Does Monetary Policy React to Stock Prices? Some International Evidence

Transcription

1 Does Monetary Policy React to Stock Prices? Some International Evidence Francesco Furlanetto DEEP, University of Lausanne Preliminary draft: October 20, 2004 Abstract This paper attempts to measure the reaction of monetary policy to the stock market. We apply the procedure of Rigobon and Sack (2003) to estimate and identify a VAR in presence of heteroskedasticity. This procedure fully takes into account the relation of endogeneity between interest rates and stock returns that is ignored in the traditional VAR literature. We found a positive and significant reaction in the US and in UK. But this reaction becomes much lower during the high tech bubble. In Japan and EU we did not find any reaction. JEL Classification: E44, E52, E58 Keywords: monetary policy, stock market, identification, VAR, heteroskedasticity 1 Introduction In the last 15 years the relationship between asset prices and monetary policy has become increasingly important. Many episodes of large swings in the stock market, in the real estate market and in the credit market happened in Japan, in the Scandinavian countries and in England in the late 80s and in the United States and, to a different degree, in all industrialized countries at the end of the 90s. 0 University of Lausanne, BFSH1 bureau 537, 1015 Dorigny, Switzerland. Francesco.Furlanetto@unil.ch 1

2 While the main fear of policy makers, the inflation rate, is now low and stable in the main developed economies, financial instability has become one of the most discussed problems in the press and in the academic literature. Borio and Lowe (2003) document two boom-bust cycles in asset prices, one from the mid-1980s to early 1990s, the other from the end of the 1990s to the present. These cycles appear to be growing in amplitude and length and are characterized by equity prices being more volatile than commercial and residential property. Large swings have been associated to strains in the financial sector and in the real economy: important recessions have been experienced after the two cycles we have described, in particular in Japan but also in many other countries. Developments in the financial markets have become increasingly important for central banks and a large debate on to what extent central banks should take into account asset prices in their strategy has begun. In this paper we try to evaluate empirically what has been in the last ten years the influence of asset prices on the strategy of monetary policy in different countries. 2 Review of the literature The relationship between monetary policy and financial variables has been considered in two strands of the literature. The first one considers the role of financial variables like stock prices, real estate prices and credit growth in the optimal strategy of monetary policy. The main question is whether financial variables should be included in the reaction function of the central bank. Bernanke and Gertler (2000) argue that the objective of a central bank is price stability and asset prices have to be taken into account only if they signal changes in expected inflation. Simulations of various kinds of monetary policy rules (including or not asset prices) in a new Keynesian model with nominal rigidities and financial accelerator show that the most stabilizing rule is one that responds strongly to inflation but does not react to asset prices variations. The authors argue that the response to asset prices has destabilizing effects because it is almost impossible to know whether a change in asset prices is due to fundamental factors or not. Cecchetti et al (2000) take the opposite view and argue that it is possible to assess the non-fundamental component in asset prices and 2

3 that a more proactive response of monetary policy to asset prices is possible. Bordo and Jeanne (2002) build a simple dynamic model where there are rich interactions between monetary policy and asset prices. In some cases a policy that tries to target asset prices is optimal: it is the case when the risk of a bust is large and the monetary authority can intervene at relatively low cost. The second strand of the literature on this subject attempts to measure empirically the reaction of monetary policy to asset prices. Bernanke and Gertler (1999) estimate by GMM a forward looking extended policy rule where the interest rate responds also to stock returns. They find that the response is negative but not significantly different from zero for United States and Japan. They take into account the endogeneity of stock returns instrumenting for the change in stock prices with lags of macroeconomic variables and stock returns. Rigobon and Sack (2003) challenge this result arguing that the endogeneity issue is not considered properly. In fact it is hard to conceive any instrument that affect the stock market without affecting the interest rate. Thus, in their opinion, this kind of regression uses weak instruments that lead to biased estimates. Rigobon and Sack try to measure the reaction of monetary policy to stock prices using a Vector autoregression (VAR) model. They fully take into account the endogeneity issue by using an appropriate identification technique based on heteroskedasticity and they estimate for the Unites States a significant positive reaction of monetary policy to stock market. Bohl, Siklos and Werner (2003) use a similar model for Germany and find a reaction that is not significant in the period Ourworkisintegratedinthissecondstrandoftheliteratureanddoes not deal with the optimal monetary policy: our objective is to extend the evidence of Rigobon and Sack to other countries and to assess the behavior of central banks (in particular the ECB) with respect to that of the FED. 3 The Rigobon and Sack s procedure 1 VAR models are the most used tool to measure the relationship between macroeconomic variables. As we are interested in interest rates and stock prices, the structure of the simplest VAR is the following: 1 This section heavily draws on Rigobon and Sack (2003). 3

