Real and nominal effects of central bank monetary policy $

Transcription

1 Journal of Monetary Economics 49 (2002) Real and nominal effects of central bank monetary policy $ Michael Kahn a, Shmuel Kandel b,c,d, Oded Sarig c,e, * a Bank of Israel, Jerusalem 91007, Israel b Tel Aviv University, Tel Aviv 69978, Israel c Wharton School of the University of Pennsylvania, Philadelphia, PA 19104, USA d CEPR, Switzerland e Arison School of Business, IDC, Herzliya 46150, Israel Received 8 December 1998; received in revised form 13 September 1999; accepted 24 October 2001 Abstract We examine the impact of monetary policy using Israeli data on nominal and indexed bonds, which allow us to decompose nominal interest rates into inflation expectations and ex ante real interest rates. We find that a monetary policy shock, introduced by raising the overnight rate the Bank of Israel charges member banks, raises real interest rates but lowers inflation expectations. Long-term real interest rates are less impacted than short-term rates. Lastly, monetary shocks affect the exchange rate between the Israeli currency and the US dollar. Our estimates are robust to numerous modifications to the basic VAR model. r 2002 Elsevier Science B.V. All rights reserved. JEL classification: E4; E5 Keywords: Monetary policy; Real interest rates; Inflation expectations $ We thank Yakov Amihud, Alex Cukierman, seminar participants in the CEPR Summer Symposium in Gerzensee, Copenhagen Business School, Hebrew University, Norwegian School of Management, Tel Aviv University, University of Cyprus, the Econometrics in Tel Aviv meetings and an anonymous referee for helpful comments and suggestions. The opinions expressed in this paper do not necessarily reflect the opinions of the Bank of Israel. *Corresponding author. Arison School of Business, IDC, P.O. Box 167, Herzliya 46150, Israel. Tel.: ; fax: address: sarig@idc.ac.il (O. Sarig) /02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S (02)

2 1494 M. Kahn et al. / Journal of Monetary Economics 49 (2002) Introduction In this paper we examine real and nominal effects of monetary policy using market data inflation expectations and real interest rates extracted from observed prices of indexed and nominal government bonds. Some of the questions that we try to answer are: Does the central bank monetary policy affect real interest rates? Does monetary policy affect inflation expectations? If the central bank monetary policy affects real interest rates or inflation expectations, is there a lag in the policy s impact on these variables? What is the magnitude of the policy s impact and how long does it last? Does the central bank monetary policy lead or respond to changes in the price level? Theory provides mixed answers to these questions. On one extreme, super neutrality implies that monetary policy does not impact real activity, which implies that, inter alia, it does not impact real interest rates. On the other hand, Keynsian analysis allows for real effects of monetary policy via its effect on real interest rates. Thus, the importance of empirical answers to these questions, both for academic research and for policy making, is self-evident. Indeed, a large body of empirical research has been devoted to estimating the real effects of monetary policy. Numerous recent studies estimate the response of macro-economic variables to monetary policy shocks using vector autoregression (VAR) models and data of many countries and across varied monetary regimes (see, for example, Edelberg and Marshall, 1996; Christiano and Eichenbaum, 1992; Christiano et al., 1996; Sims, 1992). These and other studies have yielded several empirical regularities, which are often termed puzzles. For example, the liquidity puzzle is the finding that an increase in monetary aggregates is accompanied by an increase (rather than a decrease) in nominal interest rates. 1 Another example, often referred to as the exchange rate puzzle, is the finding that an increase in non-us nominal interest rates is accompanied by a depreciation (rather than an appreciation) of the local currency. 2 While the term puzzle has been repeatedly used in reference to these findings, a simple explanation, consistent with economic theory, exists for these empirical findings. Specifically, these puzzles (as well as other puzzles discussed in Grilli and Roubini, 1996) may merely reflect the lack of a direct measure of inflation expectations. This is because, unless inflation expectations (or a proxy for these expectations) are observable, one cannot infer from an observed increase in nominal interest rates that a commensurate increase in real interest rates occurred. Consequently, it is difficult in studies that examine nominal interest rates to distinguish between the interaction of central bank policy with real interest rates and its interaction with inflation expectations. Similarly, because these studies typically analyze realized inflation rates rather than inflation expectations, they cannot examine the extent to which monetary policy leads or reacts to changes in inflation and inflation expectations. 1 See, for example, Leeper and Gordon (1992) and Reichenstein (1987). 2 See, for example, Sims (1992) and Kim and Roubini (1995).

