Empirical analysis on China’s money, income and

inflation: 1979 - 2004

Yanqun Zhang ∗

Institute of Statistics and EconometricsFree University, Berlin

May 17, 2006

Abstract

This paper aims to analyze and assess China’s monetary policy.Macroeconomic variables such as money aggregate, income, inflationand interest rate are empirically analyzed as a system. Vector errorcorrection (VEC) model and structural VAR (SVAR) model are app-lied as the statistical instruments. The empirical models are estimatedwith quarterly and seasonally unadjusted data for the period from1979Q1 to 2004Q4, which began from the China’s economic reformsuntil the latest data are available for this study. A regime shift hasbeen detected at round 1995:1. The empirical models are thereforeconstructed based on two sub-samples and for two definition of money,M1 and M2. The cointegration relations between money stock, income,inflation and interest rate, as well as the corresponding short-run dy-namic adjustments are analyzed. In addition, the information derivedfrom the moving average (MA) representations are used to identify thecommon stochastic trends and long-run impacts. Finally, impulse re-sponse analysis are conducted to trace the effects of monetary shockshitting the system.

∗The author is an associate researcher of the Institute of Quantitative and TechnicalEconomics, Chinese Academy of Social Sciences, Beijng, China, and a Ph.D. candidate inthe Free University of Berlin, Germany during 2002-2006.

1

1 Introduction

In this paper, we empirically analyze macroeconomic variables in China suchas money, income, inflation and interest rate as a system. The purposesof the empirical analysis are to identify the existence of the steady-staterelations between money stock, income, inflation and interest rate, and toinvestigate interactions within the system. In particular, we will assess theeffects of China’s monetary policy on inflation and real income.

Cointegrated VAR and structural VAR (SVAR) models are applied in theempirical investigation. The statistical models are estimated with quarterlyand seasonally unadjusted data for the period from 1979Q1 to 2004Q4, whichbegan from the China’s economic reforms until the latest data are availablefor this study.

During the sample period, the Chinese economy is in a process of tran-sition from a centrally planned to a market economy. With the reforms,the macroeconomic environment, the banking system, monetary targets andpolicy instruments all have undergone significant changes. Under these cir-cumstances, it is necessary to examine possible regime shifts in the model.Pre-test have identified a structural shift of the system occurring around1995. Consequently the empirical analysis is conducted for two separatesample periods of before and after 1995.

Since 1998, the People’s Bank of China (PBC) has officially changed theintermediate targets of the monetary policy from total credit quotas andcurrency in circulation (M0) to money supply. There are two measurementsof broad money in China, namely M1 and M2. Since 1995, the movementsof M1 and M2 have displayed divergent patterns. The PBC neverthelesshas never explicitly specified which measure of broad money to be the in-termediate target. According to the PBC’s criteria for the selection of anintermediate target, an intermediate target for monetary policy should bemeasurable, controllable and has close correlations with the ultimate policygoals, i.e., controlling inflation and promotion of economic growth. Againstthis backdrop, the empirical analysis will model M1 and M2 separately. Bymeans of this modelling strategy, the controllability of M1 and M2 and theirrelationships to inflation and real growth can be examined, respectively.

In the present study, four models are constructed. These are models forM1, M2 for two separate sample periods. For each model, we first investigatethe existence of cointegration relations between money supply, real GDP,

2

inflation and the interest rate. Then, the short run dynamics within thelong-run cointegration system will be examined to probe the monetary policyeffects on inflation and real economic growth, along with the interactions andfeedbacks within the VAR system.

For a better understanding of the effects of monetary policy, it is ne-cessary to further analyze the useful information derived from the movingaverage (MA) representation of the VAR model. By means of identifyingthe common stochastic trends and analyzing the long-run impact matrices,the driving and pulling forces of the economic system are to be inspected. Inaddition, it is of interest to analyze how the monetary shocks affect the eco-nomic system. The impulse response analysis obtained from the structuralVEC model is conducted with identified shocks.

The structure of the rest of this chapter is as follows. Section 2 is aboutthe research motivation. In section 3 the exiting literature is reviewed. Insection 4 we discuss the relevant economic theories. Section 5 is about datadescription and preliminary analysis. In section 6 we estimate the models inthe full sample period and test the potential structural shifts. In section 7at first models in the two split sub sample periods are estimated. Then wecheck model specification and determines the cointegration ranks. In section8 the single stationary relations are tested. Section 9 is about identifying thelong-run structure. Section 10 is about identifying the short-run structure.In section 11 we analyze the impulse response functions based on a Chole-ski decomposition. In section 12 we conduct long-run impact analysis. Insection 13 impulse response functions for transitory and permanent shocksare analyzed. In section 14 a summary and conclusions are presented.

2 Motivation

In this section we first briefly summarize the main changes in China’s mone-tary policy goals, intermediate targets and operational instruments. Thenwe highlight the policy debate on Chinese monetary policy, against whichwe set out the institutional background of the current research.

2.1 Evolution of China’s monetary policy: 1979-2004

In contrast to its passive role in the pre-reform period, Chinese monetarypolicy in the reform years has been deployed as a major policy tool for

3

controlling inflation and stabilizing the economy. As a consequence, themonetary objectives, intermediate targets and operational instruments ofthe monetary policy have undergone changes.

From 1984 when the PBC was formally set up unite 1994, China’s mo-netary policy was commissioned to achieve multiple objectives, namely sti-mulation of economic growth, adjustment of the economic structure andstabilization of the value of China’s currency. During this period, currenciesin circulation and total credit size have been used as the main intermediatetargets for the monetary policy. Credit quotas and cash plans were the mainpolicy instruments for the government to manage total demand.

With economic transition, Chinese monetary policy that relied on directand administrative orders became increasingly ineffective in achieving mo-netary goals, especially in controlling inflation. The high inflation in 1993proved that the total credit size was not a suitable intermediate target. Alt-hough the total credit size did not exceed the planned target as set in thecredit plan, inflation ran out of control. On the other hand, the moneysupply grew very fast at the time, which caused investment overheating anda two-digit inflation rate in 1993 and 1994. In 1996, the PBC formally usedthe money supply instead of the credit quotas as the intermediate targetfor monetary policy. In 1998, total credit size as a policy instrument forcontrolling aggregate money supply was finally abandoned.

Along with changes in the intermediate target, the PBC has also tur-ned to indirect and more market-oriented instruments, such as open marketoperations, interest rate policy, required reserves, and window guidance, etc.

The Law of People’s Bank of China issued in 1995 specifies that thegoal of the monetary policy is to ensure the stability of the value of theChinese currency hereby to promote economic growth. This implies thatprice stability is the primary goal of monetary policy.

2.2 Debates on China’s Monetary Policy

Debate 1: Which measurement of money supply should be used as theintermediate target, M1 or M2?

Since 1996, money supply has been formally announced by the PBCas the intermediate target for the monetary policy. But the PBC has notexplicitly specified which measurement of money supply, i.e. M1 or M2,

4

is the intermediate target, despite the fact that the velocity and supplyconditions of M1 and M2 are quite different. The PBC has published themoney supply plan for the target growth of M0, M1, M2, and total loans atthe beginning of each year since 1994. Dai (2002), who was then directorof the monetary policy department of the Chinese central bank, pointedout that PBC’s intermediate target actually included a group of variablesincluding M0, M1, M2 and total loans. Among them, M1 is mainly relatedto temporary price hikes and the short-run growth rate of GDP, while M2is more related to that of the long-run inflation and economic growth (Dai,2002).

Debate 2: Can the PBC control money supply?

Table 1 shows the targeted and realized growth rates of money supplyand inflation rate. From 1994 when the PBC started publication of thetarget growth rates for money supply to 2004, the realized growth of M1missed the target rate in seven years and M2 in five years, by a margin ofmore than 2.5% for both measurements. Only in three years, the discrepancybetween the realized and target growth rates of both M1 and M2 were lessthan 2%

The foundation for the PBC’s calculating the planned targets was thequantity theory:

M ∗ V = P ∗Q

where M is the total amount of money in circulation in an economy, V isthe velocity of money, P is the average price level, and Q is the total numberof items purchased with the particular kind of money represented by M .

The PBC’s planed growth rates of both narrow and broad money supplywere based on the predicted GDP growth rates and the inflation rates. Thetarget growth rate of money supply was then calculated as the sum of thetwo rates minus changes of velocity of money aggregates. Because velocity ofmoney stock is hardly a constant but displays an upward trend, the averagevelocity of the recent three years is taken as the predicted velocity (MonetaryPolice Report 2000, PBC, 2001; Dai, 2002).

Reasons for PBC’s poor record in accomplishing money supply targetsare several. One is the fact that money supply is endogenously determinedwithin the economic system, which makes the PBC incapable of fulfilling theplan of the money supply target. Another reason could be that, in practice,the PBC does not adjust the money supply to the planned targets. Xia

5

Table 1: Targeted and actual monetary policy objectives: 1994-2004Year M1 (%) M2 (%) inflation (%)

Target Actual Target Actual Actual1994 21 26.2 24 34.5 24.11995 21-23 16.8 23-25 29.5 17.11996 18 18.9 25 25.3 8.31997 18 16.5 23 17.3 2.81998 17 11.9 16-18 15.3 -2.61999 14 17.7 14-15 14.7 -1.42000 15-17 16 14-15 12.3 0.42001 13-14 12.7 15-16 14.4 0.72002 13 16.8 13 16.8 -0.82003 16 18.7 16 19.6 1.22004 17 13.6 17 14.6 3.9

Note:

1. The inflation rate is based on consumer price index.

2. Source: China Financial Yearbook, various issues.

and Liao (2002) pointed out that it seems that in actual monetary policyoperations, the PBC did not adjust money supply strictly according to theplanned targets.

This motivates the current study to systematically investigate the rela-tions between real output, money supply, and inflation in China, which hasnot been adequately discussed in the literature. Xie (2002), who was thedirector of the PBC’s research division, acknowledges that there is hardlyany research that systemically investigates the relationship between Chineseeconomic growth, money supply and inflation, and therefore it is questiona-ble to use the formula that calculates the target money supply on the basisof the predicted growth rates of GDP and target inflation rates. For thesame reason, it is debatable about the PBC’s use of money supply as theintermediate target for monetary policy (Xie, 2002).

6

2.3 Propositions examined in the empirical analysis

The current empirical study will investigate the cointegration relations andthe shout-run dynamics of the money stock and other relevant economicvariables, in order to understand the following fundamental issues that arerelevant in understanding the foundation of China’s monetary policy.

As we have explained at the beginning of this section, after about 1995monetary policy has undergone changes in terms of policy goals, interme-diate targets, and instruments. In addition, the stance of monetary policyhas changed from controlling inflation to dealing with deflation and unem-ployment. These changes suggest there could be a structural shift in themodel.

Therefore in the current research we will first examine:

1. Is there any structural break in the system? If the answer is yes,we will split the whole sample into two sub-samples, i.e. before and afterthe structural break, and construct models for the two periods separately.Because of the different movements of M1 and M2, we also need to modelM1 and M2, respectively.

2. Whether in China there exists a long run relationship between moneystock and other macroeconomic variables in the system under examination?This long run relationship can be interpreted as a money demand or supplyequation.

3. What are the responses of monetary aggregates, economic growth,inflation and other macroeconomic variables to ”excess money”? Or in otherwords, whether the excess money can stimulate real growth and increaseinflation in the long-run and short-run?

4. Is the money stock determined by money supply or demand?

5. How do real output and inflation respond to monetary shocks?

Because a structural break around 1995 has been identified in our model,we have modelled M1 and M2 in two separate periods. By examining thesimilarities and dissimilarities of the determination of inflation and the twomeasures of money stocks in the two periods, we try to answer this question:

6. Which one should be taken as the intermediate target for China’smonetary policy, M1 or M2?

7

3 Review of the Literature

In contrast to the large volume of empirical studies on money demand andthe monetary transmission mechanism in industrial countries (Lutkepohland Wolters, 1999a), the empirical analysis of Chinese money demand func-tions or monetary transmission mechanisms is scant. The existing studiesinclude Yi (1993), Hafer and Kutan (1994), Huang (1994), Qin(1994), Gi-rardin(1996), Chen (1997), Xu(1998), Qin, et al. (2004), Zhang and Wan(2004), Chow and Shen (2004), etc.

3.1 Main findings of the Literature

Against the backdrop of China’s economic transition, some of the studieshave devoted to defining the institutional variables representative of China’sreforms and the marketization process. Yi (1993) points out that the mone-tization process, accompanied by rapid income increase of both individualsand enterprise, is an important institutional variable. He uses the share ofurban population in total population as a proxy for the monetization pro-cess. When this monetization proxy is included in the estimation of themoney demand function, the model’s explanatory ability is considerably en-hanced. Qin (1994) chooses two institutional proxies to reflect the reformprocess. With these institutional variables in the model, Qin finds that thelong run income elasticity of money demand in China is close to unit, whichis lower than what has been suggested in prior empirical research. This in-dicates the existence of a long run equilibrium relationship between moneydemand and other macroeconomic variables in China.

