Information about Asia and the Pacific Asia y el Pacífico
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Appendix IV The Demand for Money in China

Author(s):
David Burton, Wanda Tseng, Kalpana Kochhar, Hoe Khor, and Dubravko Mihaljek
Published Date:
September 1994
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The Chinese authorities’ decision to accelerate reforms of the banking system and the financial sector, with a view to moving to a system of monetary control through indirect, market-based instruments, will require, inter alia, a thorough re-examination of the demand for various monetary aggregates. This is particularly true as the authorities envisage using monetary aggregates as indicative targets in guiding the conduct of monetary policy. Clearly, for a given monetary aggregate to be of use as an intermediate target in formulating and implementing policy, it is necessary that it be a reasonably stable and predictable function of a small number of key macroeconomic variables. As discussed in Section III, the role of monetary policy and the structure of the financial system in China and, more fundamentally, that of the entire economy, have undergone significant changes since the inception of market-oriented reforms in 1978. These changes suggest a priori that it would be difficult to estimate a stable demand function for money, particularly the broader aggregates, covering the entire period since reforms began.

In this appendix, the demand for three major monetary aggregates in China—currency, narrow money (Ml), and broad money (M2)—is estimated. Narrow money comprises currency111 and demand deposits held by households and enterprises, while broad money consists of narrow money plus households’ time and savings deposits. The demand functions have been estimated using quarterly data, first for the entire sample period from 1983 to 1993, and tests have been conducted for structural breaks and predictive failure. These tests indicate that the demand for all the aggregates underwent a structural change in 1988. The introduction of a secondary market in government securities in 1988, as well as other financial innovations in the period after 1988, may account for this finding, as, for the first time, agents had access to financial assets at more market-determined interest rates. Separate demand functions have therefore been estimated for each of the aggregates for the two subperiods, 1983–88 and 1989–93.

The first part of this appendix discusses the behavior of the major monetary aggregates over the sample period in relation to the determinants of money demand. The next two sections briefly outline the estimation procedure and discuss the main results, respectively. The following part presents some possible policy implications. The final sections describe the variables used, the data sources, and the different diagnostic tests that were conducted as part of the estimation procedure.

Behavior of Major Monetary Aggregates

Chart 17 presents the growth rates of currency in circulation. Ml, and M2. Note that prior to 1988, the evolution of the aggregates was broadly similar. In 1988 and again in late 1992 and 1993. when inflation accelerated sharply, the growth rate of currency in circulation was significantly higher than that of Ml or M2. This behavior can be explained by the fact that, in periods of high inflation and inflationary expectations, the demand for cash tends to rise rapidly as economic agents first substitute cash holdings for less liquid deposits to position themselves for the purchase of goods and then switch from cash into commodities or other physical assets. More generally, beginning in 1988. the growth rates of the three monetary aggregates are more divergent than in the pre-1988 period.

Chart 17.Monetary Aggregates

(Year-on-year percent change)

Source: Chinese authorities.

Chart 18 plots the growth rates of each of the aggregates in real terms against those of different measures of economic activity; it shows that the movements of currency in circulation and retail sales, and those of M1 and industrial production, are closely correlated.112 Also, real Ml and M2 clearly lead industrial production and real national income, respectively. However, the chart does not provide clear evidence of a discernible change in the behavior of real money holdings vis-à-vis the different activity variables before and after 1988.

Chart 18.Money and Economic Activity

(Year-on-year percent change)

Sources: Chinese authorities: and IMF staff estimates.

Chart 19 presents developments in the income velocity of circulation of the aggregates since 1983, There has been a near secular decline (except during the rectification period in 1989-90) in the velocity of circulation of all the aggregates. These trends are consistent with the increasing monetization of the economy that has resulted from the implementation of structural reforms in China.

Chart 19.Velocity Developments1

Sources: Chinese authorities; and IMF staff estimates.

1 Defined as nominal GNP divided by the annual averages of the relevant monetary aggregates.

Chart 20, which plots the growth rates of the monetary aggregates and retail price inflation, shows that in all cases the growth of nominal balances leads inflation; in the case of currency, the lead is short (one quarter) while, for Ml and M2, the lead appears to be between two and four quarters,113 This finding has important policy implications, in that a useful intermediate target for monetary policy should be able to give advance indication of the behavior of the ultimate targets of policy, which can be observed only with a lag. The chart also suggests that this lead-lag pattern may have changed since 1988.