4 it it 1 εt A = C (L) + B (1) s t s t 1 η t where i t is the interest rate 2, s t are stock returns, A is a 2 2 matrix that describes contemporaneous relations among the variables, c(l) is a finite order lag polynomial, ε t and η t are structural disturbances. B is a 2 2 matrix: non zero off-diagonal elements of B allow some shocks to affect both endogenous variables. The usual assumptions to achieve identification in this kind of model is to impose a triangular form to matrix A (Cholesky decomposition) and a diagonal structure to matrix B. Inthiswaythemodel is exactly identified. The triangular structure of matrix A means that in our two variables VAR one of the two variables does not react contemporaneously to the other. But this assumption, that is reasonable in other contexts, is clearly inappropriate in this case: each shock to one of the variables has immediate effect on the other in the financial markets. Rigobon and Sack build an identification procedure that allows contemporaneous relations between interest rates and asset prices and relies on the heteroskedasticity that is present in the data and that is usually not considered in VAR studies. In Figure 1 we represent the thirty day rolling variance of stock returns and interest rates in the USA: we observe that there are rich patterns that highlight the importance of modelling heteroskedasticity. Looking at the data we observe that shifts in volatility of the shocks affect the correlation between interest rates and stock returns. In Figure 1 we see that this correlation is most of the time negative but becomes positive when stock prices volatility is high. The Rigobon and Sack s procedure exploits shifts in covariance to identify the model without imposing exclusion restrictions (as in the traditional approach) that would be inappropriate. 3 2 The three month treasury bill rate is used rather than the federal funds rate. While the federal funds rate is changed every six weeks or more, the three month treasury bill rate adjusts daily reflecting expectations of future variations in the federal funds rate and is monitored by the central bank. 3 Realizations of interest rates and stock returns can be seen as the intersection between two schedules: the first is the reaction function of asset prices to changes in the interest rates (supposed to be downward sloping because an increase in the interest rate will lower the discounted value of future dividends, i.e. the value of the asset). The second is the reaction of the interest rates to an unexpected movement in the asset market. Theobjectiveoftheprocedureistoestimatetheslopeofthisschedule. Becauseof 4

5 To fully exploit the data s heteroskedasticity, it s crucial to use daily data: in lower frequency data, in fact, heteroskedasticity diminishes a lot. Rigobon and Sack estimate the following VAR: i t = βs t + θx t + γz t + ε t (2) s t = αi t + φx t + z t + η t (3) where i t is the three month interest rate (Tbill), s t is the daily return on the S&P 500 index, x t includes 5 lags of the two endogenous variables and some macroeconomic shocks (measured as monthly releases of some macro indicators less their anticipated value), z t represents some unobserved shocks 4 that affect both i t and s t and can be seen as any other macroeconomic shock other than x t or as shifts in risk preferences of the agents. ε t is a monetary policy shock, η t is a stock market shock. 5 The structure of the model is quite rich but our objective is very simple: we want to estimate the coefficient β that measures the reaction of interest rate to a stock market shock. To achieve this goal it is necessary to show that the parameter can be identified. It is important to specify the assumptions on the correlation structure of the shocks: the shocks ε t and η t and the unobserved shock z t are supposed to be orthogonal and at this stage all three can be heteroskedastic. Note that ortoghonality of ε t and η t does not imply that structural disturbances are uncorrelated: in fact the presence of z t allows correlation. We can rewrite the structural form of the VAR in the following way: 1 β α 1 it s t = θ φ x t + γzt + ε t z t + η t This system can not be estimated directly, because of the endogeneity problem discussed above and because z t is an unobservable variable, but we heteroskedasticity, endogeneity and unobservability of z t, OLS estimates are biased and so we look for a variable (an instrument) that shifts stock market curve but does not affect the monetary policy response. An increase in the variance of the stock market shock changes the covariance between stock returns and interest rates and this change plays the role of an instrument. 4 The impact of z t on s t is normalized to one. 5 Equation 2 can be interpreted as a high frequency policy reaction function or in other words as a sort of Taylor rule that includes asset prices. Equation 3 is the stock market reaction function. 5 (4)

6 can write it in reduced form: " it = s t 1 1 αβ α 1 αβ β 1 αβ 1 1 αβ # θ φ " x t αβ α 1 αβ it s t = Φx t + υ i t υ s t β 1 αβ 1 1 αβ # γzt + ε t z t + η t (5) (6) where: υ i t = υ s t = Φ = 1 1 αβ ((γ + β) z t + βη t + ε t ) 1 1 αβ ((1 + αγ) z t + η t + αε t ) " # θ φ 1 1 αβ α 1 αβ β 1 αβ 1 1 αβ In the VAR literature it s usual to recover the estimates of the structural form parameters from the reduced form residuals. Given the structure of correlations specified above, the covariance matrix of reduced form residuals is the following, : var (it ) cov (i Ω = t,s t ) = cov (i t,s t ) var (s t ) 1 (β + γ) 2 σ = 2 z + β 2 σ 2 η + σ 2 ε (1 + αγ)(β + γ) σ 2 z + βσ 2 η + ασ 2 ε (1 αβ) 2 (1 + αγ)(β + γ) σ 2 z + βσ 2 η + ασ 2 ε (1 + αγ) 2 σ 2 z + σ 2 η + α 2 σ 2 ε (7) Estimating the model in reduced form we obtain a consistent estimate for the covariance matrix of reduced form residuals. But the covariance matrix provides only three moments Ω 11, Ω 12, Ω 22. At this stage we are not able to achieve identification: the maximum number of parameters that can be identified is three but in matrix Ω we have six unknowns: α, β, γ, σ 2 z, σ 2 η, σ 2 ε. So we do not have enough restrictions to recover the structural form parameters. But heteroskedasticity can help in our task: suppose that we can identify different regimes for the covariance matrix of the reduced form residuals. 6

