In normal times, central banks implement policy primarily through steering short-term interest rates. The money supply then adjusts to changes in the demand for reserves and credit caused by the interest rate change. As illustrated in Fig. 1 above, after the collapse of Lehman Brothers in September 2008, the Eurosystem and other main central banks adopted non-standard monetary policies, which were aimed at actively influencing the evolution of their balance sheets. Hence, the reason for the creation of large reserve balances was the central bank’s policy of purchasing government bonds and other assets from the private sector. It implies that base money became an exogenous variable once it was used as a policy instrument. An alternative view is that there was an increase in the demand for currency, overnight deposits, and other liquid deposits by the public in response to the increased uncertainty. Such a flight to safety could have generated an increase in the demand for central bank money. This argument would suggest that base money was endogenous to the system. However, Taylor (2009), who addresses this issue for the United States, argues that base money is exogenous, because the increase in bank reserves

Please cite this article in press as: Jung, A. Does McCallum’s rule outperform Taylor’s rule during the financial crisis? The Quarterly Review of Economics and Finance (2017), https://doi.org/10.1016/j.qref.2017.11.005

G Model

ARTICLE IN PRESS

QUAECO-1083; No. of Pages 13

A. Jung / The Quarterly Review of Economics and Finance xxx (2017) xxx–xxx

8 Table 2 Estimated McCallum rules for the euro area. Variables Base money (mb) Equation (1) contemporaneous (OLS) forward-looking (OLS) contemporaneous (GMM) Equation (2a) contemporaneous (OLS) forward-looking (OLS) contemporaneous (GMM) Equation (2b) contemporaneous (OLS) forward-looking (OLS) contemporaneous (GMM) Equation (2c) contemporaneous (OLS) forward-looking (OLS) contemporaneous (GMM)

constant

dvmbav

pgap

ygap

−6.07 (5.17) −3.17 (8.64) 0.50 (13.54)

−2.18**(0.88) −2.21**(0.96) −1.72*(0.99)

6.64 (5.13) 7.33 (4.98) 11.65**(4.43)

−0.94 (0.69) −0.89 (0.64) −0.58 (0.56)

1.65 (2.00) 4.64* (2.32) −0.86 (2.19)

−2.55 (8.78) −2.37 (8.56) 5.15 (12.19)

−1.75**(0.85) −1.99**(0.89) −1.19 (0.82)

0.91 (1.38) 3.49 (3.40) 0.76 (1.63)

5.93 (6.08) 6.08 (5.71) 12.19***(3.92)

−1.56**(0.73) −1.20 (0.77) −1.06 (0.85)

−4.17 (3.13) −1.77 (9.37) −6.61 (4.01)

yggap

findum

R2

2.65 (1.69) 4.20 (3.75) 1.91 (2.45)

5.26 (7.35) −0.01 (6.77) 5.38 (13.01)

0.15 0.12 0.10

2.77 (8.70) 8.87 (8.14) −10.02 (13.72)

0.08 0.13 0.02

3.14 (8.00) 2.42 (7.06) 0.77 (13.46)

0.10 0.12 0.08

−9.52 (6.58) −5.05 (7.64) −18.46** (9.74)

0.10 0.06 0.02

1.65 (2.00) 4.64* (2.32) −0.86 (2.19) 0.91 (1.38) 3.49 (3.40) 0.76 (1.63)

Notes: The sample runs from 1999Q1 to 2016Q2 and effectively includes 50 observations, since the 16-quarter moving average of velocity only starts in 2003; HAC consistent errors are reported; * indicates significance at 10%; ** at 5%; *** at 1%; standard errors in brackets; the variables are explained in the text, findum is the break dummy to account for a possible break owing to the financial crisis.