Chart 20.Monetary Growth and Inflation

(Year-on-year percent change)

Sources: Chinese authorities; and IMF staff estimates.

Estimation Procedure

Conventional money demand functions are specified in a partial adjustment framework, in which current real money balances are regressed on lagged real balances, real income, and opportunity cost/rate of return variables as follows:114

where M = nominal money balances,

  • P = the general price level,
  • y = real income (or wealth),
  • r1 = the “own” rate of return on money, and
  • r2 = the rate of return on alternative assets.

For the narrower aggregates, the “own” rate of return can be expected to be close to zero. However, this may not be the case for broad money; a priori, the coefficient α3 can be expected to be positive. The coefficient α4, if significant, can be expected to be negative.

The model can then be estimated using ordinary least squares (OLS). However, as shown by several authors, OLS estimators are not consistent in the presence of nonstationary time series. Thus, although OLS estimation results may have high values for R2 and significant t-statistics, inferences based on these test statistics may not be correct.

These findings suggest that nonstationarity of the time series should be tested for, and stationarity induced, before performing regression analysis. One way to make the relevant time series stationary is by differencing, usually once or twice, and performing regressions using these differenced variables. A shortcoming of this method, however, is that information about the long-run relationships between these variables is lost, as the expected value of a stationary time series is equal to zero.

As explained in Appendix III, the development of the concept of cointegration (Engle and Granger (1987)) suggested a way to improve on this method. Most economic time series are integrated of order 1 (the shorthand notation is 1(1)), that is, their first differences are stationary, or integrated of order 0 (or 1(0)). It has also been shown that there is a way to link integrated processes and a long-run steady-state equilibrium. The idea behind the concept of cointegration is that, even though level variables are individually 1(1), that is, dominated by their long-run components, certain linear combinations of these 1(1) variables can be 1(0); in these circumstances, the long-run components of the series cancel each other out to produce a stationary time series. Such variables are then said to be cointegrated, and the vectors of coefficients of the linear combinations are called the cointegrating vectors. Under these conditions, an adjustment process is at work—the error-correction mechanism—that prevents the deviations from the long-run relationship from increasing in magnitude.

The Granger Representation Theorem demonstrates that any set of cointegrated time series has an error-correction representation, which reflects the short-run adjustment mechanism. The Engle-Granger two-step error-correction model used in this study provides a way to separate the long- and the short-run properties of the data. In the first step, as suggested by theory, the relationship between the time series is estimated by using level variables and OLS. If the estimation yields a stationary residual series, a cointegrating relationship exists between these variables, and the regression yields an estimate of the cointegrating vector.115 The reformulation of the model in first differences produces a term representing the extent of the “error” in each time period in achieving the long-run equilibrium. Thus, in the second step, the short-run adjustment or error-correction mechanism can be estimated.

Model Specification and Results

Model Specification

The general form of the long-run equations estimated in this appendix is given by

where M = nominal balances of the relevant aggregate,

  • P = the general retail price index,
  • y = real national income,116 and
  • π = quarterly inflation rate, as measured by the retail price index.

The long-run elasticity and semielasticity of real money balances with respect to real income and the opportunity cost variable are given by β1 and β32, respectively.117

The general form of the second stage error-correction equation is given by

where EC = residuals from the long-run regression.

The short-run dynamics are described by an equation whose exact specification is chosen on the basis of a general-to-specific testing-down procedure, in which insignificant lags are dropped until the most satisfactory and parsimonious representation is found.

Testing for stationarity and the order of integration of the relevant variables is done by means of unit root tests (described in detail below). The tests show that the variables are all nonstationary in level terms, but that they are integrated of order 1, or stationary, in first differences.

