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Is there a direct effect of money?
Japan and the World Economy 19 (2007) 329–337 www.elsevier.com/locate/econbase
Is there a direct effect of money? Money’s role in an estimated monetary business cycle model of the Japanese economy Ippei Fujiwara * Bank of Japan, 2-1-1 Nihonbashi-Hongokucho, Chuo-Ku, 103-8660 Tokyo, Japan Received 1 March 2006; received in revised form 24 April 2006; accepted 24 May 2006
Abstract In this paper, to study the alternative monetary transmission mechanism to the traditional interest rate channel which may even work under zero nominal interest rates, we estimate the monetary business cycle model of the Japanese economy that incorporates the direct role of money. Estimation is conducted on the system of equations in a state-space form via maximum likelihood estimation. We, however, find that the direct effect of money is extremely small in Japan. This finding is the same as those obtained for the U.S. in Ireland [Ireland, P., 2004. Money’s role in the monetary business cycle. Journal of Money, Credit and Banking 36, 969–984] and the Euro area in Andres et al. [Andres, J., Lopez-Salido, D., Valles, J., 2001. Money in an Estimated Business Cycle Model of the Euro area. Working Paper 121, Bank of Spain]. # 2006 Elsevier B.V. All rights reserved. JEL Classification: C31; E32; E52 Keywords: Direct effect of money; Cross-restriction; Maximum likelihood estimation; Dynamic stochastic general equilibrium model
1. Introduction Japanese economy has been stagnant since the burst of the bubble economy around 1990. To respond to those economic downturns, the Bank of Japan gradually lowered the overnight call rate until it hits a record low in 1996, 0.25 percent per annum. Yet, because the negative shocks were more severe than had been expected initially; magnified by the balance sheet problem due to
* Tel.: +81 3 3277 2153; fax: +81 3 3510 1265. E-mail address: [email protected]. 0922-1425/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.japwor.2006.05.003
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I. Fujiwara / Japan and the World Economy 19 (2007) 329–337
the collapse of stock and land prices, the Japanese government were not able to settle the economy on the steady growth path just by intensifying public investments. In 1997, the bankruptcy of the fourth largest securities company in Japan ‘‘Yamaichi Shoken’’ ignited financial crises. Moreover, deflationary pressure becomes manifest mainly through increasing cheaper imported goods. Although there were almost no room left for stimulating the economy by way of traditional interest rate channel literally after the introduction of zero nominal interest rate policy in February 1999, the Bank of Japan resumed new monetary policy scheme called quantitative easing as an alternative device of monetary policy to the traditional short-term interest rate control in March 2001. With this quantitative easing scheme, the Bank of Japan started to target not the overnight call rate but the outstanding balance of the current accounts at the Bank.1 It has been only several years since the introduction of the quantitative easing monetary policy. Therefore, it may not be appropriate to judge the effect of the quantitative easing as policy may effect with long lags. Recent researches with Vector Auto-regression (VAR) models, however, conclude that the effect of monetary expansion without traditional interest rate channel is extremely limited. Kimura et al. (2003) claim that although there can be found some positive effect on output and inflation from the quantitative easing, such effect is minuscule. Fujiwara (in press) shows that the effects of monetary policy either through lowering nominal interest rate or monetary expansion become significantly weaker since the traditional interest rate channel becomes almost incompetent in the middle of 1990s. The Bank of Japan’s Outlook and Risk Assessment of the Economy and Prices released in April 2003 assesses the quantitative easing policy as effective but not satisfactory such that ‘‘As seen so far, the Bank’s quantitative easing policy and ample liquidity provision have contributed to: (1) dispelling liquidity concerns, (2) reducing interest rates including those of longer-term maturities, and (3) shrinking credit spreads. Judging from such developments, the Bank’s monetary easing seems to have effectively shielded channels through which various shocks lead to liquidity concerns, thereby securing financial market stability, and have contributed to preventing the economy from stumbling into a deflationary spiral. On the other hand, the growth rate of commercial lending has been negative and bank’s financial intermediary function is still weak. Real economic activity has yet to be stimulated.’’ Thus, the quantitating easing policy seems to work as a bulwark against further deterioration, but its direct effect on output and inflation may be limited so far. Can we expect any strong direct effects from the quantitative easing? If there is any particular direct effect of money, the stagnant economic activity after the introduction of the quantitative easing could be attributed to its insufficient degree of easing. Orphanides and Wieland (2000) and Coenen and Wieland (2003) suggest that there should be changes in the risk premium caused by quantitative easing policy. As a result of changes in the composition of financial assets owned by the country as a whole, the yen should depreciate. This portfolio rebalancing effect, however, is ‘‘small enough not to be noticeable in times of non-zero interest rates’’ according to Coenen and Wieland (2003). Another possible candidate for the direct channel of the quantitative easing is simply the direct effect of money. If the real balance has some direct effects on output and
1 In Q&A: New Procedures for Money Market Operations, the Bank of Japan declares ‘‘The Bank has conducted market operations based on the guidelines set by the Monetary Policy Meeting of the Policy Board in terms of the uncollateralized overnight call rate. In the new procedures, the Monetary Policy Meeting will decide the guidelines in terms of the ‘‘outstanding balance’’ of the current accounts at the BOJ and operations will be conducted to meet the target balance.’’