coinciding with the Fed’s quantitative easing programmes was due to a shift in supply. To take potential simultaneities into account, which may arise in the contemporaneous version of the rule, we also estimate the equations again using the Generalised Method of Moments (GMM). The set of instruments are two or three lags of the endogenous variables. In this case, the J-statistics for overidentifying restrictions do not show evidence against the validity of the instruments used in the estimations. Moreover, we conduct difference-in-Sargan tests to check for the endogeneity of the regressors. However, these tests do not point to the presence of endogeneity problems for the estimated base money rules. Our results suggest that the estimates are consistent and the regressions can be performed with OLS. The estimated base money rules (Table 2) display a rather low explanatory power. Given the theoretical priors, no variant of the McCallum rule (1) or (2) seems to be strongly supported by the data. The elasticity of base velocity is estimated to be in the range of −1.50 to −2.20 (compared with −1 in the calibrated version). The response parameter ␭, which is assumed to have a value of 0.5 in the calibrated version, is considerably higher in the estimated version, but most of the times the parameter is not significant and may even display the wrong sign. Furthermore, the estimated constant typically exceeds the calibrated value of 4%, which refers to (nominal) potential output growth in equilibrium in the euro area, though it is only significant if estimated with GMM. Overall, these results suggest that the ECB’s monetary policy response throughout the financial crisis cannot be described by the McCallum rule. Since the monetary base as an instrument displays a high degree of volatility and in view of the ECB’s medium-term orientation, we examine a modified McCallum rule, which focuses on the low frequency component of base money growth as explanatory variable. We check whether the ECB may have steered the medium-term trend of the base expansion throughout the financial crisis. We therefore estimate the above rules for the euro area again using quarterly data, but explain the 6-quarter average of annual monetary base growth instead of its annual growth rate. Table 3 shows that all versions of the modified McCallum rule now have a satisfactory explanatory power. In the estimated versions, the elasticity of base velocity is estimated to be in the range [−1.6;−3] implying that the trend decline in money base velocity again somewhat exceeds the theoretical priors. The response parameter ␭ is significant and has the right sign in (2a,GMM version) and (2c). In particular, the (forward-looking and the GMM) version of variant (2c) of the McCallum rule seem to be supported by the data. For this reason, we do not consider versions ((1) and

(2b)) of the rule in the following illustration. We check that based on version ((2a), GMM) and (2c)) we obtain similar results. Moreover, in ((2a), GMM) and (2c)), the (absolute value of the) parameter of the inflation gap significantly exceeds unity, implying that the Taylor principle holds. It also suggests that, in line with its primary objective and communications, the ECB has responded to deviations of inflation from its medium-term aim. In those versions, the estimated constant is not significantly different from zero, which would be indicative of a structural decline of (nominal) potential output growth in the euro area during the financial crisis. In order to see that the ECB’s monetary policy response can be described by a modified McCallum rule, Fig. 4 shows a comparison of the modified McCallum rule with the actual outcome of the 6quarter trend of the euro area monetary base. As can be seen from the size of the residual, throughout the financial crisis the modified McCallum was fairly close to the ECB’s actual policy, as measured by the expansion of the euro area monetary base. In 2014 the residual was large and negative, thereby signalling the need for further monetary policy accommodation, as was implemented by the ECB in June 2014 with its credit easing policy and the introduction of the APP in March 2015. Though, a case in point was the ECB’s decision in March 2016 to increase its monthly purchases in public and private sector securities amount to D 80 billion. According to the modified McCallum rule the expansion of the monetary base was sufficient at that point in time. 4.2. A comparison between the McCallum rule and the Taylor rule for the euro area In this section, we compare the McCallum rule and the Taylor rule for the euro area. Because monetary policy instruments are different in both rules, it is hard to compare them directly. Therefore, a comparison requires either to transform the McCallum rule into a rule that is specified for the policy rate or to transform the Taylor rule into a rule that uses base money as instrument. In the literature, most comparisons of the Taylor and McCallum rule were made specifying the McCallum rule for the interest rate as instrument (see McCallum, 2000; Razzak, 2003). This addresses the possible criticism that base money as monetary policy instrument may be difficult to control by a central bank and that central banks have greatly relied in a short-term interest rate as policy instrument. The importance of setting policy rates beyond the zero lower nominal bound is supported by the recent moves to negative nominal policy rates, which were adopted by several major central banks including the ECB. In the present study, for the purpose of a com-

Please cite this article in press as: Jung, A. Does McCallum’s rule outperform Taylor’s rule during the financial crisis? The Quarterly Review of Economics and Finance (2017), https://doi.org/10.1016/j.qref.2017.11.005

G Model QUAECO-1083; No. of Pages 13

ARTICLE IN PRESS A. Jung / The Quarterly Review of Economics and Finance xxx (2017) xxx–xxx

9

Table 3 Estimated base money rules for the euro area (modified McCallum rule).