3 M. Kahn et al. / Journal of Monetary Economics 49 (2002) To overcome the problem that plagued prior studies, we use data from Israel where index bonds have traded since the 1950s. Using simultaneously observed prices of nominal and index government (i.e., default-free) bonds, we compute market-determined real interest rates and inflation expectations. Thus, we are able to explicitly examine the separate reactions of both real interest rates and inflation expectations to monetary policy shocks. We also examine the reaction of the central bank s monetary policy to changes in investor inflation expectations and how the short-term end and the long-term end of the term structure of real interest rates differentially react to monetary policy shocks. We find that a monetary policy shock, introduced by raising the overnight rate the Bank of Israel charges member banks by one percentage point, raises the 1-year real interest rate by roughly percentage points but lowers inflation expectations by roughly 0.6 percentage point. The effect of such a monetary policy shock on nominal interest rates, which nets the effect of the shock on real interest rates and on inflation expectations, is an immediate increase of roughly 0.3 percentage point and a longerrun decline of about 0.1%. The estimated responses to the monetary policy shocks take 3 8 months to peak and are not sensitive the inclusion of additional real variables in the estimated VAR model. We also find that the impact of a given monetary shock is smaller on long-term interest rates than on short-term interest rates. Lastly, we find that such a monetary policy shock causes a 0.1 percentage point appreciation in the exchange rate of the domestic currency the NIS. The remainder of the paper is organized as follows. In Section 2 we describe the management of monetary policy in Israel. In Section 3 we discuss the estimation methods. Section 4 includes the basic estimation results. The results of sensitivity analyses are reported in Section 5. Section 6 concludes. In Appendix A, we describe the extraction of real interest rates and inflation expectations from index and nominal bond prices. 2. Monetary policy in Israel Much of the discussion in the literature that examines the impact of monetary policy deals with the question of how to best identify monetary policy shocks (see, for example, Christiano and Eichenbaum, 1992; Strongin, 1995; Christiano et al., 1996; Cochrane, 1998). In Israel, the stated policy of the central bank (i.e., the Bank of Israel, henceforth BOI ), its application, and market references to the policy make the identification of the monetary policy control simpler. As this is the basis for our estimation of the impact of the bank s monetary policy shocks, in this section we briefly describe the BOI s policy determination and resulting actions. The BOI conducts its monetary policy by adjusting the interest rate it charges member banks on overnight loans. Changes in this rate are based, in recent years, on several indicators that, considered together, illuminate the monetary picture and indicate how necessary it is to tighten or loosen monetary policy to achieve inflation targets. 3 Among those indicators, the inflation environment is assessed by the recent rate of inflation and by inflation expectations to 12 months, which are derived from

4 1496 M. Kahn et al. / Journal of Monetary Economics 49 (2002) the government indexed-bond market. The BOI also monitors monetary aggregates, especially M1, exchange rates, capital flows, and fiscal policy. The BOI announces at the end of each month the target interest rate for the next month. In managing monetary policy, the BOI uses three instruments that are under its full or partial control. The first is the interest rate on sources that the BOI makes available to or obtains from the banking system through monetary auctions. The monetary auctions are very similar to the REPO transactions used by many central banks in conducting monetary policy. The second instrument used by the BOI is monetary loans, which are granted in quotas, and the third instrument is open market operations in nominal bonds (which are similar to Treasury bills). The quantities that were provided by the last two instruments were insignificant during our sample period. In our analysis we use innovations to the interest rate the BOI charges member banks on overnight loans to measure monetary policy shocks. To verify that this rate corresponds to the short-term rate that banks face at the margin, we compared this rate to the interest rate on inter-bank trades. The correlation between these two series is Moreover, estimating our VAR model with either series produces essentially identical results. Therefore, we use the rate that is directly determined by the BOI the overnight rate it charges member banks throughout the analysis. 3. Methodology As explained above, we use prices of index and nominal bonds to calculate monthly series of annual real interest rates and annual inflation expectations. We do so using a method developed by Kandel et al. (1996) and Yariv (1995). The method can be used with Israeli data because concurrent trading in index and nominal bonds has taken place in Israel since the end of In extracting real interest rates we do not assume any specific term structure of interest rates or any process of expectations formation. Instead, the method uses five bonds to extract ex-ante real interest rates. While it may appear that a single index bond is sufficient for the computation of a single real interest rate, this is actually not so. The reason is that index bonds compensate their holders for changes in the CPI from issuance day to maturity; yet, because the CPI is announced with a 2-week lag, the CPI is not known either at the time an index bond is bought or upon its maturity. Hence, the method uses four additional bonds to overcome problems introduced by the lag in the publication of the CPI. The details of the manner in which this is done are explained in Appendix A. The method yields an ex-ante annual real interest rate for each month for which a suitable five-tuple set of bonds exists. For each month we also observe an annual default-free nominal rate of interest. In line with previous research, we define the 3 The Israeli government has gradually adopted, starting in 1992, inflation targets. Starting in 1997 inflation targets became a stated policy of the government that the BOI is expected to achieve. 4 Prior to 1988, there were no annual nominal bonds traded in Israel.