I. Fujiwara / Japan and the World Economy 19 (2007) 329–337
331
inflation, and the expansion of base money results in the growing money supply,2 the quantitative easing policy should have some tangible influences on the real economy even without the traditional interest channel. Concerning this direct effect of money, Nelson (2002) shows that if the utility u is nonseparable in consumption C and real money holdings, M=P, such that log
@ut @C t
a1 C t þ a2 log
Mt ; Pt
then the optimized IS curve as follows is obtained after log-linearization of the first order condition: Ct ¼ b1 rrt þ
a2 Mt M tþ1 log Et log þ Et C tþ1 ; a1 Pt Ptþ1
where rr is real interest rates. The aim of this paper is to examine whether the utility function is well represented by the utility with non-separability between consumption and real money holdings. If so, we can conclude that there exist the direct effect of money in the macroeconomic dynamics of the Japanese economy. This paper is structured as follows. In the next section, we estimate a very standard dynamic stochastic general equilibrium (DSGE) model with nominal rigidity for the Japanese economy following the estimation procedure of Ireland (2004) and conclude that the non-separability between consumption and real money holdings in utility is rejected and therefore the direct effect of money has not been found in Japanese data. Finally, Section 3 summarizes the findings in this paper. 2. Estimation results Even if the existence of the direct money channel is established in a single estimation framework, it is, however, inappropriate to conclude that there exist direct channel on output and inflation from money holdings. Quite possibly, estimation on a single equation report the effect through the traditional LM curve relationship not fully captured by real interest rate as the direct effect of money. Hence, we need such a method to identify the direct effect of money properly that a system of equations should be estimated simultaneously. The seminal research by Ireland (2004) proposes a method to identify the money’s effect on dynamic macroeconomy. First, Ireland (2004) constructs a dynamic general equilibrium with non-separable utility, where ‘‘real money balances enter into a correctly-specified, forward-looking IS curve if and only if they enter into a correctly-specified, forward-looking Phillips curve,’’ and, then, evaluate such direct effects of money in IS and Phillips curve equations by maximum likelihood estimation on the DSGE model in a state-space form.3 We estimate a very standard DSGE model with nominal rigidity for Japanese data following the estimation procedure of Ireland (2004) as above. With an estimation on this model, we can 2 This latter assumption is not tested in this paper. We can, however, say that the former, which is rejected later in this paper, is the necessary condition for the direct effect of quantitative easing. 3 Recently, constructing the more data-oriented dynamic stochastic general equilibrium model has become popular. These are well-summarised in Ruge-Murcia (2002). Especially, since the seminal research by Schorfheide (2000), the Bayesian estimation of the DSGE models has been very popular among central bank economists.
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I. Fujiwara / Japan and the World Economy 19 (2007) 329–337
evaluate the direct effect of money by testing whether the utility is non-separable or not. If it is not separable, an increase in money supply will result in the rise in the output and inflation rates, even if the traditional interest rate channel is not working due to the zero nominal interest rate bound. 2.1. Model The economy consists of a representative household, a representative finished goodsproducing firm, a continuum of intermediate goods-producing firms indexed by i 2 ½0; 1, and a monetary authority. The representative household maximizes the following expected stream of utility: E0
1 X
bt at fu½ct ; ðM t =Pt Þ=et hht g;
t¼0
subject to the budget constraint as below: M t1 þ T t þ Bt1 þ W t ht þ Dt Bt =Rt þ M t ¼ ct þ ; Pt Pt where b is the subjective discount rate, a and e the preference shock, u½ the instantaneous utility function, M the nominal money holding, P the price level, T the lumpsum nominal transfer, B the amount of nominal bond, D the firm profit stemming from monopolistic competition which is attributable to the representative household, h the hours worked, W the nominal wage, and R is the nominal interest rates set by the central bank. The intermediate goods-producing firm i 4 competing in a monopolistically competitive market with the Rotemberg (1982) type adjustment cost, defined by f, maximizes its profit: E0
1 X ptþ1 Pt ðiÞ t¼0
Rtþ1
Pt
Y t ðiÞ jt Y t ðiÞ
2 f Pt ðiÞ 1 Yt ; 2 p Pt1 ðiÞ
subject to the downward sloping demand curve with elasticity u:
Pt ðiÞ Y t ðiÞ ¼ Pt
u Y t;
where Y is output, p is the inflation rate and its target level is p . The real marginal cost j is derived from the linear production function: Y t ðiÞ ¼ Z t ht ðiÞ; where Z is the labor augmenting technology. As for other agents, a representative finished goodsproducing firm just aggregates various intermediate goods to produce final goods in a perfectly competitive market and therefore obtains no profit. The monetary authority sets the short-term nominal interest rate following the Taylor type instrument rule. After obtaining the first order conditions, we log-linearize the system of equations around the steady state, which is expressed as variables without time subscript. Below is the system of equations consists of seven equations, where small variable with hat denotes the deviation from 4
Therefore, for example, YðiÞ denotes the goods produced by firm i.