Most of the empirical analyses apply an error-correction model in theireconometric formulations. Some of them use single equation error-correctionmodels which follow the methodology of Engle and Granger (1987), othersdraw on vector error-correction models which follow the maximum likelihoodmethod of Johansen (1995). Some models are based on quarterly data from1978 when China started economic reforms (Qin, 1994, Huang, 1994, Girar-din, 1996, and Chow and Shen, 2004), while in other models, annual dataare employed and the sample period starts with the beginning of the 1950swhen the People’s Republic China was just established (Yi (1994), Chen(1997), Zhang and Wan (2004), and Chow and Shen (2004)).

The aforementioned empirical research have reached a similar conclusion

8

that, in spite of considerable economic changes during the reform years, arelatively stable relationship of money demand can be found in China.

3.2 Main Problems and Shortcomings of Previous Research

Although prior work has made valuable contributions to the understan-ding of the relationship between monetary variables, output and inflation inChina, problems and shortcomings do exist.

1. Most of these empirical analyses are based on single equation estima-tion, which implicitly assumes that monetary aggregate is an endogenousvariable while other macroeconomic variables are weakly exogenous. Howe-ver, rarely any proper statistic test were conducted in previous research tojustify this assumption. The only exception is Giradin (1996), which testsfor weak exogeneity using a multiple cointegration technique, but the sampleperiod from 1988-1993 in his model is rather short. The assumption thatthere is only one cointegration relation among monetary variables, incomeand inflation is not consistent with theoretical insights underpinning inter-action of monetary policy and the real economy, hence is doubtful. Froma statistical point of view, to assume that there is only one cointegrationrelation in the information set and that the money stock is the only endoge-nous variable means imposition of many restrictions on the long-run matrix,the validity of which needs to be tested. Because single equation estimationof cointegrated vectors is problematic, if cointegrated variables are betweenthe regressors, the estimation results without testing for cointegration rankand weak exogeneity are not accurate and reliable (Ericsson, et al, 1998).

2. The sample period of most existing studies is up to 1995. As wehave analyzed in the previous section, since 1995 China’s monetary policyhas undergone sweeping changes. In this sense, the previous research hasmissed the critical shift in China’s monetary policy, which has lasting impli-cations. The current research extends the sample period to 1979-2004, i.e.from the beginning of China’s economic reforms to when the latest data areavailable for the present study. The correlation between money aggregatesand the monetary policy goal after 1995 is the focus of the examination ofthis research, with a view to shed light on the functioning of the Chinesemonetary policy.

9

4 Economic theoretical framework

In the current study, we apply the conventional static IS-LM model as theframework of the economic analysis. The static comparative solution of theconventional IS-LM model can provide useful expositional device for theanalysis of the long-run structure of a dynamic model.

4.1 Money demand function and choice of variables

Because the money demand function is in the center of interest in a mo-netary model, in this subsection we first illustrate the standard theory ofmoney demand. Then we give the explicit form of a money demand functionand explain the relevant variables, which should be included in a standardmonetary model. In the end, we discuss some issues concerning the Chinesemoney demand function.

4.1.1 The Standard Money Demand Function

According to conventional monetary theory, demand for money stems fromat least two sources: as an inventory to smooth differences between incomeand expenditure streams, and as one of several assets in a portfolio. Bothdemands lead to a long-run specification of the following form (Ericsson,1999):

Md/P = f(I,R), (1)

where Md is the nominal quantity of money demanded, P is the price level,I is a scale variable, and R is a vector of returns on various assets. Thefunction f(·, ·) is increasing in I, decreasing in those elements of R that areassociated with assets other than Md, and increasing in those elements ofR for assets regarded as Md.

Equation (1) is commonly represented with the following money demandfunction (2), which is in log-linear form, with the interest rates entering ineither logs or levels (Ericsson, 1999):

md − p = b0 + b1i + b2Rout + b3R

own + b4∆p, (2)

where b0, b1, b2, b3 and b4 are coefficients, Rout and Rown are the ratesof returns on assets other than money and on money itself. So b2 should

10

be negative and b3 positive. In empirical models, the spread Rout − Rown

is usually used to measure the opportunity costs of holding money, whichimplies that b2 and b3 have equal magnitudes but opposite signs. The infla-tion rate ∆p measures the return to holding goods instead of money, so b4

should be negative.

4.1.2 The Choice and Measurement of Variables

The choice of the measurement of money and the associated economic theorymay determine the selection of the scale variable. In the portfolio theory ofasset demand, wealth is a natural scale variable, while noting that incomemay be relevant as well. Thus, wealth is often included in models of thedemand for broad money. Because the narrow money is held mainly fortransaction demand, GDP is an appropriate scale variable for narrow moneyequations.

4.1.3 China’s Money Demand Equation

In this study, the money demand (or supply) equation for two measures ofmoney, namely M1 and M2 are to be modelled separately. In the contextof China, M1 and M2 are defined as follows:

M1 = currency in circulation + demand deposits of firms

M2 = M1 + time deposits of firms + saving deposits of households

The firms’ and households’ demand deposits M1 bear interest rate fordemand deposit. The interest rates have been strongly regulated by the PBCwith only occasional changes. Among various interest rates, the one−yeardeposit rate is generally regarded as the benchmark rate which plays a do-minant role in China’s interest rate system. The PBC adjusts the one−yeardeposit rate, here denoted as R, according to changes in inflationary conditi-ons. This will be followed by adjustments of other interest rates. When theinflation rate goes up, the PBC increases R and enlarges the gap betweenR and the interest rate for demand deposits, to reduce the demand for M1.When the inflation rate goes down, the PBC adjusts the interest rates inthe opposite direction.

In this study, R is included in the M1 demand equation to represent theopportunity costs of holding M1 rather than quasi money. The sign of R

11

in the M1 demand equation is expected to be negative. In the M2 demandfunction, the R is the own rate of return for firms and households’ timedeposits, which is a component of M2, and hence its sign could be positive,if we assume that the public are willing to hold money rather than otherfinancial or physical assets when the interest rate increases.

In the standard money demand function, the bond rate is usually inclu-ded to represent the interest rate on assets other than money. In the case ofChina, because of the underdevelopment of financial markets, bank depositsare the predominant form of financial assets.1 Therefore, only R is includedin the M2 model. Because of the unavailability of data for wealth, we usereal GDP in the M2 model as a scale variable.

In summary, the money demand functions for M1 and M2 in China areexpressed in what follows, where m1 and m2 are logarithm of M1 and M2,respectively, y is the logarithm of real GDP, p and ∆p are logarithm of CPIand its first difference, R denotes the one-year deposit rate. The followingempirical investigation is based on monetary models with four variablesm1/m2, y,∆p,R.

4.2 Potential long-run equilibria

Within the framework of the aforementioned monetary models with fourvariables, we expect to find the following potential equilibria or cointegrationrelations in the current empirical investigation.

4.2.1 Money demand or supply relation

Since in the steady state md = ms, the observed money holdings can be eit-her a realization of money demand or supply, unless adjustment takes placeimmediately (Juselius, 1996). The observed money stock can be determi-ned by demand or supply, or both. If the central bank is able to effectivelycontrol the money stock, then the observed money stock is likely to be sup-ply determined, and the demand for money has to adjust to the suppliedquantities (Juselius, 2005). In an economy with capital and credit controls,this is likely to be the case. However, if the central bank cannot control

1With the rapid development of the housing market since around 2000 when the pro-perty market reform was launched, owning real properties has become an alternativemeans for households to hold wealth.

12

the money stock, or the central bank’s money supply conforms to agents’desired money holdings, then the observed money stock could be determinedby the demand for money. This is usually the case in open and deregulatedeconomies.

Demand function for M1 If a M1 demand function exists, it shouldhave the following form:

m1d − p = b0 + b1y − b2R + b3∆p, (3)

or:

m1d − p = b4 + b5y − b6(R−∆p), (4)

with b1, b2, b5, b6 > 0. R−∆p represents the real interest rate. The signof b3 is indeterminate without further information, because on the one hand,high inflation could drive economic agents to transform quasi money intoM1 in order to increase liquidity. On the other hand, economic agents tendto keep more physical goods rather than holding money.

Demand function for M2 The M2 demand function can be representedin the following form:

md2 − p = b0 + b1y + b2R− b3∆p, (5)

ormd

2 − p = b4 + b5y + b6(R−∆p) (6)

with b1, b2, b3, b5, b6 > 0

The Central Bank’s Reaction Function During the sample periodunder examination, the main policy instrument that PBC has deployed isquantity control. According to Juselius (1996), if quantity control is adoptedas a monetary instrument, the central bank’s reaction function would includea relation between velocity and excess inflation:

(mt − pt − yt − k) = f(∆pt − π∗) + uCBm, (7)

13

where k is a constant, π∗ is the target inflation rate, and uCBm is astochastic residual. If the inflation rate is above/below the central bank’starget rate, central bank will take contractive/expansionary monetary po-licy. The money stock will be decreased or increased correspondingly. Ifthe monetary expansion effect on inflation is predominated, which meansmonetary expansion always leads to inflation, then inflation will be posi-tively cointegrated with trend-adjusted velocity. This relation results in thefollowing equilibrium:

(mt − pt − yt − b1trend− k) = b2∆pt + uCBm, (8)

with b1, b2 > 0.

If the central bank controls the money supply in order to keep a trend-adjusted velocity constant, then the following long-run steady relation exits:

(mt − pt − yt − b1trend− k) = uCBm, (9)

with b1 > 0.

Real Income Relation and the Phillips Curve If monetary expan-sion leads to inflation through demand pressure, then inflation is cointegra-ted with trend-adjusted real income. Based on the IS-LM model, the realaggregated income relation can be characterized by the following function:

yt = c1Rt + c2∆pt + c3trend + uy (10)

Where a trend variable is used to approximate the linear real producti-vity trend . Hence, the trend-adjusted real income, yt − c3trend, representsthe cyclical part of real income. If c1 < 0 and c2 = −c1, equation (10)can be interpreted as an IS relation. If c1 = 0, and c2 > 0, (10) can beinterpreted as a short-run Phillips curve. In both cases, c3 represents theaverage quarterly growth rate of real income for the sample period.

Relation between money expansion and real income If money stockis dominated by money supply, and expansion of real money always causesthe increase of the domestic aggregate demand, or alternatively, if moneystock is mainly determined by money demand, and higher transaction value

14

needs more money, then the following long-run equilibrium exits:

m1t = c0 + c1yt + um1, (11)

orm2t = c2 + c3yt + um2, (12)

with c1 > 0 and c3 > 0.

In the former case, the change of money stock is not error correctingto the deviation from the steady-state, whereas in the later case the moneydemand is negatively error correcting to the deviation from the equilibrium.

Relations between interest rate and inflation: the Fisher parityThe Fisher parity implies that the steady-state relationship between theinterest rate and the expected inflation rate is as follows:

Rt = R0 + Et(∆pt+1) + uRt (13)

Where R0 is the constant real interest rate. Et(∆pt+1) represents the ex-pected inflation rate at time t. uRt is a stochastic residual. If the realizedinflation rate is used to approximate the expected inflation rate, then theFisher parity can be modified to take the following form:

Rt = b0 + b1∆pt + ut, (14)

Where b1 > 0, and close to 1.

The liquidity effect If the excess money supply has a liquidity effect andcauses a decrease in the short-run interest rate, then the following long-runrelation might be found in the data:

(mt − pt − yt − b1trend− k) = −b2R + ut, (15)

with b1, b2 > 0.

The aforementioned steady-state relations provide theoretical underpin-nings for the investigation and interpretation of long-run relationships in thesystem. Furthermore, by analyzing the short-run dynamics of the variablesin the system, the dynamic path from one steady-state to another and theinterrelations between the variables can also be examined.

15

5 Data definition and preliminary analysis

5.1 Data definition

The definitions of the original variables is as follows:

M1t: nominal money supply of M1t

M2t: nominal money supply of M2t

GDPCt: real GDP in 1990 prices

Rt: one-year interest rate of household’s savings deposits

Pt: consumer price index, equals to 100 in 1990

The transformed variables used in the empirical VAR models are asfollows:

m1t: the real money stock of m1t, defined as log of M1t/Pt,

m2t: the real money stock of m2t, defined as log of M2t/Pt,

yt: four-quarter moving average of log of GDPCt:2

yt = (LGDPCt + LGDPCt−1 + LGDPCt−2 + LGDPCt−4)/4,

∆pt: the quarterly inflation rate in terms of CPI,

R1t: the one-quarter deposit interest rate, R1t = Rt/4

5.2 Data graphs and preliminary analysis

Figure 1 and 2 display data for m1t,m2t, yt, ∆pt, R1t in levels and in dif-ferences for the period 1978:1-2004:4, respectively. The results of HEGYseasonal unit root tests in Table 2 show that there are unit roots at 1, -1,and ±i in LGDPCt. The reason for the presence of the seasonal unit rootsmight be related to the way the data are compiled. China does not publishGDP data for individual quarters. The available quarterly GDP data are

2The reason to make this transformation is to get rid of the seasonal unit roots.