5 M. Kahn et al. / Journal of Monetary Economics 49 (2002) difference between the nominal rate of interest and the real rate of interest as inflation expectations. This definition implicitly assumes that there is no risk premium that is included in the nominal yield. 5 It is important to note that these are forward-looking inflation expectations: These expectations are extracted from asset prices that prevailed at the time these expectations were formed and reflect all the information investors had at that time. Having separated nominal interest rates, which have been analyzed in prior research, into real interest rates and inflation expectations, we proceed to study the impact of monetary policy. We do so using data generated by trading in security markets, data that immediately incorporate all anticipated effects of publicly announced actions. In particular, the real impact of monetary policy is examined mainly through its impact on the ex-ante real interest rates (which, in turn, affect real economic activity). 6 There are two main advantages to using data from financial markets. First, short-term and long-term effects are quickly incorporated into security prices (from which we extract the real interest rates we analyze) while macroeconomic series, such as the GDP series analyzed by prior studies, react much more slowly. Second, these series are much more accurately measured than most macroeconomic series, which increases the efficiency of estimating the real impact of monetary policy. Note that by using market data to extract real interest rates and inflation expectations we implicitly assume the rationality of investor expectations. Huberman and Schwert (1985) and Kandel et al. (1993) indeed find that inflation expectations so extracted are unbiased and the expectation errors uncorrelated with information known at the time these expectations are formed. Thus, neither study can reject the hypothesis that expectations extracted from Israeli bond prices are rational. While we use better data than were available for prior research, we employ a standard research method. Specifically, in the same spirit as Edelberg and Marshall (1996) and others, we estimate a fully recursive VAR model with the following order of variable types: * Type I: non-policy variables observed by the BOI when setting its monetary policy, * Type II: the BOI s monetary policy control, and * Type III: real forward interest rates of different maturities. All variable types are assumed to be endogenous. The assumed order of causality reflects the following assumption about the BOI decision making. The BOI bases its monetary policy on the whole history of all the endogenous variables as well at the contemporaneously observed macro-economic indicators (i.e., Type I variables, described below). Accordingly, the equation 5 In fact, a weaker assumption is sufficient for our analysis since any inflation risk premium that increases with the level of expected inflation does not affect our conclusions. Note also that the method assumes that there is no premium associated with the lag in the publication of the CPI. Indeed, Balsam et al. (1999) show that these premiums are virtually zero. 6 We also include, in the diagnostic analysis reported in Section 5, some direct measures of real economic activity.

6 1498 M. Kahn et al. / Journal of Monetary Economics 49 (2002) describing the dependency of the BOI monetary policy on these variables may be viewed as either the bank s feedback rule or as investors expectations of the BOI monetary policy (or both). Therefore, a change in monetary policy by the BOI in time t is the sum of: the BOI s response to changes up to time t 1 in all the model s variables, the BOI s response to time-t changes in the non-policy variables of Type I, and the BOI s monetary policy shock. In other words, we measure monetary policy shocks of time-t by changes in the BOI interest rate that are orthogonal to: * Changes in all variables (i.e., of types I, II, and III) observed prior to time t (upto time t 1), and * Contemporaneous (i.e., time t) changes in the non-policy variables on which the BOI bases its monetary policy (i.e., type I variables such as contemporaneous changes in inflation expectations). By construction, time-t monetary policy shock, which is initiated by the BOI, affects the contemporaneous (i.e., time t) changes in type-iii endogenous variables as well as all endogenous variables of later periods. In particular, inflation expectations reflect a BOI s monetary shock of time-t only in periods t þ 1 and onwards. The use of a fully recursive VAR model to estimate the impact of monetary policy versus the use of other identifying restrictions has been examined by several studies. The fully-recursive structure we use is similar to the one used by Christiano and Eichenbaum (1992), Christiano et al. (1996), Edelberg and Marshall (1996), Sims (1992), Strongin (1995), and others. However, several recent papers suggest other identifying restrictions (e.g., Bernanke and Mihov, 1995; Kim and Roubini, 1995; Kumah, 1997). Strongin (1995) compares the fully recursive structure to other restrictions on the contemporaneous error structure. He concludes that the qualitative responses of output to policy innovations are largely insensitive to the details of the contemporaneous modeling of the VARs error structure (p. 466). Yet, since in our basic VAR model we assume a particular Wald ordering of the variables (depicting the policy of the BOI described in the preceding section), to make sure that our inference does not depend on the assumed order, in Section 5 we report results estimated under different orderings. 7 Similar to Strongin (1995) findings, we find that the particular ordering we use does not appear to affect our conclusions. The basic VAR model we estimate includes the following variables: * Type I: The basic model includes only one variable EI 12 ; which is our measure of investors expectations of annual inflation. Using the method described above, we compute EI 12 as the difference between the annual nominal and real interest rates, which is the longest maturity for which matched pairs of nominal and index bonds exist. The BOI repeatedly states that it compares EI 12 to its target inflation rate. EI 12 ; therefore, depicts both the BOI s actual policy as well as investor expectations of the policy. In Section 5 s diagnostic models we also include as Type I variables 1-month-ahead inflation expectations extracted in the same 7 Section 5 reports the results of other diagnostic checks as well.

