Wicksell’s Classical Dichotomy: Is the natural rate of interest independent of the money rate of interest?

Journal of Macroeconomics 32 (2010) 366–377

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Wicksell’s Classical Dichotomy: Is the natural rate of interest independent of the money rate of interest? Michael Beenstock a,*, Alex Ilek b a b

Department of Economics, Hebrew University of Jerusalem, Israel Department of Economics, University of Frankfurt, Germany

a r t i c l e

i n f o

Article history: Received 13 January 2008 Accepted 4 June 2009 Available online 13 June 2009

JEL classification: E43 E52 Keywords: Natural rate of interest Monetary policy Event analysis Indexed bonds Neutrality of monetary policy Identification

a b s t r a c t According to Wicksell’s Classical Dichotomy the money rate of interest depends on the natural rate of interest, but the latter does not depend on the former. If this Classical Dichotomy is false monetary policy may induce hysteresis because the natural rate of interest would depend upon the money rate of interest. We use data for Israel to test Wicksell’s Classical Dichotomy. We proxy the natural rate of interest by the forward yield to maturity on indexed-linked treasury bonds. If the null hypothesis is false it is difficult to suggest persuasive instruments that would identify the causal effect of the money rate on the natural rate of interest. Our identification strategy is therefore built around quasi-experimentation and event analysis. Large and seemingly orthogonal shocks to the natural rate of interest have no measurable effect on the natural rate of interest according to non-parametric and parametric tests. Therefore, Wicksell’s Classical Dichotomy is empirically valid. Ó 2009 Elsevier Inc. All rights reserved.

1. Introduction According to the Classical Dichotomy (Patinkin 1965) real variables, such as GDP and unemployment, should be independent in the long run of nominal variables, such as the money stock or the exchange rate. Although this independence is hotly disputed in the short run, there is a surprising degree of consensus about the empirical validity of the Classical Dichotomy in the long-run. Indeed, many New Keynesian economists, such as Blanchard and Quah (1989), resort to the Classical Dichotomy to apply long-run restrictions in order to identify SVAR models of macroeconomic activity. In many instances the Classical Dichotomy is accepted as a matter of faith. However, the prediction that the ‘‘natural” or equilibrium rate of unemployment should be independent in the long run of nominal variables has been widely tested empirically. In this paper we turn our attention to the predictions of the Classical Dichotomy regarding the relationship between what Wicksell (1898) termed the ‘‘money” and ‘‘natural” rates of interest.1 In Wicksell’s ‘‘cumulative process” deviations between the money and natural rates of interest affect inflation and economic activity in the short run, but in the long run the two rates of interest move back into line. In this process it is the money rate that adjusts to the natural rate, not the other way round. Indeed the natural rate is hypothesized to be independent of the money rate. As in the Classical Dichotomy, the * Corresponding author. Tel.: +972 2 6723184; fax: +972 2 5816071. E-mail address: [email protected] (M. Beenstock). 1 Friedman (1968) borrowed Wicksell’s terminology to invent the ‘‘natural” rate of unemployment, which subsequently outshone the original concept. 0164-0704/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.jmacro.2009.06.001

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natural rate of interest is ground out in general equilibrium by real economic forces, and is therefore assumed to be independent of nominal phenomena including the money rate of interest. This Classical Dichotomy has become more important recently due to the resurgence of interest in neo-Wicksellian (or New Keynesian) monetary policy (Woodford, 2003) in which central banks chose the rate of interest rather than the money supply as the operating instrument for monetary policy. Interest rate policy responds to actual and expected deviations of inflation and output from their target values, and may be determined through a Taylor Rule or it may be based on judgment (Svennson, 2003). In either case the central bank anchors the money rate of interest to the natural rate of interest.2 This means that changes in the natural rate of interest are eventually reflected in the rate of interest set by the central bank. It is crucially important therefore for neo-Wicksellian monetary policy that the natural rate of interest be independent of the money rate. If this were not so, the real economy would lack a Classical anchor, just as would be the case if the natural rate of unemployment was not neutral with respect to monetary policy. In this case the economy would be affected by hysteresis and shocks to monetary policy would have permanent real implications via its influence on the natural rate of interest. This phenomenon is the counterpart for the natural rate of interest of arguments made by Blanchard and Summers (1986) for the natural rate of unemployment. Also, if the natural rate of interest depended upon the money rate of interest, econometric estimates of Taylor Rules in which empirical proxies for the natural rate are assumed to be exogenous, would be misspecified.3 In this context too it is important to establish that the natural rate of interest is independent of the money rate. In short, the foundations of neo-Wicksellian monetary policy would be seriously undermined if the natural rate of interest was determined by the money rate of interest. This paper has four interwoven research questions. First and foremost, we investigate empirically whether the natural rate of interest is independent of the money rate of interest. Secondly, we ask how the natural rate of interest might be measured. We suggest that the term structure of interest rates on indexed treasury bonds embodies real time information on the natural rate of interest.4 Third, we ask how the causal effect of the money rate on the natural rate might be identified econometrically. Since the money rate of interest depends on the natural rate, and rejection of the null hypothesis predicts that the natural rate depends upon the money rate, there is an obvious identification problem to be resolved in testing the null hypothesis. Fourth, we ask whether the natural rate of interest determines the money rate of interest as set by the central bank. The vast majority of empirical work on Taylor Rules ignores the role of the natural rate of interest.5 We therefore break new ground by specifying the natural rate of interest in empirical Taylor Rules. We use data for Israel to investigate this agenda empirically. We represent the money rate of interest by the rate of interest set by the Bank of Israel (BOI). We represent the natural rate of interest by the forward yield to maturity on treasury bonds that are indexed to the consumer price index. We show that our proxy for the natural rate of interest has a causal effect on the Bank of Israel’s interest rate, but the latter does not affect the natural rate of interest. Therefore, Wicksell’s Classical Dichotomy applies to the natural rate of interest.