7 The additional regimes provide new restrictions and may allow us to identify the parameters of the structural form. The problem is that for each new regime i we have three new equations but also three new unknowns σ 2 i,z, σ 2 i,η, σ 2 i,ε. But if we assume that the monetary policy shock ε is homoskedastic (so σ 2 ε is constant), for each regime we add three equations and only two unknowns. With three regimes we have nine equations and ten unknowns α, β, γ, σ 2 ε, σ 2 1,z, σ 2 1,η, σ 2 2,z, σ 2 2,η, σ 2 3,z, σ3,η 2 but this is enough to achieve partial identification and in particular we can estimate the parameter β. The hypothesis that σ 2 ε is constant is not very restrictive because it does not imply that i t is homoskedastic: the variance of the interest rate is composed also of σ 2 i,z and σ 2 i,η that change through time. The other maintained hypothesis to achieve identification is that the parameters α, β, γ are constant across regimes. This is common practice in the VAR literature, also when heteroskedasticity is not considered. So, for each regime we have the following covariance matrix: 1 (β + γ) 2 σ Ω i = 2 i,z + β 2 σ 2 i,η + σ 2 ε (1 + αγ)(β + γ) σ 2 i,z + βσ 2 i,η + ασ 2 ε (1 αβ) 2 (1 + αγ)(β + γ) σ 2 i,z + βσ 2 i,η + ασ 2 ε (1 + αγ) 2 σ 2 i,z + σ 2 i,η + α 2 σ 2 ε (8) In appendix 1 we show that with three regimes 6 onesolutionofthefollowing quadratic equation is a consistent estimator for β: where 7 : aβ 2 bβ + c =0 (9) a = Ω 31,22 Ω 21,12 Ω 21,22 Ω 31,12 b = Ω 31,22 Ω 21,11 Ω 21,22 Ω 31,11 c = Ω 31,12 Ω 21,11 Ω 21,12 Ω 31,11 A nice feature of this model is that many assumptions are testable. In fact if the model is correctly specified we should findthesameresultsforβ under 6 With four regimes we have overidentifying restrictions that allow us to estimate β by GMM. 7 Ω 31,22 is the (2,2) element of matrix Ω 31. Ω 31 = Ω 3 Ω 1. 7

8 any three regimes or using more than three regimes, given the hypothesis that the parameter β is constant in the sample. If not, the parameters are unstable across regimes, or the assumption of homoskedasticity for the monetary policy shock is not correct or there are non linearities that are not captured in the Rigobon and Sack s formulation. Thus far we proved that with at least three regimes we are able to consistently estimate the parameter β. The next question is how to determine these regimes. Rigobon and Sack use the following approach: they run the VAR (6) in reduced form and take the residuals. The two series can be interpreted as interest rate shocks and stock returns shocks. The heteroskedasticity of the shocks allows us to identify four regimes: regime 1 where both shocks have low volatility, regime 2 where interest rate shock has low volatility and stock market shock has high volatility, regime 3 where both shocks have high volatility, regime 4 where interest rate shock has high volatility and stock market shock has low volatility. To split the observations into the four regimes we adopted the following criterion: one observation is considered to have high variance if the thirty day rolling variance of the residual is more than one standard deviation over the average of the series. Rigobon and Sack admit that this approach is arbitrary but at least two arguments can justify this choice: 1) The estimates are consistent even if the regimes are badly specified. Only if the misspecification is large enough such that the system fails the following order condition, the estimates are not consistent: 8 : Ω 11,i Ω 12,j Ω11,jΩ 12,i 6=0 (10) for regimes i and j with i 6= j. This condition has an intuitive explanation: it fails if two covariances matrices are proportional i.e. if relative variances are constant across regimes. in this case some equations in our moment conditions are not independent and heteroskedasticity cannot be helpful ( for a proof of this result and more details see Rigobon (2003)). 2) The same criterion is largely used in the literature to identify period of excessive volatility in asset markets (Bordo and Jeanne, 2002). 8 In fact the parameters are neither identified because this condition is the equivalent of the rank condition that is tested in the identification literature once the order condition (number of equations equal to number of unknown to achieve just-identification) is satisfied. 8

9 4 Results for USA In this section we reproduce the results of Rigobon and Sack for the United States and we extend their analysis up to Methodology. In our first experiment the sample period is January 1985-December 1999 and the data are daily 9. The first step is to estimate the model: i t = βs t + θx t + γz t + ε t (11) s t = αi t + φx t + z t + η t (12) that we can write in reduced form as: it υ i = Φx s t + t t υ s t In their paper Rigobon and Sack include in the variable x t some observable macroeconomics shocks measured as the difference between the released value and the expected value of five monthly macroeconomic indicators: the consumer price index (CPI), the National Association of purchasing Managers survey (NAPM), non farm payrolls (NEPAY), the core producer index (PPI) and retail sales (RETL). The role of these shocks in the model is negligible and in fact we are able to reproduce the results for the United States even without them 10. In our specification the variable x t consists only of 5 lags of the two endogenous variables. Thus we run the VAR in reduced form and we take the residuals. To share the 3371 observations into the four regimes we adopted the method described in the previous section. In table 1 we observe that the covariance, that on average is slightly negative, becomes positive when the stock market shock exhibits high variance. These shifts in the covariance matrix allow us to identify the model using the estimated covariance matrices in the four regimes to recover the parameters of the structural form. In table 1 we show the estimates of the four covariance matrices Ω i for i=1 to 4. 9 All data are taken from Datastream. 10 We think that the inclusion of monthly macroeconomic shocks in a model with daily data is questionable. In the following sections we use as shocks daily variations in the trade weighted exchange rate and in the oil price index but their inclusion has also negligible effects. 9