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its steady state value, namely xˆ t means ln ðxt Þ ln ðxÞ where x is the steady state value: ˆ t Et m ˆ tþ1 Þ v2 ð1 re Þˆet þ v1 ð1 ra Þˆat ; yˆ t ¼ Et yˆ tþ1 v1 ðˆrt Et pˆ tþ1 Þ þ v2 ðm p 1 v2 v2 ˆt þ pˆ t ¼ yˆ t m eˆ t zˆt ; Et pˆ tþ1 þ c r v1 v1 v1
(1) (2)
ˆ t ¼ g 1 yˆ t g 2 rˆt þ g 3 eˆ t ; m
(3)
rˆt ¼ rr rˆt1 þ ry yˆ t þ rp pˆ t þ ert ;
(4)
aˆ t ¼ ra aˆ t1 þ eat ;
(5)
eˆ t ¼ re eˆ t1 þ eet ;
(6)
zˆ t ¼ rz zˆt1 þ ezt :
(7)
There are four exogenous shocks, namely ert, eat , eet and ezt . Each denotes monetary policy shock, preference shock, preference shock on the real balance and the technology shock, respectively, and is normally independently distributed. Parameters except for r s are computed from the deep 2
ðm=eÞð@ u=@y@mÞ , parameters and derivatives on the periodic utility function: v1 ¼ yð@@u=@y 2 u=@y2 Þ, v2 ¼ yð@2 u=@y2 Þ h i 2 2 @ u=@m r1 r 2 g 2 , g 2 ¼ ðr1Þðm=eÞ , g 3 ¼ 1 ðr 1Þg 2 and g 1 ¼ yrv mv þ v ðr1Þeð@2 u=@y@mÞruð@2 u=@m2 Þ 1
1
c ¼ u1 f . All parameters altogether must satisfy the condition in Blanchard and Kahn (1980) so that a log-linearlized model with forward-looking variables is inverted into a backwardlooking state-space form. Therefore, absolute values of r s are naturally smaller than unity. In correctly specified model from agent’s optimisation behaviour as above, real money holdings must have the direct effect on output and inflation as in Eqs. (1) and (2). Furthermore, v2 becomes positive, only when utility is non-separable between consumption and real balances. Standard dynamic new Keynesian models as in Walsh (2003) and Woodford (2003) nest to this @2 u system of equations. If v2 is zero, namely cross derivative @y@m is zero, Eqs. (1) and (2) reduce to the dynamic IS equation and the new Keynesian Phillips curve in the standard dynamic new Keynesian model: yˆ t ¼ Et yˆ tþ1 v1 ðˆrt E t pˆ tþ1 Þ þ v1ð1 ra Þˆat ; p 1 pˆ t ¼ Et pˆ tþ1 þ c yˆ zˆt : r v1 t The proper evaluation of real balance effect on economic activities, which is not captured fully in short-term nominal interest rates, can only be possible with estimation of v2 under this crossrestriction in a system of equations. On estimation procedure, three optimality conditions, (1)–(3), one decision rule, (4), and three distribution process for shocks, (5)–(7), are transformed into state-space form as follows: stþ1 ¼ Pst þ Wetþ1 ;
(8)
f t ¼ Ust ;
(9) 0
ˆ t1 pˆ t1 rˆt1 aˆ t eˆ t zˆt ert , which is the state vector, where st ¼ ½ˆyt1 m ˆ t rˆt yˆ t pˆ t 0 , et ¼ ½eat eet ezt ert 0 and P, W and U are coefficient matrices. Linear f t ¼ ½m equation system (8) is so-called the state equation while (9) is the observation equation. As shown
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in Hamilton (1994), since the system is now represented in a state-space form and data in vector f t are available, the coefficients can be obtained by maximum likelihood estimation. 2.2. Estimation results Estimation is conducted using four variables, namely the real money balance, the short-term nominal interest rate, the output and the inflation rate. The real money balance is measured as the seasonally adjusted M2+CD divided by seasonally adjusted CPI excluding perishables and population of age 16 and over, the short-term nominal interest rate is the LIBOR 3 month rate, output is the seasonally adjusted real GDP also divided by population of age 16 years and over, and the inflation rate is measured by changes in the seasonally adjusted CPI excluding perishables. All data are on quarterly bases. As a distinct upward trend is found in real money balances and output measured as above, data are either de-trended by the Hodrick–Prescott (HP) filter or time trend.5 Estimation period is set from 1982/Q1 to 1995/Q1. The starting date is chosen so as to avoid some distortional effects from the second oil shock. As for the ending date, it is set at around the Bank of Japan resumed the de-facto zero nominal interest rate policy as in the reduced form regression in Section 2. When conducting estimation, some parameters are pre-fixed. As in Ireland (2004), preliminary attempts to estimate all parameters in Eqs. (1) nd (7) are not very successful. Implausibly low v1 and c are obtained. Since the aim of this paper is to examine the existence of the direct effect of money on real economic activities, we are interested in the value of v2 . Therefore, we estimate the parameters with constrained maximum likelihood estimates with v1 and c pre-fixed as exactly examined in Ireland (2004). v1 can be considered as the parameter for intertemporal elasticity of substitution. We calibrate this parameter as 0.66 rather arbitrarily6 but following the estimated results in Nishiyama (2005).7 As for c, this can be considered as the parameter on the output gap in the new Keynesian Phillips curve and implicitly contains the information on how frequently firms can change the price. Kimura and Kurozumi (2004) estimate the new Keynesian Phillips curve in Japan for annual inflation rate and obtains the value of 0.2 for this parameter. Further, several researches on Phillips curve conducted by the Bank of Japan, such as Price Developments in Japan—A Review Focusing on the 1990s released in October 2000 which report that this value for annual inflation is around 0.2. Transforming this into quarterly bases with considering that the intertemporal elasticity of substitution is now set at 0.66, leads to that c should be set at 0.075. Tables 1 and 2 show the estimation results when the HP filtered and the time trends are eliminated respectively. Standard errors are computed from inverse of Hessian matrix. Estimation results show that reasonable values are obtained for all the parameters, and almost the same results are obtained in both cases. A minor difference can be found in the persistence of technology shock represented as rz . As the time span, when the variables are away from their steady state value, are quite different whether the HP or the time trend is considered to be the steady state path, the parameter which decides this time span, namely the persistence of shocks are naturally different. Therefore, the technology shock is very persistent in the time trend case. Other than this minor difference, the size of the parameters and their significance are almost the same. 5