2. The natural rate of interest 2.1. Previous efforts to estimate the natural rate of interest According to Wicksell (1898, p. 102) the natural rate of interest ‘‘is necessarily the same as the rate of interest which would be determined by supply and demand if no use were made of money and all lending were effected in the form of real capital goods”. Woodford (2003, p. 248) too defines the natural rate of interest in counterfactual terms. It is,”.. the equilibrium real rate of return in the case of fully flexible prices”. Wicksell’s definition differs from Woodford’s because the rate of interest in an economy with money and perfectly flexible prices will generally be different to the rate of interest in an economy without money.6 Since both concepts are counterfactual, measuring the natural rate of interest is not straightforward. Wicksell’s definition requires hypothetical data for a moneyless economy and Woodford’s definition requires hypothetical data for an economy with perfect price flexibility. Neither Wicksell nor Woodford (2003, p. 288) have suggested how in practice the natural rate of interest might be measured. Woodford’s definition requires the specification of a model and simulating the rate of interest under the assumption of price flexibility. This is the approach used by Smets and Wouters (2003) to estimate the natural rate of interest for the Euro area during 1970–2000. They solve a stochastic dynamic general equilibrium model for the Euro area under the assumption that wages and prices are perfectly flexible to obtain estimates of the natural rate of interest and other variables. Their estimated natural rates of interest7 averaged 0.44% over the period, and varied between 13% and 19%. These estimates have several implausible properties. First, the mean natural rate of interest is negative. Secondly, it is difficult to believe that the natural rate of interest can be so high or so low. Third, the variance of their estimated natural rate of interest unreasonably

2 3 4 5 6 7

See, for example, Woodford (2003, pp. 286–290) and Orphanides and Williams (2002). See Clarida et al. (1998). After the first draft of the paper we came across Bomfim (2001) who has a similar idea to ours. Orphanides and Williams (2002) and Argov et al. (2007) are rare exceptions. See, e.g. Johnson (1967), Pesek and Saving (1967) and Sidrausky (1967). We thank the authors for providing these data.

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exceeds the variance of the actual rate of interest and it typically changes by 5 percentage points from one quarter to the next. Smets and Wouters admit, ‘‘This suggests that the real rate of interest gap may be a poor guide for monetary policy”. Alternatively, virtual variables such as the natural rate of interest might be inferred from empirical data using latent variables techniques.8 This is the approach used by Laubach and Williams (2003) who specify a simple macroeconomic model and use the Kalman Filter to estimate jointly the natural rate of interest and potential output in the US over the period 1960– 2002. Using different specifications of the model, it turns out that their estimates of the natural rate of interest are not robust,9 and they conclude, ‘‘Taken together, these results cast considerable doubt on the ability to estimate the natural rate of interest with much precision in real time” (p 1066). Orphanides and Williams (2002) too reach similar conclusions. Therefore, existing suggestions to measure the natural rate of interest are far from satisfactory and in any case are not available in real time. The approach we adopt exploits financial market data, which arguably embodies information about the natural rate of interest. Specifically, we make the case, as originally suggested by Bomfim (2001), for using the forward yield to maturity on index-linked bonds as a real time estimate of the natural rate of interest. 2.2. Indexed bonds The natural rate of interest is a real variable. It is tempting, therefore, to look to the market for bonds indexed to the CPI, whose yields to maturity are expressed in real terms. Indexed treasury bonds were first issued in the United States in 1997, and in the United Kingdom in 1982, where they have played a marginal role in their respective capital markets. The same applies in Canada, Sweden, France, Australia and New Zealand. However, in Israel they have performed a major role since their introduction in 1955. In what follows Y denotes the nominal yield to maturity (m), y the real yield to maturity, c denotes the nominal coupon, r denotes real interest rates, i denotes nominal interest rates, and p denotes inflation. For simplicity we assume that all payments are annual and that the par value of the indexed bond is 1. The nominal coupon payment in year i on an indexed bond issued in year 0 is c(1 + p1)(1 + p2)  (1 + pi) and the payment on maturity is (1 + c)(1 + p1)  (1 + pm). The current price of the indexed bond is P0 which is equal to the present value of the nominal cash flows discounted by the nominal yield to maturity:

P0 ¼ c

m Qi X

s¼1 ð1 þ ps Þ

i¼1

ð1 þ YÞ

i

Qm þ

s¼1 ð1 þ ps Þ

ð1 þ YÞm

ð1Þ

Using (1 + Y)i = (1 + y)i(1 + p1)  (1 + pi), Eq. (1) simplifies to:

P0 ¼ c

m X

1

i¼1

ð1 þ yÞi

þ

1 ð1 þ yÞm

ð2Þ

Eq. (2) is in fact used by the Bank of Israel to determine real YTMs on indexed bonds. According to neoclassical term structure theory the yield to maturity on an indexed bond maturing in period t + m is

ð1 þ ymt Þm ¼ Et ð1 þ pmt Þ

m Y ½1 þ rtþi 

ð3Þ

i¼1

where E denotes the expected value operator and pm denotes the real term premium for a term of length m. Under normal circumstances10 the term premia vary directly and convergently with m. Eq. (1) states that YTMs tend to exceed the underlying spot rate expectations, which is why yield curves tend to slope upwards. The m – ahead forward rate (ft + m) is derived by using market data on the YTMs on bonds maturing m and m  1 periods ahead:

ftþm ¼

ð1 þ ymt Þm ð1 þ yðm1Þt Þm1

1

ð4Þ

and the rate of interest expected m periods ahead is equal to:

Et r tþm ¼

ð1 þ ftþm Þð1 þ pðm1Þt Þ 1 1 þ pmt

ð5Þ

Since term premia normally vary directly with m, Eq. (5) says that forward rates tend to be greater than the expected spot rates to which they refer. Suppose the effects of price stickiness dissipate after m* periods. The solution to Eq. (5) would equal

8 The Hodrick – Prescott filter is frequently used by macroeconomists to estimate ‘‘natural” latent variables. Harvey and Jaeger (1993) point out that the HP filter induces artificial trends and cycles. To our best knowledge the HP filter has not been used to estimate the natural rate of interest. 9 Their mean natural rate of interest varies from 0.9% to 2.3%. 10 For example affine theory due to Vasicek (1977) predicts increasing but convergent term premia because it is harder to predict spot rates at longer forecast horizons, and because the marginal forecast difficulty decreases. In Vasicek’s model the term premia are fixed over time whereas in Cox et al. (1985) they vary over time due to GARCH processes in the spot rate and are not necessarily monotonic.

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7

percent p.a.

6

5

4

3

2 93

94

95

96

97

98

99

00

01

02

03

04

Fig. 1. Three year forward yield to maturity on 7 year indexed treasury bonds.

the current expectation of the natural rate of interest m periods ahead provided m > m*. If m < m* the expected real rate of interest would be influenced by price stickiness, in which case it could not be considered as a natural rate of interest. The forward yield to maturity m* periods ahead on indexed bonds with maturity M  m* is equal to11:

zt ¼

M ð1 þ yMt ÞM 1 þ pMt Y ½1 þ r tþi  m ¼ Et  1 þ pm t i¼m þ1 ð1 þ ym t Þ

ð6Þ

For example, if M = 10 years and m* = 3 years, z is the current expectation of the yield to maturity on a 7-year indexed bond in 3 years time. Since the effects of price stickiness dissipate after m* years, rt + i for i > m* are natural rates of interest. Eq. (6) shows therefore that this forward yield to maturity reflects the natural rates of interest expected to prevail between 4 and 10 years ahead. If prices were perfectly flexible, i.e. m* = 0, then z is the current yield to maturity on ‘‘natural” bonds maturing M years ahead. If the term premium ratio is stable, Eq. (6) shows that changes in z would be perfectly correlated with changes in expected natural rates of interest. Although absolute term premia might vary over time, the ratio between them is likely to be more stable for two reasons. First, real term premia are likely to be more stable than nominal term premia. Secondly, real term premia shocks are likely to be positively correlated, so that pM and pm change in the same direction. Our approach draws on the neoclassical theory of the term structure of interest rates in that we assume that forward YTMs embody information on future rates of interest. Numerous empirical tests of the neoclassical theory of the term structure of interest rates have produced mixed results.12 However, this literature has been exclusively concerned with nominal YTMs, which involve predicting inflation, rather than real YTMs, which does not involve predicting inflation. The neoclassical theory may have a better chance of corroboration using real YTM’s. Although this does not constitute a proper test of the matter, we ran a ‘‘Fama Regression” in which the change in the yield to maturity on 7 year indexed bonds over 3 years is regressed on its predicted change according to the forward rate. The neoclassical theory predicts that the intercept (a) be zero and the slope coefficient (b) be unity. The estimated coefficients using ^ ¼ 1:14, respectively. Because the data are monthly and the forecast ^ ¼ 0:29 and b monthly data from 1992:1 to 2003:6 are a horizon is 36 months the residuals from the Fama Regression are expected to be autocorrelated of order MA(35) due to over^ are incorrect. Indeed the residuals are heavily auto^ and b lapping, in which case the OLS standard errors of estimate for a 13 ^ ^ is significantly positive, but not correlated. The corrected standard error of estimate for b is about 0.5, which implies that b significantly different from unity. This prima facie evidence suggests that real forward rates contain predictive information regarding the YTMs to which they refer. In summary, we use market data on the term structure of indexed bonds to calculate the forward yield to maturity, which we use to proxy the expected natural rates of interest. We cannot directly proxy the current natural rate unless we assume that prices are flexible (m* = 0). Nevertheless, we hope that finding a plausible proxy for the expected natural rate is a step forward. In principle we may infer the entire term structure of natural interest rates. However, we prefer to use the forward yield to maturity because this smoothes measurement error in the individual forward rates, which stems from the auxiliary neoclassical hypothesis used to generate the data. Since the results are insensitive to minor changes in m* we report results for m* = 3 years. In Fig. 1 we plot the 3-year forward yield to maturity on 7-year indexed bonds implied by Eq. (6) derived from the yields to maturity on 3-year and 10-year indexed treasury bonds. This forward rate rose from about 2.5% in 1992, peaked at 6% in 2002 and was about 4% in 2004. If the term premia vary over time the forward rates will contain measurement error that is

11 Eq. (6) is essentially the same as Eq. (14) in Bomfim (2001). Since Bomfim uses a linear approximation to the forward rate he corrects for duration, which is not necessary in our case. 12 For a recent review of this literature see Cuthbertson and Nitzche (2005, chapter 22). 13 Using a truncation lag of 30. Similar results are obtained for truncation lags exceeding 4. The OLS standard error is 0.2.

