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China’s monetary policy: Quantity versus price rules
Journal of Macroeconomics 31 (2009) 473–484
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Journal of Macroeconomics journal homepage: www.elsevier.com/locate/jmacro
China’s monetary policy: Quantity versus price rules q Wenlang Zhang * Research Department, Hong Kong Monetary Authority, 55th Floor, II International Finance Centre, 8 Finance Street, Central, Hong Kong
a r t i c l e
i n f o
Article history: Received 29 May 2007 Accepted 9 September 2008 Available online 23 September 2008
JEL classification: E52 E58
a b s t r a c t Two monetary policy rules, the money supply (quantity) rule and interest rate (price) rule, are explored for China in a dynamic stochastic general equilibrium model. The empirical results seem to indicate that the price rule is likely to be more effective in managing the macroeconomy than the quantity rule, favoring the government’s intention of liberalizing interest rates and making a more active use of the price instrument. Moreover, the economy would have experienced less fluctuations had interest rate responded more aggressively to inflation. Ó 2008 Elsevier Inc. All rights reserved.
Keywords: Monetary policy rules DSGE model Taylor rule
1. Introduction Compared with advanced economies, China’s monetary policy appears to be more complicated, as can be seen at least in the following two aspects. First, although the Law of People’s Bank of China (PBoC) states that the objective of monetary policy is to maintain price stability so as to promote economic growth, in reality China’s monetary policy seems to have been assigned more goals than mandated by the law. According to a speech of the PBoC governor published in a recent issue of Caijing Magazine (in Chinese, December 25, 2006), not only should monetary policy ensure price stability and promote economic growth, it is also supposed to maximize employment and achieve balance of payments equilibrium. In addition, it is expected to help promote financial liberalization and reforms. Second, unlike advanced economies which employ mainly one policy instrument, short-term interest rate recently and money supply in the earlier period, China’s monetary authority usually applies instruments of both quantity and price in nature in view of imperfect monetary policy transmission mechanism. Take the recent episode as example, in order to rein in fast growth in investment, the PBoC has raised benchmark interest rates, increased the reserve requirement ratio several times and issued a certain amount of one-year bills to selected banks whose loans were considered to have grown too fast since April 2006. The main reason that money supply gave way to interest rate as a policy instrument in numerous countries is that the latter is usually difficult to control by monetary authority. The quantity rule is rooted in the Fisher quantity theory of money and the assumption that velocity of money is relatively stable in the short run. But, as shown by Mishkin (2003, chapter 21)), the velocity of money has fluctuated too much to be seen as constant in the US from 1915 to 2002. China’s velocity of money (M2) also seems to be unstable and has increased remarkably since the early 1990s. Another assumption of the moneysupply rule is that there exists a close tie between inflation and nominal money growth. But this linkage has become looser q
The views in this paper are solely those of the author and should not be interpreted as those of Hong Kong Monetary Authority. * Tel.: +852 2878 1830; fax: +852 2878 1897. E-mail address: [email protected]
0164-0704/$ - see front matter Ó 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jmacro.2008.09.003
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W. Zhang / Journal of Macroeconomics 31 (2009) 473–484
because money demand may experience large volatility. Numerous papers have addressed this issue, see Wolters et al. (1998) for example. In fact the tie between money and inflation in China has also become looser in the past few years, mainly as a result of financial deepening. In addition, as shown in Laurens and Maino (2007), the gaps between actual and targeted money growth have been relatively large between 1994 and 2004. Evidence in this line seems to indicate that money supply should be assigned a less important role than interest rate. Indeed, as stated in the monetary policy implementation report of 2006 Q4, the PBoC is inclined to make a more active use of price-based policies and interest rate liberalization has become a main task of monetary authority. Ha and Fan (2003), for example, find that China’s investment was more sensitive to real lending rate during 1994–2002 than during 1981–1993. The research below aims at exploring two important monetary policy instruments in China, quantity and price, studying their impacts and providing some advice for policy makers. Unlike most papers on China’s policies in the literature, we will employ a dynamic stochastic general equilibrium (DSGE) model. A few macro models have been set up for China, most of which are macroeconometric models paying little attention to micro-foundations, see He et al. (2005) and Scheibe and Vines (2005) for instance. One may argue that DSGE models might not capture China’s economy well since it is not yet a perfect market economy. As argued by Scheibe and Vines (2005) and Chow (2002), however, the Chinese economy has become marketised to such a degree since 1978 that it is not inappropriate to model China’s economy in a framework of the advanced economies. In addition, as mentioned by Chow (2002), a theoretical-quantitative approach is as important as a historical-institutional one for China. The remainder of the paper is organized as follows. The second section presents some empirical evidence on China’s monetary policy. Section 3 presents the DSGE model and shows the consequential first order conditions engendered by households’ and firms’ optimization behaviors. The fourth section undertakes some numerical study of alternative monetary policies, and section five concludes the paper. 2. China’s monetary policy Although money supply has been supposed to be a dominant policy instrument in China in the past decades, as the economy becomes more market-oriented over time, the quantity rule seems to be less operable as China’s money velocity (the ratio of nominal GDP to nominal M2) and multiplier (the ratio of M2 to reserve money) have increased significantly in the past 15 years.1 This evidence has at least two implications: First, it is increasingly hard to determine money demand and as a result, hard to determine money supply. Second, it challenges China’s practice of controlling broad money by controlling base money (reserve money). In addition, the tie between money growth and inflation has loosened in the past years, with the correlation coefficient between CPI inflation and broad money growth decreasing from over 0.8 during 1992–1999 to about 0.16 during 2000–2006. In contrast, the tie between inflation and interest rate seems to have become closer, as the correlation coefficient between CPI inflation and one-year benchmark lending rate changed from 0.16 during 1992–1999 to 0.676 during 2000–2006. 2.1. Quantity rule Burdekin and Siklos (2005) claim that China seems to have followed the so-called McCallum rule.2 Assuming the annual target nominal GDP growth to be 12% (target real growth of 8% plus target inflation of 4%), Liu and Zhang (2007) find that the McCallum rule cannot capture China’s money supply well during 1991–2006, especially before 1997. The differential between the money supply simulated with the McCallum rule and the actual one was relatively large during 1991 and 1997, exceeding 40% points around 1993–1994. In fact, a main drawback of this monetary policy rule is that it does not take into account forward-looking behaviors. In addition, it does not consider inflation pressure explicitly. In the literature of DSGE models, economists usually assume money growth to be a function of technology shock, see Walsh (2003, chapter 2)), for example. This assumption is probably inappropriate for China as its money growth has been employed as an active instrument to manage the economy and can not be determined by one exogenous variable such as technology shock. Defining mt as the deviation of nominal money growth from its long-run value, we will employ the following quantity rule for China:
mt ¼ i1 mt1 i2 Et ptþ1 i3 Yb t þ vm;t 0 < i1 < 1; i2;3 > 0 where
ð1Þ
vm;t is assumed to be an AR(1) process
vm;t ¼ km vm;t1 þ t ; 0 < km < 1 b t is output gap and E is expectation operator. Such a rule dates back to where t is white noise, pt denotes inflation rate,3 Y Taylor (1979). Employing a dynamic macroeconomic model and taking money supply as policy instrument, Taylor (1979) finds that the optimal money supply can be set as a function of inflation and output gap. In a recent paper, Taylor (2000) states that
1
While the former increased from about 3 to 6, the latter rose from 2.5 to 5 in the same period. This rule reads: .t ¼ g t Dvelt þ 0:5ðg t g t1 Þ; where .t denotes the growth rate of nominal money supply, g t the target growth of nominal GDP, g t the actual growth of nominal GDP and Dvelt the growth of velocity of money. 3 One may assume it has a constant or zero target for simplicity. 2
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W. Zhang / Journal of Macroeconomics 31 (2009) 473–484
0.10
0.05
0.00
-0.05
-0.10
Actual
Simulation
-0.15
93
94
95
96
97
98
99
00
01
Fig. 1. Actual and simulated
02
03
04
05
mt .
