1Money demand in China and time-varying cointegration☆

2Haomiao ZUO a,⁎, Sung Y. PARK b

3a The Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, Fujian 361005, China4b Department of Economics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

5

7a r t i c l e i n f o 8a b s t r a c t

9Article history:10Received 24 October 201011Received in revised form 31 March 201112Accepted 8 April 201113Available online xxxx

14Many studies analyze the money demand using a (fixed coefficient) cointegrating regression15model, which may not be appropriate to deal with the money demand of a transition economy16like China. This paper investigates this issue using a time-varying cointegration approach based17on the quarterly data from 1996 to 2009. We find some interesting results: (i) the estimates of18the income elasticities are between 0.60 and 0.75, which are comparable with the previous19studies; (ii) the estimated interest rate elasticity supports the argument that the overall effect20of the interest rate on the money holding is weak although there are some mild evidences that21it has been strengthened in recent years; (iii) the substitution effect of equity asset dominates22the wealth effect, especially, during the bullish market period. Our result is robust to the23alternative choices of the scale or opportunity cost variables and shows that omission of the24stock prices in the money demand function would possibly yield a misspecification problem.25© 2011 Elsevier Inc. All rights reserved.

26JEL classification:27E4128C512930Keywords:31Money demand32Time-varying coefficient33Cointegration34Canonical cointegration regression35Chinese economy 3637

38391. Introduction

40Traditionally, the long-run money demand is of great concern to both economists and policy makers. The income elasticity41measures the speed of monetary expansion in the long-run while the interest rate elasticity represents the sensitivity of42household's willingness to hold money with respect to the change of monetary policy. Moreover, the central bank's effort for43controlling money supply and selecting valid policy instruments crucially depends on the relationship between the quantity of44money and some key indicators of real economy. Numerous efforts have been made to investigate the above issues for both45developed and developing countries in the literature, for examples, Judd and Scadding (1982), Ericsson (1998) and Sriram (2001).46Equipped with a cointegration approach introduced by Engle and Granger (1987) and further developed by Johansen (1988) and47Johansen and Juselius (1990), many recent studies perform cointegration tests to find an evidence of the long-run stability of the48money demand function. Applications along this line include Hafer and Jansen (1991), Hoffman and Rasche (1991), McNown and49Wallace (1992) for the U.S.; Bahmani-Oskooee and Bohl (2000) for Germany; Adam (1991), Johansen (1992) for the U.K.; Muscatelli50and Spinelli (2000) for Italy; Bahmani-Oskooee and Shabsigh (1996) and Bahmani-Oskooee (2001) for Japan, amongmany others. A51general consensus reached by these studies is that both the broad money (M2) and narrow money (M1) are cointegrated with52disposable incomeand interest rates aswell as someother variables. In addition to the above studies for thedeveloped countries, there53are also a few studies investigating the money demand in the developing economies, such as Baharumshah (2004) for Malaysia;

China Economic Review xxx (2011) xxx–xxx

☆ We thank an anonymous referee and the editor, whose suggestions have led to substantial improvements of the paper. We also thank Ying Fang, Ming Lin,Linlin Niu, Guochang Zhao and Tingguo Zheng and seminar participants at The Wang Yanan Institute for Economic Studies at Xiamen University, July 14th, 2010and participants at the 2010 Chinese Economists Society Annual Conference at Xiamen University, China, June 19th for suggestions and comments. Haomiao Zuogratefully acknowledges financial support from National Natural Science Foundation of China (No. 71001087).⁎ Corresponding author. Tel.: +852 2609 8001; fax: +852 2603 5805.

E-mail addresses: zuohaomiao@gmail.com (H. Zuo), sungpark@cuhk.edu.hk (S.Y. Park).

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54Thornton (1996) for Mexico; Bahmani-Oskooee (1996) for Iran, among many others. In particular, the developing economies are55significantly different in terms of economic openness, financial market maturity andmacroeconomic environment, which poses new56challenges inmodeling and estimating themoney demand function. For example, the issue of stability of the long-runmoney demand57is challenging if a country has institutional changes, which is exactly the case of China.1