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time dependent. However, this measurement error is mitigated in our case because, as mentioned, the term premia are real rather than nominal. 3. Testing Wicksell’s Classical Dichotomy 3.1. Identification Since in macroeconomics everything may depend upon everything else, it is difficult to find convincing instruments to disentangle the causal relationship between the money and natural rates of interest. For almost every conceivable instrumental variable hypothesized to affect the central bank’s rate of interest, it is possible to argue that the same variable may also affect the natural rate of interest, in which case the causal effect of the money rate on the natural rate is not identified. If Wicksell’s Classical Dichotomy is indeed false, and the natural rate of interest is affected by the money rate, it may also be influenced by inflation and other variables that affect the money rate of interest set by the central bank. The quest for convincing instruments to identify the causal effect of the central bank’s interest rate on the natural rate lies at the heart of the matter in hand. In a similar context Estrella and Mishkin (1997) and Evans and Marshall (1998) do not use instruments at all. Instead they ‘‘identify” the effect of short rates on long rates by simply assuming that there is no immediate reverse causality. They rule out a priori the possibility that there might be a causal effect running in the opposite direction from long rates to short rates. In what follows the natural rate of interest is denoted by NRI, i continues to represent the money rate of interest, which is set by the central bank. Z is a vector of variables, such as productivity and permanent income, hypothesized to determine the natural rate of interest, and X is a vector of variables, such as the inflation gap and the output gap hypothesized to determine the rate of interest set by the central bank. Z and X are assumed to be weakly exogenous. The unrestricted hypothesis for the determination of NRI is:

NRIt ¼ a þ bit þ hZ t þ cX t þ ut

ð7Þ

where u is an iid error. Wicksell’s Classical Dichotomy is valid when b = c = 0. In this case NRI does not depend on the money rate of interest or its determinants.The money rate of interest is hypothesized to be determined by a Taylor Rule:

Ii ¼ ð1  kÞðNRIi þ pi Þ þ kit1 þ /i þ ei

ð8Þ

where p continues to denote inflation, and k is an interest rate smoothing coefficient. We assume that e is iid. When X = 0 because inflation and output are on target, Eq. (8) states that the money rate of interest tends over time to equal the natural rate of interest plus the rate of inflation (p), i.e. i = NRI + p. If the null hypothesis is correct (b = c = 0) Eq. (8) is recursive to Eq. (7) implying one-way causation from the natural rate to the money rate. If the null hypothesis is incorrect because b – 0, Eqs. (7) and (8) are simultaneous, in which case neither b nor k are identified. In this case there are two channels through which X might affect the natural rate of interest; directly via c and indirectly via the effect of X on the money rate of interest. The direct effect may or may not coexist with the indirect effect. It is conceivable, though unlikely, that Wicksell’s Classical Dichotomy is valid because NRI is independent of the money rate of interest, but NRI nevertheless depends on X. Below we test for both of these effects. The identification of b requires instrumental variables that affect the money rate of interest (it) but which do not directly affect NRI. Since almost any variable that affects the money rate of interest might hypothetically affect NRI, it is impossible to think of persuasive instrumental variables that may be used to identify b. We therefore look elsewhere to identify b. In a natural or quasi experiment the treatment varies in a way that is entirely independent of the outcome. In the present context this means that the central bank alters its rate of interest for reasons that have nothing directly to do with the natural rate of interest. Indeed, this was the identification strategy used by Romer and Romer (1989) to estimate the effect of monetary policy on real economic activity. They drew their inspiration from Friedman and Schwartz (1963) who looked for shocks to monetary policy, which ‘‘..like the crucial experiments of the physical scientists, the results are so consistent and sharp as to leave little doubt about their interpretation”. Romer and Romer studied the protocols of the FOMC to identify such quasi experiments carried out by the Federal Reserve System. Just as Romer and Romer required that monetary policy be set independently of real activity, so we require that the central bank sets its rate of interest independently of the natural rate of interest. For example, the central bank might act out of panic, or it might act as a result of political pressure. If we could be sure that c = 0 X would identify b, but we cannot be sure. As Friedman and Schwartz and the Romers before us, we try to identify ‘‘large and independent monetary disturbances”, which we denote by D. Positive D means that the central bank has raised its interest rate orthogonally to the natural rate of interest. Negative D means that it has lowered its rate of interest. In principle the disturbances do not have to be large, but as we shall see, it is their very largeness that points to their independence. If D is small it not only generates less statistical resolution, it is also more difficult to be persuaded that it is indeed independent. Our focus on large disturbances is inherent to regression discontinuity design (Lee, 2005, cap 3) as a source of identification in treatment effects. Notice that D does not have to be independent of Z in Eq. (7). If, D is perfectly correlated with Z the causal effect of D on the natural rate of interest is, of course, not identified. Large disturbances are inherently less correlated with Z due to regression discontinuity.

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371

Finally, it might be thought that the residuals e from Eq. (8) might be used to identify b because they are orthogonal to the natural rate of interest and the X variables that determine the money rate of interest. This identification strategy would be valid if cov(eu) = 0. Since, common unobserved factors might affect both the money and natural rates of interest so that cov (eu) is not zero we are forced to rule out this identification strategy. 3.2. Event analysis Having identified the D’s we use a non-parametric procedure based on event analysis (e.g. Campbell et al., 1997, chapter 6) to investigate the effect of the shocks on the proxy for the natural rate of interest. We take each ‘‘event” and track our proxy for the natural rate before and after the event. According to the null hypothesis the behavior of the natural rate should be independent of the event both before and after its occurrence. If the null hypothesis is rejected we expect to see significant changes in the natural rate in the aftermath of the event. Since there is no reason why the timing and the response of the natural rate should be identical across events we use non-parametric tests to investigate qualitative rejections of the null hypothesis. Identification requires that D be orthogonal to Z in Eq. (7), so that the event analysis identifies the dynamic effect of the money rate on the natural rate. It is not necessary to specify other variables that determine the natural rate as would be required for structural estimation. The baseline in the event analysis does not have to take into account what the outcome variable would have been in the absence of the event. The estimation of treatment effects in this way does not require knowledge of structural parameters such as h, /, k and l.14 Let gj = DdYj denote the normalized15 response of the outcome variable in the jth quasi experiment where d denotes time since the shock. If the data are daily and d = 1 the response of the outcome variable is measured by the normalized change in the outcome variable during the first day after the shock. The larger is d the longer is the time frame over which the change in the outcome variable is measured. It is of course possible that there is no short-term response, i.e. when d is small, but there is a long-term response, i.e. when d is large, or vice versa. This implicitly assumes that in the absence of the shock E(DdY) = 0. According to the null hypothesis gj = 0 since shocks to the money rate should have no effect on the natural rate. We apply Wilcoxon’s signed-rank test (W), which assumes that the quasi experiments are independent, by ranking the g’s for different time frames d. W is normally distributed even when the number of experiments16 is quite small. If W > 0 exceeds its critical value we may reject the null hypothesis that g = 0 over a given time frame. Alternatively, if W < 0 exceeds its critical value we may reject the null on the grounds that the effect of the money rate on the natural rate is significantly perverse. 3.3. Time series models In addition to non-parametric event analysis we also use more standard econometric techniques for identifying the effect of quasi-experimental shocks to the money rate on the natural rate. We denote the expected real money rate of interest (r) as the money rate (i) minus expected inflation (p*): r = i  p*. In the long-run Wicksell’s model implies (up to a constant) that r = NRI. We use the following vector error correction model (VECM) to identify the causal nexus between the natural and money rates of interest.