Hamilton (1994) recommends stationarity in data when estimating a state-space model. Therefore, the coefficient on the relative risk aversion is assumed to be around 1.5. 7 Estimation of the intertemporal elasticity of substitution has usually been conducted by assuming separability in utility. Therefore, we calibrate this parameter according to the previous researches. 6
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Table 1 Parameter estimates when the HP trends are eliminated Parameter
Estimate
Standard error
b v1 v2 g1 g2 g3 c rr ry rp log(y) log(m) log ðpÞ log(r) ra re rz sa se sz sr
0.9915 0.6600 0.0112 0.0000 0.0000 0.9999 0.0750 0.8168 0.0142 0.3362 8.1503 10.3018 0.0041 0.0126 0.8172 0.9439 0.1978 0.0170 0.0063 0.0277 0.0014
0.0010 0.0602 0.0010 0.0486 0.0006 0.0574 0.0197 0.0311 0.0025 0.0121 0.0007 0.0013 0.0482 0.0356 0.1454 0.0029 0.0006 0.0045 0.0001
Table 2 Parameter estimates when the time trends are eliminated Parameter
Estimate
Standard error
b v1 v2 g1 g2 g3 c rr ry rp log(y) log(m) log ðpÞ log(r) ra re rz sa se sz sr
0.9917 0.6600 0.0017 0.0000 0.0000 0.9999 0.0750 0.7869 0.0003 0.3266 8.1656 10.3246 0.0039 0.0122 0.9544 0.9874 0.9689 0.0230 0.0102 0.0139 0.0014
0.0059 0.0097 0.0022 0.1159 0.0014 0.0337 0.0142 0.0473 0.0262 0.0962 0.0092 0.0151 0.0398 0.0132 0.0747 0.0101 0.0010 0.0028 0.0001
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The parameter of the most interest is naturally v2, which decides the non-separability in consumption and real balances in utility function and therefore defines the magnitude of direct effect of money holdings on output and inflation. In both cases, this parameter is very small and insignificant. To ensure this finding further, we examine the likelihood ratio test for the null hypothesis H0: v2 ¼ 0. Under this null hypothesis, likelihood ratio for the HP trend case is 1.3962e–008 and 7.0825e–009 for the time trend case. As the 95 percent significant level for the cumulated Chi-square distribution when the degree of freedom is set to the number of restrictions is 3.75, this null hypothesis cannot be rejected. This finding suggests that there is almost no direct role of real money balances in Japan. The same conclusion has been already obtained in Ireland (2004) for the U.S. and Andres et al. (2001) for the Euro area. Another intriguing finding is that real money balances are following almost independent dynamics from other macroeconomic variables. Parameters g 1 , g 2 and g 3 which defines the dynamics in the money demand function indicate that dynamics in real money balances are solely defined by independently distributed shocks. 3. Conclusion In this paper, since using single estimation for the evaluation of direct effect of money tends to be problematic since the endogeneity of variables is not properly considered, we first construct a DSGE model with a direct effect of money based on rigid microfoundations. Maximum likelihood estimates on such a micro-founded model support no evidence on the direct effect of money stemming from the non-separability of utility in consumption and real balances. This finding is supported by different de-trending strategies. Therefore, it seems appropriate to conclude that the direct effect of money from non-separability in utility is extremely small in Japan. The effect of the quantitative easing monetary policy on the real economic activities through this channel should be limited.8 Acknowledgements The author would like to thank Peter Ireland for sharing the MATLAB programme and technical advises and an anonymous referee for valuable inputs. Furthermore, helpful comments from Kosuke Aoki, Kanemi Ban, Yuzo Honda, Charles Yuji Horioka and seminar participants at Osaka University are also highly acknowledged. Importantly, the view in this paper should not be taken as those of the Bank of Japan nor any of its respective monetary policy or other decision making bodies. All remaining errors are clearly my own. References Andres, J., Lopez-Salido, D., Valles, J., 2001. Money in an Estimated Business Cycle Model of the Euro area. Working Paper 121, Bank of Spain. Blanchard, O.J., Kahn, C.M., 1980. The solution of linear difference models under rational expectations. Econometrica 48, 1305–1311. Coenen, G., Wieland, V., 2003. The zero-interest-rate bound and the role of the exchange rate for monetary policy in Japan. Journal of Monetary Economics 50, 1071–1101.
8
This finding is consistent with the ones in Kimura et al. (2003) and Fujiwara (in press).
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Fujiwara, I. Evaluating monetary policy when nominal interest rates are almost zero. Journal of the Japanese and International Economies, in press. Hamilton, J., 1994. Time Series Analysis. Princeton University Press, Princeton, NJ. Ireland, P., 2004. Money’s role in the monetary business cycle. Journal of Money, Credit and Banking 36, 969–984. Kimura, T., Kobayashi, H., Muranaga, J., Ugai, H. The effect of the increase in monetary base on Japan’s economy at zero interest rates: an empirical analysis in monetary policy in a changing environment, Bank for International Settlements Conference Series, 2003. Kimura, T., Kurozumi, T., 2004. Effectiveness of history-dependent monetary policy. Journal of the Japanese and International Economies 18, 330–361. Nelson, E., 2002. Direct effects of base money on aggregate demand: theory and evidence. Journal of Monetary Economics 49, 687–708. Nishiyama, S.-I., 2005. The cross-Euler Equation approach to intertemporal substitution in import demand. Journal of Applied Econometrics 20, 841–872. Orphanides, A., Wieland, V., 2000. Efficient monetary policy design near price stability. Journal of the Japanese and International Economics 14, 327–365. Rotemberg, J., 1982. Monopolistic price adjustment and aggregate output. Review of Economic Studies 49, 517–531. Ruge-Murcia, F., 2002. Methods to Estimate Dynamic Stochastic General Equilibrium Models. Discussion Paper, University of California, San Diego. Schorfheide, F., 2000. Loss function based evaluation of DSGE models. Journal of Applied Econometrics 15, 645–670. Walsh, C., 2003. Monetary Theory and Policy. MIT Press, Cambridge, MA. Woodford, M., 2003. Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton University Press, Princeton, NJ.