58Since Chinese economy is transforming from a centrally planned economy to a market oriented one, the financial system as59well as monetary policy are under transition (He, 2005; Prasad & Rajan, 2006). As pointed out by Prasad and Rajan (2006), the60China's economic reform beginning in late 1970s took incremental and experimental processes, particularly, in the financial sector.61The reform has been processed from local and small-scaled experiments to global and large-scaled experiments. This is if the result62of the experiments turned out to be satisfactory, then they have been implemented elsewhere.2 Such changes have the common63feature that the process is smooth and gradual without distinct or sharp regime shifts although the reforms themselves are very64fundamental. Even though the recent economic growth of China is remarkable, China remains as a developing economy, and,65especially, the financial market is still under-developed. For instance, the bondmarket, in particular, the corporate bondmarket, is66relatively small and inactive (Hansan, Wachtel, & Zhou, 2009). Under the strict regulation of the government, only large state67owned companies are allowed to issue bonds with high credit rankings similar to those of the government bond. This results in a68relatively low and unattractive nominal interest. Moreover, there are no financial futures and derivatives market in China. As far as69the reforms of the financial system are concerned, three important aspects of financial institutional changes are: (i) the reform of70the banking system; (ii) the exchange rate reform; and (iii) the rapid development of the capital market. The below we briefly71summarize these three important aspects.72First, since the Central Bank Law and the Commercial Bank Law were introduced in 1995, the People's Bank of China (PBC) has73been authorized to implement monetary policy although its freedom and independence have been limited. The reform of banking74system has been started from 1997 with carving out of non-performing loans (NPLs) and injecting more capital for four largest75state-owned commercial banks (SOCBs) (García-Herrero, Gavilá, & Santabárbara, 2009). Moreover, the partial privatization and76minority foreign ownership were introduced to improve the efficiency of the banking system (Berger, Hasan, & Zhou, 2009; Lin &77Zhang, 2009; Jia, 2009). By doing these, more andmore city commercial banks began to achieve better banking performance (Ferri,782009). Since 2004, the commercial banks were not restricted by the ceiling of the lending rates or the floor of deposit rates79although the floor of lending rates and the ceiling of deposit rates were not yet relaxed. Moreover, the interbank market and the80bondmarket rates had been deregulated since 1996, and the Shanghai Interbank Offered Rate (SHIBOR)was introduced in 2007 to81serve as the benchmark interest rate in the Chinese money market. All of these indicate that interest rate liberalization is on the82way although the process is rather slow (Koivu, 2009).83Second, the (market-oriented) floating exchange rate regime pegging to the basket of multiple currencies was introduced in842005. This reform allowed the exchange rate to be more flexible and more sensitive to market conditions.85Third, the most significant change in the financial sector is the rapid development of the stock market. The market86capitalizationwas 1.8 trillion RMB ($ 0.22 trillion USD)with only 3.4million investor accounts at the beginning of 1998. At the end87of 2008, the investor accounts grew to over 100millionswith total market capitalization 12 trillion RMB ($ 1.8 trillion USD). Due to88the financial under-development and relatively attractive returns from the stock market, it served as the main alternative choice89for domestic investors to the saving deposits. Traditionally, the saving deposits are the main investment channels for domestic90investors in China because of financial system repression (Prasad & Rajan, 2006). In total, household deposits reached 24.7 trillion91in RMB (or 3.6 trillion USD) at the end of the first quarter of 2009, whichwere very large amount compare to the annual GDP that is92around 30.1 trillion in RMB ($ 4.4 trillion USD in 2008). Not only the scale of savings is large, but also its proportion to the93disposable income is very high. Chamon and Prasad (2008) estimate the saving ratio (the ratio of savings to disposable income) for94urban households and report that it increased from 17% in 1995 to 24% in 2005. Although the saving ratio is high, the low or even95negative real interest rate during those periods generates quite low returns to the savings. Hence, households have strong96incentives to withdraw their money from the banks and invest them in the stock market. As a result, large amount of money tends97to transfer from the banks to the stockmarket during the bull market periods. Since the saving deposits aremeasured based on the98usual category of the broad money (M2) whereas money accounts in the stock market are not, there is clearly the substitution99effect for the broad money demand. Wu (2009) shows that share of equity assets in household holdings of financial assets varies100with the stock market cycles. During the recent two bullish markets in 2001 and 2007, these ratios were about 15% and 20%,101respectively. However, during the bearish market in 2005, it dropped to slightly about 5%. As Wu (2009) pointed out, the102expanding investment possibility is likely to influence household investors' decision in choosing between money and other103financial assets, and therefore, affecting the aggregate money demand as a whole.104Many papers study China's money demand in the process of economic transition and financial reform. The list includes Hafer105and Kutan (1994), Huang (1994), Qin (1994), Chen (1997), and Bahmani-Oskooee andWang (2007). Hafer and Kutan (1994) find106the existence of a long-run stable relationship for nominal money demand. In the broad money (M2) case, the elasticities of107income and GDP deflator are 1.33 and 1.52, respectively. This finding indicates that the velocity of money decreases as income108rises. This declining velocity of money is also observed in other developing countries (Bordo & Jonung, 1987). Furthermore, they109report that the interest rate elasticities are 0.13 and 0.15 for M0 (currency in circulation) and M2, respectively. In another study,110Huang (1994) reports that the income and deflator elasticities forM2 (nominal) are 2.12 and 1.56, respectively, while Chen (1997)111shows that the income elasticities for M0 and M2 are 1.50 and 1.93, respectively. Furthermore, Bahmani-Oskooee and Wang

1 Hansan, Wachtel, and Zhou (2009) analyze three aspects of institutional changes in China: financial development, legal institution and political system.2 Prasad and Rajan (2006) provide the advantages and potential limitations of this approach. Lau, Qian, and Roland (2001) label this as a dual-track approach.

2 H. Zuo, S.Y. Park / China Economic Review xxx (2011) xxx–xxx

Please cite this article as: Zuo, H., & Park, S.Y., Money demand in China and time-varying cointegration, China Economic Review(2011), doi:10.1016/j.chieco.2011.04.001

112(2007) show that the long-run income elasticities for M0 and M2 are 1.28 and 1.69 and the interest rate elasticities are−4.52 and113−1.54, respectively. However, their estimates of the interest rate elasticity for M2, and foreign interest rate and nominal effective114exchange rate elasticities for both M1 and M2 are not statistically significant. Table 1 provides a survey of some recent studies on115the money demand in China.116Although the above studies provide useful information about the income and interest rate elasticities, their results are not quite117consistent. Even some of the estimated interest rate elasticities turn out to have different signs. This is not surprising because China118experiences a gradual institutional transition. Under such situation the above models could confront a (smooth) structure change119problem. Since the above models are based on the assumption of the parameter constancy in the regression function, the120magnitude or sign of the estimated parameters could be dramatically changed depending on the choice of particular samples. In121order to detect the parameter inconsistency problem, Bahmani-Oskooee and Wang (2007) employ CUSUM and CUSUMSQ tests122proposed by Brown, Durbin, and Evans (1975) in combination with cointegration analysis, and they find that M1 money demand123function is stable but this is not the case for M2. Hafer and Kutan (1994) take care of the parameter inconstancy by introducing124time dummy variables. However, Hansen (1992) points out that a stability test based upon a priori specified break date is125problematic since an exogenous date choice is conditional on the data, which invalidates the conventional critical values. Thus, he126proposes a new testing procedure to overcome this problem. Even though the above mentioned tests such as CUSUM, CUSUMSQ127and Hansen (1992)'s tests can be quite helpful in detecting the date of the structural change, these tests do not provide any128guidance of further steps under alternative hypothesis. Unfortunately, for an economy under the gradual institutional transition129like China, the parameter inconstancy due to the rapid development of financial institutions and markets is a stylized fact rather130than merely assumption. Indeed, in addition to Bahmani-Oskooee and Wang (2007) and many others, Baharumshah, Mohd, and131Yol (2009) also argues that the money demand function for M2 is unstable in China unless taking stock prices into account.132In this paper, a smooth time-varying cointegrating regression approach is considered to take care of the parameter inconstancy133problem in China money demand function. The traditional cointegration method is based on the assumption of the constant134cointegrating vectors. This assumption is partly responsible for the empirical failure of the traditional cointegration approach in135many cases as pointed by Park and Hahn (1999). For example, the traditional cointegration test cannot reject the null of no136cointegrating relationship among variables even though there exists a time-varying long-run relationship. To handle this problem,137Park and Hahn (1999) propose the smooth time-varying coefficient cointegrating regression method and prove that the138estimators of the time-varying coefficients (TVC) are consistent, asymptotically efficient and normally distributed. The main139advantages of our study include: (i) we do not need assumptions on possible dates of structural breaks, which is particularly140applicable in China where reform is fundamental yet gradual with few sharp changes so that choices of break point date could be141arbitrary; (ii) while the traditional approach splits the whole sample into multiple sub-samples, we utilize the information in the

Table 1t1:1

A selective survey of some recent studies on money demand in China.t1:2

t1:3 Author(year) Sample(F) Scale variable Moneyaggregates

Interest rates Other variables Method Stability test

t1:4 Yi (1993) 52–89(a) realNI/pop(0.7–0.9 ) realM2/pop log(UP)(0.8–0.9) GDt1:5 Hafer and Kutan

