Appendix: Demand for Money

Gyorgy Szapary, Steven Dunaway, David Burton, and Mario Bléjer
Published Date:
March 1991
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This appendix summarizes the results of the estimation of models of the demand for a range of monetary aggregates originally reported in Burton and Ha (1990). The approach adopted involved testing down from a general autoregressive lag model, in which the explanatory variables were inflation and a measure of income, to a specific dynamic model. The latter was then estimated in an error correction form in which the deviations from long-run real balances (the error-correction term) were calculated from the tested-down long-run model.98

Using this approach, money demand models were estimated for six monetary aggregates: currency in circulation, household money balances, enterprise money balances, total deposits, narrow money, and broad money. For the sake of brevity the results for enterprise money balances and narrow money are not reported here. However, it may be interesting to note that the results for the demand for money by enterprises did not differ greatly from those for other aggregates and that, in particular, demand appeared to be sensitive to expected inflation. These findings suggest that, despite the apparent softness of enterprise budget constraints, enterprises as a group are sensitive to the opportunity cost of holding money.

Empirical Results

The following models were estimated with quarterly data covering the period 1983 to 1988 Q3.99

Household Money Balances

The results for household money balances are reported first as this is an aggregate for which money demand models for China have commonly been estimated (e.g., Portes and Santorum (1987) and Feltenstein and Ha (1988). The estimated error correction model is

where ût–1 is the deviation of real household balances from long-run equilibrium calculated from the tested-down version of the general lag model.100 The (expected) inflation term, Π*, is the average of current (quarterly) inflation, inflation lagged one period and inflation lagged four periods;101Y is the log of real national income;102 and D is a dummy variable for the second quarter of 1985, a period when monetary growth was sharply reduced primarily through the tightening of direct credit controls.

The estimated equation satisfies the diagnostic tests, including a Chow test for parameter stability and a Chow predictive failure test (with the sample split at the second quarter of 1985 for both tests).103 The coefficient on the error correction term, ût–1 is significant at the 1 percent level, which provides evidence that real balances, real income, and inflation are cointegrated. The underlying equilibrium relationship from which û is derived implies that the long-run income elasticity is close to 2 (Table 9), indicating an increasing role for money in the economy as the reforms progressed during the sample period;104 income elasticities greater than one are obviously not sustainable in the very long run.105 The long-run coefficient on the inflation variable (whose dimensions are percent per quarter) indicates that a 1 percentage point increase in the annual inflation rate would reduce real household money balances by about one half percentage point.

Table 9.Money Demand—Estimated Long-Run Coefficients1
Log of scale variable2Inflation variable3
Household money1.97–2.06
Currency in circulation1.66–1.01
Savings deposits1.69–4.10
Broad money1.53–3.67

Turning to the dynamics of household money demand, the results imply that a 1 percent increase in national income initially raises real household balances by just under 1 percent, while a 1 percentage point increase in II* (at an annual rate) lowers real balances on impact by 0.4 percent.106 The remaining adjustment to the long-run equilibrium appears to occur rapidly, with almost 80 percent of the deviation between actual and equilibrium money balances (lagged one quarter) eliminated in a quarter.107 A final point with regard to the dynamic structure is that the restrictions implied by the partial adjustment model are decisively rejected when the error correction model is estimated in a form similar to equation (4).

Currency in Circulation

The estimated model for currency has a more complex dynamic structure than the models for the other aggregates. The fitted equation is

where Π^ is a three quarter average of general retail price inflation. The model implies that real currency holdings at first rise in response to an increase in inflation, before declining in later periods to less than their initial value.108 The subsequent reduction in demand is brought about both through the error correction term (adjustment is quite rapid), and also through the term, Π^t2.109

The dynamic response of the demand for currency to changes in inflation indicated by the model has an intuitively plausible, “cash-in-advance,” interpretation in the Chinese context. When inflation rises with nominal interest rates held unchanged, the long-run objective of agents is to shift from both currency and deposits into consumer durables and other storable commodities. However, as noted earlier, there are no checking accounts in China and the availability of some goods has been subject to uncertainty. In these circumstances, it seems likely that agents would need to increase their cash holdings initially to put themselves in a position to purchase goods when they became available. This response pattern was particularly apparent during mid-1988 when currency holdings rose sharply as a result of large withdrawals from savings deposits, whose real return had become substantially negative with rising inflation.

It seems unlikely, however, that the relationship between currency demand and inflation is symmetric. If inflation falls, the long-run real demand for both currency and deposits would increase, but there would seem to be little reason for currency holdings to be reduced in the short term as agents attempt to shift from real goods to various forms of money.110 The properties of the estimated model probably reflect the fact that inflation was rising for most of the sample period.

As in the case of household and enterprise money balances, the restrictions implied by the partial adjustment model are rejected.