Notes: The sample runs from 1999Q1 to 2016Q2 and effectively includes 50 observations, since the 16-quarter moving average of velocity only starts in 2003; HAC consistent errors are reported; * indicates significance at 10%; ** at 5%; *** at 1%; standard errors in brackets; the variables are explained in the text, mbav refers to the 6-quarter moving average of (annualised) quarterly growth rates of the monetary base, findum is the break dummy to account for a possible break owing to the financial crisis.

parison with the Taylor rule, we rewrite the McCallum rule so that it uses the policy rate as an instrument. We attempt to apply the approach adopted by Razzak (2003), whose comparison of the McCallum rule and the Taylor rule for the United States suggests that both rules are closely related. If the relation between base money velocity and the policy rate is stable, this would enable us to substitute changes in base money by changes in the policy rate and nominal GDP in Eq. (1). Under this assumption, Razzak (2003) shows that the McCallum rule for the policy rate as instrument can be written as: rt = rt−1 + [¯vt − (1 + x ) · (x∗ − xt )]/

(5)

with the response parameter x = 0.5 and ␬ is a scaling parameter, which measures the sensitivity of base velocity to changes in the policy rate. Razzak (2003) estimates ␬ to be 50 for the United States. A large value of ␬ dampens the volatility of nominal GDP growth fluctuations and thus acts as a smoothing parameter on the policy rate. Using similar regressions as in Razzak (2003), we estimate the value for the euro area to be around 15. Nevertheless, given the short runs of genuine euro area data (since 1999), we cannot take it for granted that the (long-run) stability of this relationship is ensured. Therefore we also pursue another way of comparing the rules in the spirit of McCallum (2000), who considered an alternative

Please cite this article in press as: Jung, A. Does McCallum’s rule outperform Taylor’s rule during the financial crisis? The Quarterly Review of Economics and Finance (2017), https://doi.org/10.1016/j.qref.2017.11.005

G Model QUAECO-1083; No. of Pages 13 10

ARTICLE IN PRESS A. Jung / The Quarterly Review of Economics and Finance xxx (2017) xxx–xxx

Fig. 4. Modified McCallum rule and actual base money trend for the euro area. Note: The above McCallum rule shown refers to an estimated, forward-looking version of (2c). Source: ECB and own calculations.

version of his money base rule for a policy rate as instrument and using a nominal GDP target. This rule is similar to (1), but does not directly follow from it:

with the notations and parameters as explained above. To address changes in the macroeconomic environment throughout the financial crisis episode, we assume that the real interest rate (r*) is around zero both in (3) and (6). As suggested by Benati and Vitale (2007), the natural rate of interest in the euro area is subject to time-variation. Given the length and intensity of the financial crisis, a regime shift has occurred, when non-standard measures were aimed at reducing interest rates to historical lows. For the United States, Laubach and Williams (2016) provide evidence that during the financial crisis the natural rate has fallen to levels close to zero and has remained there. As explained, recent evidence shows that a similar reasoning applies to the euro area. Fig. 5 shows a comparison of the calibrated McCallum rule (6) with the Taylor rule (3) and the policy rate. Since rule (6) is an approximation of the base rule, which uses the policy rate as instrument, an assessment of both rules can be done relative to the policy rate (or the shadow rate). From the start of the financial crisis (in 2008Q3) until mid-2013, both rules are fairly close. Thereafter, when nominal rates approached the zero lower bound on nominal interest rates, both rules recommend a further easing of the monetary policy stance, albeit the Taylor rule called for a somewhat more aggressive move than the McCallum rule.9 In line with these indications, in June 2014 the ECB responded to the potential risk of deflation by adopting its credit easing programme and thereafter eased it stance further by means of the expanded asset purchase programme (APP).

In normal times, the level of nominal short-term interest rates can conventionally be taken as indicator of the monetary policy stance. However, against the backdrop of the financial crisis, the informative value of the short- term interest rate as a monetary policy stance indicator diminished. This was caused, in particular, by using non-standard monetary policy measures in an environment in which the scope for further policy rate cuts became increasingly constrained by the zero lower bound.10 In that environment a calculation of a shadow short-term nominal interest rate could still provide a benchmark to assess the monetary policy stance beyond the zero lower bound. A shadow rate can be understood as a metric for the stance of monetary policy in a zero lower bound environment (Krippner, 2012). Fig. 5 therefore also reports a corridor, which includes different measures of the shadow rate for the euro area. The decline in the shadow rate more clearly illustrates that the easing achieved through the APP contributed to a looser monetary policy stance relative to what interest rate cuts would have achieved alone. While different measures of the shadow rate agree on the direction, the estimated levels of the shadow rate may differ considerably owing to uncertainties surrounding the calculation of the shadow rate: i.e. uncertainty about the interest rate level at which the zero lower bound effectively gets binding and the number of latent factors considered in the underlying model (Krippner, 2015). Given the high model sensitivity of the shadow rate it remains problematic to compare a rule path with the shadow rate, since this comparison lacks the needed precision and hence may give rise to ambiguous interpretations at the zero lower bound. Moreover, as concerns the path of the rules, the results of the above analysis could be sensitive to a number of other factors, most of which would shift both rules in similar directions. One is uncertainty about the output gap. An alternative output gap measure