(1994)52–88(a) realNI(1.13) M0 I1(0.13) NIdef(2.48)

t1:6 52–88(a) realNI(1.33) M2 I1(0.15) NIdef(1.52)t1:7 Qin (1994) 78.1–92.4(q) realGDP(1.00) M0/GDPdef real

I1(−0.21–0.1)RSL , IM (−1.63–1.14) ADL,EG

t1:8 52–91(a) realNI(1.00) M0/Nidef real I1(0.01) RSL , IM (−1.65) ADL,EGt1:9 Chen(1997) 51–91(a) realNI(1.5) M0/RPI EI JJ Hansent1:10 51–91(a) realNI(1.93) M2/RPI EI JJ Hansent1:11 Deng and Liu (1999) 80.1–94.12 (m) GDP/RPI(1.29) M1/RPI real I3(−0.12) EI(−0.34) EG,ECMt1:12 Bahmani-Oskooee

and Wang(2007)83.1–02.4(q) realGDP(1.28) M1/CPI D (−4.52)

UCD (0.22)NEER( 1.181) ARDL,EG CUSUM,CUSUMSQ

t1:13 83.1–02.4(q) realGDP(1.69) M2/CPI D (−1.54)UCD (0.77)

NEER( 1.181) ARDL,EG CUSUM,CUSUMSQ

t1:14 Mehrotra(2008) 94.1–05.3(q) realGDP(1.73) M2/CPI NEER( 1.181),EI(0.967) JJt1:15 Wu (2009) 94.1–08.1(q) realGDP(0.74) M2/CPI FI(−0.082) Inf(−2.81) J, ADL,ECM RLSt1:16 Baharumshah, Mohd,

and Yol (2009)90.4–05.3(q) GDP/CPI(0.65) M2/CPI Y(−0.02) log(SP/CPI) (0.29) JJ CUSUM,CUSUMSQ

t1:17 Baharumshah, Mohd,and Masih (2009)

90.4–07.2 (q) GDP/CPI(1.06) M2/CPI F(−0.06) log(SP/CPI)(0.15),Inf(−0.059)

ARDL Hansen, CUSUM,CUSUMSQ

Note: All the scale variables and money aggregates are in logarithm forms and the values reported after the scale variables, money aggregates, interest rates andother variables are corresponding estimates of coefficients. Sample period: F: sample frequency, a, q, and m are short for annual, quarterly, and monthly,respectively. Scale variables: NI: national income, Sales: retail sales, GDP: gross domestic product, pop: population at the end of the year. Price level variables: OPI:official general retail price index, CPI: consumer price index, RPI: retail price index, GDPdef: GDP deflator, Nidef: National income deflator. Money aggregates: M0:currency in circulation, M1: narrowmoney, M2: broad money. Interest rate variables: I1: one year saving deposit rate, real I1: one year deposit savings rate minusinflation, real I3: 3-year time deposit rate minus inflation, D: deposit rate, UCD: US 3-month CD rate, FI: One-year time deposit rate for USD in China, Y: yield on UStreasury, F: foreign (US) money market rate. Other variables: UP: percentage of the urban population, SP: stock price. Inf: inflation, EI: expected inflation, NEER:nominal effective exchange rate, RSL: annual rate of savings/loan ratio, IM: monetization index. Econometric methods: GD: general differencing approach (Q1 Box-Jenkins, 1976), J: Johansen (1988), JJ: Johansen and Juselius (1990), ADL(ARDL): autoregressive distributed lag, ECM: error correction model, EG: Engle andGranger, RLS: recursive least squares. Stability test: Hansen: Hansen (1992)'s test, CUSUM: cumulative sum statistics, Brown et al. (1975), CUSUMSQ: cumulativesum of square statistics, Brown et al. (1975).t1:18

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142full sample instead of part of it. This has an advantage especially in case of China in which the sample size for time-series data is143usually small; and (iii) when a time-varying cointegrating relationship is detected, we can still interpret it as a long-run144relationship where the coefficients may help us to learn more about mechanism of the economy behind it.3

145The organization of the paper is as follows. Section 2 provides a brief explanation of the money demand model, the estimation146method and cointegration test statistics. The results of the estimation of TVC cointegrating regression along with the fixed147coefficient (FC) cointegrating regressions are reported in Section 3. Finally, Section 4 offers some concluding remarks.

1482. The model

149The traditional long-run money demand function usually takes the following form

MP

= f S;OCð Þ; ð1Þ150151152where M/P represents the demand for real money balances defined by the ratio of the selected monetary aggregate in nominal153termsM and the overall price index P, f(⋅, ⋅) denotes a function that usually takes log-linear (or semi-log-linear) form, S denotes a154scale variable reflecting the economic activity or transactions need, and OC is a variable for the opportunity cost.155For monetary aggregates, we choose the broadmoney (M2) since the People's Bank of China (PBC) considers it as an important156monetary policy instrument and announces its annual target for the growth rate of M2 until 2008. For the scale variable S, real157gross domestic product (GDP) is usually chosen as a proxy, and we also use real industrial value added (IVA) as an alternative158measure following Koivu (2009). As for opportunity cost variables, Sriram (2001) argues that institutional changes, regulation159policies as well as development of the financial markets deserve special attention. In practice, the domestic interest, foreign160interest, exchange and inflation rates are the most frequently used variables for the opportunity cost. Since China has been under161strict capital flow regulation, which include, for examples, a restriction on holding foreign currencies and a pegged nominal162exchange rate systemwith respect to U.S. dollar from 1995 through 2005, we neither introduce foreign interest rates nor exchange163rates as determinants of the money demand. Another important opportunity cost variable is the real interest rate obtained by164subtracting annual expected inflation from nominal saving deposit rate. Since saving deposit rate is set by the PBC and rarely165changes during certain periods, a large portion of variation in real interest rate is attributed to changes in inflation rate. For this166reason we also consider quarterly expected inflation rate as another measure of the opportunity cost since it could serve as the167proxy of yield on real assets.168Due to the rapid development of the stock market in recent years, a few studies introduced the stock prices as an additional169determinant of the demand for real money (Choudhry, 1996; Baharumshah, 2004; McCornac, 1991; Baharumshah, Mohd, & Yol,1702009). Using the postwar data of U.S., Reynard (2004) concludes that further studies should pay more attention to the financial171market development. Also, Baharumshah, Mohd, and Yol (2009) investigate the role of the stock prices to the money demand in172China. They show empirically that real stock prices have a positive effect on the money demand in the long-run whereas its short173run influence is negative. In view of these findings, we extend the traditional money demand function by including the stock174prices:

MP

= f S;OC; SPð Þ; ð2Þ175176177where SP denotes real stock prices.178Based on the previous studies, we consider the following linear cointegrating regression equation for themoney demand

dmj = π + α1ymj + α2rmj + α3spmj + εm + εmj; m = 1;2;3;4; j = 1;2; ⋯; T; ð3Þ179180181where dmj denotes demand for real money balance, ymj is real GDP or real IVA, rmj is real domestic interest rate, or it can be replaced182by expected inflation imj, spmj denotes real stock prices, εm is the seasonal dummies, εmj denotes the error term, and subscripts m183and j represent the quarter and year, respectively. In the above Eq. (3), α2 is the interest rate semi-elasticity since the interest rate184is measured in percentage (we use the term “interest rate elasticity” or “interest rate semi-elasticity” interchangeably unless185indicated), and α1 and α3 are the income and stock price elasticities, respectively.186According to Sriram (2001), α1 is likely to be positive to reflect the transaction or the income effect and α2 is positive for own187rate of interest or negative for the opportunity cost variable. In our case, the sign of α2 deserves more discussions. Traditionally,188money refers to cash and cash equivalents, and the interest rate is the proxy of the opportunity cost. For example, Goldfeld and189Sichel (1990) study the demand for M1 (currency plus checkable deposits) in the U.S. For narrowmoney (M1), the explicit yield is190equal to zero. Goldfeld and Sichel (1990) mention that, under this circumstance, the saving deposit rate or some short term191interest rates are proxies of opportunity cost. However, for the saving deposits, the saving rates are not variables for the192opportunity cost but own rate of interest. High interest rates would provide incentives for household to put more money in the

3 Chang and Martinez-Chombo (2003) apply this method to study the electricity demand of residential, commercial and industrial sectors in Mexico. Pen(2005) evaluates the hypothesis of stochastic convergence among five industrial countries from 1870 to 1994 and documents evidence for the existence of time-varying cointegration relationship. Moreover, Park and Zhao (2010) apply this method to analyze U.S. gasoline demand from 1976 to 2008.

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193194195196197saving deposits holding other conditions unchanged. In our case, since we are using the one year saving deposit rate as a variable198for interest rate, it is the opportunity cost for theM1 component of M2while it serves as own rate variable for the saving deposit in199M2. Thus the overall sign of α2 depends on the relative strength of two effects. Since the ratio of saving deposit in M2 to that in M1200is 1.74 at the end of 2008, we may expect a relatively stronger role of the saving deposits as own rate of interest. If this is the case,201the sign of α2 is more likely to be positive.202The sign of α3 is determined by two effects, say, the substitution and wealth effects. On one hand, when the stock prices203increase, equity assets are more likely to be substitutes for the saving deposits. If this substitution effect dominates the wealth204effect, α3 tends to be negative. On the other hand, when the nominal wealth of households increases and/or the growth of the stock205market entails more transaction needs, a large fraction of the investors' assets would be converted to more liquid alternatives to206facilitate consumption or transaction. When this wealth effect dominates the substitution effect, α3 becomes positive. Thus the207sign of α3 is a purely empirical issue.208The model (3) can be consistently estimated using the ordinary least squared (OLS) method when variables are cointegrated.209Although the OLS estimator is (super-) consistent, it is usually asymptotically biased and inefficient when there exists an210endogeneity problem in Eq. (3). Thus, generally, the statistical tests based on the OLS estimator are invalid. There are many211methods for efficient estimation of the coefficient in the previous studies, for examples, fully modified OLS (FM-OLS) (Phillips &212Hansen, 1990), the usage of sieve approximation (Saikkonen, 1992; Stock & Watson, 1993), canonical cointegrating regression213(CCR) (Park, 1992) among others.214It is quite natural to ask a question whether the long-run stable relationship is constant or time-dependent. It may be hard to215represent the long-run relationship with a constant parameter vector in the presence of structural changes. However, the216traditional cointegrating regression (3) implicitly assumes the constant long-run relationship among the time-series variables.217The parameter instability could be one of the possible reasons for the empirical failure of the traditional cointegrating regression218model. In fact, this is more prominent in the case of estimating long-run stable money demand function in China. Especially, as219demonstrated earlier, since China's reform is smooth and gradual, there are highly likely smooth structural changes of the220underlying economic structure. We should note that it might be inappropriate to introduce a dummy variable indicating a specific221date of structural change. Under the smooth structural change, the model (3) may fail to capture the presence of the long-run222stable money demand even though there exists such relationship.223In order to take care of the gradual structural changes, we allow the parameters to evolve smoothly during time horizon:

dmj = π + α1;mjymj + α2;mjrmj + α3;mjspmj + εm + εmj; m = 1;2;3;4; j = 1;2; ⋯; T; ð4Þ224225226where αi, mj, i=1, 2, 3, are assumed to be smooth functions over the time horizon. Denoting xmj=(ymj, rmj, spmj)′ and αmj=(α1, mj,227α2, mj, α3, mj)′, Eq. (4) can be represented by

dmj = π + αmj′ xmj + εm + εmj; m = 1;2;3;4; j = 1;2; ⋯; T; ð5Þ228229230where αmj=α(t/n) is assumed to be a smooth function defined on [0, 1], n is the number of observations, and t is the order or231observations in the total sample given by t=4(j−1)+m. Themodel (5) is the time-varying coefficients (TVC) version of the fixed232coefficients (FC) model (3).233Park and Hahn (1999) suggest to use the Fourier flexible form to approximate the smooth time-varying parameter αmj

αk rð Þ = βk;1 + βk;2r + ∑k

i=1βk;2i +1;βk;2 i+1ð Þ

� �ϕi rð Þ; ð6Þ

234235236where βk, j∈Rp, p is the dimension of αmj, j=1, 2, ⋯, 2(k+1), and ϕi(r)=(cos 2πir, sin 2πir)′. The αk(r) in Eq. (6) can be rewritten237as

αk = f ′k⊗Ip� �

βk; ð7Þ238239240where fk(r)=(1, r, ϕ′1(r), ⋯, ϕ′k(r))′ with r∈ [0, 1], βk=(β′k, 1, β′k, 2, ⋯, β′k, 2(k+2))′, Ip is a p×p identity matrix, and ⊗ denotes the241Kronecker product. Thus the model (4) is represented by

dmj = π + β′kxkmj + εm + εkmj; ð8Þ242243244where

xkmj = fktn

� �⊗ xmj and εkmj = εmj + α−αkð Þ t

n

� �′xkmj:

245246247The standard ordinary least square (OLS) estimators can be used to estimate the Eq. (8). However, OLS estimators are248asymptotically inefficient and have non-standard limiting distribution so that standard inference procedures cannot be applied in249this case. In order to deal with these problems Park and Hahn (1999) use the canonical cointegrating regression (CCR)

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250transformation. This transformation involves some unknown parameters, mainly the conditional and one-sided conditional long-251run variances of the residuals. However, these unknown parameters can be consistently estimated using nonparametric method252(Andrews, 1991). After obtaining the estimates of βk using the Eqs. (8), (7) can be used to recover αk. Park and Hahn (1999) show253that under certain assumptions