Summary of Main Results

There is evidence of a structural break in the late 1980s in the behavior of the demand for real balances of monetary aggregates. Some of the estimated dynamic equations—particularly those for narrow money—pass various specification tests, while others, particularly those for broad money, appear to be relatively poorly specified. This latter result is not surprising; with the rapid changes in the financial system, the holdings of broad money should undergo significant change both in terms of the long-run equilibrium relationship and the short-run dynamic behavior.118

For both subperiods, the long-run elasticities of all real monetary balances with respect to real income are greater than I. Also, the behavior of each real monetary balance with respect to real income has remained relatively stable over the two sub-periods. These balances are highly sensitive to the inflation rate, which has been used as an opportunity cost variable in the estimated equations:119 in most cases, the degree of this sensitivity declined in the second subperiod.

With respect to the behavior of currency and narrow money holdings, the evidence from the second subperiod of the sample suggests that an increase in inflationary expectations raises the demand for currency (although inflation and currency holdings are inversely related in the long run). As discussed above, this finding suggests the existence of a “cash-in-advance” constraint, because of which agents must initially increase their currency holdings in order to switch from currency into goods.120

The holdings of real Ml and M2 balances have been found to be sensitive to interest rates in the second subperiod of the sample. In particular, an increase in interest rates on one-year time deposits appears to reduce the demand for narrow money in the long run. However, the short-run dynamic equation does not reveal that changes in interest rates significantly affect changes in narrow money balances. As for M2, an increase in the own rate of interest is found to lower the demand for real M2 balances both on impact and in the long run. This counterintuitive result can arise if interest rates on time deposits, which remain administered, are increased only when the returns on alternative financial assets are increasing at a more rapid rate. To capture this effect, it would be necessary to include, in addition to the own rate of interest, interest rates on alternative financial assets.121

Currency in Circulation

Using the two-step procedure described above for the sample period 1983–88, the long-run elasticities of currency demand with respect to real income and the inflation rate have been estimated to be 1.9 and –1.2, respectively (Table 21). As discussed above, if the vector of coefficients in equation (1) is a cointegrating vector, the residual series should be 1(0), that is, stationary. Diagnostic tests on the residual series allow the rejection of the null hypothesis that the variables are not cointegrated, suggesting that the long-run demand function is well specified. The most satisfactory dynamic equation for currency demand is given in Table 22. The change in inflation rate lagged one period enters the dynamic equation with a significant negative coefficient, and the error-correction term, which has a statistically significant coefficient, indicates a moderately rapid adjustment of currency balances to their long-run equilibrium levels.

Table 21.Long-Run Currency Demand
Variable1Estimated

Coefficient
t-statisticp-value2Adjusted

R2
SER

(In percent)
Durbin-WatsonTest of

Cointegration

(p-value)
RCt (1983–88)0.985.01.98–3.663

(0.04)
Constant–7.8815.20.00
RNYt1.9023.20.00
INFLt–1.232.30.00
Long-run income elasticity1.9
Long-run semielasticity with respect to inflation–1.2
RCt (1989–93)0.983.00.353

(0.93)
–6.042

(0.00)
Constant–3.162.90.01
RCt–10.511.90.06
RNYt0.832.30.04
INFLt–0.50–0.90.38
Long-run income elasticity1.7
Long-run semielasticity with respect to inflation–1.0

RC = real currency holdings; RNY = real national income; and INFL = retail price inflation.

Probabilities of accepting the null hypotheses for the tests reported.

Durbin’s h-statistic with the p-value in parentheses.

RC = real currency holdings; RNY = real national income; and INFL = retail price inflation.

Probabilities of accepting the null hypotheses for the tests reported.

Durbin’s h-statistic with the p-value in parentheses.

Table 22.Error-Correction Equations—Currency
Variable1Estimated

Coefficient
t-statisticp-value2Adjusted

R2
SER

(In percent)
Durbin-WatsonJ-B3

(p-value)
ARCH4

(p-value)
ΔRCt (1983–88)0.483.01.960.85

(0.65)
0.08

(0.78)
Constant0.043.40.00
ΔRNYt0.522.30.03
ΔINFLt–1–0.732.10.05
ECt–1–0.462.70.02
ΔRCt (1989–93)0.722.02.021.18

(0.55)
0.01

(0.92)
Constant0.000.40.73
ΔRNYt1.295.20.00
ΔINFLt–0.481.10.31
ΔINFLt–11.002.50.03
ECt–1–0.463.00.01

RC = real currency holdings; RNY = real national income; and INFL = retail price inflation.

Probabilities of accepting the null hypotheses for the tests reported.