DNRIt ¼ p1 þ

p X

p2i DNRIti þ

i¼1

Dit ¼ j1 þ

q X i¼1

j2i Diti þ

s X

p3i Dti þ p4 ðNRIt1  rt1 Þ þ p5 Z t þ p6 X t þ wt

ð9Þ

i¼0 h X

j3i DNRIti þ j4 ðNRIt1  rt1 Þ þ j5 X t þ vt

ð10Þ

i¼0

For simplicity we assume that the VECM is of first-order: As in Eq. (7), Z in Eq. (9) is a vector of variables that determine the natural rate of interest in the long run, which, under the null hypothesis, is equal to (p1 + p5Z)/p4. The null hypothesis is rejected in the short-run if p30 – 0, it is rejected in the medium run if p31 – 0 for i = 1, 2, . . .s, and it is rejected in the long-run if p4 and p6 – 0, i.e. there is error correction from the money rate of interest to the natural rate of interest. Normally, we expect these coefficients to be positive. In short, if p3i = p4 = 0, there is no feedback from the money rate of interest to the natural rate of interest, and a permanent increase in the money rate has no effect on the natural rate. In this case we do not expect hysteresis in which case p6 = 0. As in Eq. (8), X in Eq. (10) is a vector of ‘‘Taylor Rule” variables, which tend to zero over time as targets are achieved. Eq. (10) hypothesizes that the central bank engages in interest rate smoothing via the j2 coefficients since current monetary policy depends on lagged interest rates. The j3 coefficients capture derivative error correction between the money and natural rate of interest, and j4 captures proportionate error correction. The unsmoothed solution to Eq. (10) obtained by setting differenced terms to zero is:

14 In clinical trials one does not require a complete structural model of the patients. It is merely necessary to compare the responses of the treated and the controls. Treatment effects are therefore reduced form parameters. 15 We normalize by the size of the change in the BOI’s rate of interest and its direction. 16 Owen (1962) provides exact critical values for W when the sample size is small.

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Table 1 Background data of Israel, 1990–2005. Inflation rate (percent p.a.)

Growth rate of GDP (percent p.a.)

Unemployment rate (rate percent)

Year

17.6 18.0 9.4 11.2 14.5 8.1 10.6 7.0 8.6 1.3 0.0 1.4 6.5 1.91.2 2.4

6.6 6.1 7.2 3.8 7.0 6.6 5.2 3.5 3.7 2.5 7.7 0.3-1.2 1.7 4.4 5.2

9.6 10.6 11.2 10 7.8 6.8 6.6 7.6 8.6 9.0 8.8 9.3 10.3 10.7 10.4 9.0

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

16

percent p.a.

14 12 10 8 6 4 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 Fig. 2. The Bank of Israel’s rate of interest.

i¼

j1 j5 þ NRI þ p þ X j4 j4

ð11Þ

Eq. (11) states that the central bank sets its rate of interest in line with the natural rate of interest, expected inflation, and the Taylor Rule variables. The coefficient j1 < 0 captures a potential term premium, since the central bank sets the short term, or spot rate of interest, whereas the natural rate of interest may refer to some longer maturity. In practice, however, j1 may also pick up measurement error in the Xs. Finally, the VECM does not necessarily imply that the natural and money rates of interest are nonstationary.17 Indeed, our proxy for the natural rate of interest is stationary. 4. Results 4.1. The events We have chosen 1994–2005 as the observation period since the structure of monetary policy was homogeneous during this period. The government operated inflation targets, the exchange rate was flexible,18 and BOI announced (about 10 days in advance) its rate of interest for the next month. For most of this period Jacob Frenkel was Governor of the Bank of Israel. David Klein was Governor during 2000–2004.19 As may be seen in Table 1 the rate of inflation was reduced from the teens to zero, the rate of unemployment tended to grow, and the economy grew at an average annual rate of 4%. It was during this

17

Cointegration implies error correction for nonstationary data, but error correction may exist in stationary data too. The exchange rate floated throughout the entire period, at first within a band, but the band was progressively widened. Until 1997 the float was managed, but subsequently there has been no exchange rate intervention. In June 2005 the exchange rate bands were formally abolished. 19 Stanley Fischer became Governor in May 2005. Monetary policy has been ‘‘uneventful” under his governorship, hence none of the events are from his governorship. 18

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M. Beenstock, A. Ilek / Journal of Macroeconomics 32 (2010) 366–377 Table 2 The events. Event

Date

Change in BOI interest rate

Context

1 2 3 4 5 6 7 8

August 30, 1994 November 29, 1994 June 26, 1996 August 6, 1998 October 26, 1998 November 12, 1998 December 21, 2001 June 9 and 24, 2002