Is there a direct effect of money? Money’s role in an estimated monetary business cycle model of the Japanese economy Ippei Fujiwara * Bank of Japan, 2-1-1 Nihonbashi-Hongokucho, Chuo-Ku, 103-8660 Tokyo, Japan Received 1 March 2006; received in revised form 24 April 2006; accepted 24 May 2006
Abstract In this paper, to study the alternative monetary transmission mechanism to the traditional interest rate channel which may even work under zero nominal interest rates, we estimate the monetary business cycle model of the Japanese economy that incorporates the direct role of money. Estimation is conducted on the system of equations in a state-space form via maximum likelihood estimation. We, however, find that the direct effect of money is extremely small in Japan. This finding is the same as those obtained for the U.S. in Ireland [Ireland, P., 2004. Money’s role in the monetary business cycle. Journal of Money, Credit and Banking 36, 969–984] and the Euro area in Andres et al. [Andres, J., Lopez-Salido, D., Valles, J., 2001. Money in an Estimated Business Cycle Model of the Euro area. Working Paper 121, Bank of Spain]. # 2006 Elsevier B.V. All rights reserved. JEL Classification: C31; E32; E52 Keywords: Direct effect of money; Cross-restriction; Maximum likelihood estimation; Dynamic stochastic general equilibrium model
1. Introduction Japanese economy has been stagnant since the burst of the bubble economy around 1990. To respond to those economic downturns, the Bank of Japan gradually lowered the overnight call rate until it hits a record low in 1996, 0.25 percent per annum. Yet, because the negative shocks were more severe than had been expected initially; magnified by the balance sheet problem due to
* Tel.: +81 3 3277 2153; fax: +81 3 3510 1265. E-mail address: [email protected]. 0922-1425/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.japwor.2006.05.003
330
I. Fujiwara / Japan and the World Economy 19 (2007) 329–337
the collapse of stock and land prices, the Japanese government were not able to settle the economy on the steady growth path just by intensifying public investments. In 1997, the bankruptcy of the fourth largest securities company in Japan ‘‘Yamaichi Shoken’’ ignited financial crises. Moreover, deflationary pressure becomes manifest mainly through increasing cheaper imported goods. Although there were almost no room left for stimulating the economy by way of traditional interest rate channel literally after the introduction of zero nominal interest rate policy in February 1999, the Bank of Japan resumed new monetary policy scheme called quantitative easing as an alternative device of monetary policy to the traditional short-term interest rate control in March 2001. With this quantitative easing scheme, the Bank of Japan started to target not the overnight call rate but the outstanding balance of the current accounts at the Bank.1 It has been only several years since the introduction of the quantitative easing monetary policy. Therefore, it may not be appropriate to judge the effect of the quantitative easing as policy may effect with long lags. Recent researches with Vector Auto-regression (VAR) models, however, conclude that the effect of monetary expansion without traditional interest rate channel is extremely limited. Kimura et al. (2003) claim that although there can be found some positive effect on output and inflation from the quantitative easing, such effect is minuscule. Fujiwara (in press) shows that the effects of monetary policy either through lowering nominal interest rate or monetary expansion become significantly weaker since the traditional interest rate channel becomes almost incompetent in the middle of 1990s. The Bank of Japan’s Outlook and Risk Assessment of the Economy and Prices released in April 2003 assesses the quantitative easing policy as effective but not satisfactory such that ‘‘As seen so far, the Bank’s quantitative easing policy and ample liquidity provision have contributed to: (1) dispelling liquidity concerns, (2) reducing interest rates including those of longer-term maturities, and (3) shrinking credit spreads. Judging from such developments, the Bank’s monetary easing seems to have effectively shielded channels through which various shocks lead to liquidity concerns, thereby securing financial market stability, and have contributed to preventing the economy from stumbling into a deflationary spiral. On the other hand, the growth rate of commercial lending has been negative and bank’s financial intermediary function is still weak. Real economic activity has yet to be stimulated.’’ Thus, the quantitating easing policy seems to work as a bulwark against further deterioration, but its direct effect on output and inflation may be limited so far. Can we expect any strong direct effects from the quantitative easing? If there is any particular direct effect of money, the stagnant economic activity after the introduction of the quantitative easing could be attributed to its insufficient degree of easing. Orphanides and Wieland (2000) and Coenen and Wieland (2003) suggest that there should be changes in the risk premium caused by quantitative easing policy. As a result of changes in the composition of financial assets owned by the country as a whole, the yen should depreciate. This portfolio rebalancing effect, however, is ‘‘small enough not to be noticeable in times of non-zero interest rates’’ according to Coenen and Wieland (2003). Another possible candidate for the direct channel of the quantitative easing is simply the direct effect of money. If the real balance has some direct effects on output and
1 In Q&A: New Procedures for Money Market Operations, the Bank of Japan declares ‘‘The Bank has conducted market operations based on the guidelines set by the Monetary Policy Meeting of the Policy Board in terms of the uncollateralized overnight call rate. In the new procedures, the Monetary Policy Meeting will decide the guidelines in terms of the ‘‘outstanding balance’’ of the current accounts at the BOJ and operations will be conducted to meet the target balance.’’