9 This assessment does not depend on the use of the policy rate as instrument. As explained before, around this time, the calibrated McCallum rule (2b) and the estimated rule (2c), which use the monetary base as instruments, also indicated the need for a policy easing.

10 Note that the non-standard measures have led to a different relationship between monetary policy decisions and monetary policy operations. As of 11 June 2014, the deposit rate has played a more prominent role than in the past as an indicator of the monetary policy stance.

r t = r∗ + t + (xt−1 − x∗)

(6)

Please cite this article in press as: Jung, A. Does McCallum’s rule outperform Taylor’s rule during the financial crisis? The Quarterly Review of Economics and Finance (2017), https://doi.org/10.1016/j.qref.2017.11.005

G Model QUAECO-1083; No. of Pages 13

ARTICLE IN PRESS A. Jung / The Quarterly Review of Economics and Finance xxx (2017) xxx–xxx

11

Fig. 5. The Taylor rule and the McCallum rule for the euro area. Notes: The shadow rate is shown as a corridor, which includes measures by Wu and Xia (2016), by Krippner (2016) and by Lemke and Vladu (2017) for the euro area. Source: ECB and own calculations.

computed by the OECD is around 1% lower than that of the IMF, which has been used in the present calculations of the Taylor rule. This would imply an even lower trajectory of the Taylor rule over recent quarters. Though, it is quite likely that the underlying driving factor would also increase the output growth gap in (6), thus also leading to a downward shift of the McCallum rule. Another factor is uncertainty about the equilibrium interest rate. For example, using a ten-year average of the short-term interest rate for the euro area, which is around 1.5%, instead of the assumed zero rates would imply a higher benchmark of the Taylor rule (and of the McCallum rule (6)), but otherwise would not change the path. In addition, the rule paths may also be subject to the values chosen for the target variables. Lowering (increasing) policy targets would imply a reduction (increase) in the gap(s) and therefore indicate a less (more) aggressive policy response by the central bank. However, this point is not of practical relevance, since the ECB did not change its policy target during the financial crisis. Last but not least, the results could be also sensitive to the magnitude of the monetary response factor ␭ in the money base rule and the assumed response factor of 0.5 in the Taylor rule. Increasing that factor makes the feedback from the macroeconomic variables stronger and implies a stronger reaction of the instrument to disequilibria. Since inflation and output were undershooting its target values during the financial crisis, an increase in the response factor would have made both rules call for a more aggressive easing of the policy stance compared with what is shown in Fig. 5. However, a larger response factor may not necessarily be compatible with a stable response to changes in the real economy. 5. Conclusions McCallum (2000) suggested for the case of Japan, there could be differences between his rule and the Taylor rule when monetary policy sets policy rates at very low levels. Over recent years central bank balance sheets of most major advanced economies have grown to unprecedented levels. While several central banks embarked on large-scale asset purchase programmes and paid

more attention to their balance sheet, only the Bank of Japan made the monetary base a target of its monetary policy. In an environment that is characterised by increased uncertainty, monitoring money base rules may provide policy-makers with additional insights about how the measures impact on the monetary policy stance. Our retrospective evidence for the euro area suggests that both the McCallum and the Taylor rule might have provided useful information about the policy stance of the ECB. While we find that for most of that period, both rules were fairly close to actual policy, we find no support for McCallum’s claim on the superiority of his rule especially in an environment of very low interest rates. For most of the financial crisis, both the McCallum and the Taylor rule gave similar messages about the ECB’s monetary policy during the financial crisis and were fairly close to actual policy. Our results are thus in line with an earlier assessment for the United States during normal times by Razzak (2003) who found that the classic Taylor rule and the McCallum rule are closely related. In terms of policy implications, simple rules provide information which can usefully be taken into account alongside all other relevant information in the formulation of monetary policy. Monitoring both rules can be useful from a policy perspective, since it increases the robustness of monetary policy and adds a new perspective to the assessment, because the rules have been derived for a different monetary policy instrument. At the same time, the rules are potentially sensitive to the underlying assumptions (e.g. smooth functioning of the transmission mechanism; value of the equilibrium potential output growth rate and equilibrium interest rate respectively). For that very reason, these rules may not eliminate the need for some discretion in monetary policy, in particular during crisis times, when the working of the transmission mechanism is impaired. Finally, this study has answered some questions, yet it provides some suggestions for further research. We need to understand better what domestic monetary policy can do to stabilise the economy. One avenue for further research would be to explore further the leadership role of the US Federal Reserve (Fed) in influencing global