10 Table 1: variance-covariance matrix of reduced form shocks Variance of Variance of Frequency Policy Shocks Stk mkt shocks Covariance of Obs. Regime % Regime % Regime % Regime % Subtracting the first covariance matrix from the other three we obtain the three matrices Ω i for i=1 to 3. Thesecondstepistoestimatetheparameterβ through the procedure explainedinsection3(anddetailedinappendix1). Weobtainfourdifferent estimates for the parameter using regimes 1-2-3, 1-2-4, and Under the assumptions of our model we should expect to find the same value using different regimes given that the parameter β is supposed to be stable across regimes. The third step is to compute the distribution of the estimated coefficients. The distribution is calculated by bootstrap: residuals are supposed to be normal with mean zero and variance Ω i for each regime. We simulate 1000 draws for each Ω i. For each covariance matrix we estimate β using different subsets of regimes. In the end we obtain 1000 estimates for the coefficient and we are able to compute the distribution. The four estimates for β obtained using three regimes can be compared to a GMM estimate that uses all the four regimes. With four regimes the model is overidentified. We then test that the four estimates that we obtain using three regimes are statistically equal to the GMM estimate: to do so we compute the difference between the estimates for each draw of the bootstrap. We obtain 1000 observations that represent the distribution of the difference in the estimate. This distribution should have zero mean and obviously zero should be inside the 95% confidence interval for the mean. To be coherent with the language of Rigobon and Sack we call this test test of overidentifying restrictions. Results. Our results (shown in table 2) are extremely coherent with the assumptions of the model. The estimates of the coefficient β are almost identical across regimes and quite precise. 10

11 Table 2: estimates for USA, all 1,2,3 1,2,4 1,3,4 2,3,4 Mean of distribution Std. dev. of distribution Median of distribution Mass below zero 0% 2.4% 0% 0% 0% There are mild differences with the results of Rigobon and Sack in the estimates but huge differences in the standard deviations under regimes 1,3,4 and 2,3,4 (Table 3), showing that the inclusion of the monthly macroeconomic shocks has no positive effect 11. Table 3: results of Rigobon and Sack (2003), USA All 1,2,3 1,2,4 1,3,4 2,3,4 Mean of distribution Std. dev. of distribution Median of distribution Mass below zero 0.0% 0.0% 0.0% 1.4% 1.4% Using different subsets of regimes we obtain an estimate of for the coefficient β with a standard error of (except in one case where the standard error is slightly bigger). An important check for the validity of our estimates is to compare them with the result obtained using all four regimes. The GMM estimate is very similar to our previous results (first column of table 2) and in fact the test of overidentifying restrictions is passed in each case as it is shown in table 4 11 Actually the specification without shocks achieves more stable and precise results. 11

12 Table 4: test of overidentifying restrictions, USA Confidence interval Median β GMM β 123 [ , ] β GMM β 124 [ , ] β GMM β 134 [ , ] β GMM β 234 [ , ] The major result of the Rigobon and Sack paper is that, by employing an appropriate identification procedure, the reaction of monetary policy to asset prices movements is positive and significant. A point estimate of means that a 10% rise in the S&P 500 index increases the three month interest rate by 18 basis points. Rigobon and Sack argue that this result is very plausible and corresponds to the impact of asset prices on aggregate demand through a wealth effect on consumption. The Rigobon and Sack s sample ends in December 1999: as now we have four years of additional data, we extend the analysis up to August 2003 and we find different results. Table 5: estimates for USA, All 1,2,3 1,2,4 1,3,4 2,3,4 Mean of distribution Std. dev. of distribution Median of distribution Mass below zero 0.0% 5.0% 0.7% 0.7% 0.0% The GMM estimate (shown in the first column of table 5) is much lower (0.007 compared to 0.018) and the estimates widely differ across regimes. Still they are positive and significant and the test of overidentifying restrictions (table 6) is passed in three cases out of four (even if the medians of the distributions are quite high in two cases). 12

13 Table 6: test of overidentifying restrictions, USA Confidence interval Median β GMM β 123 [ , ] β GMM β 124 [ , ] β GMM β 134 [ , ] β GMM β 234 [0.0000, ] Thus the result that the coefficient β is positive and significant is preserved but we detect some signs of instability. The specification of the model seems not robust to the extension of the sample. The most likely explanation is that the assumption of constant coefficients over the sample period is violated and that a structural break happened somewhere in the end of the nineties. To test this intuition we estimate the model for the sample period January 1998-October 2003, a period that includes the high tech bubble. A first difference with respect to the firstpartofthesampleisthatnowthe covariance is positive under all the four regimes (Table 7). It is still true that it is higher when the stock market volatility is also high. table 7: variance-covariance matrix of reduced form shocks Variance of Variance of Frequency Policy Shocks Stk mkt shocks Covariance of Obs. Regime % Regime % Regime % Regime % We obtained the following results: Table 8: estimates for USA, All 1,2,3 1,2,4 1,3,4 2,3,4 Mean of distribution Std. dev. of distribution Median of distribution Mass below zero 0.6% 0.7% 1.0% 46.3% 46.8% 13