16

Table 2: Seasonal unit root tests for the period 1978:1-2004:4

HEGY seasonal unit root testsvariable deter. lag length t(π1) t(π2) F : π3

⋂π4

m1t c, t, sd n(AIQ) = n(HQ) = 1 -2.44 -6.04** 20.78**m2t c, t, sd n(AIQ) = n(HQ) = 1 -3.49* -3.43** 7.14**LGDPCt c, t, sd n(AIQ) = n(HQ) = 1 -2.36 -2.33 2.93∆pt c, sd n(AIQ) = n(HQ) = 1 -3.25* -1.24 8.52**

Notes:

1. c, t, sd denote constant term, trend and centered seasonal dummies, respec-tively.

2. Lag order n is chosen by Akaike (AIC) and Hannan-Quinn (HQ) info criteriawith maximum lag length of 6.

3. t(π1), t(π2) and F : π3

⋂π4 indicate there are roots at 1, -1 and ±i in the

data, which indicates that there is regular, semiannual, or annual unit rootsrespectively.

4. * and ** denote significance at 5% and 1% level.

17

1980 1985 1990 1995 2000 2005

3

4

5

6 m1

1980 1985 1990 1995 2000 2005

4

6

m2

1980 1985 1990 1995 2000 2005

8

9

y

1980 1985 1990 1995 2000 2005

0.00

0.05

0.10Dp

1980 1985 1990 1995 2000 2005

0.01

0.02

0.03R1

Figure 1: Data in levels

compiled accumulatively. Therefore, we transform the real GDP data to itsfour-quarter moving average to get rid of the seasonal unit roots.

The one-year saving deposits rate Rt is transformed to one-quarter rateR1t, in order to match the quarterly inflation data ∆pt.

Several dummy variables are included in the models to capture the effectsof government intervention or regime breaks. Impulse dummies are definedas dxxqyt = 1, where xx and y denote the year and the quarter wheredxxqyt = 1, respectively, and equals 0 anywhere else. E.g. d80q1t equals 1for the first quarter of 1980 and 0 elsewhere. The step dummy is denotedas Dp97t, which equals to 1 from 1997Q1 to 2004 Q4, and 0 otherwise. Thedummy variables included in the models will be described in details whendiscussing individual model’s specifications.

18

1980 1985 1990 1995 2000 2005

−0.1

0.0

0.1

0.2 Dm1

1980 1985 1990 1995 2000 2005

−0.1

0.0

0.1

0.2 Dm2

1980 1985 1990 1995 2000 20050.000

0.025

0.050Dy

1980 1985 1990 1995 2000 2005

−0.10

−0.05

0.00

0.05 DDp

1980 1985 1990 1995 2000 2005

0.000

0.005DR1

Figure 2: Data in differences

6 Models for the full sample 1979:1-2004:4

6.1 The statistical model

The statistical model for the current empirical analysis is an unrestrictedvector autoregressive model (VAR) in the following form:

∆xt = Π(x′t−1, trend, st−1)

′+

k∑

i=1

Γi∆xt−i + ΦDt + εt (16)

Witht = 1, · · · , T, εt ∼ N(0,Ω)

where xt is a (p × 1) vector of endogenous variables, and the parametermatrices Π,Γ1, · · · ,Γk,Φ,Ω are unrestricted. Under the hypothesis thatxt is an I(1) process, Π has reduced rank r < p and can be formulatedas Π = αβ

′, where α and β are (p × r) matrices, respectively. Meanwhile,

α′⊥Γβ⊥ has full rank, where α⊥ and β⊥ are the orthogonal matrixes of

19

α and β, respectively and Γ = I − ∑k−1i=1 Γi(see section 3.3 for the VAR

representation).

In addition, in the equation (16), a trend variable is allowed to enter thecointegration space, because money supply and GDP are trending variables.st denotes a vector of exogenous variables, or un-modelled variables, suchas the shift dummies, and fixed and non-stochastic variables that need tobe included in the cointegration space. Dt contains a constant term andcentered seasonal dummies, intervention impulse dummies, as well as thecurrent and lagged differences of the variables in st. The constant term andcentered seasonal dummies are unrestricted, which means they are includedboth inside and outside the cointegration space.

6.2 Model specification and estimation

We estimate the m1 and m2 models for the full sample based on the unre-stricted cointegrated VAR model (16). For m1 and m2 models, xt contains(m1t, yt , ∆pt) and (m2t, yt , ∆pt), respectively. st includes R1 and Dp97t

for both models. In the m1 model, intervention dummies consist of impulsedummies d80q1, d84q1, d85q4, d86q4, d88q1, d88q3 and d93q1, while in them2 model, they consist of d80q1, d83q1, d84q1, d84q4, d85q1, d85q4, d88q3and d93q1. The impulse dummies are chosen according to the outliers in theresiduals of the system, which have been caused by the policy interventions.

Based on the Schwarz and Hannan-Quinn information criteria with themaximal lag length setting to be 4, the lag length for both models are set tobe 4. The residual misspecification tests turn out that there are no seriousmisspecification problems in the residuals of both models.3 Based on theseresults, the parameter nonconstancy tests are performed.

6.3 Stability tests and identification of structural changes

Before we conduct further empirical analysis, it is important to test whetherthe model is misspecified. This includes tests for residual misspecificationand parameter nonconstancy. As we have discussed in section 2.4, the im-plementation of China’s monetary policy seems to have undergone changesbefore and after the mid-1990s. Therefore it is of interest to test whether

3The misspecification tests of the two models for the full sample period is available onrequest.

20

Test for Constancy of the Log-Likelihood

1989 1991 1993 1995 1997 1999 2001 20030

1

2

3

4

5X(t)R1(t)5% C.V. (1.36 = Index)

Figure 3: The recursively calculated log-likelihood for m1 model

there is evidence from the data that a structural shift has occurred in thesample period by testing for parameter constancy. The model for the wholeperiod is used for the tests of the parameter constancy and whether there isa structural shift occurring in the sample period. For this matter, variousrecursive tests are first applied to the full-sample models to give us a visualinspection of the constancy, followed by formal statistical tests to identify astructural break.

21

Test for Constancy of the Log-Likelihood

1989 1991 1993 1995 1997 1999 2001 20030.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5X(t)R1(t)5% C.V. (1.36 = Index)

Figure 4: The recursively calculated log-likelihood for m2 model

22

Trace Test Statistics

The test statistics are scaled by the 5% critical values of the basic model1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

0.0

0.5

1.0

1.5

2.0

2.5 X(t)

H(0)|H(3) H(1)|H(3) H(2)|H(3)

1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 20040.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75 R1(t)

Figure 5: The recursively calculated trace test statistics for m1 model

23

Trace Test Statistics

The test statistics are scaled by the 5% critical values of the basic model1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25 X(t)

H(0)|H(3) H(1)|H(3) H(2)|H(3)

1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 20040.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25 R1(t)

Figure 6: The recursively calculated trace test statistics for m2 model

24

Test of Beta(t) = ’Known Beta’

1989 1991 1993 1995 1997 1999 2001 20030.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5X(t)R1(t)5% C.V. (16.9 = Index)

Figure 7: The recursively calculated test of β for m1 model, reference sampleis 1980:1-2004:4

25

Test of Beta(t) = ’Known Beta’

1989 1991 1993 1995 1997 1999 2001 20030.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0X(t)R1(t)5% C.V. (16.9 = Index)

Figure 8: The recursively calculated test of β for m1 model, reference sampleis 1995:1-2004:4

26

Test of Beta(t) = ’Known Beta’

1989 1991 1993 1995 1997 1999 2001 20030.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5X(t)R1(t)5% C.V. (16.9 = Index)

Figure 9: The recursively calculated test of β for m2 model, reference sampleis 1980:1-2004:4

27

Test of Beta(t) = ’Known Beta’

1989 1991 1993 1995 1997 1999 2001 20030.0

0.5

1.0

1.5

2.0

2.5X(t)R1(t)5% C.V. (16.9 = Index)

Figure 10: The recursively calculated test of β for m2 model, referencesample is 1995:1-2004:4

28

6.4 Recursive tests for parameter constancy

6.4.1 Tests for recursively calculated log-likelihood

CATs in RATS 2.0 provides a variety of recursive tests of parameter con-stancy. Here we present graphs of some recursive tests.

Figure 3 and Figure 4 display the forward recursively calculated log-likelihood of m1 and m2 models based on both X-form and R-form withthe line for the 5% critical value. The graphs indicate that there existspossible instabilities in the sample period.

6.4.2 Tests for recursively calculated trace test statistics

Figure 5 and 6 contain the recursively calculated trace test statistics for them1 and m2 models, respectively. They show that, two stable cointegrationrelations exist for both models from 1995. But before that, it seems the twocointegration relations are not stable in both models. In general, the figuresof recursively calculated trace test statistics suggest that there might be astructural break at around 1995:1.

6.4.3 Tests for constancy of β

Figure 7 and Figure 9 show the recursively calculated test statistics of them1 and m2 model, respectively. In the graphs the test statistic is scaled by5% critical value. The reference time is chosen to be the full sample period.Figure 7 shows that there exists a structural shift at around 1995. Becauseof our interest in the more recent economic regime, we next conduct therecursively calculated β test statistic using 1995:1-2004:4 as the referencesample period. Figure 8 and Figure 10 display that all the parts of thegraphs are above the rejection lines, which indicates that the estimated βbased on the period 1995:1-2004:4 are different from that obtained from thefull sample period.

6.4.4 Chow tests for structural changes

In addition to nonconstancy tests by means of recursive graphs, Chow testsoffer a statistical possibility for testing structural changes. Jmulti 3.1 pro-

29

Table 3: Chow tests for VAR models 1979:1-2004:4 for m1 and m2Model Break point Test Test statistic p−value

m1 1994Q4 λSS 227.5154 0.0000λBP 144.1051 0.0000

m2 1994Q4 λSS 427.9735 0.0000λBP 180.4821 0.0000

Note: λBP and λSS denote test statistics for break point Chow tests and samplesplit Chow tests, respectively. Sample range for estimation is 1980:1-2004:4

vides the program to test the sample-split, break-point and forecast Chowtests.

Table 3 reports the break point and sample split Chow tests for the m1and m2 models, assuming the breaking data is 1994Q4. All the tests rejectthe stability in m1 or m2 model, which suggests that a structural changeoccurred before and after 1994:Q4. Therefore, in the following sections wesplit the sample period into two sub-periods; one is from 1979:1 to 1994:4,and the other is from 1995:1 to 2004:4. All further empirical analysis isapplied to these two separated periods.

7 Empirical analysis for m1 and m2 models in thetwo sub-samples

The finding of a structural change allows us to split the sample into twosub-periods, i.e. before and after 1995Q1. Therefore we have four models.Hereafter, they will be denoted as m1 model 1, m2 model 1, m1 model 2,m2 model 2, respectively.

7.1 Model specifications

The statistical formulation for the four models are based on the unrestrictedcointegrated VAR model (16). To save space, the precise specification of thefour models are summarized in Table 4.

The interest rate variable R1 rarely changes and does not look like astochastic variable. We initially included it in the models as an exogenous

30

Table 4: Model specification of m1 1,2 and m2 1,2Variables model 1 model 2

m1 m2 m1 m2

xt

m1t

yt

∆pt

m2t

yt

∆pt

m1t

yt

∆pt

m2t

yt

∆pt

st - -(

R1t

Dp97t

) (R1t

Dp97t

)

Dt

d80q1d84q1d84q4d85q2d85q4d86q1d93q1d94q1

d80q1d84q1d84q4d85q1d85q4d88q3d93q1

(d03q2

) (d03q2

)

variable. However, through variable exclusion tests, we find that R1 can beexcluded in m1 and m2 model 1. The exclusion test output is reported inTable 5.

The shift dummy Dp97t is included in m1 and m2 model 2, due to theenlargement of the measurement of money stocks since 1997Q1.

7.2 Lag length determination

The choice of the lag length is mainly based on the information criteria tests.Table 6 contains the output of information criteria tests, where SC and H-Qindicate Schwarz and Hannan-Quinn information criteria, respectively. Thetest results show that for m1 model 1, 2, and m2 model 1, both SC and H-Qsuggest the same order, which is 2, 1, and 4, respectively. The residual and

31

Table 5: Testing the exclusion of R1

Models1979:1-1994:4 1995:1-2004:4

coin. rank m1 m2 m1 m2r = 1 2.264

[0.132]0.019[0.892]

4.631[0.031]

2.645[0.104]

r = 2 4.785[0.091]

2.056[0.358]

11.889[0.003]

7.115[0.029]

Note: P -values in square brackets

Table 6: Lag length Determination Tests

m1 m2Model k SC H-Q SC H-Q

4 -22.60 -24.13 -23.21 -24.74Model 1 3 -22.68 -24.02 -22.82 -24.16

2 -23.21 -24.35 -23.02 -24.171 -22.60 -23.56 -22.03 -23.194 -26.18 -28.50 -29.12 -31.52

Model 2 3 -26.42 -28.31 -28.45 -30.422 -26.64 -28.10 -28.93 -30.471 -27.54 -28.57 -29.44 -30.56

Note: SC and H-Q denote Schwartz and Hannan-Quinn information criterion, re-spectively. The maximum lag length is set to be 4

32

Table 7: Multivariate misspecification tests

Multivariate tests: 1979-1994 1995-2004m1 m2 m1 m2

Autocorrelation:LM1(9): 15.2[0.08] 11.4[0.24] 6.9[0.63] 7.7[0.56]LM4(9): 21.9[0.01] 9.7[0.37] 12.0[0.21] 12.4[0.18]Normality:χ2(6): 6.6[0.35] 4.8[0.55] 5.6[0.46] 3.02[0.80]ARCH:LM1(36): 51.3[0.05] 21.3[0.97] 32.4[0.64] 30.0[0.74]LM2(72): 74.7[0.38] 48.5[0.98] 66.5[0.66] 78.1[0.29]

recursive tests show that there is no problem with misspecification or non-constancy for the models with corresponding lag length. For the m2 model2, SC suggests order 1, but H-Q suggests order 4. The recursive estimationindicates that both VAR(1) and VAR(4) are significantly nonconstant forthe estimated β coefficients, while the misspecification tests and recursiveestimations show that VAR(2) has good properties. Therefore, we will esti-mate m1 model 1 and 2, m2 model 1 and 2 as VAR(2), VAR(1), VAR(4)and VAR(2), respectively.