1.5 1.5 1.5 1.5 2 2 2 3.5

BOI launches interest rate policy activism Phase 2 of event 1 Inflation exceeds target, but BOI response very large Exchange rate band widened LTCM crisis. Shekel weak. Phase 2 of event 5 Klein uncharacteristically agrees to economic package Klein characteristically corrects error of event 7

The implicit 7 year forward YTM and large changes in monetary interest rate - 1994-2004 6.5

6.0

Declaration of arising interest rate by 1.5 %-31/08/94

Declaration of arising interest rate by 2 %26/10/98 and 12/11/98

Declaration of arising interest rate by 1.5 %09/06/02 and by 2% 24/06/02

5.5

forward rate

5.0

4.5

4.0

3.5

3.0

Declaration of cutting interest rate by 1.5 %06/08/98

Declaration of arising interest rate by 1.5 %29/11/94 and 25/06/96

Declaration of cutting interest rate by 2 %23/12/01

2.5

2.0 01/01/1994

05/02/1995

11/03/1996

15/04/1997

20/05/1998

24/06/1999

28/07/2000

01/09/2001

06/10/2002

10/11/2003

14/12/2004

Fig. 3. Bird’s eye view of monetary events.

period that the economy absorbed mass immigration from the former Soviet Union, which added about 20% to the population during the 1990s.20 In Fig. 2 we plot the BOI’s interest rate, which serves as the money rate of interest. During the period 1994–2005 we have identified eight events (the D’s) that constitute ‘‘large and independent monetary disturbances”, and which are listed21 in Table 2. In these events BOI typically raised its rate of interest by 1.5%, when the typical change is up to 1=4 %. Only in event 7 did BOI cut interest rates. In none of these events does NRI change significantly prior to their occurrence. Since we are interested in identifying b in Eq. (7) D does not have to be independent of X, since X is specified in Eq. (7). It is of course crucial that D be independent of u in Eq. (7). In each event window we are looking for the effect of the D shock on subsequent changes in the outcome variable (NRI). For example, in the first event there was no discernable change in the forward yield to maturity on indexed bonds either before or after the shock. There was a very small increase on August 21 but this was not statistically significant. It is therefore unreasonable to claim that the bond market anticipated the shock. Some of the events were triggered by shocks overseas. For example, Event 5 followed the Ruble Crisis, which broke out on August 17, 1998 when the Russian government defaulted on its ruble bonds. At first the crisis was regarded as a parochial matter until it became clear 6 weeks later that Long Term Capital Management was threatening to fail as a result. Contagion was feared, panic struck and BOI raised interest rates twice and even broke precedent by raising interest rates in the middle of the month. There is an obvious problem of identification here. The Ruble Crisis caused BOI to raise its interest rate, and it caused bond yields to rise. The event window shows that the bond market in Israel remained steady until mid September. By contrast domestic bond markets in other emerging markets, such as Brazil, South Korea and South Africa weakened substantially. It is ironical that by the time BOI took action bond markets in these countries had more or less recovered. Therefore, events 5 and 6 were simply panic reactions, which have obvious identifying power. 20

For a review of economic developments in Israel during this period see Ben Bassat (2001). A detailed discussion of these events is in an appendix available from the authors. Daily data are used to track our proxy for the natural rate of interest during two months before and after the event. 21

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Table 3 Non-parametric test of response of NRI to event. Event

Temporary effect (1 week)

Permanent effect (1 month)

1 2 3 4 5 6

0.1 NONE NONE 0.2 First announcement NONE Second announcement 0.4 NONE First announcement NONE Second announcement 0.7

0.2 NONE 0.2 0.1 First announcement NONE Second announcement 0.2 NONE First announcement 0.7 Second announcement 0.6

7 8a 8b

Wilcoxon statistic

d W

1 1.13

3 0.89

5 0.77

10 0.89

20 0.89

30 1.6

Table 4 Taylor rule model (dependent variable: Dit).

Intercept Dit  1 Dit  4 DNRIt  4 (r  NRI)t  1 Dpet1 Dpet3 pt  1 pt  2 Dp t  3 pt1  pt4 D2Ct D2Ct  2 Growtht  1 R2 adjusted Standard error LM(2) LM(12) Forecasting test (v212 ) Chow test (Gov Klein)

Coefficient

P-value

0.2059 0.1643 0.0956 0.3548 0.0775 0.2866 0.1739 0.0131 0.0159 0.0131 0.1677 0.0484 0.0288 0.0120 0.6793 0.3846 3.14 15.41 5.638 1.877

0.0009 0.0230 0.0840 0.0471 0.0017 <0.0001 0.0016 0.0240 0.0115 0.0109 0.0029 0.0202 0.1656 0.0460

0.21 0.22 0.933 0.037

OLS May 1994–December 2005. p = monthly inflation % pa, pe = expected inflation 12 months ahead % pa (derived from capital market data), p* = target inflation % pa, C = log coincident indicator, r = i  pe, growth is a 6-month moving average of growth interpolated from quarterly GDP expressed in % pa, LM(p) is the lagrange multiplier statistic for serial correlation up to order p. Forecasting test for 2005. Chow test for Governor Klein v Governor Frenkel.