14 The estimated reaction of monetary policy to asset prices is three times lower than in the preceding period and is quite stable across different subsets of regimes even if the precision of the estimates under regimes 1,3,4 and 2,3,4 blows up considerably. Moreover, the test of overidentifying restrictions is easily passed in each case and the medians are very close to zero (Table 9). Taking these results seriously a 10% of increase in the SP500 implies an increase of the interest rate of only 6 basis point.. Table 9: test of overidentifying restrictions, USA Confidence interval Median β GMM β 123 [ , ] β GMM β 124 [ , ] β GMM β 134 [ , ] β GMM β 234 [ , ] Sensitivity analysis. The main weakness of the model is that the choice of the regimes is somewhat arbitrary: Rigobon and Sack locate residuals in the high volatility regime if the observation is at least one standard deviation over the average of the series. Our above result is referred to three quarters of a standard deviation (lim=0.75) but we show that results are largely unaffected to reasonable changes in the definition of the regimes. We compute the estimates reducing the criteria for determining high volatility observations to half of a standard deviation (lim=0.5) and increasing it to one standard deviation (lim=1): the point estimates are largely unaffected and the tests of overidentifyng restrictions are passed in both cases (see table 10 and 11 in the appendix). For sake of completeness we estimate a specification of the model that includes two macroeconomic shocks in the variable x t given by daily changes in the trade weighted exchange rate and daily changes in the world index of oil prices. The previous results are strongly confirmed: in particular the low value of the estimate in the second part of the sample. These results are presented in table 10,11,12 and 13 in the appendix. Interpretation. Thus, in the end of the nineties something has changed in the relationship between asset prices and the three month interest rate and 14

15 given that this interest rate reflect near term expectations over future monetary policy, something has changed also in the relationship between monetary policy and asset prices. This result adds some quantitative evidence to the widely held opinion that the Federal Reserve took an excessively expansionary policy in recent years or at least that it did not react to the huge swing in the stockmarket: not only it did not increase his reaction during the bubble period but worst the FED reacted less than what it had done in the recent past. The Federal Reserve Board stated several times that it considers not optimal to react to asset prices developments because the central bank is not able to detect whether these movements are due to fundamentals or to irrational exuberance. Moreover Governor Bernanke (2002) considers that only a huge increase in the interest rate (with the obvious downside consequences) can lead to some decline in the likelihood or size of a bubble and he concludes that: The FED will do best by focusing its monetary policy instruments on achieving its macro goals, price stability and maximum sustainable employment, while using its regulatory, supervisory, and lender of last resort powers to help ensure financial stability. But Governor Bernanke wrote also: Asset prices contain an enormous amount of useful and timely information about developments in the broader economy, information that should certainly be taken into account in the setting of monetary policy. For example, to the extent that a stock market boom causes, or simply forecast, sharply higher spending on consumer goods and new capital, it may indicate incipient inflationary pressures. Policy tightening might therefore be called for, but to contain the incipient inflation, not to arrest the stock market boom per se. Thus, even if the central bank does not target at all asset prices, our estimate of β should reflect at least this indirect reaction to asset prices. 12 According to our results this indirect impact has been integrated in the strategy of monetary policy up to end of the nineties but has been neglected 12 On one hand empirical evidence has shown that the speculative bubbles of the last decade had no significant impact on CPI inflation (moreover Stock and Watson (2002 ) show that asset prices have no forecasting power for CPI inflation). But on the other hand there is increasing empirical evidence that shows a significant impact of asset prices swings on aggregate demand through a wealth effect on consumption, a Tobin s q effect on investment and financial accelerator effects on investment. 15

16 in the last years. 5 Results for UK, Japan and EU We apply the Rigobon and Sack procedure to the United Kingdom, Japan and Europe and we find some analogies and some important differences. As for the USA we estimate the model: i t = βs t + θx t + γz t + ε t (13) s t = αi t + φx t + z t + η t (14) where i t is the three month interest rate, s t is the daily return on the stock market index, x t contains 5 lags of the two endogenous variables. z t, as before, is an unobserved macroeconomic shock that hits at the same time the two endogenous variables. 5.1 United Kingdom Results for United Kingdom share some important similarities with the American case leading some support to the widely held opinion that the Bank of England and the Federal Reserve implement monetary policy in a similar way. We first estimate the model for the entire sample period and we find unstable results across regimes (Table 14): Table 14: estimates for UK All 1,2,3 1,2,4 1,3,4 2,3,4 Mean of distribution Std. dev. of distribution Median of distribution Mass below zero 46.5% 29.4% 46.8% 0.6% 0.6% 16

17 Table 15: test of overidentifying restrictions, UK Confidence interval Median β GMM β 123 [ , ] β GMM β 124 [0.0000, ] β GMM β 134 [0.0063, ] β GMM β 234 [0.0061, ] The distributions are very different and we can systematically reject the test of overidentifying restrictions (Table 15). Our explanation for this unpleasant result is that the parameter β isnotconstantinthesampleperiod, as required by the assumptions of the model. Thus we reestimate the model with several different samples: in each case there is evidence of a significant reaction in the firstpartofthesampleandofzeroreactioninthesecond part of the sample. We split the sample in December 1992 because around this period the British economy was faced by a significant bubble in the real estate market and by an exchange rate crisis that forced the country to devaluate and leave the European monetary system. In table 16 we see that the covariance exibits the same pattern as in the USA in the same period: it is negative most of the time and becomes positive when stock market volatility is high. Table 16: variance covariance matrix of reduced form shocks Variance of Variance of Frequency Policy Shocks Stk mkt shocks Covariance of Obs. Regime % Regime % Regime % Regime % 17