7.3 Model misspecification tests

Table 7 and Table 8 report residual tests for the system and for individualequations. They are based on corresponding unrestricted VAR models. TheMultivariate tests are conducted using CATS in RATS 2.0, while univariatetests are performed with PcGIVE 10.0. Figures in square brackets besidethe test statistics are the corresponding p-values.

There is some evidence of fourth order autocorrelation in the residuals ofthe ∆pt equation in the m1 model 1 and for the whole system, which suggeststhat there is probably some seasonal autocorrelation left in the ∆p equationdespite the inclusion of quarterly seasonal dummies. A graphic inspection of∆p shows that the seasonal pattern seems to have changed since about 1987,perhaps because of the change in the data compilation. Quarterly inflationdata before 1987 was calculated by the National Bureau of statistics ofChina. However, the CPI quarterly statistics has been published only since

33

Table 8: Univariate misspecification TestsAutocorrelation ARCH Normality R2

AR 1-1 AR 1-4 ARCH 1-2 χ2(2)m1 model 1

m1 0.02[0.86] 1.02[0.40] 0.48[0.61] 0.86[0.64] 0.78y 0.30[0.58] 1.43[0.24] 0.96[0.38] 1.38[0.50] 0.85∆p 1.98[0.16] 3.36[0.02] 0.32[0.72] 4.48[0.10] 0.81

m2 model 1m2 0.57[0.45] 0.18[0.94] 0.41[0.66] 0.71[0.69] 0.87y 0.51[0.47] 1.56[0.20] 0.84[0.43] 1.47[0.47] 0.90∆p 1.58[0.21] 0.89[0.47] 0.005[0.99] 1.80[0.45] 0.89

m1 model 2m1 0.01[0.90] 1.15[0.35] 0.11[0.89] 0.72[0.69] 0.81y 0.21[0.64] 0.65[0.62] 0.35[0.70] 0.36[0.83] 0.60∆p 0.04[0.83] 1.39[0.26] 0.62[0.54] 2.97[0.22] 0.96

m2 model 2m2 6.56[0.02] 1.51[0.24] 0.04[0.95] 0.70[0.70] 0.80y 0.02[0.88] 1.19[0.34] 0.34[0.71] 0.08[0.95] 0.82∆p 0.94[0.34] 0.36[0.83] 0.28[0.75] 1.57[0.45] 0.97

34

1987. Because coefficients of the recursive estimated long-run cointegrationrelations and short-run adjustments turn out to be stable and constant underthe model specification, we keep this specification and further analysis will bebased on it. The F-test shows there is a problem of first order autocorrelationin the residual of the m2 equation in m2 model 2. But the LM (1) test forthe system suggests there is no autocorrelation in the system. Except forthis minor problem, the misspecification tests show that all p-values aresubstantially greater than usual significance levels, suggesting no problemof autocorrelation, ARCH or nonnormality for the system and for individualequations. The R2 values show that a large part of variations of the systemcan be explained by the chosen information set. In general, the currentmodels seems to be well behaved.

7.4 Cointegration Rank Determination

The determination of the cointegration rank is equal to determine how manystochastic trends are in the system, and it is thus crucial for the long-run andshort-run structure identification and impulse analysis. This calls for moreattention to be paid to this issue. Because of the low power of trace tests,Juselius (2005) and also Hendry and Juselius (2001) suggest the use of diffe-rent sources of information to determine the cointegration rank. The usefulinformation includes: (1) trace tests, (2) the largest roots of the companionmatrix, (3) t-values of the adjustment coefficients of the cointegration vector,and (4) the recursive graphics of the trace statistic. In the present empiricalstudies, all four information resources are applied for the determination ofthe cointegration ranks.

7.4.1 Trace tests for cointegration rank determination

Table 9 shows the results of the trace test for the determination of cointegra-tion ranks, where Trace denotes the asymptotic trace statistic correspondingto a model without shift dummies, and Trace* denotes the trace statisticwith Bartlett small sample corrections. Because R1t and the shift dummyDp97t are included in the m1 and m2 models 2 as exogenous variables, thecritical values for standard trace test are not valid and need to be simulated.CATS in RATS 2.0 automatically gives the simulated critical values whenstochastic exogenous variables are included in the cointegration space (Ju-selius, 2005, section 8.2). In the current m1 and m2 models 2, R1 does not

35

behave like a real stochastic variable, and Dp97t is a shift dummy, thereforewe use the critical values calculated in CATS in RATS 2.0 for the trace tests,but also check the cointegration ranks with further information. The resultsof trace tests suggest that the cointegration ranks for all the four modelsshould be 2.

7.4.2 The graphs of the recursive trace statistic

Following Juselius (2005, section 9.1), if the cointegration rank is r < p,then the recursively calculated components of the trace statistic should growlinearly for all i = 1, · · · , r, but stay constant for i = r + 1, · · · , p.

Figure 11, Figure 13, figure 12 and figure 14 exhibit pronounced lineargrowth in the first two cointegration relations in the R-form, but no growthin the third one, although it seems that the second cointegration vector inm1 model 2 is not very stable and the second cointegration vector in m2model 2 is not very significant. The first two linearly growing trace testcomponents correspond to two cointegration relations, while the third oneindicates a small eigenvalue, which corresponds to a unit root or near unitroot.

7.4.3 Checking the roots of the companion matrices

Following Hendry and Juselius (1999), if the rth + 1 cointegration vectoris nonstationary and is wrongly included in the model, then the largestcharacteristic root will be close to the unit circle. After restricting a reducedrank to the model, the largest characteristic roots will be significantly smallerthan one.

Table 10 shows the three largest characteristic roots for the unrestrictedmodels and the models restricted with reduced rank. In m1 models 1 and2, and m2 model 1, there is a large root for the unrestricted models. Afterrestricting the cointegration rank to be 2, the largest unrestricted roots havebeen smaller. Although in m2 model 1 the difference between 0.95 and 0.91is not very significant, but adjustment coefficients α are very significant forr = 2. This result can be regarded as evidence for two cointegration relationsin these two models. For m2 model 2, this is not the case however. Thelargest root becomes larger when r is reduced from 3 to 2. Meanwhile, theadjustment coefficients α of β

′xt−1 are significant for both r = 2 and r = 3.

36

Table 9: Trace Test for the Rank DeterminationM1 model 1

p-r r Eig.Value Trace Trace* Frac95 P-Value P-Value*3 0 0.66 102.60 90.29 42.77 0.00 0.002 1 0.38 35.64 32.03 25.73 0.00 0.001 2 0.08 5.46 4.87 12.44 0.54 0.62

M2 model 2p-r r Eig.Value Trace Trace* Frac95 P-Value P-Value*3 0 0.52 84.86 74.19 42.77 0.00 0.002 1 0.46 39.71 34.87 25.73 0.00 0.001 2 0.03 1.98 1.84 12.44 0.95 0.96

M1 model 2p-r r Eig.Value Trace Trace** Frac95 P-Value P-Value*3 0 0.77 97.88 94.05 57.31 0.00 0.002 1 0.54 39.58 38.67 35.95 0.02 0.021 2 0.21 9.20 9.13 18.15 0.55 0.59

M2 model 2p-r r Eig.Value Trace Trace** Frac95 P-Value P-Value*3 0 0.68 88.28 73.94 57.31 0.00 0.002 1 0.54 44.89 36.29 35.95 0.00 0.041 2 0.32 15.10 11.18 18.15 0.12 0.36

Note: trace and trace* denote standard trace statistics and the trace statistics withBartlett corrections for small sample, respectively. Frac95 denotes the 95% quantilefrom the asymptotic table generated in CATS in RATS 2.0. The value of Frac95for the model 1 corresponds to that in the asymptotic table generated with a trendin the cointegration relations, while that for the model 2 is generated with a trendand a random exogenous variable in the cointegration relations

37

Trace Test Statistics

The test statistics are scaled by the 5% critical values of the basic model1987 1988 1989 1990 1991 1992 1993 1994

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25 X(t)

H(0)|H(3) H(1)|H(3) H(2)|H(3)

1987 1988 1989 1990 1991 1992 1993 19940.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00 R1(t)

Figure 11: Recursive trace test statistic M1 1979:1-1994:4

Table 10: Modulus of the 3 largest roots of the companion matricesModel 1

coin.ranks m1 m2unrestricted 0.902 0.902 0.498 0.947 0.914 0.914

2 1.000 0.711 0.539 1.000 0.909 0.9091 1.000 1.000 0.634 1.000 1.000 0.842

Model 2coin.ranks m1 m2

unrestricted 0.993 0.534 0.0912 0.769 0.769 0.5632 1.000 0.886 0.014 1.000 0.857 0.4691 1.000 1.000 0.788 1.000 1.000 0.719

38

Trace Test Statistics

H(0)|H(3) H(1)|H(3) H(2)|H(3)

The test statistics are scaled by the 5% critical values of the basic model1999 2000 2001 2002 2003 2004

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00X(t) = R1(t)

Figure 12: Recursive trace test statistic M1 1995:1-2004:4

39

Trace Test Statistics

The test statistics are scaled by the 5% critical values of the basic model1987 1988 1989 1990 1991 1992 1993 1994

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25 X(t)

H(0)|H(3) H(1)|H(3) H(2)|H(3)

1987 1988 1989 1990 1991 1992 1993 19940.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00 R1(t)

Figure 13: Recursive trace test statistic M2 1979:1-1994:4

40

Trace Test Statistics

The test statistics are scaled by the 5% critical values of the basic model2001 2002 2003 2004

0.4

0.6

0.8

1.0

1.2

1.4

1.6 X(t)

H(0)|H(3) H(1)|H(3) H(2)|H(3)

2001 2002 2003 20040.4

0.6

0.8

1.0

1.2

1.4

1.6 R1(t)

Figure 14: Recursive trace test statistic M2 1995:1-2004:4

41

This can be regarded as evidence that some variables contain a near I(2)unit root (Juselius, 1999).

7.4.4 Concluding remarks

In this subsection, various information has been applied to testing the coin-tegration ranks of the four models. Evidence for the existence of two coin-tegration relations in the m1, m2 model 1 and m1 model 2 are quite clear.Whereas evidence for two cointegration relations in the m2 model 2 seemsweak, which implies that the cointegration rank in this model could be oneor two. In the following analysis, we first restrict all four models with r = 2.After imposing restrictions on long-run cointegrations, we further examinethe plausibility of the rank choice by means of inspecting the stability ofthe long-run cointegration and short-run adjustment coefficients, as well aschecking the economic meaning of the restricted long-run relations.

7.5 Weak exogeneity for the long-run parameters β

Before we further impose restrictions on the VAR models, we test for theweak exogeneity for the long-run parameters β.

Table 11 gives the results of weak exogeneity tests for both r = 2 and r =1. It shows that no variable is weakly exogenous in the m1 models for bothr. In the m2 model 1 and 2, the results depend on the choice of cointegrationrank. If r = 1 then m2t or yt is weakly exogenous in both models. If r = 2,then no variable is weakly exogenous in m2 model 1. We further test thejoint weakly exogenous for m2 model 1 and 2 by setting r = 1. The resultsare χ2(2) = 29.658[0.000] for m2 model 1 and χ2(2) = 1.562[0.458] for m2model 2, where p-values are in square brackets. The results indicate that,in m2 model 2, by setting r = 1, both m2t and yt would have acted as twoindependent driving forces for ∆pt, while ∆pt is a fully adjusting variable.m2t in m2 model 2 is found to be weakly exogenous independent of thechoice of r. When we examine the estimated residual correlation matrixΩ (see table 17), we find the residual correlation between equation m2t

and ∆pt is as large as -0.78, which indicates that current effects betweenthe variables are perhaps neglected in the reduced VAR model. Becausethe identification of the short-run structure may change the adjustmentcoefficients α of the cointegration relations β

′xt, we further estimate all

four models in the full system. In order to check for the robustness of the

42

Table 11: Testing for weakly exogenous variablesModel 1

m1 m2coin. rank m1t yt ∆pt m2t yt ∆pt

r = 1 24.376[0.000]

4.683[0.030]

5.746[0.017]

1.611[0.204]

3.108[0.078]

5.008[0.025]

r = 2 24.422[0.000]

22.051[0.000]

19.451[0.000]

33.541[0.000]

32.994[0.000]

21.331[0.000]

Model 2m1 m2

coin. rank m1t yt ∆pt m2t yt ∆pt

r = 1 7.568[0.006]

11.419[0.001]

9.428[0.002]

0.043[0.835]

1.559[0.212]

10.040[0.002]

r = 2 12.453[0.002]

24.454[0.000]

29.867[0.000]

0.179[0.914]

12.921[0.002]

13.694[0.001]

estimates of β coefficients, we have estimated m2 model 2 based on boththe full system and the partial system conditioning on m2t given r = 2.The difference between the estimates of the β coefficients obtained from thetwo systems is negligible, which justifies our further estimation m2 model 2being based on the full system.