J-B = Jarque-Bera test for normality of residuals.

ARCH = Test for autoregressive conditional heteroskedasticity.

RC = real currency holdings; RNY = real national income; and INFL = retail price inflation.

Probabilities of accepting the null hypotheses for the tests reported.

J-B = Jarque-Bera test for normality of residuals.

ARCH = Test for autoregressive conditional heteroskedasticity.

Table 21 also indicates that, for the 1989-93 sub-period, the long-run elasticity and semielasticity of currency demand with respect to income and the inflation rate have been estimated as 1.7 and -1.0, respectively. These estimated values are not very different from those for the first subperiod; however, the short-run dynamics, especially with respect to inflation, are quite complex and markedly different from those estimated for the 1983-88 subperiod. In particular, the estimated short-run response of currency demand to an increase in inflation in the previous quarter is complicated: an increase in the current period rate of inflation induces a reduction in real currency holdings. The difference in response to inflationary developments between the two periods may be attributable to the greater options available to households in the later period, in particular the availability of higher-yielding financial assets, combined with the cash-in-advance constraint. This response is particularly evident in 1992-93 when currency holdings rose sharply, owing to shifts by households from deposits whose real returns had become highly negative into stocks and other financial instruments. The size of the error-correction coefficient is comparable to the one estimated for the 1983-88 subperiod.122

Narrow Money

The estimated long-run elasticity and semi-elasticity of narrow money with respect to income and inflation in the 1983-88 subperiod are 1.5 and –1.5, respectively (Table 23). The short-run error-correction equation is given in Table 24. The error-correction coefficient is larger than in the case of currency demand, implying that narrow money balances adjust faster to disequilibrium than do currency holdings. However, the diagnostic tests suggest that this equation is relatively poorly specified.

Table 23.Long-Run Narrow Money Demand
Variable1Estimated

Coefficient
t-statisticp-value2Adjusted R2SER

(In percent)
Durbin-WatsonTest of

Cointegration

(p-value)
RMIt (1983–88)0.965.01.99–4.031

(0.02)
Constant–4.038.00.00
RNYt1.5319.10.00
INFLt–1.513.00.01
Long-run income elasticity1.5
Long-run semielasticity with respect to inflation–1.5
RMlt (1988–93)0.094.02.08–4.435

(0.01)
Constant–3.646.10.00
RNYt1.4818.30.00
INFLt–0.942.50.03
IRt–0.034.60.00
Long-run income elasticity1.5
Long-run semielasticity with respect to inflation–0.9
Long-run semielasticity with respect to interest rates–0.03

RMI = real narrow money holdings; RNY = real national income; INFL = retail price inflation; and IR = real interest rate.

Probabilities of accepting the null hypotheses for the tests reported.

RMI = real narrow money holdings; RNY = real national income; INFL = retail price inflation; and IR = real interest rate.

Probabilities of accepting the null hypotheses for the tests reported.

Table 24.Error-Correction Equations—Narrow Money
Variable1Estimated Coefficientt-statisticp-value2Adjusted R2SER (In percent)Durbin-Watsonj-B3 (p-value)ARCH4 (p-value)
ΔRMIt (1983–88)0.364.01.931.14

(0.50)
0.00

(0.98)
Constant0.010.90.39
ΔRNYt0.912.40.03
ΔINFLt–0.691.40.18
ECt–1–0.783.10.01
ΔRMIt (1989–93)0.702.01.960.18

(0.91)
0.01

(0.94)
Constant0.033.90.00
ΔRNYt0.843.10.01
ΔRNYt–1,–0.512.30.04
ΔINFLt–0.852.20.05
ΔINFLt–11.564.80.00
ECt–1–0.442.00.06

RMI = real narrow money holdings; RNY = real national income; and INFL = retail price inflation.

Probabilities of accepting the null hypotheses for the tests reported.

J-B = Jarque-Bera test for normality of residuals.

ARCH = Test for autoregressive conditional heteroskedasticity.

RMI = real narrow money holdings; RNY = real national income; and INFL = retail price inflation.

Probabilities of accepting the null hypotheses for the tests reported.

J-B = Jarque-Bera test for normality of residuals.

ARCH = Test for autoregressive conditional heteroskedasticity.