M⁎−1=2nk Π α̂k

�� �−Π αð Þ� �

→dℕ 0;ω2⁎ Ipd

� �as n→∞;

254255256where Π(α)=(α(r1), ⋯, α(rd))′ and Π α̂k

� �= αk r1ð Þ; ⋯;αk rdð Þð Þ′ for ri∈ [0, 1], i=1, ⋯, d, Ipd is a pd×pd identity matrix, Mnk

⁎ is a257pd×pd matrix, ω⁎

2 is the conditional long-run variance of the residuals from the transformed regression. For more details on this258method, see Park and Hahn (1999).259The two tests proposed by Park and Hahn (1999), both of which are based on the Wald-type variable addition tests (see Park,2601990), will be employed to check whether themodel is correctly specified. The first test performs under the null hypothesis of TVC261model against the alternative that the regression is spurious. The test statistic is given by

τ� = RSSTVC−RSSsTVCω̂2

⁎

;

262263264where RSSTVC and RSSTVC

s are the sum of squared residuals from Eq. (5) and (5) augmentedwith s additional superfluous regressors265and ω̂2

⁎ is a consistent estimator of ω⁎2. Under the null that the TVC model is correctly specified, τ⁎ is asymptotically chi-square

266distributed with s degree of freedom. Under the alternative, the statistic would diverge.267As mentioned in Park and Hahn (1999), the fixed coefficient model would become a spurious regression if the true model is268TVC model. Thus, the test statistic under the null that the fixed coefficient model is cointegrated takes the following form

τ1� = RSSFC−RSSsFC

ω̂2⁎

;

269270271where RSSFC and RSSFC

s are the sum of the squared residuals from the regression (3) and (3) with s additional superfluous272regressors, respectively. Under the null, the limit distribution is chi-square distribution with s degree of freedom, otherwise it273diverges.

2743. Empirical analysis

2753.1. Data description

276We consider the quarterly data from 1996Q1 through 2009Q1. For the scale variable, we use real GDP. The National Bureau of277Statistics (NBS) of China provides nominal GDP and its growth rates at constant prices. We also consider real industrial value278added (IVA) as the scale variable in order to check the robustness of the estimation results. As for the price variable, the consumer279price index (CPI) is chosen to deflate GDP, IVA, M2 and stock prices. The Shanghai composite stock index published by the280Shanghai Stock Exchange is the proxy for the stock prices in our analysis. The real interest rate is obtained by subtracting expected281inflation rate from one-year saving deposit rate,4 where the expected inflation is an average inflation rate in the previous year282assuming that the agents have the belief that their best guess of inflation rate in the next year would be the one at the current year,283i.e., the inflation rate follows a random walk process. The stock price index is obtained from the China Stock Market Accounting284Research Database (CSMAR). Other macro data used in our analysis are obtained from the China Premium Database in the CEIC.285Those databases use the raw data from the People's Bank of China (PBC), the National Bureau of Statistics (NBS) and Shanghai286Stock Exchange (SSE).5

287All series are plotted in Fig. 1. From Fig. 1, we can observe that real M2, GDP and IVA have increasing time trends and seasonal288patterns. Thus, we consider seasonal dummies in the FC and TVC models. In Fig. 2, three different interest rate measures, seven289days China Interbank Offering Rate (CHIBOR), three months CHIBOR and one year saving deposit rate (with tax adjustment) are290plotted at quarterly frequency. The difference among these measures is that the one year saving deposit rate is set by the central291bank, which changes infrequently and the CHIBOR rates are more market oriented interest rates which change with market292conditions on a daily basis. Despite their difference, the short term CHIBOR rates follow the similar pattern as official interest rate293set by the central bank and seldom deviate much. Furthermore, the interbank rate is vulnerable to short term market condition294such as initial public offers in the stock market as pointed out by Hong et al. (2009). For this reason the short term interest rate is295not considered in our study. From Fig. 2, we can also observe that nominal interest rate is unusually high before 2000 and296decreases sharply thereafter. In Fig. 1, we can observe that the real interest rate is negative sometimes. This is due to high inflation297rates since 2004. For the real stock priceswe can observe that the periods 1996–2001 and 2006–2008 are two bullish periods in the

4 In China, interest earned on savings deposits was taxed at a rate of 20 percent since November 1, 1999, which decreased to 5 percent since August 15, 2007.Our interest rate is net of this tax.

5 CSMAR is also included in Wharton Research Data Services. The macroeconomic variables used could also be found in other databases which have access toPBC, NBS and SSE in China. Moreover, the computer programs used are available upon request from the authors.

6 H. Zuo, S.Y. Park / China Economic Review xxx (2011) xxx–xxx

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298Chinese stockmarket, and the period 2001–2006 is a bearish period. Recent bearish periods in 2008 and 2009 are the consequence299of international financial crisis.300We perform unit root tests for all series using the Augmented Dickey–Fuller (ADF) and the Kwiatkowski, Phillips, Schmidt and301Shin (KPSS) tests (Dickey & Fuller, 1981; Kwiatkowski, Phillips, Schmidt, & Shin, 1992). For ADF test, Bayesian information302criterion (BIC) with maximum lag length equals 10 is employed to pick the optimal lag length. For KPSS test, we use spectral GLS-303detrended AR method with Modified Akaike information criterion (AIC) as criterion to choose the lag. The results are reported in304Table 2. While the null hypothesis of ADF test is the time-series has a unit-root, the null of KPSS test is that the time-series is305stationary. At the usual 10% significance level, Table 2 shows that there are strong evidences supporting the presence of unit root in306all variables. For the robust check, we also perform unit root tests for the seasonally adjusted series and obtain the same results.307Similar to Smyth and Inder (2004), we also use Zivot and Andrews (1992) and Lumsdaine and Papell (1997) methods to test308the unit root hypothesis under possible structural breaks. Both tests treat structural break dates to be endogenously determined. In309these tests, one can also consider possible structural breaks in intercept and trend terms. The test proposed by Lumsdaine and310Papell (1997) is more general compared to Zivot and Andrews (1992) since it takes care of the possibility of two endogenous break

1996 1998 2000 2002 2004 2006 2008

1996 1998 2000 2002 2004 2006 2008 1996 1998 2000 2002 2004 2006 2008

1996 1998 2000 2002 2004 2006 2008 1996 1998 2000 2002 2004 2006 2008

1996 1998 2000 2002 2004 2006 20084.

04.

55.

05.

56.

0

Rea

l M2

10.0

10.5

11.0

Rea

l GD

P

8.5

9.0

9.5

10.0

Rea

l IV

A

−4

−2

02

46

Rea

l int

eres

t rat

e

−10

010

20

Exp

ecte

d in

flatio

n

2.0

2.5

3.0

3.5

Rea

l sto

ck p

rices

Fig. 1. Time series plot. Note: The figure plots the real M2, real GDP, real IVA and real stock price in logarithm, real interest rate and expected inflation inpercentages.