Other events were triggered by political shocks. For example, event 7 followed extraordinary political pressure on Governor Klein, who quite uncharacteristically cut interest rates massively. Having realized his error, this lead to event 8 when interest rates were raised by a record amount. Fig. 3 provides a bird’s eye view of the events. 4.2. Non-parametric tests of Wicksell’s Classical Dichotomy Visual examination of each of the events does not suggest that the 3-year ahead forward yield to maturity on 7-year indexed bonds responds to interest rate policy. In Table 3 we classify the results for our experiments. The Wilcoxon test statistic is initially positive (when d = 1 day) but it falls well below its critical value. When a wider window up to 30 days is used W turns out to be negative, but never approaches statistical significance. Our main conclusion is that event analysis does not suggest that ‘‘large and independent monetary disturbances” affect the expected natural rate of interest. 4.3. The effect of the natural rate of interest on the money rate In Table 4 we report an estimate of Eq. (10) using monthly data. The main question is whether given other determinants of interest rate policy, does the natural rate of interest affect BOI’s rate of interest? The dynamic specification of Table 4 has been estimated using the general-to-specific methodology (Hendry, 1995), which nests down from an unrestricted dynamic model to the restricted model reported in Table 4. The X variables to which BOI is hypothesized to react are similar to those

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Table 5 Testing Wicksell’s Classical Dichotomy (dependent variable is NRI). Variable

Coefficient

P-value

Intercept DNRIt  1 DNRIt  2 (r  NRI)t  1 Dt Dt  1 Dt  2 Dt  3 Dt  4 Di t  1 Di t  2 Di t  3 Di t  4 R2 adjusted LM

0.0732 0.3899 0.2566 0.0022 0.0333 0.0466 0.0281 0.0203 0.0367 0.0273 0.0589 0.0266 0.0459 0.0882 14.421

0.8258 0.0001 0.0080 0.8520 0.3248 0.4335 0.6499 0.7491 0.5260 0.6607 0.4115 0.7080 0.4237 0.2746

OLS May 1994–December 2005. Controls for 4 lags on debt/GDP and X variables from Table 4. LM is lagrange multiplier statistic for up to 12th order serial correlation.

reported by Sussman (2004), Melnick (2005) and Argov et al. (2007). They include the rate of economic growth, the BOI’s coincident indicator of economic activity, inflation, expected inflation, and target inflation. Note that the variables that feature in Table 4 were known at the time BOI set its rate of interest for the following month. The signs of these variables are as expected. Table 4 shows that BOI reacts to changes in expected inflation.22 so that the Taylor Rule is forward-looking. However, it is also backward-looking since lagged inflation matters too. We found that BOI responds to the change in the official inflation target rather than its level. Indeed, specifying inflation or expected inflation in terms of deviations from the official inflation target seriously harms the goodness-of-fit. This suggests that BOI operated an implicit inflation target that was different to the official target. BOI also reacted to the real economy in a counter cyclical fashion. It raised interest rates when its coincident indicator of economic activity increased and when the economy grew more rapidly. An important novelty in Table 4 is that we introduce our proxy for the natural rate of interest into the model. Table 4 shows that BOI reacts to lagged changes in the natural rate of interest and that there is error correction from the natural rate to the (real) money rate. Indeed, the error correction coefficient is 0.08 and is highly statistically significant. Therefore, in the long-run the natural rate drives the money rate, on a one-to-one basis (up to a constant). There is both short-term and long-term error correction from the natural rate to the money rate. The model implies that following a permanent increase in the natural rate of interest by one percentage point, the Bank of Israel raises its rate of interest by 0.16% after 3 months, 0.77% after 6 months and almost 1% after 14 months. It therefore takes about a year for the Bank of Israel to respond fully to changes in the natural rate of interest. The specification in Table 4 implies23 that BOI has a strong preference for smoothing its interest rate policy, as reflected in the estimated error correction coefficient of 0.077. The unsmoothed Taylor Rule24 implied by Table 4 and Eq. (10) is:

i ¼ 2:66 þ r n þ p þ 0:37p þ 0:154growth

ð12Þ

which states that BOI anchors its rate of interest to the natural rate of interest, the reaction coefficient to inflation (actual and expected) is 1.37 so that, as expected by the Taylor Principle, it raises its rate of interest by more than inflation, and it raises its rate of interest by 0.15% if the rate if the growth rate rises by 1% pa. In Eq. (10) we expected j1 < 0 because our measure of the natural rate of interest embodies a term premium. The estimated term premium is 2.66% per year according to Eq. (12). All the variables that feature in Table 4 are weakly exogenous, therefore estimation by OLS is appropriate. They are weakly exogenous because we condition on lagged state variables and because the lagrange multiplier test statistics for serial correlation (LM) indicate that there is no trace of serial correlation in the errors. Had this not been the case, the lagged state variables might have been correlated with the current residuals in which case OLS would be inconsistent and estimation by GMM or IV would have been necessary. The same would have applied had Table 4 included current state variables. The forecasting test statistic has a p-value which is close to unity implying that the Taylor Rule model in Table 4 predicted the Bank of Israel’s monetary policy almost perfectly during 2005, despite the fact that in May 2005 Governor Stanley Fischer took over from Governor Klein.25 22

Expected inflation is calculated by BOI as the difference between 12 month yields on nominal and indexed bonds. An alternative specification (not shown) expresses inflation as deviations from target. In this case the NRI effect is weaker. Misspecification tests fail to discriminate between the two models. 24 Obtained by setting differenced terms to zero and solving for i. 25 Indeed, the Chow forecasting test statistic is not significant when the sample period is extended into 2008. However, the Chow structural break test suggests that a structural break in monetary policy might have occurred when Governor Klein took over from Governor Frenkel in 2000. Klein’s ECM coefficient turns out to be smaller than Frenkel’s, implying that he adjusted the rate of interest to the natural rate more slowly than his predecessor, his monetary policy was less countercyclical, and he ran a smoother interest rate policy. 23