18 Table 17: estimates for UK lim=0.5 UK lim 0.5 All 1,2,3 1,2,4 1,3,4 2,3,4 Mean of distribution Std. dev. of distribution Median of distribution Mass below zero 4.5% 7.7% 4.5% 26.7% 28.8% Theestimateofβ, as shown in table 17, is around meaning that an increase of 10% in the stock market index causes an increase in the three month interest rate of 13 basis point. The estimated coefficient looks of the same order of magnitude as the one estimated for the United States. The GMM estimate is positive and significantly different from zero, the test of overidentifying restrictions is passed in all cases (Table 18) and the medians are very close to zero. Table 18: test of overidentifying restrictions, UK Confidence interval Median β GMM β 123 [ , ] β GMM β 124 [ , ] β GMM β 134 [ , ] β GMM β 234 [ , ] The result is confirmed by the sensitivity analysis that we present in the appendix (Table 19 and 20) As for the United States we enlarge the criterion to be considered an high volatility observation and we estimate the model including daily variations in the exchange rate and in the oil price index. table 21: variance-covariance matrix of reduced form shocks Variance of Variance of Frequency Policy Shocks Stk mkt shocks Covariance of Obs. Regime % Regime % Regime % Regime % 18

19 In the second part of our sample (January 1993-August 2003) the covariance follows the opposite pattern with respect to the preceding period (Table 21). The coefficient is negative and not significantly different from zero (Table 22). The estimates are similar across different subsets of regimes and in fact the test of overidentifying restrictions is easily passed, the distributions are centered around zero (Table 23). The sensitivity analysis, presented in the appendix (Table 24 and 25) confirms the result. Table 22: estimates for UK lim. 0.5 All 1,2,3 1,2,4 1,3,4 2,3,4 Mean of distribution Std. dev. of distribution Median of distribution Mass below zero 86.7% 85.1% 86.7% 52.2% 52.9% Table 23: test of overidentifying restrictions, UK Confidence interval Median β GMM β 123 [ , ] β GMM β 124 [ , ] β GMM β 134 [ , ] β GMM β 234 [ , ] An interesting feature that we found in all our estimates is that the role of common shocks in the second part of the sample is negligible: Table 26: estimates for UK , without common shock Regimes Regimes Regimes Regimes 1,2 1,3 1,4 All Mean of distribution Std. dev. of distribution Median of distribution Mass below zero 80.6% 80.6% 62% 80.6% 19

20 The role of the common shock is crucial in the American case and can take into account episodes of flight to quality when interest rate and stock prices decreases at the same time because of an increase in risk aversion of the agents. These results seem to confirm the likelihood of American and British monetary policy. But an important difference is that, while in the American case there is evidence of low reaction since the end of 1990s, in the British case this tendency begins around the mid 1990s and is much stronger given that in the British case the estimates are even negative. Finally we can roughly compare our results to the estimates of Chadha, Sarno and Valente (2003). Through a GMM estimation of a forward looking augmented Taylor rule they find a value of (s.e ) for the reaction of interest rate to stock prices in the period Our results are consistent: in fact estimating our model for the period we find a reaction of (s.e ). The problem is that the result is not stable. 13 Our explanation for this instability, as we argued in the beginning of this section, is that the reaction was positive and significant in the firstpartof the sample and was negative and not significant in the second part of the sample. Thus on average we confirm the result of Chadha, Sarno and Valente but we highlight the different behavior in the two subsamples. 5.2 Japan For Japan we used daily data for the period august 1991-august We observe low heteroskedasticity in the interest rate shock and high heteroskedasticity in the stock market shock. The covariance shifts sign and becomes positive when interest rate shock has high variance (in the USA it is the case when the stock market shock has high variance). In table 27 we summarize the characteristics of the four regimes: 13 The estimates widely differ across regimes and the sensitivity analysis reveals that they are not robust to changes in the definition of the regimes. 14 In Figure 3 we represent the thirty day rolling variance of stock returns and interest rates. We observe the correlation that shifts sign quite often. 20

21 Table 27: variance-covariance matrix of reduced form shocks Variance of Variance of Frequency Policy Shocks Stk mkt shocks Covariance of Obs. Regime % Regime % Regime % Regime % The results are quite different with respect to the United States: the estimate of β is almost zero in each subsample and more than half of the draws of the bootstrap have negative sign (Table 28). It seems that the Bank of Japan did not react at all to asset prices. The results are very stable using different subsets of regimes, the coefficient is always almost zero or slightly negative and the estimates have very low standard error. As indicated by theory, the GMM estimate (first column of table 28) is very similar to the others. Table 28: estimates for Japan, All 1,2,3 1,2,4 1,3,4 2,3,4 Mean of distribution Std. dev. of distribution Median of distribution Mass below zero 57.9% 46.4% 63.4% 65.6% 67.8% All tests of overidentifyng restrictions are easily passed Table 29: test of overidentifying restrictions, Japan Confidence interval Median β GMM β 123 [ , ] β GMM β 124 [ , ] β GMM β 134 [ , ] β GMM β 234 [ , ]