1996 1998 2000 2002 2004 2006 2008 20100

2

4

6

8

10

12

14

Year

Per

cent

age

Seven day CHIBORThree months CHIBOROne year saving deposit rate (tax adjusted)

Fig. 2. Different interest rate measures in China.

7H. Zuo, S.Y. Park / China Economic Review xxx (2011) xxx–xxx

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311points instead of only one (for technical details, refer to Zivot and Andrews (1992), Lumsdaine and Papell (1997), Ben-David,312Lumsdaine, and Papell (2003).313We consider two model specifications for these tests: T1 and T2. T1 allows for possible structural breaks in the intercept term314while T2 allows for breaks in both the intercept and trend terms. Following Lumsdaine and Papell (1997), we use the data-driven315method to select the lag order k. We start with k=8. If the last lag term is significant, we choose that lag order for the test.316Otherwise, we reduce k by 1 and repeat the above procedure. The critical values are obtained from Zivot and Andrews (1992) and317Ben-David et al. (2003).318The results are shown in Table 2. From Table 2, we observe that ZA test (Zivot & Andrews, 1992) rejects the null of unit root for319real stock prices in case of T1. Under T2, ZA test rejects the null of unit root for expected inflation at 5% significant level. If we use LP320test (Lumsdaine & Papell, 1997), the unit root hypothesis of real stock price is rejected for T1. However, if we consider two break321points for T2, no evidence of rejecting the null of unit root hypothesis is found.322We found that the evidence of rejecting the unit root hypothesis is relativelyweak. Especially, if we consider the LP test with T2,323which is the most general set-up in Ben-David et al. (2003), there is no evidence against unit root hypothesis for all the series at32410% significant level. In addition to the results found by ADF and KPSS tests, these results further show the existence of unit root in325all variables we considered in our analysis.

3263.2. Model estimation and economic interpretation

327We estimate four versions of themoney demandmodels: real money balance determined by real GDP, the interest rate and the328stock prices (S1); the model when the scale variable is replaced by real IVA (S2); the model when the opportunity cost variable is329replaced by expected inflation (S3); themodel when the stock prices are excluded (S4). S1 is the benchmark model, and S2 and S3330are for the robust check of our results. S4 is used to analyze the usual money demand function. For each model, we rely on BIC to331choose the optimal lag truncation order of trigonometric functions in Eq. (6) when we estimate the regression Eq. (8). In practice,332we choose the constant term, the linear trend and the first pair of trigonometric functions for models S1–S3, and we choose the333constant term, the linear trend and the first eight pairs of trigonometric functions for model S4. Using these specifications, we first334estimate βk and recover the time-varying coefficient αk using Eq. (7). The estimation results for S1 and S2–S4 are reported in Figs. 3335and 4, respectively. In these figures the estimates of coefficients are plotted in solid lines, and their 90% confidence intervals336(confidence bands) are represented by dashed lines.337Before we interpret the estimation results, we check whether the time-varying cointegrating regression specifications are338appropriate using the test statistics τ⁎ and τ1⁎. Test statistics τ⁎ and τ1⁎ are reported in Table 3. When we perform the test, the339polynomial terms t, t2, t3 and t4 are considered as the superfluous regressors.340For models S1–S3, the test statistic τ1⁎ rejects the null of FC model in favor of TVC model and, moreover, the test statistic τ⁎

341cannot reject the TVC model at 1% significance level. Both of them imply that there exist time-varying long-run relationships342among the variables. For the last model, we reject the legitimacy of both FC and TVC models.

3433.2.1. Time-varying income elasticity344For the income elasticity, many previous studies report different estimates. Yi (1993) uses annual data from 1952 to 1989 and345reports that the estimated income elasticities are between 0.7 and 0.9. With similar sample periods and frequencies, Hafer and346Kutan (1994) obtain 1.33 for nominal M2, and Chen (1997) reports 1.93 for real M2. Using quarterly data from 1983 to 2002,347Bahmani-Oskooee and Wang (2007) obtain 1.69 while Mehrotra (2008) find it to be 1.73 using the quarterly data from 1994 to3482005. With slightly longer sample periods, Wu (2009) finds the estimate to be 0.74 (1994 to 2008), and Baharumshah, Mohd, and349Yol (2009) obtain 0.65 (1990 to 2005). Our estimates are between 0.60 and 0.75, which are comparable with previous studies350using post-1990 data on a quarterly basis.

Table 2t2:1

Unit-root tests.t2:2t2:3 Variables Demeaned series Detrended series T1 T2

t2:4 ADF KPSS ADF KPSS ZA LP ZA LP

t2:5 Real M2 −0.94[0] 19.18[8] −2.87[0] 5.91[10] −2.71[8] −3.97[8] −3.89[8] −5.56[4]t2:6 Real GDP 0.02[4] 0.40[4] −2.59[4] 4.20[4] −3.95[8] −4.29[8] −3.34[8] −4.27[8]t2:7 Real IVA −1.04[4] 17.78[5] −2.74[4] 0.23[6] −3.43[4] −3.94[4] −3.49[4] −4.06[4]t2:8 Real stock price −2.43[1] 5.77[1] −2.74[1] 0.60[1] −4.96[4] −6.35[4] −5.01[4] −6.19[4]t2:9 Real interest rate −2.43[0] 5.18[0] −2.95[0] 0.78[0] −3.49[4] −5.84[7] −3.88[5] −6.11[7]t2:10 Expected inflation −2.15[3] 3.30[3] −3.07[6] 1.72[3] −4.04[6] −4.49[6] −5.26[6] −5.63[6]t2:11 10% critical values −2.60 0.35 −3.18 0.12 −4.58 −5.89 −4.82 −6.48t2:12 5% critical values −2.92 0.46 −3.50 0.15 −4.80 −6.16 −5.08 −6.75

Note: ADF and KPSS are, respectively, the Augmented Dicky–Fuller and Kwiatkowski, Phillips, Schmidt and Shin test statistics for the null hypothesis that the seriesare nonstationary or stationary, respectively. The numbers in brackets in ADF and KPSS denote the selected lag lengths. ZA and LP are, respectively, the testsproposed by Zivot and Andrews (1992) and Lumsdaine and Papell (1997). The numbers in brackets in ZA and LP denote the selected lag lengths. T1 denotes forallowing structural breaks in intercept terms and T2 allows for structural breaks in both intercept and trend terms.t2:13

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351In addition, in Fig. 3, an increasing, although not monotonic, pattern of the income elasticity is also observed. This pattern352indicates that, in recent years, given 1% growth in real income, people are likely to holdmore assets falling into the category of M2.353This finding is consistent with the fact that the saving ratio also shows an increasing pattern in recent years. Chamon and Prasad354(2008) claim that households' precautionary saving motives to cover the housing expenditure, education and health care become355stronger in recent years, and people prefer to postpone their consumption by saving a large portion of their disposable income in356the banks (around 24% in 2005).357We have to note that the above increasing pattern is not affected by changing covariates. As we can see in the first subplot of358Fig. 4, the shape of the time-varying elasticity remains unchanged with slightly different magnitudes with alternative choices of359other covariates. We can reach the conclusion that our result is robust to alternative choices of the scale variables.