such a rule can still be relevant for emerging market economies. Here we consider expected inflation rate to highlight the PBoC’s increasing concerns over inflation expectations in recent issues of monetary policy implementation reports. The parameter i1 reflects the smoothing effect in money supply as central banks usually feature some smoothing behavior to avoid drastic economic fluctuations brought about by sudden changes in policies. Let M t denote nominal money supply with growth rate .t , we know
Mt ¼ ð1 þ .t ÞM t1 ) mt ¼
1 þ .t mt1 1 þ pt
where mt ¼ MPtt with Pt denoting price level. Following Liu and Zhang (2007) we set i1 at 0.8, i2 ¼ 1:0 and i3 ¼ 0:5, suggesting that the monetary authority responds actively to expected inflation, with a lower response to output.4 Measuring mt by the deviation of actual money (M2) growth from its HP trend, we show the actual mt and that simulated with the above equation in Fig. 1. This figure shows that the simulated series can capture the actual series relatively well except in 1994 when actual money growth was very high. Comparing the simulated series in Fig. 1 and the McCallum rule in Liu and Zhang (2007), one may claim that the rule in Eq. (1) captures China’s money growth rule better. Measuring vm;t with the residuals in Eq. (1) we obtain the estimate of km ¼ 0:75. 2.2. Interest rate rule Taylor (1993) proposes that short-term interest rate can be set as function of output gap and inflation. Liu and Zhang (2007) find that the standard Taylor rule can not capture China’s interest rate well during 1992 and 2006, especially before 1996. In particular, the differential between the actual one-year lending rate and the simulated interest rate can be as large as 30% points in 1994. Below we will employ a modified Taylor rule for China:5
b t ¼ k1 R b t1 þ ð1 k1 Þ½k2 ðEt ptþ1 pt Þ þ k3 pt þ k4 Y b t þ v ; R R;t
1 > k1 > 0; k2;3;4 > 0
ð2Þ
b t and R b t denote output gap and the deviation of short-term rate from its steady state, respectively. The shock v is where Y R;t assumed to follow an AR(1) stochastic process:
vR;t ¼ kR vR;t1 þ tt ; 0 < kR < 1 with tt being a white noise. As for the parameters, we estimate the equation with GMM with quarterly data of 1994–2006 and obtain the following b t1 þ 0:65ðEt ptþ1 pt Þ þ 0:10pt þ 0:15 Y b t . The actual and fitted series are shown in Fig. 2. This rule b t ¼ 0:75 R specification:6 R 4 In an alternative version they consider contemporary rather than expected inflation. Here we follow their original version to capture the PBoC’s increasing concerns over inflation expectations. We have also estimated this equation with quarterly data of the past ten years by GMM and find that the estimates of i1 , i2 and i3 are 0.76, 0.94 and 0.47, respectively, close to the above values. In addition, we have tried to estimate an quantity rule considering contemporary inflation in addition to expected inflation and found that the coefficient of contemporary inflation is insignificant. 5 Such a rule can be considered as a combination of the rules of Clarida et al. (1998) and Smets and Wouters (2002). While the former consider inflation expectations, the latter highlight changes in inflation and output. One may also consider a long-run real interest rate in the rule and our simulation results below should not be affected as long as the long-run real rate is constant. 6 We use the percentage deviations of one-year base lending rate, CPI inflation and real GDP from their HP filter trends to measure their deviations from steady states. Xie and Luo (2002) find that the coefficients of output gap and expected inflation are 0.52 and 0.13, respectively. Our estimation seems to indicate that China’s monetary authority has paid more attention to inflation over time.
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W. Zhang / Journal of Macroeconomics 31 (2009) 473–484 0.20
0.15
ACTUAL FITTED
0.10
0.05
0.00
-0.05
-0.10
-0.15
-0.20 94
95
96
97
98
99
00
01
02
03
04
05
06
Fig. 2. Actual and simulated interest rate rules.
seems to have captured China’s interest rate rule better than the original Taylor rule without expectation and smoothing shown in Liu and Zhang (2007). The differential between the actual and the simulated series is less than 2% points most of the time. Measuring vR;t with the residuals from the above equation we obtain the estimate of kR ¼ 0:51. 3. A dynamic stochastic general equilibrium model 3.1. Households There exists a continuum of households, indexed by k, k 2 ð0; 1Þ. Household k maximizes the following objective function
Et
1 X
bi U k;tþi
i¼0
with
U k;t ¼
1c 1 1 M k;t 1 ðC k;t hC t1 Þ1r þ N1þg 1r 1 c Pt 1 þ g k;t
s.t.
Mk;t Bk;t M k;t1 Bk;t1 W k;t þ þ C k;t þ Ik;t ¼ þ þ Nk;t þ r ct K k;t þ Dk;t þ T k;t Pt P t Rt Pt Pt Pt
ð3Þ
The household enters period t with capital stock K k;t , nominal money balance M k;t1 and coupon bond Bk;t1 . Rt and r ct denote gross return of bond and rental rate of capital, while C k;t , Ik;t and N k;t denote real consumption, investment and labor supply in period t, respectively. The parameter h is referred to as habit parameter, so that hC t1 denotes the external habit stock with C t being aggregate consumption. r denotes the coefficient of relative risk aversion of households, c the inverse of the elasticity of money holdings with respect to interest rate. g denotes the inverse of the elasticity of work effort with respect to real wage. W k;t is nominal wage. Each household is assumed to own an equal share of firms and receives an aliquot share of real aggregate profits Dk;t . T k;t denotes the real net transfer from government in period t. Assuming complete contingent claims markets for labor income, and identical initial endowments of capital, bonds and money, all optimality conditions will be the same across households, except for labor supply and wage. We can, therefore, drop the index k for all variables but labor and wage. The first-order conditions (FOCs) with respect to C t and Bt read
bEt
ðC tþ1 hC t Þr Pt Rt ¼ 1; ðC t hC t1 Þr Ptþ1
ð4Þ
while the FOC with respect to M t reads
c Mt Rt 1 ¼ ðC t hC t1 Þr Rt Pt
ð5Þ
Given the capital stock accumulation equation
K tþ1 ¼ ð1 dÞK t þ It
ð6Þ
W. Zhang / Journal of Macroeconomics 31 (2009) 473–484
477
with d denoting depreciation rate, we have the following FOC with respect to investment and capital stock
1 ¼ bEt
r C t hC t1 ð1 d þ r ctþ1 Þ C tþ1 hC t
ð7Þ
In addition, the aggregate labor supply N t is assumed to be a CES function of differentiated labor provided by household k with the Dixit-Stiglitz elasticity of substitution among differentiated labor services being l(>1). The demand for differentiated labor then reads
Nk;t ¼
W k;t Wt
l
Nt
In each period all households can adjust their wages, but only 1 n fraction of households can adjust their wages optimally, with the rest n fraction of households setting their wages according to the rule7
W k;t ¼ V t1 W k;t1 t where V t ¼ PPt1 ¼ 1 þ pt . The household which can optimize the wage in period t then chooses the optimal wage W k;t to maximize the following objective function:8
Et
( ) 1 X U c ðt þ i; tÞ ðbnÞi ðW k;t X ti Nk;tþi;t Ptþi C tþi;t Þ þ UðC tþi;t ; Nk;tþi;t Þ ; Ptþi i¼0
where U c ðt þ i; tÞ denotes the marginal utility of consumption at t þ i of workers that optimize at t, and N k;tþi;t the hours worked at t þ i at the wage set at time t:
Nk;tþi;t ¼
l W k;t X ti Ntþi W tþi
with X ti ¼ 1, for i ¼ 0 and X ti ¼ V t V tþ1 V tþ2 ; . . . ; V tþi1 , for i P 1. The FOC with respect to W k;t then results in
2
W k;t
31þl1 g lð1þgÞ i 1þg X ti ðbnÞ N i¼0 tþi W tþi 6 l 7 ¼4 5 : l l 1 P1 i X ti X ti Et i¼0 ðbnÞ W tþi U ðt þ i; tÞN c tþi P tþi Et
P1
ð8Þ
The above equation shows that one can replace W k;t with W t since all households have the same optimal wage. Based on the above FOC and the following aggregate wage equation: 1
W t ¼ ½ð1 nÞðW t Þ1l þ nðV t1 W t1 Þ1l 1l ;
ð9Þ
one can then obtain the following linearized real wage equation:
^t -
U
with
^ t1 þ pt1 Þ ð1 þ bÞð1 þ glÞnpt þ ð1 þ glÞnbEt ð^ tþ1 þ ptþ1 Þ ¼ ð1 þ glÞnðh i r b t1 Þ bt C bt þ þ ð1 bnÞð1 nÞ g N ðC 1h
1 -t ¼ WPtt and U ¼ ð1þbÞð1þglÞnþð1bnÞð1nÞ .
3.2. Firms 3.2.1. Final goods Final good Y t (subject to perfect competition) is assumed to be a CES function of the intermediate goods Y j;t produced by a continuum of firms indexed by j 2 ð0; 1Þ, with the elasticity of substitution between varieties of intermediate goods being h. Let Pj;t denote the price of intermediate goods j at time t, the demand for intermediate goods j then reads
Y j;t ¼
h Pj;t Yt Pt
7 There are also economists assuming that this group of households set wage according to last-period wage inflation or a combination of last-period price and wage inflation rate. Here we follow Sbordone (2006). assuming households that can not set wage optimally set their wages according to last-period price inflation. This assumption seems to capture China’s situation better than others because China’s officially released wage growth data reflect only the wage dynamics of a small part of employees. Migrant workers’ salaries, for example, are not well shown in the existing data. 8 Following Sbordone (2006), we assume the household maximizes the expected stream of discounted utility from the new wage.