I. Fujiwara / Japan and the World Economy 19 (2007) 329–337
331
inflation, and the expansion of base money results in the growing money supply,2 the quantitative easing policy should have some tangible influences on the real economy even without the traditional interest channel. Concerning this direct effect of money, Nelson (2002) shows that if the utility u is nonseparable in consumption C and real money holdings, M=P, such that log
@ut @C t
a1 C t þ a2 log
Mt ; Pt
then the optimized IS curve as follows is obtained after log-linearization of the first order condition: Ct ¼ b1 rrt þ
a2 Mt M tþ1 log Et log þ Et C tþ1 ; a1 Pt Ptþ1
where rr is real interest rates. The aim of this paper is to examine whether the utility function is well represented by the utility with non-separability between consumption and real money holdings. If so, we can conclude that there exist the direct effect of money in the macroeconomic dynamics of the Japanese economy. This paper is structured as follows. In the next section, we estimate a very standard dynamic stochastic general equilibrium (DSGE) model with nominal rigidity for the Japanese economy following the estimation procedure of Ireland (2004) and conclude that the non-separability between consumption and real money holdings in utility is rejected and therefore the direct effect of money has not been found in Japanese data. Finally, Section 3 summarizes the findings in this paper. 2. Estimation results Even if the existence of the direct money channel is established in a single estimation framework, it is, however, inappropriate to conclude that there exist direct channel on output and inflation from money holdings. Quite possibly, estimation on a single equation report the effect through the traditional LM curve relationship not fully captured by real interest rate as the direct effect of money. Hence, we need such a method to identify the direct effect of money properly that a system of equations should be estimated simultaneously. The seminal research by Ireland (2004) proposes a method to identify the money’s effect on dynamic macroeconomy. First, Ireland (2004) constructs a dynamic general equilibrium with non-separable utility, where ‘‘real money balances enter into a correctly-specified, forward-looking IS curve if and only if they enter into a correctly-specified, forward-looking Phillips curve,’’ and, then, evaluate such direct effects of money in IS and Phillips curve equations by maximum likelihood estimation on the DSGE model in a state-space form.3 We estimate a very standard DSGE model with nominal rigidity for Japanese data following the estimation procedure of Ireland (2004) as above. With an estimation on this model, we can 2 This latter assumption is not tested in this paper. We can, however, say that the former, which is rejected later in this paper, is the necessary condition for the direct effect of quantitative easing. 3 Recently, constructing the more data-oriented dynamic stochastic general equilibrium model has become popular. These are well-summarised in Ruge-Murcia (2002). Especially, since the seminal research by Schorfheide (2000), the Bayesian estimation of the DSGE models has been very popular among central bank economists.
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evaluate the direct effect of money by testing whether the utility is non-separable or not. If it is not separable, an increase in money supply will result in the rise in the output and inflation rates, even if the traditional interest rate channel is not working due to the zero nominal interest rate bound. 2.1. Model The economy consists of a representative household, a representative finished goodsproducing firm, a continuum of intermediate goods-producing firms indexed by i 2 ½0; 1, and a monetary authority. The representative household maximizes the following expected stream of utility: E0
1 X
bt at fu½ct ; ðM t =Pt Þ=et hht g;
t¼0
subject to the budget constraint as below: M t1 þ T t þ Bt1 þ W t ht þ Dt Bt =Rt þ M t ¼ ct þ ; Pt Pt where b is the subjective discount rate, a and e the preference shock, u½ the instantaneous utility function, M the nominal money holding, P the price level, T the lumpsum nominal transfer, B the amount of nominal bond, D the firm profit stemming from monopolistic competition which is attributable to the representative household, h the hours worked, W the nominal wage, and R is the nominal interest rates set by the central bank. The intermediate goods-producing firm i 4 competing in a monopolistically competitive market with the Rotemberg (1982) type adjustment cost, defined by f, maximizes its profit: E0
1 X ptþ1 Pt ðiÞ t¼0
Rtþ1
Pt
Y t ðiÞ jt Y t ðiÞ
2 f Pt ðiÞ 1 Yt ; 2 p Pt1 ðiÞ
subject to the downward sloping demand curve with elasticity u:
Pt ðiÞ Y t ðiÞ ¼ Pt
u Y t;
where Y is output, p is the inflation rate and its target level is p . The real marginal cost j is derived from the linear production function: Y t ðiÞ ¼ Z t ht ðiÞ; where Z is the labor augmenting technology. As for other agents, a representative finished goodsproducing firm just aggregates various intermediate goods to produce final goods in a perfectly competitive market and therefore obtains no profit. The monetary authority sets the short-term nominal interest rate following the Taylor type instrument rule. After obtaining the first order conditions, we log-linearize the system of equations around the steady state, which is expressed as variables without time subscript. Below is the system of equations consists of seven equations, where small variable with hat denotes the deviation from 4
Therefore, for example, YðiÞ denotes the goods produced by firm i.