7 M. Kahn et al. / Journal of Monetary Economics 49 (2002) method, the money supply ðm1þ; the real exchange rate, and the actual inflation rate in the preceding 12 months. * Type II: In the basic model, we measure the BOI s monetary policy by the monthly average of the nominal interest paid by member banks on overnight deposits N BOI : Other studies (reviewed in Strongin, 1995) suggest that monetary aggregates (e.g., M1; total reserves, non-borrowed reserves) may also be used to proxy for the central bank s policy control. Accordingly, in Section 5 we examine the use of M1 to proxy for the BOI s monetary control. * Type III: We use the 1-year real yield to maturity ðr 1 Þ and the real forward rates calculated from the yields to maturity of index bonds maturing in five ðr 5 Þ and ten ðr 10 Þ years. The use of forward rates (rather than yields to maturity) neutralizes the double counting inherent in the use of yields to maturity. This is because, when using yields to maturity, the estimated impact of a monetary policy shock on short-term yields is also included in the estimated impact on the yields of longer-term instruments. 4. Results In this section we report the VAR estimates of the effects of changes in the BOI s monetary policy on nominal and real variables. The basic system we estimate includes the following variables: * Expectations of inflation over the next 12 months EI 12 * Annualized nominal effective BOI over-night interest rate N BOI * Annual real interest rates 1, 5, and 10 years forward R 1 ; R 5 ; R 10 where all variables are monthly averages of daily observations and the system is estimated with 2 lags. 8 In Table 1 we present the sample statistics of these series and in Fig. 1 we plot the series. In the plots one can observe a pick in the BOI interest rate in the last quarter of This sharprise in interest rates was instigated by a mini-run on the Israeli currency, the NIS, which the BOI defended by raising the interest rates on NIS-denominated overnight loans. The rise in the BOI s rate was accompanied by a drop in inflation expectations, which remained low even after the BOI interest rate returned to lower levels. In fact, real interest rates rose as the BOI lowered its overnight rate since inflation expectations declined faster than the lowering of the BOI nominal interest rate. The estimated system of equations is reported in Table 2. The residuals of the system are plotted in Fig. 2 and in Table 3 we report the covariances and the correlations of the residual series. The estimated coefficients illustrate the advantage of VAR response function estimates over simple regression estimates: Due to high 8 Using one lag or three lags in the estimation does not affect our results. We choose two lags since this is the minimum lag that reflects the BOI s policy of considering changes in inflation expectations when setting its monetary policy. Longer lags yield estimated models with lower values for Akaike Information Criteria.

8 1500 M. Kahn et al. / Journal of Monetary Economics 49 (2002) Table 1 Summary statistics of main sample series Mean Median Maximum Minimum S.D. Skewness Kurtosis EI N BOI R R R The above data series are of monthly averages of daily observations in Israel during the period of January 1989 December The series are: EI 12 ¼ monthly inflation expectations for the next 12 months extracted from nominal and index bond yields. N BOI ¼ the annualized nominal rate charged by the Bank of Israel on member banks overnight loans. R 1 ¼ the annualized yield to maturity of a 1-year index bond (i.e., the 1-year real rate of interest). R 5 ; R 10 ¼ the annualized 5-year and 10-year, respectively, forward real rates of interest. 28 BOI interest rate 30 Inflation expectations Real interest rate, 1 year Real forward rate, year Real forward rate, year Fig. 1. Plot of main sample series autocorrelations in the explanatory variables and response lags being longer than the lags included in the regression equations, the estimated coefficients appear to be insignificantly related to the endogenous variables. Yet, the response function estimates, which are reported below, do show significant impacts.

9 M. Kahn et al. / Journal of Monetary Economics 49 (2002) Table 2 Coefficient estimates in the basic VAR model EI 12 N BOI R 1 R 5 R 10 EI 12 ð 1Þ ( ) (8725) (5794) (4288) (6288) EI 12 ð 2Þ ( ) (8773) (5826) (4311) (6322) N BOI ð 1Þ ( ) (9456) (6280) (4647) (6814) N BOI ð 2Þ (9616) (7476) (4965) (3674) (5388) R 1 ð 1Þ (5260) ( ) ( ) (9652) ( ) R 1 ð 2Þ (3332) ( ) ( ) (8916) ( ) R 5 ð 1Þ ( ) (6666) ( ) ( ) ( ) R 5 ð 2Þ ( ) (7677) ( ) ( ) ( ) R 10 ð 1Þ (1341) ( ) ( ) (8155) ( ) R 10 ð 2Þ (1365) ( ) ( ) (8164) ( ) C ( ) ( ) (8701) ( ) ( ) Adj. R The above estimates are of a fully recursive VAR model with the following variables (in their order in the VAR model): EI 12 ¼ monthly inflation expectations for the next 12 months extracted from nominal and index bond yields. N BOI ¼ the annualized nominal rate charged by the Bank of Israel on member banks overnight loans. R 1 ¼ the annualized yield to maturity of a 1-year index bond (i.e., the 1-year real rate of interest). R 5 ; R 10 ¼ the annualized five-year and ten-year, respectively, forward real rates of interest. The model is estimated with two lags. Numbers in parenthesis in the explanatory variables designate the lag of the variable. Numbers in parenthesis in the table (under each estimate) are the asymptotic standard errors of the estimated coefficients. The estimates reported in Table 3 indicate that the residuals of the inflation expectation series and the BOI s overnight rate s residuals are hardly correlated both statistically (the correlation coefficient is not different from zero at 10% significance) and economically. The BOI s monetary policy residuals are only significantly