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W. Zhang / Journal of Macroeconomics 31 (2009) 473–484
3.2.2. Intermediate goods Intermediate goods Y j (subject to monopolistic competition) is assumed to be produced with the following production function: a Y jt ¼ Z t Naj;t K 1 j;t ;
0 < a < 1;
where N j;t and K j;t denote labor and capital used for producing Y j;t . Z t denotes technology shock subject to the following path
ln Z t ¼ j ln Z þ ð1 jÞ ln Z t1 þ et ; with Z being the mean of Z t and
0 < j < 1;
ð10Þ
et a white noise. The FOCs with respect to Nj;t and K j;t are
a1 N -t ¼ aut Z t j;t K j;t c 1a 1 -t a rt ut ¼ Zt a 1a
ð11Þ ð12Þ
where ut denotes the real marginal cost. 3.2.3. Price setting Here we follow Christiano et al. (2005) and Smets and Wouters (2002) assuming that in each period all firms can adjust their prices, but only 1 x fraction of firms are allowed to adjust their prices optimally, and the remaining x fraction adjust their prices as P j;t ¼ V t1 Pj;t1 . Firm j which can re-optimize its price at t chooses the optimal price Pj;t to maximize the present value of its real profits. The optimal price then reads
P P tþi h h i Et 1 Pj;t h i¼0 x Ktþi utþi ð Pt Þ Y tþi X ti ¼ P1 i h 1 Et i¼0 x Ktþi utþi ðPtþi Þh1 Y tþi X ti1h Pt
ð13Þ
Pt
where Ktþi denotes the stochastic discount factor bi ð Ctþit Þr . One can drop the index j in P j;t as the optimal price is the same for each firm j. From C
Y j;t ¼
Pj;t Pt
h
Yt
ð14Þ
and assuming symmetric equilibrium with respect to intermediate goods, we know that the aggregate price at t is 1
Pt ¼ ½ð1 xÞðPt Þ1h þ xðV t1 Pt1 Þ1h 1h :
ð15Þ
From Eqs. (13) and (15) we can derive the following linearized Phillips curve:
pt ¼
x 1 þ bx
2
pt1 þ
2 x bx þ bx2 Et ptþ1 þ ð1 xÞð1 bxÞu^t : 1 þ bx2
ð16Þ
4. Policy analysis 4.1. Linearized equations One can calculate the steady states of the variables of interest from the series of FOC conditions derived above. The steady state of Rt , for example, is R ¼ 1b according to Eq. (4). Assuming general equilibrium and employing the quantitative monetary policy rule, one can then log-linearize relevant equations around the steady states of variables:
bt ¼ C
h b 1 b tþ1 1 h ð R b t Et ptþ1 Þ C t1 þ Et C 1þh 1þh ð1 þ hÞr
ð17Þ
b t1 þ Et C b t ¼ hC b tþ1 1 h Et ^r c C tþ1
ð18Þ
b t þ ð1 aÞðh 1Þ bI t b t ¼ 1 þ aðh 1Þ C Y h h
ð19Þ
b t þ ð1 aÞ K b t þ aN bt bt ¼ Z Y
ð20Þ
r
W. Zhang / Journal of Macroeconomics 31 (2009) 473–484
b tþ1 ¼ ð1 dÞ K b t þ dbI t K
pt ¼ ^t -
U
x 1 þ bx2
pt1 þ
2 x bx þ bx2 Et ptþ1 þ ð1 xÞð1 bxÞu^t 1 þ bx2
^ t1 þ pt1 Þ ð1 þ bÞð1 þ glÞnpt þ ð1 þ glÞnbEt ð^ tþ1 þ ptþ1 Þ ¼ ð1 þ glÞnðh i b t hC b t1 Þ b t þ r ðC þ ð1 bnÞð1 nÞ g N 1h
^t ¼ m
r ð1 hÞc
bt C
rh b 1b C t1 R ð1 hÞc c t
479
ð21Þ ð22Þ
ð23Þ
ð24Þ
^ t1 pt þ mt ^t ¼ m m
ð25Þ
mt ¼ i1 mt1 i2 Et ptþ1 i3 Yb t þ vm;t
ð26Þ
b t ¼ ð1 jÞ Z b t1 þ et Z
ð27Þ
bt ^ t þ ð1 aÞ^r ct Z ^ ¼ au
ð28Þ
b t ¼ ^r c þ K bt ^t N t
ð29Þ
In the case of interest rate rule, one then replaces Eqs. (24)–(26) with Eq. (2). 4.2. Parameterization As is known, it is quite challenging to parameterize a macro model for China because (a) China’s data are relatively scarce and (b) China has been shifting from a planning economy to a market one, suggesting possible structural changes in the past decade. In view of this problem, economists have usually chosen to estimate single equations rather than a simultaneous system for China. In the research below we will follow this line of literature, estimating some of the parameters with available data and assigning values to others according to related works in the literature. Equations will be estimated separately for variable sample periods according to data availability.9 Following Walsh (2003), we set r ¼ 2. Estimating Eq. (18) with data of 1993–2005 by GMM we obtain h ¼ 0:61 (t-st. 110.24).10 a and d are set at 0.4 and 0.04, respectively, following the estimates of He et al. (2007). Setting a ¼ 0:4 and estimating (19) with data of 1993–2007 one can figure out h ¼ 4:61.11 The average (annual) nominal interest rate is 0.08 from 1978 to 2005, which might justify a quarterly rate of 0.02 in the steady state and b ¼ 0:98 since R ¼ 1b. The GMM estimation of Eq. (22) with data of 1995 to 2005 shows that x ¼ 0:84 (t-st. 24.10). Our estimation of the Phillips curve looks close to that of Funke (2005) who estimates the new Keynesian Phillips curve for China with various methodologies. Following the estimates of Liu (2007) we set g ¼ 6:16, n ¼ 0:6 and l ¼ 2. The estimation of Eq. (24) with data of 1992-2006 shows that c is 3.13 (t-st. 1.92).12 Using total factor productivity (TFP) data from He and Zhang (2008) we obtain the estimate of j ¼ 0:5.13 The main parameters are summarized in Table 1. 4.3. Simulations Next, we will solve the above linear dynamic system by methods of undetermined coefficients with the algorithm developed by Uhlig (1999). Uhlig (1999) divides all variables into three categories: endogenous state variables Ut , jump variables Wt and exogenous stochastic processes Zt , with Ut , Wt and Zt being vectors of a1 , a2 and a3 elements, respectively. Then the linearized system can be arranged as follows:
9
Estimations are undertaken with quarterly data. When quarterly data are not available, we convert annual data into quarterly data with Eviews. Consumption in this equation is proxied with retail sales as consumption data from national account are annual. Consumption gap is measured with percentage deviation of actual retail sales from its HP-filter trend. Return to capital is proxied by the marginal product of capital estimated by He et al. (2007). 11 Output gap, consumption and investment gaps are measured with the percentage deviations of the actual values of output, consumption (national account data of total consumption) and investment (gross capital formation) from their HP-filter trends. 12 Real money gap is measured by the percentage deviation of real broad money from its HP-filter trend. 13 While He et al. (2007) estimate TFP growth for China with the Cobb-Douglas production with national data, He and Zhang (2008) estimate TFP growth with the Malmquist index using panel data. The latter seems to outperform the former since the production function approach assumes production is always conducted on the frontier and may overestimate TFP growth. 10
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W. Zhang / Journal of Macroeconomics 31 (2009) 473–484
Table 1 Parameterization h
r
a
x
b
n
g
l
h
c
j
d
0.61
2.0
0.40
0.84
0.98
0.60
6.16
2.0
4.61
3.13
0.5
0.04
0.6
Output
Percent Deviation from Steady State
0.5
Inflation
0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -1
0
1
2
3
4
5
6
7
8
5
6
7
8
Years after Shock
Percent Deviation from Steady State
1
Output
0.8
0.6
0.4
0.2
0
-0.2 Inflation -0.4 -1
0
1
2
3
4
Years after Shock
0.15 Inflation
Percent Deviation from Steady State
0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 -0.25 -0.3
Output -0.35 -1
0
1
2
3
4
5
6
7
Years after Shock
Fig. 3. Impulse responses to shocks with quantity rule.
8
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W. Zhang / Journal of Macroeconomics 31 (2009) 473–484
0 ¼ AUt þ BUt1 þ C Wt þ DZt ;
ð30Þ
0 ¼ Et ½F Utþ1 þ GUt þ HUt1 þ J Wtþ1 þ K Wt þ LZtþ1 þ MZt
ð31Þ
Ztþ1 ¼ NZt þ z;tþ1 ;
ð32Þ
Et ½z;tþ1 ¼ 0;
where C is assumed to be of size a4 a2 , a4 P a2 and of rank a2 , F is of size ða1 þ a2 a4 Þ a1 . N is assumed to have only stable eigenvalues. Then one may express Ut and Wt as
Percent Deviation from Steady State
1
0.5
0
-0.5
-1
-1.5 -1
Inflation Output 0
1
2
3
4
5
6
7
8
5
6
7
8
5
6
7
8
Years after Shock
Percent Deviation from Steady State
1.2
1
Output
0.8
0.6
0.4
0.2
0 Inflation -0.2 -1
0
1
2
3
4
Years after Shock
Percent Deviation from Steady State
0.05 0 Inflation -0.05 -0.1 -0.15 -0.2 -0.25 -0.3 -0.35
Output
-1
0
1
2
3
4
Years after Shock Fig. 4. Impulse responses with interest rate rule.