Please cite this article in press as: Jung, A. Does McCallum’s rule outperform Taylor’s rule during the financial crisis? The Quarterly Review of Economics and Finance (2017), https://doi.org/10.1016/j.qref.2017.11.005

G Model QUAECO-1083; No. of Pages 13 12

ARTICLE IN PRESS A. Jung / The Quarterly Review of Economics and Finance xxx (2017) xxx–xxx

interest rate cycles and balance sheet expansions. An important question is whether a flexible exchange rate regime still allows other central banks to pursue a monetary policy rule independently from the Fed and whether international spillovers call for a deviation from the simple rules considered in this study. Another important avenue for which further research is needed concerns the optimal degree of policy coordination in an environment of low interest rates. Appendix A

Table A1 Data sources. Monetary base Interest rates Inflation, GDP Output gap (contemporaneous) ECB staff forecasts SPF forecasts

ECB MFI statistics and ECB real-time database ECB statistics Eurostat and ECB real-time database IMF, OECD hand collected from ECB website (real-time) hand collected from ECB website (real-time)

References Anderson, R., & Rasche, R. (2001). The remarkable stability of monetary base velocity in the United States, 1919–1999. Federal Reserve of St. Louis Working Paper No. 2001-008A. Anderton, B., Aranki, T., Dieppe, A., Elding, C., Haroutunian, S., Jacquinot, P., Jarvis, V., Labhard, V., Rusinova, D., & Szörfi, B. (2014). Potential output from a euro area perspective. ECB Occasional Paper Series No. 156. Asso, P., Kahn, G., & Leeson, R. (2010). The Taylor rule and the practice of central banking. Fed Kansas Research Working Paper No. 10-05. Beck, G., & Wieland, V. (2007). Money in monetary policy design: A formal characterization of ECB-style cross-checking. Journal of the European Economic Association, 5, 524–533. Beck, G., & Wieland, V. (2008). Central bank misperceptions and the role of money in interest-rate rules. Journal of Monetary Economics, 55, 1–17. Beckmann, J., Belke, A., & Dreger, C. (2017). The relevance of international spillovers and asymmetric effects in the Taylor rule. Quarterly Review of Economics and Finance, 64(2), 162–170. Belke, A., & Cui, Y. (2010). US–Euro area monetary policy interdependence: New evidence from Taylor rule-based VECMs. The World Economy, 25, 778–797. Belke, A., & Klose, J. (2011). Does the ECB rely on a Taylor rule during the financial crisis? Comparing ex-post and real time data with real time forecasts. Economic Analysis and Policy, 41(2), 147–171. Belke, A., & Klose, J. (2013). Modifying Taylor reaction functions in the presence of the zero-lower-bound – Evidence for the ECB and the Federal Reserve. Economic Modelling, 35, 515–527. Benati, L., & Vitale, G. (2007). Joint estimation of the natural rate of interest, the natural rate of unemployment, expected inflation, and potential output. ECB Working Paper Series No. 797. Benhabib, J., Schmitt-Grohé, S., & Uribe, M. (2001). The perils of Taylor rules. Journal of Economic Theory, 96, 40–96. Bernanke, B. (2010). Monetary policy and the housing bubble. In Speech given at the American Economic Association Annual Meeting. Bernanke, B., & Boivin, J. (2003). Monetary policy in a data-rich environment. Journal of Monetary Economics, 50(3), 525–546. Beyer, A., & Reichlin, L. (2006). The role of money – money and monetary policy in the twenty-first century. In Fourth ECB central banking conference. Frankfurt: ECB. Beyer, R., & Wieland, V. (2017). Instability, imprecision and inconsistent use of equilibrium real interest rate estimates. Frankfurt: Goethe University. Institute for Monetary and Financial Stability Working Paper No. 110. Blattner, T., & Margaritov, E. (2010). Towards a robust monetary policy rule for the euro area. ECB Working Paper Series No. 1210. Blinder, A. (2010). Quantitative easing: entrance and exit strategies. Federal Reserve Bank of St. Louis Review, 92(6), 465–479. Carpenter, S., & Demiralp, S. (2010). Money, reserves, and the transmission of monetary policy: Does the money multiplier exist? Journal of Macroeconomics, 34(1), 59–75. Christiano, L., & Rostagno, M. (2001). Money growth monitoring and the Taylor rule. NBER Working Paper No. 8539. Cour-Thimann, P., & Winkler, B. (2012). The ECB’s non-standard monetary policy measures: the role of institutional factors and financial structure. Oxford Review of Economic Policy, 28(4), 765–803. Dieppe, A., Küster, K., & McAdam, P. (2005). Optimal monetary policy rules for the euro area: an analysis using the area wide model. Journal of Common Market Studies, 43(3), 507–537. Dueker, M., & Fischer, A. (1998). A guide to nominal feedback rules and their use for monetary policy. Federal Reserve Bank of St. Louis Review, 80(4), 55–63.