10 1502 M. Kahn et al. / Journal of Monetary Economics 49 (2002) Expected Inflation (EI12) BOI Interest (N BOI) One-year Real Rate (R 1) 3 Five-year Real Forward Rate (R 5) Ten-year Real Forward Rate (R 10) Fig. 2. Plot of estimated residuals in basic VAR model. correlated with the residuals of the 1-year real interest rates, which they precede in the sequence of effects we estimate. This means that simultaneous shocks to the system do not seem to be a major concern in our estimation of the impact of monetary policy shocks.

11 M. Kahn et al. / Journal of Monetary Economics 49 (2002) Table 3 Covariance and correlation matrices of shocks in the estimated system EI 12 N BOI R 1 R 5 R 10 Covariance matrix EI N BOI R R R Correlation matrix EI N BOI R R R The above estimates are the correlation and covariance matrices of the residuals of a fully recursive VAR model with the following variables (in their order in the VAR model): EI 12 ¼ monthly inflation expectations for the next 12 months extracted from nominal and index bond yields. N BOI ¼ the annualized nominal rate charged by the Bank of Israel on member banks overnight loans. R 1 ¼ the annualized yield to maturity of a 1-year index bond (i.e., the 1-year real rate of interest). R 5 ; R 10 ¼ the annualized 5-year and 10-year, respectively, forward real rates of interest. The model is estimated with two lags. Response to One S.D Innovations + _ 2 S.E Fig. 3. The reaction of the Bank of Israel to changes in investor inflation expectations. First we report, in Fig. 3, the estimated reaction of the central bank monetary control the overnight interest it charges banks to a one standard deviation increase (which is about 1.35 percentage points) in investor inflation expectations. The observed reaction to a one standard deviation increase in inflation expectations accumulates to about half a percentage point increase in the bank s nominal interest rate, peaking about 4 months after the shock to the expectations. These estimates

12 1504 M. Kahn et al. / Journal of Monetary Economics 49 (2002) Response to One S.D Innovations + 2 S.E. _ Fig. 4. The reaction of nominal interest rates to monetary policy shocks. suggest that, as the BOI s officials state and as specified in our estimated system, the bank s interest-rate policy responds to changes in inflation expectations, albeit with a few months lag. Next we report the estimated response of interest rates to monetary policy shocks. As discussed in the introduction, prior research on the effect of central bank monetary policy has examined the reaction of nominal interest rates to monetary policy shocks. To make our results comparable to those reported by previous studies, we also estimate the VAR model with nominal interest rates replacing the real interest rates in the basic VAR model (still including the inflation expectations extracted from the concurrently-observed prices of nominal and index bonds). In Fig. 4 we plot the response of nominal interest rates to monetary policy shocks. The estimated reaction to a one-standard-deviation shock (i.e., a 1.05 percentage point increase) to the BOI overnight interest rate is a 0.3 percentage point increase in the 1- year nominal interest rate, peaking about 2 months after the change in the BOI interest. This estimated response function is similar, both in shape and in magnitude, to the response function estimated by Edelberg and Marshall (1996) using US data and a similar VAR model. One may be surprised by the relatively small reaction of nominal interest rates to shocks to the interest rate charged by the central bank given the substitutability of money-market instruments and 1-year instruments. This, however, is not as surprising as it seems. Since changes in nominal interest rates are the net of two effects the effect on real interest rates and the effect on expected inflation, the small impact of a monetary policy shock on nominal interest rates nets these two effects, which are in opposite directions. 9 The advantage of using our data is that we can 9 The negative correlation between real interest rates and inflation expectations is documented in Fama (1990) and in Kandel et al. (1996).

13 M. Kahn et al. / Journal of Monetary Economics 49 (2002) Response to One S.D Innovations + 2 S.E. _ 0.8 Response of Real Interest Rates Response of Inflation Expectations Fig. 5. The reaction of real interest rates and inflation expectations to monetary policy shocks. decompose the nominal interest rate into the real rate and the expected inflation and separately estimate the effect of the central bank s policy on the two components. In Fig. 5 we present the estimated reactions of real interest rates and of inflation expectations to a one-standard-deviation increase in the BOI s overnight interest rate. Fig. 5 shows that, indeed, real interest rates and inflation expectations react in opposite directions to an increase in the BOI s overnight rate. As one might expect, an increase in the central bank s rate lowers investors inflation expectations. This suggests that the BOI s monetary policy is considered credible by investors. On the other hand, an increase in the BOI s rate also raises the real rate of interest (to 1-year maturity). This finding suggests that monetary policy has a real effect on the