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W. Zhang / Journal of Macroeconomics 31 (2009) 473–484
Table 2 Response coefficients of inflation to shocks
Quantity rule Price rule
Monetary policy
Technology
Real wage
0.264 0.840
0.192 0.123
0.019 0.002
Monetary policy
Technology
Real wage
0.584 1.423
0.963 0.961
0.328 0.300
Table 3 Response coefficients of output to shocks
Quantity rule Price rule
Ut ¼ S1 Ut1 þ S2 Zt Wt ¼ S3 Ut1 þ S4 Zt :
ð33Þ ð34Þ
We will explore how the two policy rules differ from each other from two perspectives: (a) which policy instrument is more powerful assuming a shock to each of them separately, and (b) under which policy rule the economy experiences less fluctuations assuming the economy faces shocks of other main economic variables than monetary policy since less fluctuations in inflation and output imply a lower loss to the central bank.14 The impulse responses of inflation and output gap to b t and real wage are presented in Fig. 3.15 shocks in money growth, technology Z The upper panel shows that a positive shock from nominal money growth will lead to a half percentage point increase in inflation in the first two quarters, together with a 0.6% point upturn in output, followed by a slide in GDP by about 0.3% point in the second year. This suggests that although money can lead to a temporary expansion in GDP, it may result in an output reduction in the medium term. The middle panel shows that output will increase by over 0.9% point in the first year following a positive technology shock, while inflation may decline by 0.3% point in the meantime. Inflation declines because supply increases due to productivity improvement. In the lower panel we show the reactions of inflation and output to a percentage point deviation of real wage from its steady state. Clearly, while inflation increases by 0.1% point, output may decrease by 0.33% point. The impulse responses of output and inflation to money growth, technology and real wage when interest rate rather than money supply is employed as policy instrument are shown in Fig. 4. Comparing Fig. 3 with Fig. 4, one may have the following findings: (a) the price instrument seems to be more powerful than the quantity instrument, and (b) facing similar shocks from main variables in the economy, inflation and output may experience less fluctuations when the price rule rather than the quantity rule is in operation. Point (a) can be seen by comparing the upper panels of the two figures. While a shock in interest rate may lead to decreases of inflation and output of between one and 1.5% points, a shock in money growth leads to increases in inflation and output of about 0.5–0.6% point. This can also be partly reflected by the response coefficients of inflation and output gap to monetary policy (relevant elements in S2 and S4 ). The response coefficients of inflation to shocks in money growth and interest rate are 0.264 and 0.840, respectively (Table 2). Meanwhile, the response coefficients of output gap to shocks in money growth and interest rate are 0.584 and 1.423, respectively (Table 3). In fact, observers of China’s economy have argued that impacts of interest rate on the economy have been underestimated as small-and-medium size and private enterprizes are much less likely to get loans from banks than large-size and state-owned enterprizes (SOEs) when monetary tightening occurs. In order to get the same amount of loans as SOEs the former may have to pay extra costs other than interest. Point (b) can be seen by comparing the middle and lower panels of Figs. 3 and 4. Clearly, while a shock in technology may lead to an increase in output of similar size in both figures, inflation experiences less fluctuations in Fig. 4. Moreover, both inflation and output converge to their steady states much faster in Fig. 4. We get similar findings with respect to a shock in real wage. While output decreases by about 0.33% point in Fig. 3, it slides by less than 0.3% point in Fig. 4. Likewise, inflation experiences much less fluctuations in Fig. 4. Moreover, both inflation and output converge to their steady states faster in Fig. 4 than in Fig. 3. One can also see this point from the response coefficients of inflation and output to technology and real wage under different policy rules. As shown in Tables 2 and 3, the response coefficients of inflation and output to shocks in technology and real wage are lower in magnitude under the price rule than under the quantity rule. Some economists argue that China should have been more aggressive in interest rate policy. Take the recent episode of monetary policy as example, although the PBoC has raised interest rate gradually, real interest rate still remains quite low and even negative. The inactive policy stance of the authority has been argued by some commentators to be partly responsible for upsurges (or bubbles) in stock prices since 2006. Moreover, inflation remains elevated. Artificially low costs of cap-
14
Woodford (2003) shows the links between quadratic loss functions of inflation and output and households’ objective functions. One may also see the reactions of inflation and output to shocks in other variables than real wage and technology. We have also simulated shocks for some other variables, inflation for example, and find that the main findings remain essentially unchanged. 15
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Percent Deviation from Steady State
1.2
1 Output 0.8
0.6
0.4
0.2
0 Inflation -0.2 -1
0
1
2
3
4
5
6
7
8
5
6
7
8
Years after Shock
Percent Deviation from Steady State
0.1
0.05
0 Inflation -0.05
-0.1
-0.15
-0.2
-0.25 -1
Output 0 1
2
3
4
Years after Shock
Fig. 5. Impulse responses with more aggressive interest rate rule.
ital have not only led to wastes of resources but may have fueled volatility of economy. In fact, Taylor (1993) sets the coefficient of inflation at above one and that of output gap at 0.5. Taylor (1999) further raises the coefficient of output gap to unity. In the interest rate rule employed above, we have used the estimated coefficients of inflation and output gap. Next, we will conduct an counterfactual experiment by assuming that interest rate reacts more aggressively to inflation and output gap. Namely, we raise the coefficient of expected inflation ðk2 Þ to 1.0 to see how inflation and output may have responded to various shocks in the economy. The simulation results are shown in Fig. 5. Comparing Fig. 4 with Fig. 5, one finds that the economy would have experienced less fluctuations if interest rate had been more aggressive. For example, while output declines by about 0.3% point in the presence of a wage shock in Fig. 4, it declines by less than 0.25% point in Fig. 5. Inflation and output also fluctuate less in the wake of a technology shock in Fig. 5 than in Fig. 4. Looking at the response coefficients of inflation and output to technology and real wage provides us clearer evidence. For example, while the response coefficient of output gap to real wage is 0.300 in Fig. 4, it is 0.242 in Fig. 5. 5. Conclusions Monetary policy with money supply as instrument seems to become more difficult to conduct in China than before, as money multiplier and velocity have been increasing noticeably and the linkage between money supply and inflation becomes weaker over time. Experiments in a DSGE model based on data in the past decade indicate that effects of a price rule on the economy seem to have become more significant than those of a quantity rule. Moreover, the economy may experience less fluctuations in the presence of shocks from main macroeconomic variables when the price rule is employed to manage the macroeconomy. The findings seem to favor the government’s intention of liberalizing interest rates and making a more active use of the price instrument in recent years as the economy becomes more market-oriented.