As discussed above, changes in administered interest rates were made more frequently during 1989-93 than in the earlier period. Also, with the increasing availability of a wider range of financial instruments for household and enterprise savings, as well as with the introduction of secondary market trading in government securities, the demand for monetary aggregates can be expected to have been more sensitive to interest rate changes during the later period. For this reason, interest rates on one-year time deposits were included in the estimation of the demand functions for Ml (and M2, as discussed below) in the second subperiod.

For the 1989–93 subperiod, the estimated long-run elasticity with respect to income is 1.5—the same as in the earlier sample period—but the semi-elasticity with respect to inflation is –0.9, compared with—1.5 in the earlier period. Furthermore, the long-run demand for narrow money is found to be sensitive to changes in the interest rate on one-year time deposits.123

As for the short-run dynamics in the second sub-period, the change in income in the current period, t as well as in the previous period, (t – 1), enters the equation significantly but with opposite signs. In particular, the coefficient for the current period change in income is positive while that for the term ΔRNYt–1 is negative, implying that the impact of an increase in income on narrow money demand is smaller when income growth is accelerating. As for the impact of inflation, the current period change in inflation has a negative impact on narrow money demand, while the change in inflation lagged one period has a positive impact. This latter effect probably arises for the same reason as in the case of currency demand. The error-correction term is statistically significant but considerably smaller than in the earlier subperiod, implying a less rapid adjustment to disequilibria in narrow money holdings.

Broad Money

The long-run elasticities of broad money with respect to income and the inflation variable in the 1983–88 subperiod are estimated to be 1.8 and –2.2, respectively (Table 25). The estimated error-correction equation describing the short-run behavior of broad money holdings indicates that, as in the case of M1, the error-correction term (Table 26) is quite large and statistically significant, suggesting a relatively rapid adjustment of broad money balances to their long-run equilibrium.

Table 25.Long-Run Broad Money Demand
Variable1Estimated Coefficientt-statisticp-value2Adjusted R2SER (In percent)Durbin- WatsonTest of Cointegration (p-value)
RM2t (1983–88)0.984.02.08–4.661

(0.01)
Constant–5.5111.90.00
RNYt1.8124.60.00
INFLt–2.214.80.00
Long-run income elasticity1.8
Long-run semielasticity with respect to inflation–2.2
RM2t(1989–93)0.994.02.05–4.611bottom(0.01)
Constant–3.575.70.00
RNYt1.5818.30.00
INFLt–1.545.60.00
IRt–0.056.80.00
Long-run income elasticity1.6
Long-run semielasticity with respect to inflation–1.5
Long-run semielasticity with respect to interest rate–0.05

RM2 = real broad money holdings; RNY = real national income; INFL = retail price inflation; and IR = real interest rate.

Probabilities of accepting the null hypotheses for the tests reported.

RM2 = real broad money holdings; RNY = real national income; INFL = retail price inflation; and IR = real interest rate.

Probabilities of accepting the null hypotheses for the tests reported.

Table 26.Error-Correction Equations—Broad Money
Variable1Estimated Coefficientt-statisticp-value2Adjusted R2SER (In percent)Durbin-WatsonJ-B3(p-value)ARCH4 (p-value)
ΔRM2t(1983–88)0.384.01.960.57

(0.75)
0.50

(0.50)
Constant0.021.30.20
ΔRNYt1.043.00.01
ΔINFLt–1.232.80.01
ECt–1–0.783.10.01
ΔRM2t (1989–93)0.552.01.950.77

(0.68)
0.13

(0.72)
Constant0.044.40.00
ΔRNYt0.230.90.39
ΔINFLt–1.192.10.05
ΔIRt–0.022.70.02
ECt–1–0.22–0.90.40

RM2 = real broad money balances; RNY = real national income; INFL = retail price inflation; and IR = real interest rates.

Probabilities of accepting the null hypotheses for the tests reported.

J-B = Jarque-Bera test for normality of residuals.

ARCH = Test for autoregressive conditional heteroskedasticity.

RM2 = real broad money balances; RNY = real national income; INFL = retail price inflation; and IR = real interest rates.

Probabilities of accepting the null hypotheses for the tests reported.

J-B = Jarque-Bera test for normality of residuals.