22 In the appendix (table 30, 32 and 33) we present the sensitivity analysis. We reestimate the model without the common shock z t,usingadifferent window for the inclusion of observations in the high volatility regimes, adding shocks to exchange rate and oil prices. The reaction is always inexistent. One can argue that the result of no reaction in the Japanese monetary policy is due to the extremely low level of the interest rate in Japan in the last seven years. No matter what happens in the stock market the interest rate level is so low that monetary policy is prevented from reacting by the zero bound and so it is logical to find zero reaction (at least in periods of declining asset prices). To investigate this idea we estimate the model up to 1996 when the zero interest bound started to become binding but we do not obtain a different picture: results are largely unaffected(table 31). Even if now the sign of the coefficient is positive, the magnitude is still very low. table 31: estimates for Japan All 1,2,3 1,2,4 1,3,4 2,3,4 Mean of distribution Std. dev. of distribution Median of distribution Mass below zero 38.9% 54.4% 31.2% 56.1% 47.5% Chadha, Sarno and Valente (2003) find a value of (s.e ) for the period in a Taylor rule framework. Our results are consistent with their findings. 5.3 European Union We now present the results for the EU. 15 the sample period is January august 2003, data are daily. In table 34 we see that the covariance is positive but very low under all the four regimes. 15 In figure 4 we represent the thirty day rolling variance of stock returns and interest rates. We observe that correlation is positive most of the time. 22

23 Table 34: variance-covariance matrix of reduced form shocks Variance of Variance of Frequency Policy Shocks Stk mkt shocks Covariance of Obs. Regime % Regime % Regime % Regime % Estimating the model we obtain the following results: Table 35: estimates for EMU lim.1 all 1,2,3 1,2,4 1,3,4 2,3,4 mean of distribution Std. dev. of distribution median of distribution mass below zero 48.8% 35.9% 26.7% 52.9% 52% Table 36: test of overidentifying restrictions, EMU Confidence interval Median β GMM β 123 [ , ] β GMM β 124 [ , ] β GMM β 134 [ , ] β GMM β 234 [ , ] Results for EU are similar to Japan. The ECB s reaction turns out to be absolutely insignificant. Estimates are less precise under regimes and but in general are very coherent with the assumptions of the model. All tests of overidentifying restrictions are easily passed and so the five distributions are statistically equal. 23

24 The estimates are robust to changes in the criteria to consider the regimes and to the introduction of macroeconomic shocks (results are presented in the appendix, table 37, 38 and 39). The size of our sample is small, due to the introduction of the euro in 1999, but is sufficient to draw some lessons on European monetary policy. Governor Trichet (2002) said explicitly that it is not opportune to introduce asset prices in the central bank s reaction function and our result confirms this attitude. A topic of discussion is whether we should find some sign of indirect reaction due to the wealth effect in consumption, the Tobin s Q effect on investment and the balance sheet channel effect on investment. Governor Trichet recognizes that recent changes in asset prices have influenced private spending more than past swings, because of the more widespread share ownership in a number of industrialized countries, but considers that this impact is still low compared to the United States. And in fact our results show no sign of indirect reaction during the high tech bubble. 6 Conclusion In this paper we evaluated empirically what has been the reaction of monetary policy to asset prices in the four major world economies. The main results can be summarized in the following four points. 1) We found positive and significant reaction in United States (up to the end of the 1990s) and United Kingdom (up to the mid 1990s). This result highlights a similar behavior in the strategy of the Federal Reserve and of the Bank of England. Our result is of the same order of magnitude of the findings in Rigobon and Sack (2003) and Chadha, Sarno and Valente (2003). 2) We found a much lower reaction of the Federal Reserve during the high tech bubble period, even if this reaction is still positive and significant. In the same period the Bank of England and the European Central Bank did not react at all to asset prices. 3) The behavior of the Bank of Japan is constant over time and shows a negative but not significant reaction to asset prices. 4) The role of the common shock z t is crucial to distinguish policy reaction from shifts in risk preferences in the periods of positive reaction but does not play any role during the recent period. 24

25 References [1] Bernanke, Ben and Mark Gertler (2000), Monetary policy and asset price volatility, NBER working paper 7559 [2] Bernanke, Ben and Mark Gertler (2001), Should central banks respond to movements in asset prices?, American economic review papers and proceedings [3] Bohl, Martin, Pierre Siklos and Thomas Werner (2003), Did the Bundesbank react to stock price movements?, Discussion paper 14/03, economic Research Centre of the Deutsche Bundesbank. [4] Bordo, M. and Olivier Jeanne (2002), Boom-busts in asset prices, economic instability and monetary policy, NBER working paper 8966 [5] Borio, C. and P. Lowe (2002), asset prices, financial and monetary stability: exploring the nexus, BIS working paper 114 [6] Cecchetti, Stephen G., Hans Genberg, John Lipsky and Sushil Wadhawani (2000), Asset prices and central bank policy, Geneva reports on the world economy, CEPR [7] Chadha, Jagjit S., Lucio Sarno and Giorgio Valente (2003), Monetary policy rules, asset prices and exchange rates, CEPR working paper 4114 [8] Rigobon, Roberto (2003) Identification through heteroskedasticity, forthcoming Review of economics and Statistics. [9] Rigobon, Roberto and Brian Sack (2003), Measuring the reaction of monetary policy to the stock market, Quarterly journal of economics 25