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We have also conducted a counterfactual study assuming that the monetary authority had reacted more aggressively to inflation than estimated with data. The experiments seem to indicate that the economy would have experienced less fluctuations had interest rate been more aggressive. References Burdekin, R.C.K., Siklos, P.L., 2005. What has driven Chinese monetary policy since 1990? Investigating the People’s Bank’s policy rule. East-West Center Working Paper No. 85. Chow, G., 2002. China’s Economic Transmission. Blackwell Publishers Ltd., Oxford, 1990. Christiano, L.J., Eichernbaum, M., Evans, C.L., 2005. Nominal rigidities and the dynamic effects of a shock to monetary policy. Journal of Political Economy 113 (1), 1–45. Clarida, R., Gali, J., Gertler, M., 1998. Monetary policy rules in practice: some international evidence. European Economic Review 42, 1033–1067. Funke, M., 2005. Inflation in mainland China—modelling a roller coaster ride. Hong Kong Institute for Monetary Research, Working Paper 15/2005. Ha J., Fan K., 2003. The monetary transmission mechanism in the mainland. Research memorandum 11/2003, Hong Kong Monetary Authority. He, D., Zhang, W., 2008. How dependent is China’s economy on exports? Hong Kong Monetary Authority working paper. He, X., Wu, H., Cao, Y., Liu, R., 2005. China-QEM: A Quarterly Macroeconometric Model of China. Social Sciences Academic Press, Beijing. He, D., Zhang, W., Shek, J., 2007. How efficient has been China’s investment? Empirical evidence from national and provincial data. Pacific Economic Review 12 (5), 597–617. Laurens, B.J., Maino, R., 2007. China: Strengthening monetary policy implementation. IMF Working Paper, WP/07/14. Liu, B., 2007. Developing a DSGE model for China and its application in monetary policy. PBoC Research Bureau (in Chinese). Liu, L., Zhang, W., 2007. A model based appraoch to monetary policy analysis for China. Hong Kong Monetary Authority Working Paper 18/2007. Mishkin, F.S., 2003. The Economics of Money. Banking and Financial Markets. Addison Wesley. Sbordone, A.M., 2006. US wage and price dynamics: a limited-information approach. International Journal of Central Banking 2 (3), 155–191. Scheibe, J., Vines, D., 2005. After the revaluation: Insights on Chinese macroeconomic strategy from an estimated macroeconomic model. Manuscript St Antony’s College and Department of Economics. University of Cambridge. Smets, F., Wouters, R., 2002. An estimated dynamic stochastic general equilibrium model of the euro area. Journal of the European Economic Association 1 (5), 1123–1175. Taylor, J.B., 1979. Estimation and control of a macroeconomic model with rational expectations. Econometrica 47 (5), 1267–1286. Taylor, J.B., 1993. Discretion versus policy rules in practice. Carnegie-Rochester Conference Series on Public Policy 39, 195–214. Taylor, J.B., 1999. A historical analysis of monetary policy rules. In: Taylor, J.B. (Ed.), Monetary Policy Rules. University of Chicago Press, Chicago. Taylor, J.B., 2000. Using monetary policy in emerging market economies. Standford University, Unpublished. Uhlig H., 1999. A toolkit for analyzing nonlinear dynamic stochastic models easily. Department of Economics, Humboldt University. Walsh, C.E., 2003. Monetary Theory and Policy. The MIT Press, Cambridge, Massachusetts. Wolters, J., Teräsvirta, T., Lütkepohl, D.H., 1998. Modelling the demand for M3 in the united Germany. The Review of Economics and Statistics 80 (3), 399– 409. Xie, P., Luo, X., 2002. Taylor rule and its empirical tests in China’s monetary policy. Economic Research Journal 3, 3–12 (in Chinese).
Contents lists available at ScienceDirect
Journal of Macroeconomics journal homepage: www.elsevier.com/locate/jmacro
China’s monetary policy: Quantity versus price rules q Wenlang Zhang * Research Department, Hong Kong Monetary Authority, 55th Floor, II International Finance Centre, 8 Finance Street, Central, Hong Kong
a r t i c l e
i n f o
Article history: Received 29 May 2007 Accepted 9 September 2008 Available online 23 September 2008
JEL classification: E52 E58
a b s t r a c t Two monetary policy rules, the money supply (quantity) rule and interest rate (price) rule, are explored for China in a dynamic stochastic general equilibrium model. The empirical results seem to indicate that the price rule is likely to be more effective in managing the macroeconomy than the quantity rule, favoring the government’s intention of liberalizing interest rates and making a more active use of the price instrument. Moreover, the economy would have experienced less fluctuations had interest rate responded more aggressively to inflation. Ó 2008 Elsevier Inc. All rights reserved.
Keywords: Monetary policy rules DSGE model Taylor rule
1. Introduction Compared with advanced economies, China’s monetary policy appears to be more complicated, as can be seen at least in the following two aspects. First, although the Law of People’s Bank of China (PBoC) states that the objective of monetary policy is to maintain price stability so as to promote economic growth, in reality China’s monetary policy seems to have been assigned more goals than mandated by the law. According to a speech of the PBoC governor published in a recent issue of Caijing Magazine (in Chinese, December 25, 2006), not only should monetary policy ensure price stability and promote economic growth, it is also supposed to maximize employment and achieve balance of payments equilibrium. In addition, it is expected to help promote financial liberalization and reforms. Second, unlike advanced economies which employ mainly one policy instrument, short-term interest rate recently and money supply in the earlier period, China’s monetary authority usually applies instruments of both quantity and price in nature in view of imperfect monetary policy transmission mechanism. Take the recent episode as example, in order to rein in fast growth in investment, the PBoC has raised benchmark interest rates, increased the reserve requirement ratio several times and issued a certain amount of one-year bills to selected banks whose loans were considered to have grown too fast since April 2006. The main reason that money supply gave way to interest rate as a policy instrument in numerous countries is that the latter is usually difficult to control by monetary authority. The quantity rule is rooted in the Fisher quantity theory of money and the assumption that velocity of money is relatively stable in the short run. But, as shown by Mishkin (2003, chapter 21)), the velocity of money has fluctuated too much to be seen as constant in the US from 1915 to 2002. China’s velocity of money (M2) also seems to be unstable and has increased remarkably since the early 1990s. Another assumption of the moneysupply rule is that there exists a close tie between inflation and nominal money growth. But this linkage has become looser q
The views in this paper are solely those of the author and should not be interpreted as those of Hong Kong Monetary Authority. * Tel.: +852 2878 1830; fax: +852 2878 1897. E-mail address: [email protected]
0164-0704/$ - see front matter Ó 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jmacro.2008.09.003
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because money demand may experience large volatility. Numerous papers have addressed this issue, see Wolters et al. (1998) for example. In fact the tie between money and inflation in China has also become looser in the past few years, mainly as a result of financial deepening. In addition, as shown in Laurens and Maino (2007), the gaps between actual and targeted money growth have been relatively large between 1994 and 2004. Evidence in this line seems to indicate that money supply should be assigned a less important role than interest rate. Indeed, as stated in the monetary policy implementation report of 2006 Q4, the PBoC is inclined to make a more active use of price-based policies and interest rate liberalization has become a main task of monetary authority. Ha and Fan (2003), for example, find that China’s investment was more sensitive to real lending rate during 1994–2002 than during 1981–1993. The research below aims at exploring two important monetary policy instruments in China, quantity and price, studying their impacts and providing some advice for policy makers. Unlike most papers on China’s policies in the literature, we will employ a dynamic stochastic general equilibrium (DSGE) model. A few macro models have been set up for China, most of which are macroeconometric models paying little attention to micro-foundations, see He et al. (2005) and Scheibe and Vines (2005) for instance. One may argue that DSGE models might not capture China’s economy well since it is not yet a perfect market economy. As argued by Scheibe and Vines (2005) and Chow (2002), however, the Chinese economy has become marketised to such a degree since 1978 that it is not inappropriate to model China’s economy in a framework of the advanced economies. In addition, as mentioned by Chow (2002), a theoretical-quantitative approach is as important as a historical-institutional one for China. The remainder of the paper is organized as follows. The second section presents some empirical evidence on China’s monetary policy. Section 3 presents the DSGE model and shows the consequential first order conditions engendered by households’ and firms’ optimization behaviors. The fourth section undertakes some numerical study of alternative monetary policies, and section five concludes the paper. 2. China’s monetary policy Although money supply has been supposed to be a dominant policy instrument in China in the past decades, as the economy becomes more market-oriented over time, the quantity rule seems to be less operable as China’s money velocity (the ratio of nominal GDP to nominal M2) and multiplier (the ratio of M2 to reserve money) have increased significantly in the past 15 years.1 This evidence has at least two implications: First, it is increasingly hard to determine money demand and as a result, hard to determine money supply. Second, it challenges China’s practice of controlling broad money by controlling base money (reserve money). In addition, the tie between money growth and inflation has loosened in the past years, with the correlation coefficient between CPI inflation and broad money growth decreasing from over 0.8 during 1992–1999 to about 0.16 during 2000–2006. In contrast, the tie between inflation and interest rate seems to have become closer, as the correlation coefficient between CPI inflation and one-year benchmark lending rate changed from 0.16 during 1992–1999 to 0.676 during 2000–2006. 2.1. Quantity rule Burdekin and Siklos (2005) claim that China seems to have followed the so-called McCallum rule.2 Assuming the annual target nominal GDP growth to be 12% (target real growth of 8% plus target inflation of 4%), Liu and Zhang (2007) find that the McCallum rule cannot capture China’s money supply well during 1991–2006, especially before 1997. The differential between the money supply simulated with the McCallum rule and the actual one was relatively large during 1991 and 1997, exceeding 40% points around 1993–1994. In fact, a main drawback of this monetary policy rule is that it does not take into account forward-looking behaviors. In addition, it does not consider inflation pressure explicitly. In the literature of DSGE models, economists usually assume money growth to be a function of technology shock, see Walsh (2003, chapter 2)), for example. This assumption is probably inappropriate for China as its money growth has been employed as an active instrument to manage the economy and can not be determined by one exogenous variable such as technology shock. Defining mt as the deviation of nominal money growth from its long-run value, we will employ the following quantity rule for China:
mt ¼ i1 mt1 i2 Et ptþ1 i3 Yb t þ vm;t 0 < i1 < 1; i2;3 > 0 where
ð1Þ
vm;t is assumed to be an AR(1) process
vm;t ¼ km vm;t1 þ t ; 0 < km < 1 b t is output gap and E is expectation operator. Such a rule dates back to where t is white noise, pt denotes inflation rate,3 Y Taylor (1979). Employing a dynamic macroeconomic model and taking money supply as policy instrument, Taylor (1979) finds that the optimal money supply can be set as a function of inflation and output gap. In a recent paper, Taylor (2000) states that
1
While the former increased from about 3 to 6, the latter rose from 2.5 to 5 in the same period. This rule reads: .t ¼ g t Dvelt þ 0:5ðg t g t1 Þ; where .t denotes the growth rate of nominal money supply, g t the target growth of nominal GDP, g t the actual growth of nominal GDP and Dvelt the growth of velocity of money. 3 One may assume it has a constant or zero target for simplicity. 2
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0.10
0.05
0.00
-0.05
-0.10
Actual
Simulation
-0.15
93
94
95
96
97
98
99
00
01
Fig. 1. Actual and simulated
02
03
04
05
mt .
