This article reexamines the demand for money during hyperinflation using a model that allows the relative price of capital goods to vary. We assume that relative price fluctuations reflect interactions between the real and monetary sectors. While the expected inflation rate reflects intertemporal price changes, it is the relative price of the capital good.
Our theory concludes that demand for money depends negatively on both the expected inflation rate and the relative price of capital goods to consumption goods. As a result, relative price movements have an ambiguous effect on how money demand responds to expected inflation. On the one hand, an increase in the relative price increases effective cost inflation.
We use data on the Chinese hyperinflation (January 1946 to April 1949) to uncover empirical evidence on the importance of the relative price effect on the demand for money. In particular, when the relative price rises, expected inflation has a more negative effect on money demand. Thus, estimates of traditional Cagan money demand, which ignore relative price and interactive effects, may underestimate the welfare costs of hyperinflation.
Equation (4) determines the efficiency of intertemporal consumption, while (5) determines the relative price of a capital good relative to a consumer good.
Comparative-Static Analysis
The equation system together with (1) characterizes the individual decision policy functions of the optimal control problem (PA) of the representative agent. This indicates a modified golden rule that determines the optimal accumulation of the physical capital stock. Our generalized cash-in-advance model thus adds two additional factors to determine the optimal capital accumulation: the relative price (q) and the expected inflation (via the term associated with non-zero θ).
Therefore, it can be concluded that both the expected inflation rate and the relative price of the capital asset have negative effects on the demand for money. For the case of Stockman (1981), where θ*q=1 and v = 1, the magnitude of the relative price effect (on the demand for money) is larger than that of the expected inflation effect. In general, the greater the share of capital goods subject to the cash prepayment constraint, the greater the magnitude of expected inflation and relative price effects on real money balances.
7 Tallman and Wang (1995) interpret shocks to the relative price ratio as a proxy for real price increases. In contrast, the relative price variable in this paper is a cost of capital proxy and is used for comparative static results. It is thus clear that while the effect of the relative price or cost of capital on money demand remains negative, the variable velocity factor magnifies the negative effect of expected inflation.
Therefore, there is an acceleration of the negative effect of inflation on the demand for money as inflation becomes higher. In this case, the cost of inflation is fully absorbed by the changes in the transaction frequency, and holdings of real money therefore become independent of the inflation rate as it increases without limit. It is also interesting to see from these two equations that in addition to the level of inflation and the level of the relative price, there are others.
Our theory concludes that money demand depends negatively on both the expected inflation rate and the relative price level. However, the effect of relative price on the response of money demand to expected inflation is unclear. Omitting the real concerns represented by changes in relative price and these interacting terms may mismeasure the effect of inflation on money demand, leading to biased welfare estimates.
Empirical Evidence
In our application, a larger number indicates a depreciation of the currency and therefore indicates the expectation of further inflation in the future. Separately, in Figure 1 we present evidence that the ratio of WPI to CLI increased substantially during the hyperinflationary period. In the benchmark case of an inflation expectations model as described above, we do not include contemporaneous values of money supply growth in the inflation forecast.
However, to avoid the potential problem related to the endogeneity of money supply creation, we only use lagged values of the money supply growth rates in the inflation forecast equation (although the addition of contemporaneous money growth to the regression does not change the main implications of the results).11 . The SIC results suggest the following specification for the inflation prediction equation: one lag of the inflation rate, the current value and two lagged values of the money growth rate, and the current log level of exchange rate. We note that we have considered alternative specifications of the inflation forecast equation: (i) incorporating simultaneous money supply creation and (ii) specifying the current exchange rate in logged differences.
These unusual coefficient values in the inflation prediction equation come from our use of the logarithm of the black market exchange rate. We also took into account less (one) and more (three) lagged values of the money growth rate and found virtually identical results, which are therefore omitted from the paper. 14 Frenkel (1977) used the forward nominal exchange rate premium to forecast inflation during the German hyperinflation.
The results performed with the index as the geometric mean of the series were practically unchanged. We note that the only non-stable result for the change from WPI to CLI as a deflator is the negative and significant impact of the relative price measure. We have also considered the relative price ratio transformed as the natural logarithm of the ratio.
Based on the Fisher equation, the direct measure of the interest rate semi-elasticity of money demand is β1. For the specifications that include non-linear interaction terms, the direct measure of the semi-elasticity ranges from -1.5 to -2.1. The magnitude of this semi-elasticity is positively related to the Harberger triangle measure of the welfare cost of inflation.
Therefore, our results suggest that the welfare costs of Chinese hyperinflation appear larger once the nonlinear interaction terms are included. In Figure 2 we present the time series model of semi-elasticity measures that clearly depend on the time series of expected inflation and relative price.
Concluding Remarks
The theoretical model suggests that an increase in expected inflation raises the effective cost of capital, ρ[1+θ ρ*( + +n π)]q. The reduction in capital through substitution of assets will encourage balance holdings of real money in a second-order way. The estimated coefficients for the interaction terms are all positive, suggesting that second-order asset substitution effects dominate the effect via the indirect marginal benefit mentioned above.
In addition, the lack of viable alternative stores of wealth in China may have increased the demand for capital goods such as pure inventory capital, motivated solely by hyperinflation. For future work, it may be interesting to apply our theoretical and empirical framework to other hyperinflationary experiences, such as the German hyperinflation after World War I and the 1980s episodes in Israel and several Latin American countries. On the one hand, one can examine the robustness of the inclusion of relative price variables and non-linear interactive terms to explain the money demand behavior during hyperinflationary episodes.
On the other hand, one can compare and contrast the interactive effects between the real and monetary sectors, which can help to understand the transmission mechanism of monetary disturbances in the absence of a credible central bank. Π is the inflation rate, MG is the money growth rate, and EG is the natural logarithm of the dollar-CNC exchange rate. The DW statistic is biased towards the non-rejection of the null hypothesis of no autocorrelation of the errors when a lagged dependent variable is present.
Notes: In addition to the notes in Table 1, Q is the relative price measured by the ratio of WPI to CPI. The dependent variable is the natural logarithm of real money balances, log(M/P), with WPI used as the price deflator (P). The two-stage least squares estimation procedure is used to jointly estimate the money demand and inflation expectations equation.
The instruments are lagged values of the dependent and independent variables, a constant and lagged inflation and money growth. As in Table 1 except for the inclusion of the contemporaneous value of money supply growth. We have fewer observations to have sufficient degrees of freedom for out-of-sample forecasts.
Coefficient estimates: two-stage IV procedure – 1) generate “out-of-sample” inflation forecasts (baseline specification (i.e. lagged money growth, log exchange rate) Notes: As in Table 1, except that EG is the differentiated logarithm in the dollar-CNC exchange rate.