26 A Appendix 1 To show how to estimate β under three regimes we begin by subtracting the first covariance matrix from the other two and we have: Ω 21 = Ω 2 Ω 1 = 1 = (1 αβ) 2 (β + γ) 2 σ 2 21,z + β 2 σ 2 21,η (1 + αγ)(β + γ) σ 2 21,z + β σ 2 21,η (1 + αγ)(β + γ) σ 2 21,z + β σ 2 21,η (1 + αγ) 2 σ 2 21,z + σ 2 (1 21,η (1 Ω 31 = Ω 3 Ω 1 = 1 = (1 αβ) 2 (β + γ) 2 σ 2 31,z + β 2 σ 2 31,η (1 + αγ)(β + γ) σ 2 31,z + β σ 2 31,η (1 + αγ)(β + γ) σ 2 31,z + β σ 2 31,η (1 + αγ) 2 σ 2 31,z + σ 2 (1 31,η Let θ = 1+αγ. From the two estimated covariance matrices above we can β+γ write the six following equations where Ω 21,11 is the (1,1) element of the matrix Ω 21 : (β + γ) 2 σ 2 21,z + β2 σ 2 21,η =(1 αβ)2 Ω 21,11 (19) (1 θ (β + γ) 2 σ 2 21,z + β σ2 21,η =(1 αβ)2 Ω 21,12 (20) θ 2 (β + γ) 2 σ 2 21,z + σ2 21,η =(1 αβ)2 Ω 21,22 (21) (β + γ) 2 σ 2 31,z + β 2 σ 2 31,η =(1 αβ) 2 Ω 31,11 (22) θ (β + γ) 2 σ 2 31,z + β σ2 31,η =(1 αβ)2 Ω 31,12 (23) θ 2 (β + γ) 2 σ 2 31,z + σ2 31,η =(1 αβ)2 Ω 31,22 (24) From the six equations above we obtain: θ = Ω 21,12 β Ω 21,22 Ω 21,11 β Ω 21,12 (25) 26

27 θ = Ω 31,12 β Ω 31,22 (26) Ω 31,11 β Ω 31,12 which is a system of two equations in two unknowns (β, θ). Solving this system we can have an estimate for β, the parameter of interest, and an estimate µθ that combines α, β and γ (that s why we achieve only partial identification). 16 Substituting (25) in (26) we have the following quadratic equation for our estimate of β: where: aβ 2 bβ + c =0 (27) a = Ω 31,22 Ω 21,12 Ω 21,22 Ω 31,12 b = Ω 31,22 Ω 21,11 Ω 21,22 Ω 31,11 c = Ω 31,12 Ω 21,11 Ω 21,12 Ω 31,11 The quadratic equation has always a real solution and after some tedious algebra we can rewrite it in the following way 16 Rigobon and Sack choose the root using the following criterion: if the two roots have different sign they select the positive one, if they have the same sign they choose the smaller in absolute value. From a theoretical point of view we expect β to be small and positive but we do not have an à priori for 1 θ = β+γ 1+αγ. We can choose as a guide the GMM estimate that is for β and -0,9090 for θ for the United States, and so it is reasonable that if we find only one positive root this has to be β and that if the two roots have the same sign β is the smaller one, otherwise our model would be completely misspecified. We used the Rigobon and Sack selection criterion for Japan, Uk and EU but we find estimates very different in each subset of regimes with standard errors very big: the model seemed to be completely misspecified. We tried to modify the regimes, to estimate the model for different samples but the problem was always present. The GMM estimate was many times lower than the others under three regimes. And these other estimates were very different across different sets of regimes. So we tried to use a simpler procedure for the selection of the roots: we choose the root that is lower in absolute value. In case of different sign we do not force β to be positive as Rigobon and Sack. We based our decision on the GMM estimates that are for β and 2 for θ. This slight modification matters a lot for the Japanese case: under this new selection procedure the results are much better: the estimates are very similar across subsets of regimes, the standard errors are low, the test of overidentifying restriction is easily passed in each case, the GMM estimate is very similar to the others. 27

28 where: (1 + αγ) dβ 2 (2β + αγβ + γ) dβ + β (γ + β) d (28) d = σ 2 z3σ 2 η2 σ 2 z3σ 2 η1 σ 2 z1σ 2 η2 σ 2 z2σ 2 η3 + σ 2 z1σ 2 η3 + σ 2 z2σ 2 η1 Provided that d is different from zero, the equation has two solutions 17 : β = β (29) β = 1 θ = β + γ (30) 1+αγ Thusweareabletoestimateconsistentlyβ provided that we choose the right solution of the quadratic form and that we have at least three regimes for the covariance matrix. If we have four regimes the model is overidentified and the parameters can be estimated by GMM The moment conditions are: AΩ i A 0 = Γσ 2 z,iγ Ω ε,i (31) where Ω i is the covariance matrix of reduced form residuals that can be estimated in the data in regime i, σ 2 z,i is the variance of the common unobservable shocks in regime i and Ω ε,i is the covariance matrix of the structural disturbances which is also diagonal. Solving the system we obtain conditions 25 and 26 but also the additional restriction: θ = Ω 41,12 β Ω 41,22 Ω 41,11 β Ω 41,12 (32) Now the model is overidentified: we have three equations and two parameters to estimate and so we can use the GMM methodology. We look for the β that minimizes the difference between the three expressions for θ 17 Itcanbeprovedthattherearealwaysrealsolutions to this equation because the Delta is always positive. 1 β 18 A = α 1 γ Γ = 1 28