such a rule can still be relevant for emerging market economies. Here we consider expected inflation rate to highlight the PBoC’s increasing concerns over inflation expectations in recent issues of monetary policy implementation reports. The parameter i1 reflects the smoothing effect in money supply as central banks usually feature some smoothing behavior to avoid drastic economic fluctuations brought about by sudden changes in policies. Let M t denote nominal money supply with growth rate .t , we know
Mt ¼ ð1 þ .t ÞM t1 ) mt ¼
1 þ .t mt1 1 þ pt
where mt ¼ MPtt with Pt denoting price level. Following Liu and Zhang (2007) we set i1 at 0.8, i2 ¼ 1:0 and i3 ¼ 0:5, suggesting that the monetary authority responds actively to expected inflation, with a lower response to output.4 Measuring mt by the deviation of actual money (M2) growth from its HP trend, we show the actual mt and that simulated with the above equation in Fig. 1. This figure shows that the simulated series can capture the actual series relatively well except in 1994 when actual money growth was very high. Comparing the simulated series in Fig. 1 and the McCallum rule in Liu and Zhang (2007), one may claim that the rule in Eq. (1) captures China’s money growth rule better. Measuring vm;t with the residuals in Eq. (1) we obtain the estimate of km ¼ 0:75. 2.2. Interest rate rule Taylor (1993) proposes that short-term interest rate can be set as function of output gap and inflation. Liu and Zhang (2007) find that the standard Taylor rule can not capture China’s interest rate well during 1992 and 2006, especially before 1996. In particular, the differential between the actual one-year lending rate and the simulated interest rate can be as large as 30% points in 1994. Below we will employ a modified Taylor rule for China:5
b t ¼ k1 R b t1 þ ð1 k1 Þ½k2 ðEt ptþ1 pt Þ þ k3 pt þ k4 Y b t þ v ; R R;t
1 > k1 > 0; k2;3;4 > 0
ð2Þ
b t and R b t denote output gap and the deviation of short-term rate from its steady state, respectively. The shock v is where Y R;t assumed to follow an AR(1) stochastic process:
vR;t ¼ kR vR;t1 þ tt ; 0 < kR < 1 with tt being a white noise. As for the parameters, we estimate the equation with GMM with quarterly data of 1994–2006 and obtain the following b t1 þ 0:65ðEt ptþ1 pt Þ þ 0:10pt þ 0:15 Y b t . The actual and fitted series are shown in Fig. 2. This rule b t ¼ 0:75 R specification:6 R 4 In an alternative version they consider contemporary rather than expected inflation. Here we follow their original version to capture the PBoC’s increasing concerns over inflation expectations. We have also estimated this equation with quarterly data of the past ten years by GMM and find that the estimates of i1 , i2 and i3 are 0.76, 0.94 and 0.47, respectively, close to the above values. In addition, we have tried to estimate an quantity rule considering contemporary inflation in addition to expected inflation and found that the coefficient of contemporary inflation is insignificant. 5 Such a rule can be considered as a combination of the rules of Clarida et al. (1998) and Smets and Wouters (2002). While the former consider inflation expectations, the latter highlight changes in inflation and output. One may also consider a long-run real interest rate in the rule and our simulation results below should not be affected as long as the long-run real rate is constant. 6 We use the percentage deviations of one-year base lending rate, CPI inflation and real GDP from their HP filter trends to measure their deviations from steady states. Xie and Luo (2002) find that the coefficients of output gap and expected inflation are 0.52 and 0.13, respectively. Our estimation seems to indicate that China’s monetary authority has paid more attention to inflation over time.
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W. Zhang / Journal of Macroeconomics 31 (2009) 473–484 0.20
0.15
ACTUAL FITTED
0.10
0.05
0.00
-0.05
-0.10
-0.15
-0.20 94
95
96
97
98
99
00
01
02
03
04
05
06
Fig. 2. Actual and simulated interest rate rules.
seems to have captured China’s interest rate rule better than the original Taylor rule without expectation and smoothing shown in Liu and Zhang (2007). The differential between the actual and the simulated series is less than 2% points most of the time. Measuring vR;t with the residuals from the above equation we obtain the estimate of kR ¼ 0:51. 3. A dynamic stochastic general equilibrium model 3.1. Households There exists a continuum of households, indexed by k, k 2 ð0; 1Þ. Household k maximizes the following objective function
Et
1 X
bi U k;tþi
i¼0
with
U k;t ¼
1c 1 1 M k;t 1 ðC k;t hC t1 Þ1r þ N1þg 1r 1 c Pt 1 þ g k;t
s.t.
Mk;t Bk;t M k;t1 Bk;t1 W k;t þ þ C k;t þ Ik;t ¼ þ þ Nk;t þ r ct K k;t þ Dk;t þ T k;t Pt P t Rt Pt Pt Pt
ð3Þ
The household enters period t with capital stock K k;t , nominal money balance M k;t1 and coupon bond Bk;t1 . Rt and r ct denote gross return of bond and rental rate of capital, while C k;t , Ik;t and N k;t denote real consumption, investment and labor supply in period t, respectively. The parameter h is referred to as habit parameter, so that hC t1 denotes the external habit stock with C t being aggregate consumption. r denotes the coefficient of relative risk aversion of households, c the inverse of the elasticity of money holdings with respect to interest rate. g denotes the inverse of the elasticity of work effort with respect to real wage. W k;t is nominal wage. Each household is assumed to own an equal share of firms and receives an aliquot share of real aggregate profits Dk;t . T k;t denotes the real net transfer from government in period t. Assuming complete contingent claims markets for labor income, and identical initial endowments of capital, bonds and money, all optimality conditions will be the same across households, except for labor supply and wage. We can, therefore, drop the index k for all variables but labor and wage. The first-order conditions (FOCs) with respect to C t and Bt read
bEt
ðC tþ1 hC t Þr Pt Rt ¼ 1; ðC t hC t1 Þr Ptþ1
ð4Þ
while the FOC with respect to M t reads
c Mt Rt 1 ¼ ðC t hC t1 Þr Rt Pt
ð5Þ
Given the capital stock accumulation equation
K tþ1 ¼ ð1 dÞK t þ It
ð6Þ
W. Zhang / Journal of Macroeconomics 31 (2009) 473–484
477
with d denoting depreciation rate, we have the following FOC with respect to investment and capital stock
1 ¼ bEt
r C t hC t1 ð1 d þ r ctþ1 Þ C tþ1 hC t
ð7Þ
In addition, the aggregate labor supply N t is assumed to be a CES function of differentiated labor provided by household k with the Dixit-Stiglitz elasticity of substitution among differentiated labor services being l(>1). The demand for differentiated labor then reads
Nk;t ¼
W k;t Wt
l
Nt
In each period all households can adjust their wages, but only 1 n fraction of households can adjust their wages optimally, with the rest n fraction of households setting their wages according to the rule7
W k;t ¼ V t1 W k;t1 t where V t ¼ PPt1 ¼ 1 þ pt . The household which can optimize the wage in period t then chooses the optimal wage W k;t to maximize the following objective function:8
Et
( ) 1 X U c ðt þ i; tÞ ðbnÞi ðW k;t X ti Nk;tþi;t Ptþi C tþi;t Þ þ UðC tþi;t ; Nk;tþi;t Þ ; Ptþi i¼0
where U c ðt þ i; tÞ denotes the marginal utility of consumption at t þ i of workers that optimize at t, and N k;tþi;t the hours worked at t þ i at the wage set at time t:
Nk;tþi;t ¼
l W k;t X ti Ntþi W tþi
with X ti ¼ 1, for i ¼ 0 and X ti ¼ V t V tþ1 V tþ2 ; . . . ; V tþi1 , for i P 1. The FOC with respect to W k;t then results in
2
W k;t
31þl1 g lð1þgÞ i 1þg X ti ðbnÞ N i¼0 tþi W tþi 6 l 7 ¼4 5 : l l 1 P1 i X ti X ti Et i¼0 ðbnÞ W tþi U ðt þ i; tÞN c tþi P tþi Et
P1
ð8Þ
The above equation shows that one can replace W k;t with W t since all households have the same optimal wage. Based on the above FOC and the following aggregate wage equation: 1
W t ¼ ½ð1 nÞðW t Þ1l þ nðV t1 W t1 Þ1l 1l ;
ð9Þ
one can then obtain the following linearized real wage equation:
^t -
U
with
^ t1 þ pt1 Þ ð1 þ bÞð1 þ glÞnpt þ ð1 þ glÞnbEt ð^ tþ1 þ ptþ1 Þ ¼ ð1 þ glÞnðh i r b t1 Þ bt C bt þ þ ð1 bnÞð1 nÞ g N ðC 1h
1 -t ¼ WPtt and U ¼ ð1þbÞð1þglÞnþð1bnÞð1nÞ .