8 Identifying the long-run structure.

8.1 Testing for Single Stationarity Hypotheses

Before formally identifying the long-run structure β′xt, we first test the

stationarity of a single hypothetical cointegration relation, and leaving theremaining r − 1 relations unrestricted. The tests for single stationarity hy-potheses can be regarded as a preliminary attempt to imposing restrictionson the long-run structure, because systematically testing the stationarityof all possible relations helps to spot relevant information for an identifiedlong-run structure. If a hypothetical cointegration relation is rejected by thesingle stationarity test, it could never be included in the long-run structureβ′xt (Juselius, 2005, section 10.4). On the other hand, the single cointegra-

tion relationship can be regarded as a potential equilibrium relationship inthe final long-run structure.

43

The hypotheses to be investigated are of the form β = Hφ1, ψ1, i.e.we test for whether a single restricted relation lies in the cointegration space,while leaving the other relations unrestricted. The test procedure deals withnonlinear estimation problems and is provided by CATS in RATS 2.0 (fordetailed test procedures, see Juselius, 2005, section 10.4).

Tables 12, 13, 14 and 15 show the outcome of tests for the stationarity ofthe potential single relations in m1, m2 model 1 and model 2, respectively.The null hypotheses, or the potential long-run steady-states as illustratedin Section 4, are categorized into four groups, i.e. relations relating to realmoney, real income, the velocity and the inflation rate.

In the real money group, except for m2 model 2 (H30), all the otherthree hypotheses regarding the stationarity of trend-adjusted real moneystocks (H1,H9,H17) can be rejected. Tests for H2,H10,H18 and H31 showthat the real money stock is cointegrated with real income in model 1, butnot in model 2. In m1 and m2 model 1 and m1 model 2, trend-adjustedreal money is positively cointegrated with inflation rate ( see H3, H11, H19).But this is not the case for m2 model 2 (see H32).4

In the group of real income, we test stationarity of trend-adjusted realincome , Phillips curve and IS type relationships. H4, H12, H20 and H33

show that trend-adjusted real income is nonstationary in all four models. Inm1 and m2 models 1, trend-adjusted real income is positively cointegratedwith inflation ( H5 and H13 ), which indicates a Phillips curve type relation,while in the m1 and m2 models 2, trend-adjusted real income is cointegratedwith inflation, but with negative sign ( H21 and H34 ). In the m1 andm2 models 2, the stationarity of the relation between trend-adjusted realincome and the real interest rate are tested by H22 and H35. This relationis nonstationary in m1 model 2 ( H22 ) and stationary in m2 model 2 (H35),but with ’wrong’ signs for IS type relations.

In the group of velocity relations, tests for H6 and H14 show that trend-adjusted velocity in m1 and m2 models 1 is stationary, but with relativelysmall p-values. When the inflation rate is added to the relations denoted byH6 and H14, which indicates the relation between the trend-adjusted velocityand inflation, the coefficients of the inflation are significant. In addition,the p-values rise from 0.21 and 0.09, respectively, to 1, by construction (H7

4This result should not come as a surprise, because a combination of a stationarycomponent (trend-adjusted real money, H30) and a nonstationary component (inflationrate, see H40) is nonstationary.

44

and H15), which indicates that trend-adjusted velocity shares a commonstochastic trend with inflation in some degree, and can be cancelled out bya linear combination. In m1 model 2, the trend-adjusted velocity is notstationary (H23), but is strongly positively cointegrated with the inflationrate (H24) and negatively cointegrated with the real interest rate (H26).In m2 model 2, H36 is the combination of H30 and H33. The p-values ofthe tests for H30 and H33 are 0.16 and 0.00, respectively, hence it is notsurprising that the test for H36 has a lower p-value (0.06). H37 can beregarded as a combination of H30 and H34, or H36 and H40.

The inflation rate in H37 is not significant, which makes H37 close toH36. H36 indicates the trend-adjusted velocity, which is only borderlineacceptable. The test for H38 shows that there is a negative cointegrationrelation between trend-adjusted velocity and interest rate in m2 model 2.

The tests for the group of inflation and the real interest rate show thatinflation (H8, H16, H27, H40) is not stationary in all four models. The realinterest rate (H28, H41) or the relations between inflation and the interestrate with freely estimated coefficients (H29, H42) are also nonstationary inm1 and m2 models 2, which indicates that Fisher parity does not exist inthe Chinese data, probably because the interest rate as a policy variable isheavily regulated by the PBC during the sample period.

8.2 Restrictions on the long-run structure

In the previous section, we have tested various hypotheses of stationarity forsingle relations, in order to spot the potential cointegration relations betweenvariables. In this section, we formally impose restrictions on the long-runstructure and test the joint stability of cointegrations in the systems.

Tables 16 and 17 report the restrictions imposed on the cointegrationspaces and the corresponding short-run adjusted coefficients for m1 and m2models 1 and models 2. We illustrate the test results for the four modelsone by one as follows.

8.2.1 m1 model 1979:1-1994:4

The restricted long-run relations are the combination of hypotheses H2 andH5 in the table 12. The first cointegration vector represented by H5 indicatesthat the expansion of m1 always leads to an increase of real income. The

45

Table 12: Testing the stationary of single relations m1 model 1

m1t yt ∆pt trendt χ2(υ) p− value

Real money relationsH1 1 0 0 −0.029

[−26.022]χ2(1)=10.394 0.001

H2 1 −1.292[−41.333]

0 0 χ2(1) = 0.224 [0.636]

H3 1 0 −10.156[−12.697]

−0.027[−19.513]

− −Real income relationsH4 0 1 0 −0.022

[−24.173]χ2(1) = 24.581 [0.000]

H5 0 1 −6.914[−19.657]

−0.021[−33.195]

− −Velocity relationsH6 1 -1 0 −0.007

[−8.813]χ2(1) = 1.535 [0.215]

H7 1 -1 −3.242[−4.220]

−0.006[−6.082]

- -

InflationH8 0 0 1 0 χ2(2)=12.834 [0.002]

46

Table 13: Testing the stationary of single relations m2 model 1

m2t yt ∆pt trendt χ2(υ) p− value

Real money relationsH9 1 0 0 −0.039

[−40.521]χ2(1)= 19.115 [0.000]

H10 1 −1.715[−71.713]

0 0 χ2(1) = 0.826 [0.364]

H11 1 0 −12.320[−12.433]

−0.036[−35.754]

− −Real income relationsH12 0 1 0 −0.027

[−17.603]χ2(1)= 29.625 [0.000]

H13 0 1 −3.829[−4.093]

−0.015[−22.825]

− −Velocity relationsH14 1 -1 0 −0.017

[−31.953]χ2(1) = 2.840 [0.092]

H15 1 -1 −3.829[−4.277]

−0.015[−23.174]

- -

Inflation rateH16 0 0 1 0 χ2(2)=13.236 [0.001]

47

Table 14: Testing the stationary of single relations for m1 model 2

m1t yt ∆pt R1t Dp97t trendt χ2(υ) p− value

Real money relationsH17 1 0 0 0 −0.283

[−4.871]−0.034[−16.243]

χ2(2) = 18.111 [0.000]

H18 1 −0.501[−0.868]

0 0 −1.393[−4.435]

0 χ2(2) = 19.074 [0.000]

H19 1 0 −12.025[−17.038]

0 −0.237[−5.181]

−0.037[−24.190]

χ2(1)= 0.159 [0.690]

Real income relationsH20 0 1 0 0 0 −0.020

[−37.700]χ2(3) = 28.261 [0.000]

H21 0 1 2.836[14.078]

0 0 −0.019[−63.155]

χ2(2) = 3.585 [0.167]

H22 0 1 2.618[11.546]

−2.618[−11.546]

0 −0.021[−71.521]

χ2(2)= 7.079 [0.029]

Velocity relationsH23 1 -1 0 0 −0.591

[−4.499]−0.008[−1.667]

χ2(2)=18.988 [0.000]

H24 1 -1 −15.088[−20.677]

0 −0.257[−4.611]

−0.017[−8.955]

χ2(1) = 0.418 [0.518]

H25 1 -1 0 33.411[6.373]

−0.046[−0.680]

0.001[0.270]

χ2(1) = 4.589 [0.032]

H26 1 -1 −10.456[−15.523]

10.456[15.523]

−0.183[−4.774]

−0.011[−8.027]

χ2(1) = 1.960 [0.162]

Inflation and real interest rateH27 0 0 1 0 0 0 χ2(4) = 9.001 [0.061]H28 0 0 1 -1 0 0 χ2(4) = 23.492 [0.000]H29 0 0 1 −0.082

[−0.497]0 0 χ2(3)= 8.874 [0.031]

48

Table 15: Testing the stationary of single relations for m2 model 2

m2t yt ∆pt R1t Dp97t trendt χ2(υ) p− value

Real money relationsH30 1 0 0 0 −0.102

[−7.167]−0.036[−76.836]

χ2(2) = 3.559 [0.169]

H31 1 −1.849[−52.684]

0 0 −0.085[−4.057]

0 χ2(2) = 8.449 [0.015]

H32 1 0 0.794[1.121]

0 −0.089[−4.050]

−0.036[−74.155]

χ2(1)=3.271 [0.070]

Real income relationsH33 0 1 0 0 0 −0.020

[−83.601]χ2(3) = 19.824 [0.000]

H34 0 1 1.654[11.632]

0 0 −0.019[−160.923]

χ2(2) = 2.773 [0.250]

H35 0 1 1.578[11.520]

−1.578[−11.520]

0 −0.020[−211.082]

χ2(2) = 2.649 [0.266]

Velocity relationsH36 1 -1 0 0 −0.083

[−5.389]−0.017[−33.045]

χ2(2) = 5.603 [0.061]

H37 1 -1 −0.986[−1.270]

0 −0.095[−3.979]

−0.017[−32.706]

χ2(1) = 5.227 [0.022]

H38 1 -1 0 4.397[2.721]

−0.062[−3.625]

−0.015[−17.591]

χ2(1)= 0.499 [0.480]

H39 1 -1 −2.011[−2.709]

2.011[2.709]

−0.101[−5.327]

−0.016[−24.238]

χ2(1) = 2.448 [0.118]

Inflation and real interest rateH40 0 0 1 0 0 0 χ2(4)= 16.983 [0.002]H41 0 0 1 -1 0 0 χ2(4) = 20.724 [0.000]H42 0 0 1 −0.408

[−1.927]0 0 χ2(3) = 15.813 [0.001]

49

Table 16: Identifying long-run structure: 1979:1-1994:4

m1 model m2 modelThe cointegrating vectors:

β1 β2 β1 β2

m1t 1.0 0.0 m2t 1.0 0.0yt −1.292

[−41.333]1.0 yt −1.715

[−71.713]1.0

∆pt 0.0 −6.615[−11.237]

∆pt 0.0 −8.202[−8.833]

trendt 0.0 −0.021[−32.414]

trendt 0.0 −0.021[−30.389]

The adjustment coefficients:α1 α2 α1 α2

∆m1t −0.084[−1.828]

0.200[5.205]

∆m2t −0.037[−0.933]

0.282[6.825]

∆yt 0.037[5.299]

−0.005[−0.883]

∆yt 0.047[6.803]

−0.006[−0.913]

∆2pt 0.075[2.960]

0.098[4.650]

∆2pt 0.114[4.914]

0.020[0.816]

The residual correlation matrix Ω:∆m1t 0.028 ∆m2t 0.02∆yt 0.38 0.004 ∆yt -0.16 0.003∆2pt -0.42 0.004 0.015 ∆2pt -0.34 0.23 0.012Test of overidentifying restrictionsχ2(1) = 0.224 [0.636] χ2(1) = 0.826 [0.364]

Notes:

1. p− values are in square brackets.

2. in Ω the standard errors are on the diagonal, cross-correlations are on theoff-diagonal elements.