ARCH = Test for autoregressive conditional heteroskedasticity.

For the subperiod 1989-93, the most satisfactory long-run broad money demand function included the interest rate on time deposits, which can be interpreted as an own rate on broad money balances. The income elasticity of broad money is 1.6, which is similar to that estimated for the earlier subperiod. The estimated semielasticity with respect to inflation is -1.5, significantly smaller than that in the earlier subperiod. In addition, the estimated own interest semielasticity is negative and statistically significant. This perverse result could arise from the fact that, although interest rates on bank deposits have been adjusted with greater frequency, they remain administered. In such circumstances, it is likely that the adjustments of deposit interest rates have typically occurred when interest rates on alternative financial assets (including those offered by fund-raising schemes outside the financial sector) have been rising by greater margins, and have therefore been insufficient to cause agents to maintain their real holdings of M2 balances.124

The estimated dynamic error-correction equation shows that the short-nm response of broad money—unlike that of currency and narrow money—to inflationary developments is unchanged. Another notable feature of the results is that, although the estimated coefficient is very small, an increase in the own rate on broad money tends to lower holdings of broad money, even in the short run. The error-correction term, while having the correct sign, is not statistically significant.125

Possible Policy Implications

The existence of relatively stable long-run demand functions for the monetary aggregates in the post-1988 period points to the feasibility of monetary targeting. At the same time, however, the difficulty in obtaining well-specified short-run dynamic equations—especially the response of narrow and broad money to changes in interest rates and other opportunity cost variables—suggests that these aggregates will have to be monitored closely, particularly as interest rates become increasingly flexible and market determined. It would also be advisable for the authorities to continue to monitor credit developments closely.

Another issue that needs to be clarified with respect to the move to monetary targeting is the controllability of the monetary aggregates, that is, the relationship between operating instruments and monetary aggregates. The Chinese authorities have expressed the intention to use excess reserves of the banking system as the operating instrument to regulate the growth of their intermediate targets, namely, the monetary aggregates. However, given the wide-ranging implementation of institutional reforms in the financial sector, it would be prudent for the authorities to watch closely the relationship of excess reserves to the intermediate targets and to supplement excess reserves with other variables, including PBC credit to banks and foreign exchange reserves, as operating instruments.

Notes on Data Sources and Definitions

The sample covers the period 1983-93. All data are quarterly and have been seasonally adjusted prior to estimation. Data on currency, narrow money, and broad money have been provided by the authorities and deflated by the retail price index. In that connection, it should be noted that the Chinese authorities publish only an annual retail price index: for higher frequencies, all published data are in the form of percentage changes over the previous 12-month period. A monthly price index has been constructed by assuming that the price levels increased smoothly during the base year of 1980, so that the implied average inflation during those 12 months was the same as the actual average annual inflation, as measured by the published price index. The rest of the price index has been constructed by applying the published 12-month percentage changes to the levels established for 1980. The implied annual average percentage changes have then been calculated and compared with the published annual price index as a way of verifying the interpolation procedure.126

Also, the authorities do not publish monthly or quarterly data on GNP or any other broad measure of economic activity. In this appendix, the methodology described in Burton and Ha (1990) has been followed to construct a quarterly series for national income. Annual national income data in nominal terms have been divided into three components: (1) agriculture; (2) industry, construction, and transportation; and (3) commerce. These components have then been converted into real terms by using the corresponding annual sectoral deflators. Next, quarterly data have been interpolated for each of these components on the basis of the seasonal pattern for the corresponding year in related variables for which quarterly data are available. For the agriculture component of national income, quarterly real rural household incomes have been used to interpolate the quarterly series. For industry, transportation, and construction, the variable used has been quarterly real industrial production, while commerce has been interpolated on the basis of quarterly real retail sales. The interpolated quarterly components of real national income have then been added together to obtain a quarterly real national income series. Again, the implied annual average percentage changes have been calculated and compared with the annual percentage changes as reported by the authorities as a check.

Finally, given that interest rates were changed only infrequently prior to 1988. inflation—as measured by movements in the retail price index—has been used as a proxy for the rate of return/opportunity cost of holding money balances in the 1983-88 subperiod. For the period after 1988. the equations for M1 and M2 have been estimated with the difference between the interest rate on one-year time deposits and the inflation rate as the relevant opportunity cost/rate of return variable.