3603.2.2. Time-varying interest rate elasticity361For the interest rate elasticity, lots of studies show quite inconsistent estimation results. Hafer and Kutan (1994) show that the362interest rate elasticity is 0.15 but not statistically significant. Bahmani-Oskooee andWang (2007)obtain−1.54 but not significant363neither. Baharumshah, Mohd, and Yol (2009) report that the estimated interest rate elasticity is insignificant, and they exclude it364from their cointegrating regression equation.Wu (2009) reaches the similar conclusion that the interest rate plays an insignificant365role in the cointegrating regression.366There are many potential reasons for the insignificance of the interest rate elasticity estimates. First, Chen (1997) points out367that themajor interest rates of saving deposits in China are set by the central bank directly in advance and rarely change over time.368Second, as mentioned in Koivu (2009), although the centrally planned credit rationing (a predetermined and direct control of369commercial banks credit plan performed by the central bank) have been abandoned in 1998, the central bank still uses a window370guidance policy to influence the decision of commercial banks. Furthermore, the majority of bank loans still flows to the state-371owned companies (SOEs) (Prasad & Rajan, 2006; García-Herrero et al. (2009). All these facts result in the severe restriction of the372market mechanism. Lastly, as mentioned before, due to the financial depression and capital flow regulation, saving deposit is the373main investment channel for domestic investors. Observing that the official interest rate does not respond to market effectively,374Wu (2009) argues that interest rate does not play a significant role in affecting money holdings. Qin, Quising, He, and Liu (2005),

Income elasticity

1996 1998 2000 2002 2004 2006 2008

1996 1998 2000 2002 2004 2006 2008

1996 1998 2000 2002 2004 2006 2008

0.60

0.65

0.70

0.75

Interest rate elasticity

−0.

010.

010.

020.

03

Stock price elasticity

−0.

15−

0.05

0.05

Fig. 3. The time-varying coefficients of model S1. Note: This figure plots the estimates of income elasticity, interest rate elasticity and real stock price elasticity ofmodel S1 (solid line) and their corresponding 10% confidence bands (dashed lines), respectively.

9H. Zuo, S.Y. Park / China Economic Review xxx (2011) xxx–xxx

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Income elasticity

1996 2000 2004 2008

1996 2000 2004 2008

1996 2000 2004 2008 1996 2000 2004 2008

1996 2000 2004 2008 1996 2000 2004 2008

1996 2000 2004 2008 1996 2000 2004 2008

0.60

0.65

0.70

0.75

−0.

010.

010.

03

Model S2Interest rate elasticity Stock price elasticity

−0.

20−

0.10

0.00

Income elasticity

0.70

0.75

0.80

−0.

010

−0.

005

0.00

00.

005

Model S3Expected inflation elasticity Stock price elasticity

−0.

100.

000.

10

Income elasticity

0.82

0.86

0.90

0.94

−0.

040.

000.

040.

08

Model S4Interest rate elasticity

Fig. 4. The estimates of time-varying elasticities under model S2–S4. Note:The top, middle and bottom panel depicts the estimates of time-varying co-efficients insolid lines and their corresponding 10% confidence bands in dashed lines for model S2, S3 and S4, respectively.

Table 3t3:1

Model specification tests.t3:2t3:3 Model Test statistics

t3:4 τ⁎ τ1⁎

t3:5 S1: The scale variable is real GDP 10.8405 1512.16t3:6 S2: The scale variable is real IVA 3.0660 2603.39t3:7 S3: The opportunity variable is expected inflation 5.1538 1014.78t3:8 S4: The real stock price is excluded 21.0237 104025t3:9 1% critical value 13.2767

Note: τ1⁎ and τ⁎ are the test statistics for the null hypothesis that the variables are fixed coefficient cointegrating regression and time-varying coefficientcointegrating regression, respectively. The additional superfluous regressors are time polynomial terms, t, t2, t3 and t4. If the null hypothesis is true, thecorresponding statistics converges to χ4

2 in distribution. Otherwise, it will diverge as the sample size increases.t3:10

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375Bahmani-Oskooee andWang (2007), Baharumshah, Mohd, and Yol (2009) and Baharumshah, Mohd, and Masih (2009) reach the376similar conclusion in their studies.377Although, traditionally, interest rate is a rather weak monetary policy instrument in China, its effect becomes stronger with378progress of the interest rate liberalization. Koivu (2009) uses more recent data and argues that the interest rate policy begins to379influence the economy to a larger extent than before. More specifically, he splits the whole sample into two different sub-samples380and estimates models with each sub-sample to show the changing role of the interest rate policy. Our results of the time-varying381interest rate elasticity estimates support previous findings without splitting the sample. The estimated time-varying interest rate382elasticities are between −0.01 and 0.04 and they are significant over the recent time horizons. The interest rate elasticity383estimates turn to be positive after 2004, which implies a relatively stronger role of saving deposits in M2 demand.384There are some evidences for the recent stronger effect of the interest rate policy. First, as mentioned before, the commercial385banks are not restricted by the ceiling of the lending rates or the floor of the deposit rates since 2004. Second, as mentioned in386Koivu (2009), the ownership structure of the commercial bank has been changing from the original state-ownership to more387market oriented one. This provides more freedom to the commercial banks in the sense of issuing loans through the market388mechanism. Third, with the development of the financial and housing markets, more investment alternatives are available for389domestic investors in more recent years. This is necessary for the interest rate to have impacts on household saving decision.390Otherwise, even if households want to reallocate their assets in response to the change of the interest rate, they may be391constrained by investment opportunities.392We also consider another proxy of the opportunity cost, the quarterly expected inflation rate. As shown in Fig. 2, the fact that393nominal interest rate stays low level and roughly the same over time since 2004 suggests a large portion of the variation of real394interest rate comes from the changes in expected inflation rate. That is the reason why we choose the expected inflation rate as395another proxy, and the similar choices have been made by Chen (1997), Mehrotra (2008), Deng and Liu (1999), among many396others. Furthermore, according to economic theory, households would prefer to transfer saving deposits to real assets during high397inflation periods if the nominal interest rate is unattractive. Thus, the corresponding coefficient should be negative.398The estimates of the time-varying elasticities have been depicted in the second panel of Fig. 4. We could draw at least two399conclusions under this model specification. First, the shape of the income and stock price elasticities remain unchanged but the400values of the income and stock price elasticities are larger and smaller (in absolute value) compared with those of S1. Second,401similar to the case of real saving rate, the elasticity of expected inflation remains insignificant over a large portion of the time402horizon. The negative sign after 2004 is not surprising as we mentioned the above.