50

Table 17: Identifying long-run structure, 1995:1-2004:4

m1 model m2 modelThe cointegrating vectors:

β1 β2 β1 β2

m1t 1.0 0.0 m2t 1.0 0.0yt −1.608

[−24.062]1.0 yt -1.0 1.0

∆pt −11.752[−11.595]

2.696[11.711]

∆pt 0 1.632[11.747]

R1t 11.752[11.595]

0.0 R1t 5.717[3.535]

0.0

Dp97t −0.133[−5.850]

0.0 Dp97t −0.061[−3.495]

0

trendt 0.0 −0.019[−63.876]

trendt −0.014[−16.224]

−0.019[−164.134]

The adjustment coefficients:α1 α2 α1 α2

∆m1t −0.205[−3.387]

−0.872[−4.273]

∆m2t −0.010[−0.096]

0.247[0.903]

∆yt 0.033[5.987]

0.139[7.375]

∆yt 0.049[5.034]

0.045[1.769]

∆2pt 0.113[4.645]

0.086[1.041]

∆2pt 0.119[2.173]

−0.804[−5.671]

The residual correlation matrix Ω:∆m1t 0.017 ∆m2t 0.012∆yt 0.42 0.001 ∆yt 0.533 0.001∆2pt -0.28 -0.058 0.006 ∆2pt -0.782 -0.403 0.006Test of overidentifying restrictions:χ2(3) = 3.686 [0.297] χ2(3) = 2.957[0.398]

Notes:

1. p− values are in square brackets.

2. in Ω the standard errors are on the diagonal, cross-correlations are on theoff-diagonal elements.

51

relation can be regarded as a money supply equation, because m1 is notsignificantly error correcting to this cointegration vector. The second onerepresented by H5 indicates a short-run Phillips curve relation.

The corresponding adjustment coefficients show that m1 is not errorcorrecting to the excess money as measured by the deviation from the moneysupply relation. Whereas, excess money seems to have significantly increasedthe real aggregate demand and the inflation rate.

The deviation from the short-run Phillips curve as given by the secondcointegration vector has positive effects on inflation as expected. Moreover,m1 is significantly and negatively error correcting to the deviation from thesecond cointegration vector, which can be interpreted as the monetary policyreaction effect.

The overidentifying restrictions on the long-run structure are acceptablewith a p-value of 0.63.

8.2.2 m2 model 1979:1-1994:4

The restrictions imposed on the long-run structure and the correspondingadjustment coefficients in m2 model 1 are similar to that in m1 model 1,except that in the inflation equation the error correction of the second coin-tegration vector is not significant.

The overidentifying restrictions on the long-run structure are acceptablewith a p-value of 0.36.

8.2.3 m1 model 1995:1-2004:4

In m1 model 2, the two restricted long-run relations can be regarded asthe combination of a modified relation represented by H26 with a relationrepresented by H21 in the table 14. The first cointegration vector looks likea money demand relation. Because m1 is negatively error correcting to thedeviation from this cointegration vector, we can further confirm that therelation can be interpreted as a money demand relation. Moreover, excessmoney has significant positive effects on real aggregate demand and theinflation rate.

The second cointegration vector indicates that trend-adjusted real in-come is negatively cointegrated with inflation, which might be interpreted

52

as a partial real income relation. In order to get an economic interpretablereal income relation, more variables need to be included in the informationset.

The adjustment coefficients show that m1 is positively error correcting tothe deviation of the second cointegration vector, which indicates a monetarypolicy reaction effect. In other words, when there exists excess inflation interms of deviation from modified velocity, the central bank takes measuresto reduce the money supply. In addition, the deviation from the secondcointegration vector has positive effects on the real income.

The overidentifying restrictions on the long-run structure is acceptablewith a p-value of 0.30.

8.2.4 m2 model 1995:1-2004:4

The two cointegration relations in m2 model 2 are the combination of mo-dified H38 and H34 in Table 15. The first cointegration vector indicatesthat the modified velocity ( the coefficient of y is freely estimated) is ne-gatively cointegrated with the interest rate R1t, which implies that excessmoney supply has long-run liquidity effects on the interest rate, i.e. thereis a negative transmission effect between the interest rate and monetary ex-pansion, as the standard IS-LM model would predict. The correspondingadjustment coefficients show that the excess money measured as the devia-tion from this cointegration vector increases the real income and inflationsignificantly, whereas m2 is not error correcting to it. The second cointegra-tion vector is similar to the second cointegration vector in the m1 model 2,which reflects that real income is negatively correlated with inflation. Ad-justment coefficients show that only inflation is negatively error correctingto this cointegration vector.

The overidentifying restrictions on the long-run structure is acceptablewith a p-value of 0.40.

In Tables 16 and 17, the estimated residual correlation matrices for thecorresponding models are reported. We find that in m2 model 2, thereexists a large correlation between residuals of the equations of ∆m2 and∆2p, which implies that current effects may exist in this model. Hence,although m2 seems to be weakly exogenous for the long-run coefficients inm2 model 2, we still keep it as an endogenous variable before we analyzethe short-run structure of the model.

53

8.3 Graphs of the cointegration vectors

Figures ??-?? in the Appendix display the graphs of the identified cointe-grations for the four models. All eight cointegration relationships seem tobe mean-reverting and stationary.

8.4 Recursive Estimation of α and β

Having estimated restricted long-run β coefficients and their correspondingloading factors α, we now examine the constancy of these parameters usingrecursive methods. Figure 21-?? in the appendix exhibit the forward recur-sively estimated α and β for the four models. It can be seen that exceptsome nonconstancy occurring in the beginning of the short sample period,the estimated α and β are in general constant. Figure ??-?? display therecursively calculated LR-tests for restrictions on the four models, whichindicate that the restrictions imposed on the α and β are acceptable.

9 Identifying the Short-run Structure

9.1 The procedure and guideline for identifying the short-run structure

We next impose a short-run structure on the system of unrestricted short-run reduced-form equations, which are estimated in the previous section.The statistical formulation takes the following form:

A0∆xt = α∗β′xt−1 +

k−1∑

i=1

Γ∗i ∆xt−i + Φ∗Dt + Bvt (17)

t = 1, · · · , T, vt ∼ N(0,Ω∗)

In the unrestricted short-run reduced form models, A0 = I, which isequivalent to imposing p− 1 zero restrictions on each row of A0 and henceis exactly identified. We note that the short-run structure of the current esti-mated unrestricted reduced form system is over-parameterized with manyinsignificant coefficients. In addition, some of the correlations of standar-dized residuals are rather large, which may be caused by ignorance of the

54

current effects. In this section we try to impose general restrictions on A0

or B, which might make the short-run structure overidentified.

The error correction terms that are calculated from the identified long-run cointegration vectors before identifying the short-run structure are inclu-ded as stationary components in the VEC models. This strategy is justifiedby the super consistent property of estimated β (Juselius, 2005, Section13.1).

In the models of present research, there are no prior hypotheses or theoryabout the current effects. Hence we impose overidentifying short-run re-strictions through simplification searching rather than a stringent economicidentification. The guiding principle is the plausibility of the results, inparticular plausible estimates of the coefficients of the equilibrium error cor-rection terms α, as well as the reduction of the residual cross-correlations.

The search for the short-run structure is performed with PcGive 10.0following the approach suggested by Lutkepohl and Wolters (1999b). First,we eliminate the most insignificant short-run parameters according to thelowest t-values but keep the error correction terms in the systems. Thenwe try to consider the current effects of the system by including currentvariables in the equations of other variables. Then we continually eliminatethe insignificant variables. If finally the error correction terms are provedto be insignificant, they are also eliminated. The estimation of the fullsystem is conducted using FIML contained in PcGive 10.0. Next, we conductthe overidentifying restriction tests to make sure that the reductions areacceptable. By means of examining the economic plausibility of the currenteffects, as well as checking whether the estimated residual cross-correlationsare reduced by including current variables, we can decide on the structuralmodels that are sensible to our research interest.

9.2 Estimated structural models

In what follows, we give the identified parsimonious structural models form1, m2 model 1, 2, respectively. To save space, constant terms and seasonaldummies are not reported. The standard errors are in parentheses under-neath the parameters. All reduced-form models have been tested with LRtests of over-identifying restrictions, and proved to have no over-identifyingproblem.

55

9.2.1 Structural m1 model 1

∆m1 equation in the m1 model 1

∆m1t = − 0.91(0.22)

∆2pt + 0.31(0.043)

ec2t−1 + 0.65(0.38)

∆yt−1 + 0.55(0.15)

∆2pt−1

+ 0.11(0.019)

(d84q4t − d85q2t) + 0.06(0.03)

d85q4t + 0.11(0.03)

d93q1t + ut

AR(1-1): F(1,45) = 1.75 [0.19] AR(1-4): F(4,42) = 1.42 [0.24]ARCH(1-1): F(1,54) = 0.04 [0.83] ARCH(1-4): F(4,44) = 1.34 [0.26]Normality: χ2(2) = 1.43 [0.48]

∆y equation in the m1 model 1

∆yt = 0.03(0.0065)

ec1t−1 + 0.545(0.064)

∆yt−1 + 0.015(0.005)

d80q1t + 0.039(0.0047)

d84q1t

+ 0.016(0.0048)

d85q1t − 0.022(0.0053)

d85q4t + ut

AR(1-1): F(1,45) = 5.31 [0.02] AR(1-4): F(4,42) = 2.52 [0.05]ARCH(1-1): F(1,54) =0.04 [0.83] ARCH(1-4): F(4,44) = 0.66 [0.61]Normality: χ2(2) = 1.46 [0.48]

∆2pt equation in the m1 model

∆2pt = 0.07(0.025)

ec1t−1 + 0.10(0.016)

ec2t−1 + 0.1(0.06)

∆m1t−1 + 0.09(0.019)

d80q1t

+ 0.06(0.018)

d93q1t + 0.07(0.018)

d94q1t + ut

AR(1-1): F(1,54) = 0.27 [0.60] AR(1-4): F(4,42) = 3.82 [0.01]ARCH(1-1): F(4,48) = 0.72 [0.57] ARCH(1-4): F(4,44) = 0.31 [0.86]Normality: χ2(2) = 5.02 [0.08]

56

where

ec1t = m1t − 1.29yt

ec2t = yt − 6.61∆pt − 0.02trend

9.2.2 Structural m2 model 1

∆m2 equation in the m2 model 1

∆m2t = − 1.3(0.21)

∆2pt + 0.25(0.032)

ec2t−1 − 0.16(0.082)

∆m2t−2 − 0.093(0.068)

∆m2t−3

− 0.55(0.45)

∆yt−2 + 0.78(0.53)

∆yt−3 + 0.42(0.2)

∆2pt−1 + 0.5(0.14)

∆2pt−3

+ 0.075(0.034)

d84q4t + 0.1(0.03)

d85q4t + 0.19(0.033)

d93q1t + ut

AR(1-1): F(1,38) = 3.80 [0.05] AR(1-4): F(4,35) = 1.05 [0.39]ARCH(1-1): F(1,45) = 1.24 [0.27] ARCH(1-4): F(4,39) = 1.08 [0.37]Normality: χ2(2) = 0.54 [0.76]

∆y equation in the m2 model 1

∆yt = 0.044(0.006)

ec1t−1 − 0.038(0.016)

∆m2t−1 + 0.49(0.074)

∆yt−1 + 0.093(0.013)

∆yt−2

+ 0.031(0.018)

∆2pt−3 + 0.017(0.019)

d80q1t + 0.039(0.0047)

d84q1t + 0.025(0.004)

d85q1t

+ 0.016(0.004)

d84q4t − 0.017(0.004)

d85q4t + ut

AR(1-1): F(1,38) = 3.22 [0.08] AR(1-4): F(4,35) = 2.71 [0.04]ARCH(1-1): F(1,45) = 0.24 [0.62] ARCH(1-4): F(4,39) = 0.69 [0.60]Normality: χ2(2) = 2.27 [0.32]

∆2pt equation in the m2 model 1

57

∆2pt = 0.092(0.018)

ec1t−1 0.43(0.0017)

∆yt−1 − 0.87(0.075)

∆2pt−1 − 0.67(0.07)

∆2pt−2

− 0.54(0.07)

∆2pt−3 + 0.084(0.014)

d80q1t + 0.026(0.014)

d85q1t + 0.066(0.013)

d88q3t

+ 0.069(0.015)

d93q1t + ut

AR(1-1): F(1,38) = 4.49 [0.05] AR(1-4): F(4,35) = 1.51 [0.21]ARCH(1-1): F(1,45) = 0.82 [0.36] ARCH(1-4): F(4,39)= 0.26 [0.89]Normality: χ2(2) = 0.68 [0.71]

where

ec1t = m1t − 1.71yt

ec2t = yt − 8.20∆pt − 0.02trend

9.2.3 Structural m1 model 2

∆m1 equation in the m1 model 2

∆m1t = − 0.14(0.065)

ec1t−1 − 0.72(0.22)

ec2t−1 + 0.083(0.02)

∆Dp97t + ut

AR(1-1): F(1,30) = 0.57 [0.45] AR(1-4): F(4,27) = 1.01 [0.41]ARCH(1-1): F(1,31) = 0.12 [0.72] ARCH(1-4): F(4,25) = 0.39 [0.80]Normality: χ20.49 [0.78]