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333
its steady state value, namely xˆ t means ln ðxt Þ ln ðxÞ where x is the steady state value: ˆ t Et m ˆ tþ1 Þ v2 ð1 re Þˆet þ v1 ð1 ra Þˆat ; yˆ t ¼ Et yˆ tþ1 v1 ðˆrt Et pˆ tþ1 Þ þ v2 ðm p 1 v2 v2 ˆt þ pˆ t ¼ yˆ t m eˆ t zˆt ; Et pˆ tþ1 þ c r v1 v1 v1
(1) (2)
ˆ t ¼ g 1 yˆ t g 2 rˆt þ g 3 eˆ t ; m
(3)
rˆt ¼ rr rˆt1 þ ry yˆ t þ rp pˆ t þ ert ;
(4)
aˆ t ¼ ra aˆ t1 þ eat ;
(5)
eˆ t ¼ re eˆ t1 þ eet ;
(6)
zˆ t ¼ rz zˆt1 þ ezt :
(7)
There are four exogenous shocks, namely ert, eat , eet and ezt . Each denotes monetary policy shock, preference shock, preference shock on the real balance and the technology shock, respectively, and is normally independently distributed. Parameters except for r s are computed from the deep 2
ðm=eÞð@ u=@y@mÞ , parameters and derivatives on the periodic utility function: v1 ¼ yð@@u=@y 2 u=@y2 Þ, v2 ¼ yð@2 u=@y2 Þ h i 2 2 @ u=@m r1 r 2 g 2 , g 2 ¼ ðr1Þðm=eÞ , g 3 ¼ 1 ðr 1Þg 2 and g 1 ¼ yrv mv þ v ðr1Þeð@2 u=@y@mÞruð@2 u=@m2 Þ 1
1
c ¼ u1 f . All parameters altogether must satisfy the condition in Blanchard and Kahn (1980) so that a log-linearlized model with forward-looking variables is inverted into a backwardlooking state-space form. Therefore, absolute values of r s are naturally smaller than unity. In correctly specified model from agent’s optimisation behaviour as above, real money holdings must have the direct effect on output and inflation as in Eqs. (1) and (2). Furthermore, v2 becomes positive, only when utility is non-separable between consumption and real balances. Standard dynamic new Keynesian models as in Walsh (2003) and Woodford (2003) nest to this @2 u system of equations. If v2 is zero, namely cross derivative @y@m is zero, Eqs. (1) and (2) reduce to the dynamic IS equation and the new Keynesian Phillips curve in the standard dynamic new Keynesian model: yˆ t ¼ Et yˆ tþ1 v1 ðˆrt E t pˆ tþ1 Þ þ v1ð1 ra Þˆat ; p 1 pˆ t ¼ Et pˆ tþ1 þ c yˆ zˆt : r v1 t The proper evaluation of real balance effect on economic activities, which is not captured fully in short-term nominal interest rates, can only be possible with estimation of v2 under this crossrestriction in a system of equations. On estimation procedure, three optimality conditions, (1)–(3), one decision rule, (4), and three distribution process for shocks, (5)–(7), are transformed into state-space form as follows: stþ1 ¼ Pst þ Wetþ1 ;
(8)
f t ¼ Ust ;
(9) 0
ˆ t1 pˆ t1 rˆt1 aˆ t eˆ t zˆt ert , which is the state vector, where st ¼ ½ˆyt1 m ˆ t rˆt yˆ t pˆ t 0 , et ¼ ½eat eet ezt ert 0 and P, W and U are coefficient matrices. Linear f t ¼ ½m equation system (8) is so-called the state equation while (9) is the observation equation. As shown
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in Hamilton (1994), since the system is now represented in a state-space form and data in vector f t are available, the coefficients can be obtained by maximum likelihood estimation. 2.2. Estimation results Estimation is conducted using four variables, namely the real money balance, the short-term nominal interest rate, the output and the inflation rate. The real money balance is measured as the seasonally adjusted M2+CD divided by seasonally adjusted CPI excluding perishables and population of age 16 and over, the short-term nominal interest rate is the LIBOR 3 month rate, output is the seasonally adjusted real GDP also divided by population of age 16 years and over, and the inflation rate is measured by changes in the seasonally adjusted CPI excluding perishables. All data are on quarterly bases. As a distinct upward trend is found in real money balances and output measured as above, data are either de-trended by the Hodrick–Prescott (HP) filter or time trend.5 Estimation period is set from 1982/Q1 to 1995/Q1. The starting date is chosen so as to avoid some distortional effects from the second oil shock. As for the ending date, it is set at around the Bank of Japan resumed the de-facto zero nominal interest rate policy as in the reduced form regression in Section 2. When conducting estimation, some parameters are pre-fixed. As in Ireland (2004), preliminary attempts to estimate all parameters in Eqs. (1) nd (7) are not very successful. Implausibly low v1 and c are obtained. Since the aim of this paper is to examine the existence of the direct effect of money on real economic activities, we are interested in the value of v2 . Therefore, we estimate the parameters with constrained maximum likelihood estimates with v1 and c pre-fixed as exactly examined in Ireland (2004). v1 can be considered as the parameter for intertemporal elasticity of substitution. We calibrate this parameter as 0.66 rather arbitrarily6 but following the estimated results in Nishiyama (2005).7 As for c, this can be considered as the parameter on the output gap in the new Keynesian Phillips curve and implicitly contains the information on how frequently firms can change the price. Kimura and Kurozumi (2004) estimate the new Keynesian Phillips curve in Japan for annual inflation rate and obtains the value of 0.2 for this parameter. Further, several researches on Phillips curve conducted by the Bank of Japan, such as Price Developments in Japan—A Review Focusing on the 1990s released in October 2000 which report that this value for annual inflation is around 0.2. Transforming this into quarterly bases with considering that the intertemporal elasticity of substitution is now set at 0.66, leads to that c should be set at 0.075. Tables 1 and 2 show the estimation results when the HP filtered and the time trends are eliminated respectively. Standard errors are computed from inverse of Hessian matrix. Estimation results show that reasonable values are obtained for all the parameters, and almost the same results are obtained in both cases. A minor difference can be found in the persistence of technology shock represented as rz . As the time span, when the variables are away from their steady state value, are quite different whether the HP or the time trend is considered to be the steady state path, the parameter which decides this time span, namely the persistence of shocks are naturally different. Therefore, the technology shock is very persistent in the time trend case. Other than this minor difference, the size of the parameters and their significance are almost the same. 5