3.2. Firms 3.2.1. Final goods Final good Y t (subject to perfect competition) is assumed to be a CES function of the intermediate goods Y j;t produced by a continuum of firms indexed by j 2 ð0; 1Þ, with the elasticity of substitution between varieties of intermediate goods being h. Let Pj;t denote the price of intermediate goods j at time t, the demand for intermediate goods j then reads
Y j;t ¼
h Pj;t Yt Pt
7 There are also economists assuming that this group of households set wage according to last-period wage inflation or a combination of last-period price and wage inflation rate. Here we follow Sbordone (2006). assuming households that can not set wage optimally set their wages according to last-period price inflation. This assumption seems to capture China’s situation better than others because China’s officially released wage growth data reflect only the wage dynamics of a small part of employees. Migrant workers’ salaries, for example, are not well shown in the existing data. 8 Following Sbordone (2006), we assume the household maximizes the expected stream of discounted utility from the new wage.
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3.2.2. Intermediate goods Intermediate goods Y j (subject to monopolistic competition) is assumed to be produced with the following production function: a Y jt ¼ Z t Naj;t K 1 j;t ;
0 < a < 1;
where N j;t and K j;t denote labor and capital used for producing Y j;t . Z t denotes technology shock subject to the following path
ln Z t ¼ j ln Z þ ð1 jÞ ln Z t1 þ et ; with Z being the mean of Z t and
0 < j < 1;
ð10Þ
et a white noise. The FOCs with respect to Nj;t and K j;t are
a1 N -t ¼ aut Z t j;t K j;t c 1a 1 -t a rt ut ¼ Zt a 1a
ð11Þ ð12Þ
where ut denotes the real marginal cost. 3.2.3. Price setting Here we follow Christiano et al. (2005) and Smets and Wouters (2002) assuming that in each period all firms can adjust their prices, but only 1 x fraction of firms are allowed to adjust their prices optimally, and the remaining x fraction adjust their prices as P j;t ¼ V t1 Pj;t1 . Firm j which can re-optimize its price at t chooses the optimal price Pj;t to maximize the present value of its real profits. The optimal price then reads
P P tþi h h i Et 1 Pj;t h i¼0 x Ktþi utþi ð Pt Þ Y tþi X ti ¼ P1 i h 1 Et i¼0 x Ktþi utþi ðPtþi Þh1 Y tþi X ti1h Pt
ð13Þ
Pt
where Ktþi denotes the stochastic discount factor bi ð Ctþit Þr . One can drop the index j in P j;t as the optimal price is the same for each firm j. From C
Y j;t ¼
Pj;t Pt
h
Yt
ð14Þ
and assuming symmetric equilibrium with respect to intermediate goods, we know that the aggregate price at t is 1
Pt ¼ ½ð1 xÞðPt Þ1h þ xðV t1 Pt1 Þ1h 1h :
ð15Þ
From Eqs. (13) and (15) we can derive the following linearized Phillips curve:
pt ¼
x 1 þ bx
2
pt1 þ
2 x bx þ bx2 Et ptþ1 þ ð1 xÞð1 bxÞu^t : 1 þ bx2
ð16Þ
4. Policy analysis 4.1. Linearized equations One can calculate the steady states of the variables of interest from the series of FOC conditions derived above. The steady state of Rt , for example, is R ¼ 1b according to Eq. (4). Assuming general equilibrium and employing the quantitative monetary policy rule, one can then log-linearize relevant equations around the steady states of variables:
bt ¼ C
h b 1 b tþ1 1 h ð R b t Et ptþ1 Þ C t1 þ Et C 1þh 1þh ð1 þ hÞr
ð17Þ
b t1 þ Et C b t ¼ hC b tþ1 1 h Et ^r c C tþ1
ð18Þ
b t þ ð1 aÞðh 1Þ bI t b t ¼ 1 þ aðh 1Þ C Y h h
ð19Þ
b t þ ð1 aÞ K b t þ aN bt bt ¼ Z Y
ð20Þ
r
W. Zhang / Journal of Macroeconomics 31 (2009) 473–484
b tþ1 ¼ ð1 dÞ K b t þ dbI t K
pt ¼ ^t -
U
x 1 þ bx2
pt1 þ
2 x bx þ bx2 Et ptþ1 þ ð1 xÞð1 bxÞu^t 1 þ bx2
^ t1 þ pt1 Þ ð1 þ bÞð1 þ glÞnpt þ ð1 þ glÞnbEt ð^ tþ1 þ ptþ1 Þ ¼ ð1 þ glÞnðh i b t hC b t1 Þ b t þ r ðC þ ð1 bnÞð1 nÞ g N 1h
^t ¼ m
r ð1 hÞc
bt C
rh b 1b C t1 R ð1 hÞc c t
479
ð21Þ ð22Þ
ð23Þ
ð24Þ
^ t1 pt þ mt ^t ¼ m m
ð25Þ
mt ¼ i1 mt1 i2 Et ptþ1 i3 Yb t þ vm;t
ð26Þ
b t ¼ ð1 jÞ Z b t1 þ et Z
ð27Þ
bt ^ t þ ð1 aÞ^r ct Z ^ ¼ au
ð28Þ
b t ¼ ^r c þ K bt ^t N t
ð29Þ
In the case of interest rate rule, one then replaces Eqs. (24)–(26) with Eq. (2). 4.2. Parameterization As is known, it is quite challenging to parameterize a macro model for China because (a) China’s data are relatively scarce and (b) China has been shifting from a planning economy to a market one, suggesting possible structural changes in the past decade. In view of this problem, economists have usually chosen to estimate single equations rather than a simultaneous system for China. In the research below we will follow this line of literature, estimating some of the parameters with available data and assigning values to others according to related works in the literature. Equations will be estimated separately for variable sample periods according to data availability.9 Following Walsh (2003), we set r ¼ 2. Estimating Eq. (18) with data of 1993–2005 by GMM we obtain h ¼ 0:61 (t-st. 110.24).10 a and d are set at 0.4 and 0.04, respectively, following the estimates of He et al. (2007). Setting a ¼ 0:4 and estimating (19) with data of 1993–2007 one can figure out h ¼ 4:61.11 The average (annual) nominal interest rate is 0.08 from 1978 to 2005, which might justify a quarterly rate of 0.02 in the steady state and b ¼ 0:98 since R ¼ 1b. The GMM estimation of Eq. (22) with data of 1995 to 2005 shows that x ¼ 0:84 (t-st. 24.10). Our estimation of the Phillips curve looks close to that of Funke (2005) who estimates the new Keynesian Phillips curve for China with various methodologies. Following the estimates of Liu (2007) we set g ¼ 6:16, n ¼ 0:6 and l ¼ 2. The estimation of Eq. (24) with data of 1992-2006 shows that c is 3.13 (t-st. 1.92).12 Using total factor productivity (TFP) data from He and Zhang (2008) we obtain the estimate of j ¼ 0:5.13 The main parameters are summarized in Table 1. 4.3. Simulations Next, we will solve the above linear dynamic system by methods of undetermined coefficients with the algorithm developed by Uhlig (1999). Uhlig (1999) divides all variables into three categories: endogenous state variables Ut , jump variables Wt and exogenous stochastic processes Zt , with Ut , Wt and Zt being vectors of a1 , a2 and a3 elements, respectively. Then the linearized system can be arranged as follows:
9
Estimations are undertaken with quarterly data. When quarterly data are not available, we convert annual data into quarterly data with Eviews. Consumption in this equation is proxied with retail sales as consumption data from national account are annual. Consumption gap is measured with percentage deviation of actual retail sales from its HP-filter trend. Return to capital is proxied by the marginal product of capital estimated by He et al. (2007). 11 Output gap, consumption and investment gaps are measured with the percentage deviations of the actual values of output, consumption (national account data of total consumption) and investment (gross capital formation) from their HP-filter trends. 12 Real money gap is measured by the percentage deviation of real broad money from its HP-filter trend. 13 While He et al. (2007) estimate TFP growth for China with the Cobb-Douglas production with national data, He and Zhang (2008) estimate TFP growth with the Malmquist index using panel data. The latter seems to outperform the former since the production function approach assumes production is always conducted on the frontier and may overestimate TFP growth. 10
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Table 1 Parameterization h
r
a
x
b
n
g
l
h
c
j
d
0.61
2.0
0.40
0.84
0.98
0.60
6.16
2.0
4.61
3.13
0.5
0.04
0.6
Output
Percent Deviation from Steady State
0.5
Inflation
0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -1
0
1
2
3
4
5
6
7
8
5
6
7
8
Years after Shock
Percent Deviation from Steady State
1
Output
0.8
0.6
0.4
0.2
0
-0.2 Inflation -0.4 -1
0
1
2
3
4
Years after Shock
0.15 Inflation
Percent Deviation from Steady State
0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 -0.25 -0.3
Output -0.35 -1
0
1
2
3
4
5
6
7
Years after Shock
Fig. 3. Impulse responses to shocks with quantity rule.