All variables, except for inflation and interest rates, are expressed in logarithms.

Explanation of Diagnostic Tests

In this analysis, a standard Chow test—an F-test for parameter stability over the two specified subperiods—has been used to test for structural breaks. The null hypothesis is that the coefficient estimates in the two subperiods are the same. Predictive failure tests or out-of-sample prediction tests have also been conducted to determine whether a new observation lies inside the confidence interval for the forecast.

The order of integration of the variables used in this analysis has been tested by means of unit root tests. Generally speaking, these involve testing the null hypothesis that α=1(or that the process y has a unit root) in the following regression:

By subtracting yt–1 from both sides of the equation, it can be rewritten as

In theory, the null hypothesis of the presence of a unit root could be tested by using the t-statistic for the estimated coefficient of yt–1. In practice, however, two problems arise with this general procedure. First, under the null hypothesis that the process has a unit root, the t-statistic does not have a standard t-distribution and is not asymptotically normally distributed. Thus, specially calculated critical values are required. Second, these specially calculated critical values depend on the specific form of the 1(1) or nonstationary process that yt, is under the null hypothesis. In particular, the values would differ if the process were a pure random walk or a random walk with drift. To take account of these possibilities, a slightly modified version of the above regression has been run to test for unit roots. This test is referred to as the augmented Dickey-Fuller (ADF) test and is based on the following equation, which includes a time trend:

The null hypothesis is that λ = 0 or that the process yt has a unit root. Table 27 presents results of the ADF tests for the variables of interest in this model in levels and first differences. As noted above, the results show that the null hypothesis that the variables are nonstationary cannot be rejected at the 1 percent significance level. The tests performed on the first differences show that the variables are all 1(1).

Table 27.Unit Root Tests
Variable(k.n)ADF(k.n)1p-value2
Narrow money (RM1)341.1–1.2520.90
Broad money (RM2)341.1–1.7660.74
Currency (RQ)341.1–1.7160.76
National income (RNY)41.1–1.9530.65
Retail prices (RP)41.11.8000.72
Retail sales (RS)41.1–2.3890.41
Industrial production (IP)41.1–1.3900.87
ΔRM140.1–4.6650.00
ΔRM240.1–4.7470.00
ΔRC40.1–4.6080.00
ΔRNY40.1–6.4020.00
ΔRP40.1–3.6180.04
ΔRS40.1–7.3730.00
ΔIP40.1–7.5870.00

ADF is the augmented Dickey-Fuller unit root test, k denotes the degrees of freedom, and n denotes the number of l(I) series to be tested.

The p-values are the probabilities of accepting the null hypothesis in equation (1).

Nominal variables deflated by the retail price index.

ADF is the augmented Dickey-Fuller unit root test, k denotes the degrees of freedom, and n denotes the number of l(I) series to be tested.

The p-values are the probabilities of accepting the null hypothesis in equation (1).

Nominal variables deflated by the retail price index.

In addition to these tests, a variety of tests have been employed to check the properties of the dynamic error-correction equations. In the case of all reported test statistics, the p-values shown represent the probability of accepting the null hypothesis.

Serial correlation of the residuals has been tested for by using the Durbin-Watson statistic or, in the presence of a lagged dependent variable, the Durbin’s h-statistic. The null hypothesis for both tests is that there is no first-order serial correlation in the error term.

The Jarque-Bera test for normality of the residuals is a Lagrange multiplier test for excessive skewness and kurtosis of the residuals relative to a normal distribution; it is distributed as x2(2).

A test for first-order auto regressive conditional heteroskedasticity (ARCH) of the residuals was conducted. Autoregressive conditional heteroskedasticity arises when the variance of the error terms follows an autoregressive process; in a regression of the type yt = β xt + t, the variance of t is given by α0 + α12t–1. The ARCH statistic tests the null hypothesis that α1 is equal to zero and is distributed as x2(1).