Esanov, A., Merkl, C., & de Souza, L. (2005). Monetary policy rules for Russia. Journal of Comparative Economics, 33, 484–499. European Monetary Institute. (1995). Annual report 1994. Frankfurt: EMI. Friedman, M. (1968). The role of monetary policy. American Economic Review, 58(1), 1–17. Giles, D., & Godwin, R. (2012). Testing for multivariate cointegration in the presence of structural breaks: p-values and critical values. Applied Economic Letters, 19, 1561–1565. Hafer, R., Haslag, J., & Hein, S. (1996). Implementing monetary base rules: the currency problem. Journal of Economics and Business, 48, 461–472. Hammond, G. (2012). State of the art of inflation targeting. Centre for Central Banking Studies handbook No. 29. Bank of England. Hofmann, B., & Bogdanova, B. (2012). Taylor rules and monetary policy: A global Great Deviation? BIS Quarterly Review, (September), 37–49. Holston, K., Laubach, T., & Williams, J. (2017). Measuring the natural rate of interest: International trends and determinants. Journal of International Economics, 108, S59–S75. Issing, O. (2006). The ECB’s monetary policy strategy: Why did we choose a Two Pillar approach? In Paper presented at the fourth ECB central banking conference on the role of money: Money and monetary policy in the twenty-first century. Jackson, H. (2015). The international experience with negative policy rates. Bank of Canada Staff Discussion Paper No. 2015-13. Johansen, S. (1991). Estimation and hypothesis testing of cointegration vectors in Gaussian Vector Autoregressive Models. Econometrica, 59(6), 1551–1580. Johansen, S., Mosconi, R., & Nielsen, B. (2000). Cointegration analysis in the presence of structural breaks in the deterministic trend. Econometrics Journal, 3, 216–249. Jung, A. (2013). Policymakers’ interest rate preferences: Recent evidence for three monetary policy committees. International Journal of Central Banking, 9(3), 145–192. Krippner, L. (2012). Measuring the stance of monetary policy in zero lower bound environments. Economics Letters, 118, 135–138. Krippner, L. (2015). Zero lower bound term structure modelling: A practitioner’s guide. New York: Palgrave Macmillan. Krippner, L. (2016). Comparison of international monetary policy measures. Reserve Bank of New Zealand., available at. https://www.rbnz.govt.nz/research-andpublications/research-programme/additional-research/measures-of-thestance-of-united-states-monetary-policy/comparison-of-internationalmonetary-policy-measures Laubach, T., & Williams, J. (2016). Measuring the natural rate of interest redux. Journal of Business Economics, 51(2), 57–67. Lemke, W., & Vladu, A. (2017). Below the zero lower bound – A shadow-rate term structure model for the euro area. ECB Working Paper No. 1991. Lucas, R. E. (1976). Econometric policy evaluation: A critique. Carnegie-Rochester Conference Series on Public Policy, 1, 19–46. Lucas, R. E. (2007). Central banking: Is science replacing art? In European Central Bank Monetary policy: A journey from theory to practice. Frankfurt: ECB. Masuch, K., Nicoletti-Altimari, S., Rostagno, M., & Pill, H. (2003). The role of money in monetary policy making Bank for International Settlements. pp. 158–191. Monetary policy in a changing environment (Vol. 19). McCallum, B. T. (1988). Robustness properties of a rule for monetary policy. Carnegie Rochester Conference Series on Public Policy, 29, 173–204. McCallum, B. T. (2000). Alternative monetary policy rules: A comparison with historical settings for the United States, the United Kingdom, and Japan. Federal Reserve Bank of Richmond Economic Quarterly, 86(1), 49–79. McCallum, B. T. (2001). Should monetary policy respond strongly to output gaps? American Economic Review, 91(2), 258–262. McCallum, B. T., & Nelson, E. (2005). Targeting vs. instrument rules for monetary policy. Federal Reserve Bank of St Louis Review, 87(5), 597–611. Orphanides, A. (2001). Monetary policy rules based on real-time data. American Economic Review, 91, 964–985. Orphanides, A. (2003). Historical monetary policy analysis and the Taylor rule. Journal of Monetary Economics, 50(5), 983–1022. Orphanides, A. (2007). Taylor rules. Finance and economics discussion paper No. 2007-18. Board of Governors of the Federal Reserve System. Orphanides, A., Porter, R., Reifschneider, D., Tetlow, R., & Finan, F. (2000). Errors in the measurements of the output gap and the design of monetary policy. Journal of Economics and Business, 52(1/2), 117–141. Papademos, L., & Stark, J. (Eds.). (2010). Enhancing monetary analysis. Frankfurt: ECB. Patra, M., & Kapur, M. (2012). Alternative monetary policy rules for India. IMF Working Paper No. WP/12/118. Razzak, W. (2003). Is the Taylor rule really different from the McCallum rule? Contemporary Economic Policy, 21(4), 445–457. Reis, R. (2012). Exit strategies and the Federal Reserve. In Presented at the annual conference of the American Economic Association , available at. http://www. columbia.edu/∼rr2572/papers/09-AEI.pdf Rudebusch, G. (2005). Assessing the Lucas critique in monetary policy models. Journal of Money, Credit and Banking, 37(2), 245–272. Sack, B., & Wieland, V. (2000). Interest-rate smoothing and optimal monetary policy: A review of recent empirical evidence. Journal of Economics and Business, 52(1–2), 205–228. Scharnagl, M., Gerberding, C., & Seitz, F. (2010). Should monetary policy respond to money growth? New results for the euro area. International Finance, 13(3), 409–441.