Hamilton (1994) recommends stationarity in data when estimating a state-space model. Therefore, the coefficient on the relative risk aversion is assumed to be around 1.5. 7 Estimation of the intertemporal elasticity of substitution has usually been conducted by assuming separability in utility. Therefore, we calibrate this parameter according to the previous researches. 6
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Table 1 Parameter estimates when the HP trends are eliminated Parameter
Estimate
Standard error
b v1 v2 g1 g2 g3 c rr ry rp log(y) log(m) log ðpÞ log(r) ra re rz sa se sz sr
0.9915 0.6600 0.0112 0.0000 0.0000 0.9999 0.0750 0.8168 0.0142 0.3362 8.1503 10.3018 0.0041 0.0126 0.8172 0.9439 0.1978 0.0170 0.0063 0.0277 0.0014
0.0010 0.0602 0.0010 0.0486 0.0006 0.0574 0.0197 0.0311 0.0025 0.0121 0.0007 0.0013 0.0482 0.0356 0.1454 0.0029 0.0006 0.0045 0.0001
Table 2 Parameter estimates when the time trends are eliminated Parameter
Estimate
Standard error
b v1 v2 g1 g2 g3 c rr ry rp log(y) log(m) log ðpÞ log(r) ra re rz sa se sz sr
0.9917 0.6600 0.0017 0.0000 0.0000 0.9999 0.0750 0.7869 0.0003 0.3266 8.1656 10.3246 0.0039 0.0122 0.9544 0.9874 0.9689 0.0230 0.0102 0.0139 0.0014
0.0059 0.0097 0.0022 0.1159 0.0014 0.0337 0.0142 0.0473 0.0262 0.0962 0.0092 0.0151 0.0398 0.0132 0.0747 0.0101 0.0010 0.0028 0.0001
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The parameter of the most interest is naturally v2, which decides the non-separability in consumption and real balances in utility function and therefore defines the magnitude of direct effect of money holdings on output and inflation. In both cases, this parameter is very small and insignificant. To ensure this finding further, we examine the likelihood ratio test for the null hypothesis H0: v2 ¼ 0. Under this null hypothesis, likelihood ratio for the HP trend case is 1.3962e–008 and 7.0825e–009 for the time trend case. As the 95 percent significant level for the cumulated Chi-square distribution when the degree of freedom is set to the number of restrictions is 3.75, this null hypothesis cannot be rejected. This finding suggests that there is almost no direct role of real money balances in Japan. The same conclusion has been already obtained in Ireland (2004) for the U.S. and Andres et al. (2001) for the Euro area. Another intriguing finding is that real money balances are following almost independent dynamics from other macroeconomic variables. Parameters g 1 , g 2 and g 3 which defines the dynamics in the money demand function indicate that dynamics in real money balances are solely defined by independently distributed shocks. 3. Conclusion In this paper, since using single estimation for the evaluation of direct effect of money tends to be problematic since the endogeneity of variables is not properly considered, we first construct a DSGE model with a direct effect of money based on rigid microfoundations. Maximum likelihood estimates on such a micro-founded model support no evidence on the direct effect of money stemming from the non-separability of utility in consumption and real balances. This finding is supported by different de-trending strategies. Therefore, it seems appropriate to conclude that the direct effect of money from non-separability in utility is extremely small in Japan. The effect of the quantitative easing monetary policy on the real economic activities through this channel should be limited.8 Acknowledgements The author would like to thank Peter Ireland for sharing the MATLAB programme and technical advises and an anonymous referee for valuable inputs. Furthermore, helpful comments from Kosuke Aoki, Kanemi Ban, Yuzo Honda, Charles Yuji Horioka and seminar participants at Osaka University are also highly acknowledged. Importantly, the view in this paper should not be taken as those of the Bank of Japan nor any of its respective monetary policy or other decision making bodies. All remaining errors are clearly my own. References Andres, J., Lopez-Salido, D., Valles, J., 2001. Money in an Estimated Business Cycle Model of the Euro area. Working Paper 121, Bank of Spain. Blanchard, O.J., Kahn, C.M., 1980. The solution of linear difference models under rational expectations. Econometrica 48, 1305–1311. Coenen, G., Wieland, V., 2003. The zero-interest-rate bound and the role of the exchange rate for monetary policy in Japan. Journal of Monetary Economics 50, 1071–1101.
8
This finding is consistent with the ones in Kimura et al. (2003) and Fujiwara (in press).
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Fujiwara, I. Evaluating monetary policy when nominal interest rates are almost zero. Journal of the Japanese and International Economies, in press. Hamilton, J., 1994. Time Series Analysis. Princeton University Press, Princeton, NJ. Ireland, P., 2004. Money’s role in the monetary business cycle. Journal of Money, Credit and Banking 36, 969–984. Kimura, T., Kobayashi, H., Muranaga, J., Ugai, H. The effect of the increase in monetary base on Japan’s economy at zero interest rates: an empirical analysis in monetary policy in a changing environment, Bank for International Settlements Conference Series, 2003. Kimura, T., Kurozumi, T., 2004. Effectiveness of history-dependent monetary policy. Journal of the Japanese and International Economies 18, 330–361. Nelson, E., 2002. Direct effects of base money on aggregate demand: theory and evidence. Journal of Monetary Economics 49, 687–708. Nishiyama, S.-I., 2005. The cross-Euler Equation approach to intertemporal substitution in import demand. Journal of Applied Econometrics 20, 841–872. Orphanides, A., Wieland, V., 2000. Efficient monetary policy design near price stability. Journal of the Japanese and International Economics 14, 327–365. Rotemberg, J., 1982. Monopolistic price adjustment and aggregate output. Review of Economic Studies 49, 517–531. Ruge-Murcia, F., 2002. Methods to Estimate Dynamic Stochastic General Equilibrium Models. Discussion Paper, University of California, San Diego. Schorfheide, F., 2000. Loss function based evaluation of DSGE models. Journal of Applied Econometrics 15, 645–670. Walsh, C., 2003. Monetary Theory and Policy. MIT Press, Cambridge, MA. Woodford, M., 2003. Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton University Press, Princeton, NJ.