14 1506 M. Kahn et al. / Journal of Monetary Economics 49 (2002) economy through its impact on the real cost of capital in the economy and the resulting effect on firms investment decisions. Note that the estimated impact of an increase in the BOI overnight rate on the nominal interest rate (Fig. 4) is smaller than the estimated separate impact on the determinants of the nominal rate on the real interest rate and on inflation expectations. Prior studies estimated the effect of central bank policy on inflation by including the series of realized inflation rates. Unlike inflation expectations, however, realized subsequent inflation is affected by additional factors, not all of which are known when the monetary shock happens. Assuming rational inflation expectations, actual inflation differs only by white noise from the inflation expectations formed when the monetary shock occurs. Therefore, when estimating the model with subsequent actual inflation rather than with contemporaneous inflation expectations, one obtains unbiased, albeit less powerful, estimates of the impact of monetary policy on inflation. Fig. 6 reproduces the plots in Fig. 5 with realized inflation during the following 12- month period. The estimated response function of the actual inflation rate is similar to the response function estimated with inflation expectations. This is in accordance with Huberman and Schwert (1985) and Kandel et al. (1993) findings that inflation expectations extracted from index and nominal bonds are unbiased. Yet, as actual inflation series contain more (white) noise than the inflation expectation series, the response function is estimated less accurately (i.e., with larger standard errors) than the estimated reaction of inflation expectations to the same change in the BOI s overnight interest. This means that our data, which allows us to use market information to proxy for inflation expectations, allows for more powerful tests of the effects of monetary policy on the economy. The central bank s policy affects interest rates at the very short end of the maturity spectrum. However, monetary policy may also impact longer-term real interest rates via investor substitution across maturities. In other words, because investors consider yields across the whole maturity spectrum when choosing investment portfolios, the monetary policy may impact long-term real interest rates and real economic activity. In Fig. 7 we report the estimated impact of a one-standarddeviation increase in the BOI s rate (i.e., an increase of 1.05 percentage point) on real interest rates for 1-, 5-, and 10-year maturities. Recall that we use the forward real rates of interest. By doing so we neutralize the effect of a change in the short-term spot rates on longer-term spot rates that exists because long-term spot rates contain the short-term yields as well the forward yield from the short maturity to the long maturity. For example, suppose that a monetary shock impacts interest rates upto 10 years forward. In this case, the 10-year spot rate, which is the product of the one through ten annual forward rates, is affected by the sum of the individual effects of the shock on the forward rates of years one through ten. On the other hand, by using forward rates we separately estimate the impact of a monetary policy shock on the real interest rate of individual years one, five, and ten. All estimated reactions are plotted using the same scale to facilitate easy comparison of the impact of the BOI s monetary policy shocks on the term structure of real rates of interest.

15 M. Kahn et al. / Journal of Monetary Economics 49 (2002) Response to One S.D Innovations + _ 2 S.E. Response of Real Interest Rates Response of Actual Inflation Fig. 6. The reaction of real interest rates and actual inflation to monetary policy shocks. Fig. 7 shows that the estimated reaction of the 5-year real interest is roughly six times lower than the reaction of the 1-year real interest rate to a given change in the BOI s overnight rate. The reaction of the 10-year real rate is not significantly different from zero either statistically or economically. This suggests that the central bank s monetary policy real impact is largely concentrated in the short-term end of the term structure of real interest rates. This does not mean that monetary policy shocks do not affect long-term spot rates: Long-term spot real interest rates are affected by monetary policy to the extent that long-term spot rates reflect short-term spot rates (as well as the forward rates between the short and the long maturities). In sum, it appears that, in the Israeli economy, monetary policy shocks * lower one-year-ahead inflation expectations,

16 1508 M. Kahn et al. / Journal of Monetary Economics 49 (2002) Response to One S.D Innovations + 2 S.E. _ 0.8 Response of One Year Real Rate Response of The Fifth Year Forward Real Rate Response of the Tenth Year Forward Real Rate Fig. 7. The reaction of real interest rates to monetary policy shocks. * increase real interest rates, mostly in the short-term end of the term structure of real interest rates: 1 5 years forward, and * little affect the long-term end of the real interest rate term structure.