4033.2.3. Time-varying real stock price elasticity404Traditionally, stock market prices have not been considered as a determinant of the money demand until Friedman (1988).405According to Friedman (1988), the stock prices may exert a positive wealth effect and a negative substitution effect. There are406mainly three channels contributing to a positive wealth effect: (i) an increase in the stock prices would yield an increase in407nominal wealth. This results in a positive effect on themoney demand to facilitate consumption; (ii) the better the condition of the408stock market is, the more money is needed in order to facilitate transactions; (iii) since higher stock prices imply higher future409expected returns and, in turn, higher risks (assuming investors' preference of risk to be constant), investors are willing to shift the410large proportion of their wealth to risk free ones such as cashes or saving deposits. The substitution effect works exactly in the411opposite direction. As the stock prices rise, equity would becomemore desirable, and therefore, the demand for money decreases.412The whole effect depends on the relative magnitude of both effects. Choudhry (1996) studies the relationship between the stock413prices and money demand (real M2) in the U.S. and Canada from 1955 to 1989 using Johansen's cointegration method and finds414that the stock price elasticities are negative and positive in Canada and U.S., respectively. He further argues that there is no strong

1998 2000 2002 2004 2006 2008 20100

2000

4000

6000

Sto

ck p

rice

Time

Stock price and the number of investor accounts

0

5000

10000

15000

The

num

ber

of in

vest

or a

ccou

ts

Stock priceThe number of investor accounts

Fig. 5. Stock price and total number of investors. Note: This figure plots the Shanghai composite stock price (left scale) and number of investor accounts in China’sstock market (in 10 thousands, right scale).

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417418419420421422423424425426427428429430431432433434evidence supporting a long-run stable money demand function without considering real stock prices. Caruso (2006) shows that435the wealth effect dominates from 1913 to 1980 while the substitution effect dominates in the last two decades in Italy.436Baharumshah, Mohd, and Yol (2009) estimate a positive stock price elasticity of 0.287 in China.437In order to get some general idea, the stock prices and the number of investors' accounts in China are plotted in Fig. 5. In Fig. 5,438we can observe that more investors entered the stock market during the bullish periods of the stock market while the number of439investors' accounts was non-increasing during the bearish market periods. Thus we can say that the third channel of the wealth440effect may not be dominant in China. The relative strength of the wealth effect may mainly depend on the other two channels.441As we mentioned the above, since a large amount of saving deposits enjoys quite low real interest rate, and financial markets442are not well developed in China, the stock market can be the natural alternative choice. As pointed out by Wu (2009), the443proportion of equity assets in the total financial assets increased from 5% in 2005 to above 20% in 2007. The shift of the saving444deposit and equity shares can be inferred from Fig. 6. We can observe that during two bullish market periods, 1996–2001 and4452006–2008, the growth of the saving deposits increases moderately or even decreases sharply around 2007.6 On the contrary,446during the bearish periods, the growth of the saving deposits increases tremendously. Since themoney in the stock accounts is not447classified as the broad money (M2), a massive amount of money transferring from the banks to the stock market constitutes a448strong substitution effect for the demand for M2. This effect is particularly strong during the bullish market. However, for the

1996 1998 2000 2002 2004 2006 2008 20100

1000

2000

3000

4000

5000

6000

Sto

ck p

rice

Time

The stock price and saving growth

−1

−0.5

0

0.5

1

1.5

2x 104

Gro

wth

of s

avin

g de

posi

ts

Growth of saving depositsStock price

Fig. 6. Stock price and growth of savings. Note: This figure plots the Shanghai composite stock price (left scale) and change of saving deposits in banking system (in100 million RMB, right scale).

1996 1998 2000 2002 2004 2006 2008

−0.

2−

0.1

0.0

0.1

0.2

0.3

0.4

0.5

Stock priceStock price elasticityLower and upper bound for stock price elasticity

Fig. 7. The stock price and real stock price elasticity. Note: The figure plots the Shanghai composite stock index (divided by 10000), the stock price elasticity and thecorresponding 10% confidence intervals.

6 Year 2007 is a year of exceptionally high stock returns. See Monetary Policy Report, 2007 and other issues published by PBC.

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449450451452bearish market periods, we cannot observe some specific trends. In Fig. 7, we find that when the stock prices reach its peak, the453stock price elasticities are more likely to be negative and, moreover, reach its bottom. For the bearish market, the stock price454elasticities are positive or insignificant.455To further investigate the role of the stock prices, we estimate both the TVC and FC models excluding real stock prices in the456regression equation. The result of TVC model is shown in the last subplot of Fig. 4. This graph shows rather wriggled estimates of457elasticities. Unfortunately, model specification tests reject both TVC and FC models which implies that the exclusion of the stock458prices from the money demand function may yield model misspecification. This implies that the long-run equilibrium between459money demand and its determinants cannot be captured by either the fixed coefficient approach or the time-varying one without460including the stock prices in the regression equation.

4614. Concluding remarks

462Many previous studies investigate the long-run equilibrium of the money demand using traditional cointegrating regression463approach. However, the fixed coefficient approach may fail to capture the long-run relationship when economic condition and464policy regimes are changing over time. This is especially the case in a transition economy like China, where smooth structural465changes are present. As a result, the usage of traditional (fixed coefficient) parameter cointegrating regression approach may not466be appropriate. In order to study the long-run relationship of themoney demand function in China, we analyze themoney demand467in China using the smooth time-varying cointegrating approach and find the existence of long-run time-varying stable468relationship.469Using recent data set, we find (i) the estimates of income elasticities are around 0.6–0.75, which are comparable with existing470studies; (ii) our interest rate elasticity estimates are between−0.01 and 0.04. This finding is consistent with the fact that the role471of the interest rate policy is weak in China and households' insensitivity to monetary policy changes, although there are somemild472evidences that its role has been strengthened in recent years; (iii) considering the stock prices as an additional covariate in the473money demand equation helps to explain the demand of real money balances.We observe that the substitutional effect dominates474the wealth effect, especially, during the bullish market period.475We identify and highlight the role of the stock prices in themoney demand. The strong substitution effect of equity assets is the476result of underdeveloped financial market, unattractive real interest rate and high saving ratio. Even in a transition economy with477immature financial market like China, asset price is one of important determinants inmoney demand analysis. More efforts should478be devoted to explore how this phenomenon would affect the monetary policy in China.

479References

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