Savings and Time Deposits

Given the different dynamic behavior of currency to household and enterprise money, a model for total deposits (defined as broad money minus currency) was also estimated. The fitted error correction model

is similar to those for enterprise and household money, although it differs in that it includes an acceleration term in inflation. The underlying long-run model indicates a greater responsiveness to inflation than either household or enterprise money. It seems likely that this reflects the relatively low estimated inflation elasticity of the currency component of the latter two aggregates. The restrictions implied by the partial adjustment model are rejected at the 1 percent level.

Broad Money

The estimated error correction model for broad money is

The inflation variable is the same as in the model for household money balances, namely an average of the current, one-period, and four-period lagged inflation rates. Dummy variables for 1984 Q4 and 1985 Q2 are also included.111 The restrictions implied by the partial adjustment model could not be rejected at the 5 percent level, although they were rejected at the 10 percent level.

Concluding Observations

The results presented above suggest the existence, for a range of monetary aggregates, of relatively stable demand relationships that might be helpful in guiding monetary policy. It is noteworthy that, for most aggregates, the standard real partial adjustment model is decisively rejected, indicating that a more complex dynamic structure is required to characterize the data adequately.

In all cases, the long-run income elasticity is greater than unity. As noted in the main text, this could reflect the monetization of the economy under the reforms as the coordination of economic activity has increasingly taken place through markets, or, alternately, a rising degree of repressed inflation that has been correlated with real income growth. However, another feature of the results is that real balances appear to be sensitive to expected inflation as proxied by the inflation rate of the general retail price index. This suggests that agents are able to adjust the level of their real balances to changes in opportunity costs, and hence tends to undermine the argument that a substantial amount of money holdings is involuntary.112

Although the estimated models passed a limited range of stability tests (the extent of the testing was limited by the small number of observations), the nature of money demand in China is likely to evolve as the economic system, particularly the financial sector, develops. For instance, the introduction of checking accounts would be likely to affect the dynamics of the demand for currency. In addition, the dynamic structure of the models almost certainly reflects a combination of both the dynamics of adjustment to long-run equilibrium and the structure of expectations formation mechanisms; the latter are likely to evolve if the processes generating the variables in question change (the Lucas critique).

An issue that remains to be addressed is the impact of changes in interest rates on the demand for various aggregates; expected inflation is the only opportunity cost variable in the estimated equations because of the very limited variability of interest rates during the sample period. It is likely that a reduction in deposit interest rates would have a similar effect on the demand for deposits to that of an increase in inflation. The consequences for the demand for currency in the present circumstances, however, would probably be more complex. In particular, the long-run demand for currency would be likely to rise, but possibly by less than the short-run increase, as agents temporarily increased their currency holdings as a transitional stage in the substitution from deposits into commodities. The response of currency to an increase in deposit rates, however, would be unlikely to involve a larger short-run than long-run decline in demand, and hence might not be symmetric. Since interest rate policy in China has become more active over the past two years, it may soon be possible to investigate this question empirically.

This methodology is described in Hendry and Richard (1982) and C.L. Gilbert (1986). For discussions of its application to the demand for money see Cuthbertson (1985) and Ericsson (1986).

The data are described in detail in Burton and Ha (1990).

Similar results were obtained using the residual from the direct estimation of the long-run model.

This formulation was indicated by the general lag model.

If real national income is replaced by household cash income, which grows more slowly than real national income (possibly owing to an increasing amount of under-reporting of incomes in the household survey), the coefficient is not significant. This indicates that household money balances, household cash income, and the inflation variable are not cointegrated.

The tests are described in the annex in Burton and Ha. For the Chow tests, the break point was chosen because it coincided (approximately) with the implementation of a substantial price liberalization and enterprise reform.

Monetization was not tested directly because a reasonable proxy variable that would capture the extent to which transactions were conducted in the monetary economy was not available.

It is not unusual, however, to find income elasticities greater than one in developing countries.

A 1 percentage point increase in actual inflation in a quarter (at an annual rate) would have only one third the impact on real balances.

If the first difference of real income or inflation has a nonzero mean, the model in general does not converge to its long-run equilibrium unless certain parameter restrictions are imposed (see Currie (1981)). Instead, the model converges to some constant distance from long-run equilibrium. The problem, which applies even more severely to the partial adjustment model, arises because the long-run equilibrium to which the model converges is specified in terms of the current levels of explanatory variables even though they may exhibit trend growth. For an approach in which the future path of the explanatory variables is explicitly taken into account, see Cuthbertson and Taylor (1987).

Currency is less responsive in the long run to change in expected inflation than other aggregates.

Similar results were obtained in a model in which the two inflation terms were quarterly inflation lagged one period and lagged four periods, with the former variable entering with a positive coefficient and the second term with a negative coefficient.

It is possible that agents would initially increase holdings of interest-earning deposits at the expense of cash.

The exclusion of the dummy variables has little effect on the estimated coefficients, although it does sharply reduce the R2.

As noted earlier, however, the sensitivity of money demand to expected inflation does not rule out the possibility that under a partially liberalized price system, the price level is lower than if prices were fully liberalized.

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