17 5. Diagnostic checks M. Kahn et al. / Journal of Monetary Economics 49 (2002) A typical criticism of the fully recursive VAR method to estimate response functions is that when shocks to endogenous variables are not independent, it is difficult to interpret the impact of an individual shock on the system. In particular, correlated shocks may make the estimated response functions depend on the order in which the endogenous variables are included in the model. To assess how robust our results are, in this section we present some diagnostic checks using different specifications of the VAR model. In our analysis, we focus on the joint evolution of inflation expectations and the BOI s overnight rate. We assume that shocks to inflation expectations affect all concurrent endogenous variables but are not affected by the concurrent monetary policy shock: A monetary shock in a given month is assumed to affect inflation expectations only in the subsequent month. A possible criticism of the basic model may be that this is a valid identifying restriction for short-term inflation but not necessarily for long-term inflation. While we believe that inflation expectations are concurrently formed to all horizons, to examine this possibility we re-estimate the model replacing annual inflation expectations with expectations of next month s inflation. 10 The 1-month-ahead inflation expectations are extracted from nominal and index bond prices in the same manner done for the annual inflation expectations but with bonds that mature in a month. In Fig. 8 we present the same response functions presented in Figs. 3 and 5 but with 1-month-forward inflation expectations replacing the annual inflation expectations used to generate Figs. 3 and 5. In Fig. 8 we present the response functions using the same scales as the original response functions graphs. As is evident, the two estimated response functions of the BOI to innovations in inflation expectations are virtually the same when annual and monthly inflation expectations are used. Similarly, the estimated reaction of real interest rates to a monetary shock is not affected by the way inflation expectations are measures. The only difference entailed by using 1-month-ahead inflation expectations instead of 1-year-ahead expectations is that indeed a given monetary shocks impacts less 1-month-ahead inflation expectations than year-ahead inflation expectations. Next we examine whether the order of the variables in the VAR model impacts the estimates of their impulse response functions. To see this, we re-estimate the response functions reversing the order of the two main variables of our analysis the BOI over-night rate and inflation expectations. In other words, we re-estimate the response functions with the sequence N BOI ; EI 12 ; R 1 ; R 5 ; and R 10 instead of the sequence EI 12 ; N BOI ; R 1 ; R 5 ; and R 10 : In Fig. 9 we plot the estimated response functions of inflation expectations and 1-year real interest rates to monetary policy shocks under the modified order of variables. Comparing Fig. 9 to Fig. 5 it is immediately apparent that the order of the variables expected inflation shocks first or monetary shocks first little affects the estimated reaction functions. Similar response functions, which are not presented here to save space, are estimated when 10 We are thankful to the referee for suggesting this solution.

18 1510 M. Kahn et al. / Journal of Monetary Economics 49 (2002) Response to One S.D Innovations + 2 S.E. _ Response of BOI to innovations in Inflation Expectations Response of Real Interest rates to Monetary Shocks Response of Inflation Expectations to Monetary Shocks - - Fig. 8. The reaction of the Bank of Israel to changes in investor inflation expectations and the reaction of inflation expectations and real interest rates to monetary policy shocks using short-term inflation expectations.

19 M. Kahn et al. / Journal of Monetary Economics 49 (2002) Response to One S.D Innovations + 2 S.E. _ 0.8 Response of Real Interest Rates Response of Inflation Expectations Fig. 9. The reaction of real interest rates and inflation expectations to monetary policy shocks when monetary policy precedes inflation expectations. concurrent shocks to real interest rates are also supposed to affect the BOI s monetary policy. Hence, the assumed Wald ordering of the model s endogenous variables does not seem to affect the estimated response of real interest rates and of inflation expectations to monetary policy shocks. One of the issues debated in the literature on the impact of monetary policy on interest rates is which variable is best to use to measure monetary policy shocks. The two major alternatives are to measure these shocks by changes in interest rates or by changes in monetary aggregates. While the BOI officially states its policy in terms of

20 1512 M. Kahn et al. / Journal of Monetary Economics 49 (2002) interest rates, to examine the potential impact of measuring monetary policy shocks by changes in monetary aggregates we re-estimate the basic model with the money supply ðm1þ replacing the BOI s interest rate ðn BOI Þ: The difficulty with measuring changes in monetary policy by shocks to the money supply is that the money supply may reflect, besides monetary policy changes, other shocks to the economy. Thus, we expect that the modified model will result less accurate estimates than the basic model. In Fig. 10 we plot the estimated response functions of 1-year real interest rates and inflation expectations to monetary policy shocks when these shocks are measured by changes in M1: Since a tightening of the monetary policy corresponds to an increase in N BOI and a decrease in M1; the estimated response functions using M1 and using N BOI should be of the opposite sign. Comparing Fig. 10 and Fig. 5 we can clearly see that this is the case. Moreover, as expected, the standard errors in Fig. 10 are larger than the standard errors in Fig. 5, suggesting that it is better to use N BOI to measures monetary policy shocks in Israel. 11 In the basic model we estimate the impact of monetary policy shocks using only data from the financial markets. As argued in Section 3, the advantage of these data is that they are observable on a continuous basis and that financial asset prices continuously reflect all information. We now augment the basic model with some non-financial variables that may impact interest rates and inflation expectations. If these variables are also correlated with the monetary policy of the BOI, their omission may erroneously lead us to conclude that the BOI s monetary policy affects the interest rates and inflation expectations. The variables we include correspond to those variables suggested by prior theoretical and empirical research to be either determinants of inflation rates or determinants of the central bank s monetary policy. The additional variables are: * DPOP ¼ growth in the population, measured by the annualized growth rate in the adult population in Israel over the preceding 6 months. The Israeli Central Bureau of Statistics (CBS) estimates this variable quarterly. We use the quarterly estimate for each month of the quarter to capture the exogenous change in the Israeli population. * UNEMP ¼ the unemployment rate. This variable is also estimated by the CBS quarterly. We use this variable to capture weakness in the labor market, which may dampen inflation pressures. * DEXCH ¼ the change in the monthly average of the exchange rate of the NIS against a basket of foreign currencies weighted by their relative weight in the Israeli foreign trade. We use this variable to capture the potential impact of the cost of imports on the inflation rate. * FUNDING ¼ the net new issues of government securities during the month. We use this variable to capture monthly variation in the government s demand in the financial markets. 11 Estimating the VAR model with both M1 and N BOI does not materially change these conclusions.