∆y equation in the m1 model 2

∆yt = 0.028(0.0064)

ec1t−1 + 0.13(0.022)

ec2t−1 + ut

AR(1-1): F(1,30) = 1.32 [0.25] AR(1-4): F(4,27) = 0.83 [0.51]ARCH(1-1): F(1,31) = 0.58 [0.45] ARCH(1-4): F(4,25) = 0.55 [0.69]Normality: χ2(2) = 0.95 [0.62]

58

∆2p equation in the m1 model 2

∆2pt = 0.085(0.012)

ec1t−1 + ut

AR(1-1): F(1,30) = 0.67 [0.41] AR(1-4): F(4,27) = 1.53 [0.22]ARCH(1-1): F(1,31) = 0.16 [0.68] ARCH(1-4): F(4,25)= 0.69 [0.607]Normality: χ2(2) = 4.06 [0.13]

where

ec1t = m1t − 1.60yt − 11.75(R1t −∆pt)− 0.13Dp97t

ec2t = yt + 2.69∆pt − 0.02trend

9.2.4 Structural m2 model 2

∆m2 equation in the m2 model 2

∆m2t = − 0.69(0.33)

∆2pt − 0.35(0.18)

ec2t−1 0.013(0.0094)

∆Dp97t + 0.024(0.012)

d03q2t + ut

AR(1-1): F(1,23) = 4.88 [0.03] AR(1-4): F(4,20) = 1.51 [0.23]ARCH(1-1): F(1,32) = 0.45 [0.50] ARCH(1-4): F(4,26) = 0.51 [0.72]Normality: χ2(2) = 0.78 [0.67]

∆y equation in the m2 model 2

∆yt = 0.054(0.008)

ec1t−1 + 0.28(0.10)

∆yt−1 + 0.0042(0.001)

∆Dp97t−1 − 0.006(0.001)

d03q2t + ut

AR(1-1): F(1,23) = 4.08 [0.05] AR(1-4): F(4,20) = 1.88 [0.15]ARCH(1-1): F(1,32) = 0.66 [0.42] ARCH(1-4): F(4,26) = 0.06 [0.99]Normality: χ2(2) = 0.22 [0.89]

59

∆2pt equation in the m2 model 2

∆2pt = 0.12(0.04)

ec1t−1 − 0.61(0.08)

ec2t−1 + 1.4(0.58)

∆yt−1 − 0.017(0.008)

d03q2t + ut

AR(1-1): F(1,23) = 1.94 [0.17] AR(1-4): F(4,20) = 0.88 [0.48]ARCH(1-1): F(1,32)= 0.03 [0.85] ARCH(1-4): F(4,26) = 2.86 [0.04]Normality: χ2(2) = 1.58 [0.45]

where

ec1t = m2t − yt + 5.71R1t − 0.061Dp97t − 0.014trendt

ec2t = yt + 1.63∆pt − 0.02trend

The structural models show that inflation has current negative effectson real money stock in all the models, except in the m1 model 2, where thestructure of the unrestricted VEC model is too simple to identify the currenteffect of inflation on money stock. When the current effect of inflation istaken into account in the ∆m2 equation of m2 model 2, m2 becomes errorcorrecting to the second cointegration vector. In general, the significanceand sign of the error correction terms in the four models are reasonable andhave not been significantly changed by imposing the short-run structures.

10 Impulse response analysis

Impulse response analyses are conducted in this section to trace the respon-ses of variables when the system is hit by a shock. Through the impulseresponse analysis we can also examine the plausibility using the currentmodels as framework for policy analysis.

The impulse response analyses are based on the parsimonious VAR mo-dels, which are achieved by eliminating insignificant components on theright-hand sides of the equations of the system. The exogenous variablesand deterministic terms are treated as fixed in the impulse response analysis,because they are considered to be constant and not affected by the impulseshitting the system. The residuals are orthogonalized by the Choleski decom-position. Because the structural analysis in the previous section shows that

60

inflation seems to have an instantaneous effect on money stock, we chose theorder of the variables for the Choleski decomposition as yt, ∆pt,m1t/m2t.This implies that the shock on yt has instantaneous effects on itself, infla-tion, and money stock, the shock on inflation has instantaneous effects onitself and money stock, while the shock on the money stock has only aninstantaneous effect on itself. Because such an assumption is relatively ar-bitrary, we also check the sensibility of the impulse responses by means ofusing other orders of variables.

The impulse response analysis is performed with Jmulti 3.1. Bootstrap-ping method are applied to calculate the confidence intervals for the calcu-lated responses. If zero is not included within the confidence intervals, theresponses are supposed to be significant. The number of the bootstrap re-plications is set to be 2000. Confidence intervals for the individual impulseresponse coefficients are estimated at the 95% significant level.

Graphs 15-18 are the impulse response functions of m1 and m2 model 1and 2. The impulses are the orthogonalized standard deviations of estimatedresiduals of the models. The variables in the columns indicate the equationsto which impulses are attached, while the variables in the rows indicatesthe response functions to the impulses. The graphs show that almost allthe responses are in line with theoretical expectations. For example, whenan impulse hits the real money stock, it will increase real income and infla-tion in all the four models except the insignificant response of real incomein m1 model 2. This result can be taken as evidence that money supplyis effective in stimulating the real income and controlling inflation for bothm1 and m2 during the two sub-sample periods. An impulse hitting infla-tion tends to decrease real money stock in all four models. This suggeststhat the Chinese central bank has adopted a cautious monetary policy toprevent inflation running out of control for both periods. The impulse onthe real income increases itself, inflation and real money stock at least fora short period, except for the response of real money stock in m2 model 2where m2 decreases in the beginning but increases after about four quarters.These findings are robust to other variable orders chosen for conducting theCholeski decomposition.

In general, the impulse response functions of the four models are inline with economic theories. Therefore, the current models can be takenas a sensible framework for further policy analysis. The impulse responseanalyses can also provide the following conclusions. First, inflation can beregarded as monetary phenomenon in China for the whole sample period,

61

Figure 15: Impulse responses of m1 model 1979:1-1994:4

although in the later period the Chinese economy has experienced deflationfrom about 1998-2002. Second, the Chinese monetary authorities are verycautious in controlling inflation. This is reflected in the fact that, exceptfor m1 model 2, in all the other models money stock decreases significantlyin response to an inflation impulse. In m1 model 2, m1 declines in thebeginning but not statistically significant, possibly due to the fact that inthe second sample period, m1 is more determined by money demand.

11 Long-run impact analysis

We now investigate the long-run impact matrices of unanticipated shocksto the four models based on the moving average representation of the VAR

62

Figure 16: Impulse responses of m2 model 1979:1-1994:4

63

Figure 17: Impulse responses of m1 model 1995:1-2004:4

64

Figure 18: Impulse responses of m2 model 1995:1-2004:4

65

formulation.

As pointed out in Section 3.6, VAR models can be represented in thefollowing moving average form:

xt = Ct∑

i=1

(εi + ΦDt) +∞∑

i=0

C∗(εt−i + φDt−i) + A0,

= Ct∑

i=1

(εi + ΦDt) + C∗(L)εt + C∗(L)ΦDt + A0 (18)

Where:

C = β⊥(α′⊥Γβ⊥)−1α′⊥ (19)

and α⊥ and β⊥ are the orthogonal complements to α and β, respectively.(α⊥ : α) and (β⊥ : β) are regular matrices. α⊥ and β⊥ can be calculatedbased on the unrestricted estimates of α and β. Long-run impact matrix Ccan be uniquely calculated from α⊥ and β⊥, although α⊥ and β⊥ are notuniquely estimated. The estimated C matrices contain useful informationabout the overall effects of the stochastic driving forces in the system.

We choose the residuals εit from the unrestricted VECM models as esti-mates of the unanticipated shocks associated with variable xi, because theconditional expectation Et−1∆xt|∆xt−1, β

′xt−1 has optimal properties

as a predictor of ∆xt (Juselius, 1999).

11.1 Long-run impact analysis for the full sample

In previous section, we have identified that there exists structural shifts inthe estimated β in m1 and m2 models for the whole sample period 1979:1-2004:4. In order to derive constant coefficients of the cointegration relations,we have empirically investigated the models in the split samples, i.e. beforeand after 1995Q1. On the other hand, because the long-run impact matrixis independent of the identification of α or β, the long-run impact matrixC might be constant even if the estimates of α and β are nonconstant. Inthis section, we investigate the long-run impact based on the whole sample

66

period.5

Table 18 shows the long-run impact matrices of m1 and m2 models forthe whole sample period, with the assumption that there exists one or twocointegration relations. An interesting finding is that the cumulated shocksin m1 are insignificant for any of the variables in the system, which meansthat m1 is a fully adjusting variable. Contrary to m1, the unanticipatedshocks in m2 have significant and positive long-run impact on m2, realincome and inflation.

If the estimated residuals associated with the money stock can be inter-preted as monetary policy shocks, this finding might imply that expansio-nary monetary policy in terms of increasing m2 supply has long-run positiveeffects on m2, real income and inflation, whereas that in terms of increasingm1 has no such long-run effect.

In particular, the finding is robust in the sense that it is independent onthe choice of the cointegration rank.

12 Impulse response functions for transitory andpermanent shocks

12.1 Estimate of B matrices

The impulse response analysis for transitory and permanent shocks are con-ducted based on m1 and m2 models in the full sample with cointegrationrank to be 2. The estimated matrix B (normalized at the largest coeffi-cient in each row) defines how the orthogonalized permanent and transitoryshocks are associated with the estimated VAR residuals through the equa-tion ut = Bεt, where ut and εt are structural shocks and VAR estimatedresiduals, respectively.

The estimated B and the transformation relations between structuralshocks and estimated VAR residuals for the two models is given in equations(20) and (21)6

5Because of the large cross-correlations existing in the residual covariance matrices,the long-run impact analyses based on the two sub sample periods seem not to be veryplausible and reliable

6Because by construction the SVAR restrictions are just-identifying, there is no testfor estimated B

67

Table 18: The long-run impact matrices for 1979:1-2004:4

m1 model, r = 2 m2 model, r = 2∑εm1i

∑εyi

∑ε∆pi

∑εm2i

∑εyi

∑ε∆pi

m1t 0.031[0.319]

2.700[3.478]

−1.295[−6.195]

m2t 0.194[3.771]

1.477[4.459]

−0.458[−3.782]

yt 0.011[0.319]

0.940[3.478]

−0.451[−6.195]

yt 0.194[3.771]

1.472[4.459]

−0.457[−3.782]

∆pt −0.001[−0.319]

−0.130[−3.478]

0.062[6.195]

∆pt 0.011[3.771]

0.080[4.459]

−0.025[−3.782]

m1 model, r = 1 m2 model, r = 1∑εm1i

∑εyi

∑ε∆pi

∑εm2i

∑εyi

∑ε∆pi

m1t −0.201[−0.781]

−3.595[−1.624]

−2.106[−3.798]

m2t 0.515[4.963]

−0.172[−0.376]

0.021[0.251]

yt 0.107[1.003]

3.552[3.875]

−0.115[−0.500]

yt 0.359[4.660]

0.619[1.822]

−0.209[−3.332]

∆pt 0.010[0.785]

0.178[1.647]

0.102[3.775]

∆pt 0.169[4.052]

−0.736[−4.006]

0.212[6.271]

Note: t-values are in square brackets.

us,1i

us,2i

ul,1i

=

−0.003 0.123 1.0001.000 0.563 −0.6240.011 −0.480 1.000

εm1i

ε∆pi

εyi

(20)

us,1i

us,2i

ul,1i

=

−0.038 0.091 1.0001.000 1.768 −1.3450.132 −0.310 1.000

εm2i

ε∆pi

εyi

(21)

Where us,t and ul,t denote transitory and permanent shocks, respectively.

68

12.2 Impulse response functions for transitory and perma-nent shocks

Based on the estimated B matrices, the transitory and permanent shocks inthe m1 model are defined as:

us,1 ≈ εy + 0.12ε∆p

us,2 = εm1 + 0.56ε∆p − 0.62εy

ul,1 ≈ εy − 0.48ε∆p

and that in the m2 model are defined as:

us,1 ≈ εy + 0.09ε∆p

us,2 = εm2 + 1.76ε∆p − 1.34εy

ul,1 ≈ εy + 0.13εm2 − 0.31ε∆p

In both m1 and m2 models, there are two transitory shocks and one per-manent shock. In order to identify the two transitory shocks, one exclusionrestriction need to be imposed on the matrix C0, which describes the im-mediate effect of the structural shocks on the variables. The restriction onmatrix C0 in m1 and m2 model are given as follows, respectively:

C0,m1 =

−0.174 2.171 0.6270.665 0.052 −0.9780.321 −0.000 0.122

and

C0,m2 =

0.496 1.453 1.5010.192 −0.191 0.1260.829 −0.000 −0.753

The exclusion restriction imposed on the C0 matrix in the m1 and m2models is equivalent to assuming that the second transitory shock has nocurrent effect on yt. Based on the estimated B matrix and the identificationrestriction imposed on the C0 matrix, the impulse response functions for aone standard deviation of transitory and permanent shocks in m1 and m2models are calculated and depicted in Figure 19 and 20, respectively.