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4.4. Parametric test of Wicksell’s Classical Dichotomy We estimated Eq. (9) using a variety of alternatives for the Z and X variables. The former included expected yields to maturity on 10-year bonds issued by the US Treasury, the rate of growth of per capita income in Israel, and the ratio of government debt to GDP. The latter included the X variables in Table 4. Our main results are reported in Table 5. In none of these specifications did the p5 and p6 parameter estimates turn out to be even remotely statistical significant. The latter means that there is no direct evidence of hysteresis on the natural rate of interest, in which case c = 0 in Eq. (7). The former means that we have been unable to discover the exogenous variables (Z) that drive the natural rate of interest. Although we find no direct evidence of hysteresis, there will be indirect hysteresis if in Eq. (5) b – 0 or p3 – 0 in Eq. (9). In Table 5 we allow up to four lags on the D shocks including the contemporaneous effect. Although these coefficients are negative none of them is statistically significant. Nor are they jointly significant. Therefore, both in the short-run and in the long-run there is no evidence that shocks to the money rate of interest affect the natural rate of interest. The same applies to the coefficients on the lagged changes in the money rate of interest. Finally, there is no error correction since the coefficient of r  NRI does not approach statistical significance in which case p4 is zero. The only statistically significant coefficients are the autoregressive parameters (p2) at lags 1 and 2. At one level these none-results are disappointing, because we have been unable to determine the variables that drive the natural rate of interest. On the other hand, they are encouraging because they show that we cannot reject Wicksell’s Classical Dichotomy, and that this result is robust with respect to alternative specifications. In Table 5 m* = 3 years, which assumes that it takes 3 years for the effect of price stickiness to dissipate. We could not find a causal effect of the BOI’s interest rate on forward YTMs on indexed bonds when m* > 3, suggesting that price stickiness does not take longer than 3 years to dissipate.

5. Conclusion To test Wicksell’s Classical Dichotomy we use the forward yield to maturity on indexed bonds to proxy expected ‘‘natural” yields to maturity. In the absence of convincing exclusion restrictions on potential instrumental variables, we use quasi experimentation and event analysis to identify the effect of monetary policy on the natural rate of interest. We select events in which the Bank of Israel changed its interest rate in a quasi-experimental manner. We use non-parametric and parametric tests to investigate the causal effect of the BOI’s interest rate policy on the expected natural rate of interest. These tests turned out to be negative, confirming the empirical validity of Wicksell’s Classical Dichotomy. Our results show that whereas there is no causal effect of the money rate of interest on the natural rate of interest, there is a causal effect of the natural rate on the money rate. This result confirms Taylor Rule theory, which predicts that the natural rate of interest anchors the money rate of interest. It takes about 14 months for the Bank of Israel to adjust the money rate of interest to developments in the natural rate. It also means that the natural rate of interest serves as a strongly exogenous regressor in Taylor Rule regressions. Therefore, to estimate Taylor Rules (for Israel) it is not necessary to find instrumental variables for the natural rate of interest. The empirical confirmation of Wicksell’s Classical Dichotomy implies that interest rate policy is not hysterical; it should not affect the level of output and other real variables in the long run because it does not affect the natural rate of interest. References Argov, E., Binyamini, A., Elkayam, D., Rozenshtrom, I., 2007. A Small Macroeconomic Model to Support Inflation Targeting in Israel. Bank of Israel, Monetary Department, Jerusalem. Ben Bassat, A. (Ed.), 2001. The Israeli Economy 1985–1998: From Government Intervention to Market Economics. Am Oved, Tel Aviv (Hebrew). Blanchard, O.J., Summers, R., 1986. Hysteresis and the European unemployment problem. NBER Macroeconomics Annual. MIT Press, Cambridge. Blanchard, O.J., Quah, D., 1989. The dynamic effects of aggregate demand and supply disturbances. American Economic Review 79, 655–673. Bomfim, A.N., 2001. Measuring Equilibrium Interest Real Rates: What Can We Learn from Yields on Indexed Bonds? Working Paper 2003-15, Federal Reserve Board. Campbell, J.Y., Lo, A.W., MacKinlay, A.C., 1997. The Econometrics of Financial Markets. Princeton University Press. Clarida, R., Gali, J., Gertler, M., 1998. The science of monetary policy: a New Keynesian perspective. Journal of Economic Literature, 37. Cox, J.C., Ingersoll, J.E., Ross, S.A., 1985. A theory of the term structure of interest rates. Econometrica 53, 385–407. Cuthbertson, K., Nitzche, D., 2005. Quantitative Financial Analysis, second ed. John Wiley, England. Estrella, A., Mishkin, F.S., 1997. The predictive power of the term structure of interest rates in Europe and the United States: Implication for the European Central Bank. European Economic Review, 41. Evans, C.L., Marshall, D.A., 1998. Monetary policy and the term structure of nominal interest rates: evidence and theory. Federal Reserve Bank of Chicago. Friedman, M., 1968. The role of monetary policy. American Economic Review 58, 1–17. Friedman, M., Schwartz, A.J., 1963. A Monetary History of the United States. Princeton University Press. Harvey, A.C., Jaeger, A., 1993. Detrending, stylized facts and the business cycle. Journal of Applied Econometrics 8, 231–247. Hendry, D.F., 1995. Dynamic Econometrics. Oxford University Press, Oxford. Laubach, T., Williams, J.C., 2003. Measuring the natural rate of interest. Review of Economics and Statistics 85, 1063–1070. Lee, M.-J., 2005. Micro-econometrics for Policy, Program and Treatment Effects. Oxford University Press. Melnick, R., 2005. A glimpse into the Governor’s chambers: the case of Israel. Bank of Israel Economic Review 77, 77–104 (in Hebrew). Orphanides, A., Williams, J.C., 2002. Robust monetary policy rules with unknown natural rates. Brooking Papers on Economic Activity 2, 63–118. Patinkin, D., 1965. Money, Interest and Prices, second ed. Harper & Row, New York. Pesek, B.P., Saving, T.R., 1967. Money, Wealth and Economic Theory. Macmillan, New York.

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