8
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W. Zhang / Journal of Macroeconomics 31 (2009) 473–484
0 ¼ AUt þ BUt1 þ C Wt þ DZt ;
ð30Þ
0 ¼ Et ½F Utþ1 þ GUt þ HUt1 þ J Wtþ1 þ K Wt þ LZtþ1 þ MZt
ð31Þ
Ztþ1 ¼ NZt þ z;tþ1 ;
ð32Þ
Et ½z;tþ1 ¼ 0;
where C is assumed to be of size a4 a2 , a4 P a2 and of rank a2 , F is of size ða1 þ a2 a4 Þ a1 . N is assumed to have only stable eigenvalues. Then one may express Ut and Wt as
Percent Deviation from Steady State
1
0.5
0
-0.5
-1
-1.5 -1
Inflation Output 0
1
2
3
4
5
6
7
8
5
6
7
8
5
6
7
8
Years after Shock
Percent Deviation from Steady State
1.2
1
Output
0.8
0.6
0.4
0.2
0 Inflation -0.2 -1
0
1
2
3
4
Years after Shock
Percent Deviation from Steady State
0.05 0 Inflation -0.05 -0.1 -0.15 -0.2 -0.25 -0.3 -0.35
Output
-1
0
1
2
3
4
Years after Shock Fig. 4. Impulse responses with interest rate rule.
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W. Zhang / Journal of Macroeconomics 31 (2009) 473–484
Table 2 Response coefficients of inflation to shocks
Quantity rule Price rule
Monetary policy
Technology
Real wage
0.264 0.840
0.192 0.123
0.019 0.002
Monetary policy
Technology
Real wage
0.584 1.423
0.963 0.961
0.328 0.300
Table 3 Response coefficients of output to shocks
Quantity rule Price rule
Ut ¼ S1 Ut1 þ S2 Zt Wt ¼ S3 Ut1 þ S4 Zt :
ð33Þ ð34Þ
We will explore how the two policy rules differ from each other from two perspectives: (a) which policy instrument is more powerful assuming a shock to each of them separately, and (b) under which policy rule the economy experiences less fluctuations assuming the economy faces shocks of other main economic variables than monetary policy since less fluctuations in inflation and output imply a lower loss to the central bank.14 The impulse responses of inflation and output gap to b t and real wage are presented in Fig. 3.15 shocks in money growth, technology Z The upper panel shows that a positive shock from nominal money growth will lead to a half percentage point increase in inflation in the first two quarters, together with a 0.6% point upturn in output, followed by a slide in GDP by about 0.3% point in the second year. This suggests that although money can lead to a temporary expansion in GDP, it may result in an output reduction in the medium term. The middle panel shows that output will increase by over 0.9% point in the first year following a positive technology shock, while inflation may decline by 0.3% point in the meantime. Inflation declines because supply increases due to productivity improvement. In the lower panel we show the reactions of inflation and output to a percentage point deviation of real wage from its steady state. Clearly, while inflation increases by 0.1% point, output may decrease by 0.33% point. The impulse responses of output and inflation to money growth, technology and real wage when interest rate rather than money supply is employed as policy instrument are shown in Fig. 4. Comparing Fig. 3 with Fig. 4, one may have the following findings: (a) the price instrument seems to be more powerful than the quantity instrument, and (b) facing similar shocks from main variables in the economy, inflation and output may experience less fluctuations when the price rule rather than the quantity rule is in operation. Point (a) can be seen by comparing the upper panels of the two figures. While a shock in interest rate may lead to decreases of inflation and output of between one and 1.5% points, a shock in money growth leads to increases in inflation and output of about 0.5–0.6% point. This can also be partly reflected by the response coefficients of inflation and output gap to monetary policy (relevant elements in S2 and S4 ). The response coefficients of inflation to shocks in money growth and interest rate are 0.264 and 0.840, respectively (Table 2). Meanwhile, the response coefficients of output gap to shocks in money growth and interest rate are 0.584 and 1.423, respectively (Table 3). In fact, observers of China’s economy have argued that impacts of interest rate on the economy have been underestimated as small-and-medium size and private enterprizes are much less likely to get loans from banks than large-size and state-owned enterprizes (SOEs) when monetary tightening occurs. In order to get the same amount of loans as SOEs the former may have to pay extra costs other than interest. Point (b) can be seen by comparing the middle and lower panels of Figs. 3 and 4. Clearly, while a shock in technology may lead to an increase in output of similar size in both figures, inflation experiences less fluctuations in Fig. 4. Moreover, both inflation and output converge to their steady states much faster in Fig. 4. We get similar findings with respect to a shock in real wage. While output decreases by about 0.33% point in Fig. 3, it slides by less than 0.3% point in Fig. 4. Likewise, inflation experiences much less fluctuations in Fig. 4. Moreover, both inflation and output converge to their steady states faster in Fig. 4 than in Fig. 3. One can also see this point from the response coefficients of inflation and output to technology and real wage under different policy rules. As shown in Tables 2 and 3, the response coefficients of inflation and output to shocks in technology and real wage are lower in magnitude under the price rule than under the quantity rule. Some economists argue that China should have been more aggressive in interest rate policy. Take the recent episode of monetary policy as example, although the PBoC has raised interest rate gradually, real interest rate still remains quite low and even negative. The inactive policy stance of the authority has been argued by some commentators to be partly responsible for upsurges (or bubbles) in stock prices since 2006. Moreover, inflation remains elevated. Artificially low costs of cap-
14
Woodford (2003) shows the links between quadratic loss functions of inflation and output and households’ objective functions. One may also see the reactions of inflation and output to shocks in other variables than real wage and technology. We have also simulated shocks for some other variables, inflation for example, and find that the main findings remain essentially unchanged. 15
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Percent Deviation from Steady State
1.2
1 Output 0.8
0.6
0.4
0.2
0 Inflation -0.2 -1
0
1
2
3
4
5
6
7
8
5
6
7
8
Years after Shock
Percent Deviation from Steady State
0.1
0.05
0 Inflation -0.05
-0.1
-0.15
-0.2
-0.25 -1
Output 0 1
2
3
4
Years after Shock
Fig. 5. Impulse responses with more aggressive interest rate rule.
ital have not only led to wastes of resources but may have fueled volatility of economy. In fact, Taylor (1993) sets the coefficient of inflation at above one and that of output gap at 0.5. Taylor (1999) further raises the coefficient of output gap to unity. In the interest rate rule employed above, we have used the estimated coefficients of inflation and output gap. Next, we will conduct an counterfactual experiment by assuming that interest rate reacts more aggressively to inflation and output gap. Namely, we raise the coefficient of expected inflation ðk2 Þ to 1.0 to see how inflation and output may have responded to various shocks in the economy. The simulation results are shown in Fig. 5. Comparing Fig. 4 with Fig. 5, one finds that the economy would have experienced less fluctuations if interest rate had been more aggressive. For example, while output declines by about 0.3% point in the presence of a wage shock in Fig. 4, it declines by less than 0.25% point in Fig. 5. Inflation and output also fluctuate less in the wake of a technology shock in Fig. 5 than in Fig. 4. Looking at the response coefficients of inflation and output to technology and real wage provides us clearer evidence. For example, while the response coefficient of output gap to real wage is 0.300 in Fig. 4, it is 0.242 in Fig. 5. 5. Conclusions Monetary policy with money supply as instrument seems to become more difficult to conduct in China than before, as money multiplier and velocity have been increasing noticeably and the linkage between money supply and inflation becomes weaker over time. Experiments in a DSGE model based on data in the past decade indicate that effects of a price rule on the economy seem to have become more significant than those of a quantity rule. Moreover, the economy may experience less fluctuations in the presence of shocks from main macroeconomic variables when the price rule is employed to manage the macroeconomy. The findings seem to favor the government’s intention of liberalizing interest rates and making a more active use of the price instrument in recent years as the economy becomes more market-oriented.
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