69

Steps 1 to 29

LM1

DP

Y

Trans(1) Trans(2) Perm(1)

-0.024

-0.020

-0.016

-0.012

-0.008

-0.004

0.000

0.004

-0.0025

0.0000

0.0025

0.0050

0.0075

0.0100

0.0125

-0.0006

0.0000

0.0006

0.0012

0.0018

0.0024

0.0030

0.0036

0.0042

-0.0050

-0.0025

0.0000

0.0025

0.0050

0.0075

0.0100

0.0125

0.0150

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

-0.0002

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0000

0.0025

0.0050

0.0075

0.0100

0.0125

0.0150

0.0175

0.0200

0.0225

-0.006

-0.004

-0.002

0.000

0.002

0.004

0.006

0.000

0.002

0.004

0.006

0.008

0.010

0.012

Figure 19: Impulse response functions for the transitory and permanentshocks in m1 model

By the construction of the transitory and permanent shocks, the twotransitory shocks have no long-run impact, while the permanent shock haslong-run impact on all the variables.

Figure 19 and 20 display similar pictures. The first transitory shockconsisting of residuals from equations yt and ∆pt has transitory positiveeffects on real income and inflation, but transitory negative effects on moneystock. Therefore, we might interpret this shock as a demand shock. Thenegative response of the money stock can be interpreted as the monetarypolicy reaction. The second transitory shock, which contains residuals ofmoney stock, real income and inflation, seems like a money supply shock,which increases money stock and inflation immediately, and real incomea period later. The only permanent shock has permanently increased themoney stock and real income, but initially decreased the inflation, and onlyslightly increased the inflation in the long-run, which makes it much like asupply shock, according to the Blanchard and Quah’s (1988) interpretationof supply disturbances.

In their paper, Blanchard and Quah interpret the supply and demand

70

Steps 1 to 32

LM2

DP

Y

Trans(1) Trans(2) Perm(1)

-0.014

-0.012

-0.010

-0.008

-0.006

-0.004

-0.002

0.000

0.002

-0.002

0.000

0.002

0.004

0.006

0.008

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

-0.0050

-0.0025

0.0000

0.0025

0.0050

0.0075

0.0100

0.0125

0.0150

0.0175

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

-0.00025

0.00000

0.00025

0.00050

0.00075

0.00100

0.00125

0.00150

0.00175

0.000

0.005

0.010

0.015

0.020

0.025

0.030

-0.012

-0.010

-0.008

-0.006

-0.004

-0.002

0.000

0.002

0.004

0.000

0.002

0.004

0.006

0.008

0.010

0.012

Figure 20: Impulse response functions for the transitory and permanentshocks in m2 model

disturbance as follows (in Abstract):

If we interpret fluctuations in GNP and unemployment as dueto two types of disturbances: disturbances that have a permanenteffect on output and disturbances that do not. We interpret thefirst as supply disturbances, the second as demand disturbances.

They characterize the effects of supply disturbances as follows (pp. 2):

The effect of supply disturbances on output increases steadilyover time, to reach a peak after two years and a plateau afterfive years. ’Favorable’ supply disturbances may initially increaseunemployment.

Being aware that interpreting residuals in small dimensional systemsas ’structural’ disturbances is always perilous (Blanchard and Quah, 1988,Juselius, 2005, et al.), we regard the aforementioned economic interpretationof transitory and permanent shocks only as a very tentative attempt.

71

13 Summary and Conclusions

To conclude, we will first report the results of our empirical investigationsfor the hypotheses raised in the beginning of this chapter. Then we willsummarize the main findings of the current study and discuss some relatedissues.

13.1 Answers to the propositions

1. Is there any structural break in the monetary transmission mechanism inChina during 1979:1-2004:4?

We do find evidence of a structural break in the estimates of the long-runcointegration coefficients β and the corresponding short-run loading factorsα before and after 1995Q1. When the models are separately estimated inthe split sample period, estimates of α and β turned out to be constant.

2. Are there long-run relationships between money stock, real income,inflation and other macroeconomic variables? If yes, are they money demandor supply relationship?

In the first period, we find cointegration relations between money stockand real income, which can be interpreted as money supply relations. Thiscorrelation implies that money supply and real income have the same sto-chastic trend, and hence can be cancelled out by a linear combination. Inthe second period, there exists a money demand function for m1. But inthe m2 model, there is a correlating relation between velocity and interestrate, which seems still to be a supply relation. In other words, m1 is largelydetermined by money demand in the second period, while m2 is still supplydetermined.

3. How do real income and inflation adjust to the monetary expansion?

In all four models, excess money of m1 and m2 has a positive short-runeffect on real income and inflation. This is the evidence that the Chinesemonetary policy is effective in adjusting aggregate demand and in controllinginflation by means of controlling money supply in the whole sample period.Or in other word, inflation can be regarded as monetary phenomena duringthe whole sample period.

4. How does the money supply react to excess inflation?

72

We also find that m1 and m2 negatively respond to excess inflation inboth periods, which reflects the fact that PBC’s has taken cautionary mone-tary policy to prevent inflation, and furthermore, the cautionary monetarypolicy has not changed during the whole sample period.

5. Do unanticipated shocks of m1 or m2 have long-run impacts on realincome and inflation?

Only the unanticipated shocks of m2 have long-run positive impacts onm2, real income and inflation. The unanticipated shocks of m1 have nolong-run impacts for any variable.

6. Which one should be taken as the intermediate target, M1 or M2?

In the short-run, both excess m1 and m2 have a positive impact onreal income and inflation, whereas only expansionary shocks in m2 have along-run impact on real income and inflation. This means, in the long-runto take m2 as intermediate target of monetary policy is more relevant. Inaddition, in the second period, m1 is largely determined by money demand,which implies that the PBC cannot directly control m1 but can only indi-rectly adjust m1 through adjusting the deposit rate. To qualify to be anintermediate target, it is usually required to be measurable, controllable andrelevant to the monetary target. According to these criteria, m2 seems tobe more suitable as the intermediate target for monetary policy than m1,especially in the long-run.

13.2 Other Interesting Findings

The empirical investigation also provides us with some other interestingfindings that are worth mentioning.

1. In the first period, there exists a short-run Phillips curve type rela-tion, which suggests that excess aggregate demand pressure causes inflation.In the second period, we find cointegration relation between trend-adjustedreal income and inflation, but with a ’wrong’ sign, i.e. they are negativelycointegrated. Juselius (2005) has also found similar cointegration relationin a monetary model including five variables based on Danish data. Sheinterprets this relation as a partial real income relation. When more infor-mation is added to the original model, she has found a standard Phillipscurve relation between inflation, the unemployment rate and real bond rate.In our current models, the similar relations seem to exist as well, and further

73

investigation using more information is required in this regard.

2. The PBC has adjusted the interest rate in the recent period morefrequently than it did in the first period. Our empirical investigation showsthat the interest rate variable can be excluded from the models in the firstperiod, but not in the second period. In the later period, the interest rateis a indispensable component of the monetary relations, and seems to haveinfluenced by the monetary expansion in the long-run. This gives the evi-dence that the interest rate policy is now playing an increasingly importantrole in China.

3. The PBC has claimed to take money supply as the intermediate tar-get of the monetary policy since 1995. The planed target of money supplyis supposed to be calculated based on the quantity theory and exchangeequation. If the PBC has controlled money supply according to the planedtarget, then we expect to find a long-run relation between real money supplyand real income, and money stock should adjust to the deviation from theequilibrium. In our empirical models in the second sample period, we didn’tfind such long-run equilibria and the corresponding short-run adjustments.Instead, we find the growth rate of money supply m1 and m2 react signifi-cantly negative to the current increase of inflation and the excess inflationin the previous period. This finding might be interpreted as evidence that inpractice, the PBC has not adjusted money supply according to the plannedtarget but rather according to the inflation target.

74

Reference:

Blanchard, O.J. and Quah, D. (1988). ”The dynamic effects of aggre-gate and supply disturbances”, NBER working papers, National Bureau ofEconomic Research, No. 2737

Chen, Baizhu (1997). ”Long-run money demand and inflation in China”,Journal of Macroeconomics, Vol. 19, No. 3, pp. 609-617.

Chinese monetary policy committee (2002). ”Studies on China’s mone-tary policy transmission mechanism” in Xie, Ping and Jiao, Jinpu (eds.):Disputations on China’s monetary policy (in Chinese), Finance Press ofChina.

Chow, Gregory C and Shen, Yan (2004). ”Money, price level and outputin the Chinese macro economy”. working paper, Peking University.

Dai, Genyou (2002). ”Some theoretical and empirical issues on China’smonetary policy”, in Xie, Ping and Jiao, Jinpu (eds.): Disputations onChina’s monetary policy (in Chinese), Finance Press of China.

Engle, R.F. and Granger, C.W.J. (1987). ”Co-integration and errorcorrection: representation, estimation, and testing”. Econometrica, Vol.55, No. 2, pp. 251-276.

Doornik, J.A. and Hendry, D.F. (1995). PcFiml 8.0, Interactive econo-metric modeling of dynamic systems. Chapman and Hall press.

Ericsson, NR. (1999). ”Empirical modeling of money demand”, inLutkephol H. and Wolters J. (eds.): Money Demand in Europe, Physica-Verlag

Dennis, Jonathan G. (2006). CATS in RATS, cointegration analysis oftime series, version 2. Published by Estima, Evanston, Illinois, USA.

Girardin, Eric (1996). ”Is there a long run demand for currency inChina?” Economics of Planning, Vol. 29, issue 3, pp. 169-184.

Hafer, R.W. and Kutan, A.M. (1994), ”Economic reforms and long-run money demand in China: implications for monetary policy”. SouthernEconomic Journal, Vol. 60.

Hendry, D.F. (1995). Dynamic Econometrics, Oxford University Press.

Hendry, D.F. and Juselius. K. (1999). ”Explaining cointegration Ana-lysis: Part one”. Download from www.econ.ku.dk/okokj/.

75

Hendry, D.F. and Juselius. K. (2001). ”Explaining cointegration Ana-lysis: Part two”. Download from www.econ.ku.dk/okokj/.

Huang, Guobo (1994). ”Money demand in China in the reform period:an error correction model”. Applied Economic, 26, pp.713-719.

Johansen, S.(1996). Likelihood-based inference in cointegrated vectorautoregressive models, 2nd edition, Oxford University Press.

Juselius, K. (1996). ”An empirical analysis on the changing role of theGerman Bundesbank after 1983”. Oxford Bulletin of Economics and Stati-stics, 58,4

Juselius, K. (1999). ”Changing monetary transmission mechanism wi-thin the EU”. in Lutkephol H. and Wolters J. (eds.): Money Demand inEurope, Physica-Verlag.

Juselius, K. (2005). The Cointegrated VAR model: methodology andapplications, manuscript, will be published by Oxford University Press

Lutkepohl H. (1993). Introduction to Multiple Time Series Analysis,2nd edition, Springer-Verlag.

Lutkepohl H. and Wolters J. (eds.) (1999a). Money Demand in Europe,Physica-Verlag.

Lutkepohl H. and Wolters J. (1999b). ”A money demand system forGerman M3”, in Lutkephol H. and Wolters J. (eds.): Money Demand inEurope, Physica-Verlag.

Lutkepohl H. and Kratzig M.(2004), Applied Time Series Econometrics,Cambridge University Press.

Qin, Duo (1994). ”Money demand in China: The effect of economicreform”. Journal of Asian Economics, Vol. 5, No. 2, pp. 253 - 271

Qin, Duo (2003). ”Determinants of household savings in China and theirrole in quasi-money supply”. Economics of Transition 11(3): pp. 513-537.

Qin, Duo, Quising, P., He, Xinhua, and Liu, Shiguo (2005). ”Modelingmonetary transmission and policy in China”. Journal of Policy modeling,Vol. 27, issue 2, pp. 157-175.

Xia, Bin and Liao, Qian (2002). ”Money supply is not suitable to bethe intermediate target of monetary policy”, in Xie, Ping and Jiao, Jinpu(eds.): Disputations on China’s monetary policy (in Chinese), Finance Press

76

of China.

Xie, Ping (2002). ”The challenges facing China’s monetary policy in thenew century”, in Xie, Ping and Jiao, Jinpu (eds.): Disputations on China’smonetary policy (in Chinese), Finance Press of China.

Xu, Yingfeng (1998), ”Money demand in China, a disaggregate ap-proach”. Journal of Comparative Economics, Vol. 26, pp. 544-564.

Yi, Gang (1993). ”Towards estimating the demand for money in China”.Economics of Planning, Vol. 26. issue 3, pp. 243-270.

Yu, Yongding (2001). ”A review of China’s macroeconomic developmentand polices in the 1990s”. China and World Economy, No. 6, 2001, pp. 3-12.

Zhang, Yin and Wan, Guanghua (2004). ”Output and price fluctuati-ons in China’s reform years, what role did money play?”. Research Paper,No. 2004/56, World Institute for Development Economic Research, UniteNations University. www.wider.unu.edu

77