References

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111Despite considerable financial innovation in recent years, currency remains the principal medium of exchange in China and a variable to which policymakers still pay attention.
112In the empirical analysis presented later in this appendix, real retail sales and industrial production are also used as scale variables in the demand functions for currency and M1. As the results are similar to the ones obtained using national income, only the latter are reported here.
113This finding is also consistent with that reported in Appendix II.
114Such a model can be derived from transactions demand, portfolio balance, and “overlapping generations” approaches to money demand (See Laidler (1985), Goldfeld and Sichel (1990), Goodfriend (1985), Blanchard and Fischer (1989), and Cuthbertson and Taylor (1987)). Note that this formulation imposes the restriction that money balances are homogenous of degree I with respect to prices. Alternatively, nominal balances can be written as functions of prices, real income, and opportunity cost/rate of return variables.
115The Engle-Granger approach used in this study has the advantage of transparency in obtaining and interpreting the results. However, its drawback is that the estimated cointegrating vector may not be unique. In general, in an n-variate model, there exist (n—1) possible cointegrating vectors: therefore, the cointegrating vector estimated using the Engle-Granger methodology is not necessarily unique and may be a linear combination of the true conintegrating vectors. Johansen (1988) and Johansen and Juselius (1990) have developed a maximum likelihood procedure that allows the researcher to test for the number of cointegrating vectors that exist and to estimate separately the coefficients of the different vectors. If there is more than one possible cointegrating vector, the choice between the vectors is generally made on the basis of prior theoretical assumptions about the signs and/or the magnitude of the coefficients. In this paper, the Johansen procedure is used only to test for the number of cointegrating vectors. The actual values of the vector are estimated by using the Engle-Granger procedure.
116See below for the method used to construct this variable.
117For some of the equations, the most satisfactory first-step equation took the following form:(M/P)t=β0+β1yt+β2βt+β3(M/P)t-1+ϵt.
In these cases, the long-run elasticities with respect to scale and opportunity cost variables are given by β1/(1–β3) and β2/(1–β3), respectively.
118Many of the key series used in the empirical analysis are constructed by using strong assumptions. The results should therefore be viewed with an additional measure of caution, as they may be strongly influenced by the idiosyncracies of the data and the methodology underlying their construction.
119As argued by Burton and Ha (1990), this finding tends to undermine the argument that a substantial amount of money holdings in China was involuntary. One reason for this could be the introduction of the “two-track” pricing system relatively early in the reform process. Under this system, farmers and enterprises were required lo sell products up to the plan amount to the state at fixed prices but could sell additional output on the free market. This system implies that individuals and enterprises were buying and selling goods on the margin at market-related prices. Thus, it was unlikely that money holdings were “involuntary.” The results of several studies of repressed inflation or forced savings (Feltenstein and Ha (1991) and Portes and Santorum (1987)) suggest that the magnitude of repressed inflation in China was limited.
120This is a reflection of the backwardness of the payments system, which continues to rely on cash as a main instrument of transaction.
121The lack of a sufficiently long time series for interest rates on alternative, longer-term financial assets precludes their inclusion in this analysis.
122Burton and Ha (1990) found that the long-run elasticities of currency demand with respect lo income and the inflation variable were 1.66 and –1,01, respectively—broadly similar to the results obtained in this study. However, the estimated short-run dynamics are considerably different. This is partly attributable to Burton and Ha’s use of an expected inflation term that is the average of inflation in the current period and inflation lagged one and four periods. The authors noted that this formulation was indicated by the general lag model that they fitted to the inflation process. In contrast, the finding in the present paper is that the stochastic process describing the behavior of inflation (and expectations) is best approximated by an autoregrcssive process of order 1. This would imply that the expectations for inflation in period (t + 1), formed at time t. would be equal to actual inflation in period t.
123The interest rate variable is specified as the annual rate on one-year time deposits. Thus, the estimated coefficient shows the contemporaneous response in real narrow money holdings in a given quarter to a change in the annual percentage rate on time deposits. That is, an increase of 1 percentage point in the annual interest rate on time deposits in a given quarter would lower real M1 balances by 0.03 percent in that quarter.
124This suggests that the differential between the own rate and alternative rates may be a more appropriate variable to be used.
125As argued in Kremers and Lane (1992), it is possible that finding a relatively low and statistically insignificant error-correction term reflects specification errors in both the long- and short-run equations.
126Burton and Ha (1990) constructed an index based in 1982, but the implied annual average percentage changes are considerably different from those provided by the authorities.

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