21 M. Kahn et al. / Journal of Monetary Economics 49 (2002) Response to One S.D Innovations + 2 S.E. _ 0.8 Response of Expected Inflation Response of One-year Real Interest Rates Fig. 10. The reaction of real interest rates and inflation expectations to monetary policy shocks when monetary policy shocks are measured by M1: The summary statistics of these additional variables are reported in Table 4. One notable aspect of the Israeli economy in the sample period is evident from the growth of the Israeli population: During a 2-year period (mid 1990 through mid 1992) Israel s population grew very rapidly due to immigration from the Communist block. At its peak, the annualized growth rate was 8.6%. This corresponded to relatively high unemployment in 1991 and 1992, unemployment that subsided afterwards as the new immigrants were absorbed into the work force. This means

22 1514 M. Kahn et al. / Journal of Monetary Economics 49 (2002) Table 4 Summary statistics of additional sample series Mean Median Maximum Minimum S.D. Skewness Kurtosis DPOP UNEMP DEXCH FUNDING The above data series are of monthly observations in Israel during the period of January 1989 December The series are: DPOP ¼ growth in the population measured by the annualized growth rate in the adult population in Israel over the preceding six months. This variable is estimated quarterly by the Israeli Central Bureau of Statistics (CBS). We use the quarterly estimate for each month of the quarter. UNEMP ¼ the unemployment rate. This variable is also estimated by the CBS quarterly. EXCH ¼ the change in the monthly average of the exchange rate of the NIS against a basket of foreign currencies weighted by their relative weight in the Israeli foreign trade. FUNDING ¼ the net new issues of government securities during the month. that our non-financial series, which include these abnormal years in terms of employment, may yield atypical estimates of the relations between real variables and financial variables. When we re-estimate the basic model, which is based on financial data only, excluding these years, the estimated model parameters and response functions are little affected. We augment the basic model with the additional variables where DPOP is added as an exogenous variable and all other variables are entered as endogenous Type-III variables. The estimated response functions of the real interest rate and of inflation expectations to monetary policy shocks under the augmented model are plotted in Fig. 11. As is evident from the figure, the estimated response functions are hardly affected by the augmentation of the basic model. Moreover, we obtain virtually the same estimated response functions when we insert the additional variables before the BOI s interest rate, i.e., when we add these variables as Type-I variables. Next, in Fig. 12, we plot the estimated impact of monetary policy shocks on unemployment, NIS exchange rate, and net government funding in the augmented model. Neither the unemployment rate nor the net government funding appears to be affected by monetary policy shocks. It is possible that we cannot detect these effects since we use monthly data so that measurement of changes in unemployment or in government funding needs is too noisy to yield any reliable estimates. On the other hand, the NIS exchange rate, which is observed daily and can respond quickly to monetary policy shocks, responds significantly to monetary policy shocks. Specifically, a one standard deviation shock to N BOI (which is about a 1.05 percentage point shock) results in a devaluation of the NIS of about 0.1 percentage point. Lastly, the estimated VAR model includes all variables in a linear form. We also estimate the basic model with all the variables included both in linear and quadratic terms. The resulting estimated response functions of inflation expectations and of real interest rates to monetary policy shocks are virtually the same as the response functions estimated with linear effects only.

23 M. Kahn et al. / Journal of Monetary Economics 49 (2002) Response to One S.D Innovations + 2 S.E. _ 0.8 Response of Real Interest Rate Response of Expected Inflation Fig. 11. The reaction of real interest rates and inflation expectations to monetary policy shocks estimated within an augmented model. In sum, the estimated impact of monetary policy shocks on inflation expectations and on real interest rates seems to be robust to reasonable modifications to the estimated model. 6. Conclusions In this paper we examine the impact of monetary policy on interest rates and real economic activity using a fully recursive VAR model and Israeli data. Specifically,

24 1516 M. Kahn et al. / Journal of Monetary Economics 49 (2002) Response to One S.D Innovations + _ 2 S.E. Response of Unemployment Response of the NIS Exchange Rate Response of Government Funding Fig. 12. The reaction of unemployment, NIS exchange rate, and government net funding to monetary policy shocks. we examine the effect of monetary policy shocks on real interest rates and on inflation expectations. Unlike prior studies, we are able to separately estimate the impact of monetary policy on real interest rates and on inflation expectations since