Please cite this article in press as: Jung, A. Does McCallum’s rule outperform Taylor’s rule during the financial crisis? The Quarterly Review of Economics and Finance (2017), https://doi.org/10.1016/j.qref.2017.11.005

G Model QUAECO-1083; No. of Pages 13

ARTICLE IN PRESS A. Jung / The Quarterly Review of Economics and Finance xxx (2017) xxx–xxx

Stark, T., & Croushore, D. (1998). Evaluating McCallum’s rule when monetary policy matters. Journal of Macroeconomics, 20(3), 451–485. Stuart, A. (1996). Simple monetary policy rules. Bank of England Quarterly Bulletin, (August), 281–287. Sun, S., Gan, C., & Hu, B. (2012). Evaluating McCallum rule as policy guideline for China. Journal of the Asia Pacific Economy, 17(3), 527–545. Taylor, J. (1993). Discretion versus policy rules in practice. Carnegie Rochester conference series on public policy, 39, 195–214. Taylor, J. (2009). The need to return to a monetary framework. Business Economics, 44(2), 63–72.

13

Taylor, J. (2012). Monetary policy rules work and discretion doesn’t: a tale of two eras. Journal of Money Credit and Banking, 44(6), 1017–1032. Williams, J. (2012). Monetary policy, money, and inflation. FRBSF Economic Letter, published on 9 July 2012. Woodford, M. (2001). The Taylor rule and optimal monetary policy. American Economic Review, Papers and Proceedings, 91(2), 232–237. Wu, C., & Xia, F. (2016). Measuring the macroeconomic impact of monetary policy at the zero lower bound. Journal of Money, Credit and Banking, 48(2–3), 253–291.

Please cite this article in press as: Jung, A. Does McCallum’s rule outperform Taylor’s rule during the financial crisis? The Quarterly Review of Economics and Finance (2017), https://doi.org/10.1016/j.qref.2017.11.005