# Money demand during hyperinflation and stabilization: Bolivia, 1980-1988.

I. INTRODUCTION

The stability of demand-for-money equations has been at issue in both econometric research and policy analysis. The academic debates about the relative merits of the traditional, buffer-stock, and the error-correction models of demand for money have centered on parameter stability.(1) In policy discussion, the scope for remonetization following stabilization depends on the upward shift in the demand for money and the consequent predictability of higher money demand with lower rates of inflation.(2) Only an increased demand for money would make further credit expansion non-inflationary.

Inflation uncertainty has a pervasive effect in the money-price nexus. High inflation uncertainty makes money a riskier asset, depressing the demand for money on a long-term and possibly short-term basis. This impact on the demand for money means that policies influencing inflation will have an additional effect through their impact on inflation uncertainty, as well as on expected inflation.

This paper examines the role of inflation uncertainty in a dramatic case study: Bolivia during the 1980s. This was a decade of extreme macroeconomic instability. Annual inflation rates reached over 20,000 percent, motivating a subsequent stabilization which drove annual inflation rates down to less than 25 percent, where they have remained for more than five years. Perhaps more than any other country in recent history, Bolivia has undergone a dramatic structural shift in its macroeconomic policy regime. To what extent did the demand for money shift during this period in its sensitivity to expected inflation, inflation uncertainty, and to underlying monetary disequilibria? As the inflation stabilization progressed, how fast did the money-demand parameters react to this new regime change? Was there scope for remonetization in Bolivia following the now famous stabilization plan of August 1985, the New Economic Plan introduced by President Victor Paz Estenssoro?(3)

Previous literature on the demand for money has explored the role of inflation uncertainty with ambiguous results.(4) Klein |1977~ observed that inflation-rate uncertainty reduced the average and marginal productivity of real cash balances in providing monetary services. Effectively, a greater volume of real cash balances is required to obtain the same "quality-adjusted" level of cash balances. While the impact on the demand for money is theoretically uncertain because the income and substitution effects work in opposite directions, Klein provided empirical evidence that inflation uncertainty (measured by a moving five-year variance around a moving ten-year trend, with data from 1880 to 1972) actually increased the demand for money in the United States. Around the same time, Boonekamp |1978~ presented a two-period mean-variance model of money and bond demand, highlighting the potential importance of a hedging role in the demand for money in the face of inflation uncertainty.

Related to aspects of both of these two approaches, and working with a capital-asset pricing model (CAPM), Sweeney |1988~ drew on University of Michigan survey data on inflationary expectations to resolve the theoretical ambiguity of the impact Of inflation uncertainty. His results, based on post-war quarterly U.S. data, contrasted with those of Klein by showing a negative impact of inflation uncertainty on money demand.

In his study of the demand for money in the six hyperinflations originally examined by Cagan |1956~, Khan |1977~ measured inflation uncertainty by the absolute value of the change in inflation. His model assumed that inflation uncertainty would affect the demand for money not directly, but by altering the adaptive expectations parameter in the adjustment of inflation expectations. His empirical estimates implied a negative impact of inflation uncertainty on the demand for money during accelerating inflation.

Engle |1982~ introduced the concept of ARCH (autoregressive conditional heteroskedastic) models with a specific application to inflation expectations. Using United Kingdom data, he argued that such models provided a better measure of inflation uncertainty than the approaches of Klein and Khan. Evans |1991~ recently suggested that Engle's approach should be augmented by allowing for time-varying parameters in the model for inflation.

Our approach draws on all of this literature. Like Baba, Hendry and Starr |1992~, we model the demand for money as an error-correction process. Like Klein |1977~ and Sweeney |1988~, we allow inflation uncertainty to enter the demand for money directly, following Engle |1982~ as well as Bollerslev |1986~ in using a generalized ARCH (GARCH) model of inflation to generate the estimate of inflation uncertainty. In the spirit of Khan |1977~ and Evans |1991~, we allow the possibility of time-varying adjustment coefficients, estimated with Kalman filtering. While these elements are thus not new individually, the combination of all three has not hitherto been applied to the demand for money in the context of high inflation and subsequent stabilization.

Our results show that both expected inflation and inflation uncertainty influence the demand for money. The time-varying parameter analysis shows that the reaction to monetary disequilibria was significantly more rapid during hyperinflation.

Section II describes our empirical methodology and section III contains the results of our analysis. The last section is the conclusion.

II. A GARCH MODEL WITH ERROR CORRECTION

Our method of empirical analysis combines three approaches: first, a generalized autoregressive conditional heteroskedastic (GARCH) estimation of inflation variance variable, ||sigma~.sup.2~; second, an error-correction model of money demand; and third, estimation of time-varying coefficients of the error-correction model with Kalman filtering.

To obtain a proxy for inflation uncertainty we estimate a GARCH random walk model for inflation. Tests appearing in Table I, Panel A, discussed below, confirm that the rate of inflation has a unit root. We assume that our GARCH estimate of the conditional variance is correlated with inflation uncertainty. We also assume that this has both a short-term and a long-term effect on money demand. The following equations represent our GARCH model:(5)

|Mathematical Expression Omitted~,

|Mathematical Expression Omitted~

where p represents the logarithm of the price level, |delta~|p.sub.t~ period t inflation, ||epsilon~.sub.t~ the random error term, and |Mathematical Expression Omitted~ the squared error at time t-1 and ||sigma~.sup.2~ the conditional variance of inflation. Given an initial specification for ||sigma~.sup.2~ at time t = 0, equations (1) and (2) are estimated by a maximum-likelihood process to obtain the conditional variance parameters {||gamma~.sub.i~}.(6) Given these parameters and an initial starting value, inflation uncertainty, proxied by ||sigma~.sup.2~, is generated for each period by forward recursion. The GARCH process for the inflation uncertainty is similar to the one estimated by Bollerslev |1986~.(7)

The long-run equilibrium or optimal demand for money (m - p)* depends on the expected rate of inflation |pi~ and on inflation uncertainty, ||sigma~.sup.2~.(8) The long-run model is an extension of Cagan |1956~, with the inclusion of the uncertainty variable. Since the inflation uncertainty term is estimated from a random-walk model of inflation, for consistency with this measure of inflation variance, expected inflation |pi~ for time (t + 1) is set equal to |delta~p. The long-run money demand is given by the following expression:

|Mathematical Expression Omitted~.

We test this specification of equilibrium for the cointegration of real balances (m - p) with |pi~, and ||sigma~.sup.2~, plus a time trend, tr. Cointegration implies the existence of a stationary vector |upsilon~ which is a linear combination TABULAR DATA OMITTED of (m - p), |pi~, and ||sigma~.sup.2~ as well as a constant and trend term. We obtain this vector |upsilon~ by a regression of (m - p) on |pi~ and ||sigma~.sup.2~, and setting |upsilon~ = (m - p) - (m - p)*, where (m - p)* is the optimal level of real balances, generated by a least squares estimation of the parameters of equation (3).(9)

In our study, we do not use a "scale variable" (representing transactions) in the money demand model, nor an "opportunity cost" variable other than the rate of inflation. We ignore the scale variable since we wish to work with monthly data during the hyperinflation episodes, when adjustment becomes rapid, and data for income are not available as monthly series in Bolivia. Similarly, variables for interest rates or other rates of return were severely distorted during the hyperinflation, so that the expected rate of inflation is the only available indicator of the costs of holding money.

With three or more variables in the cointegration equation given by (3), Johansen and Juselius |1990~ have shown that there may be more than one cointegrating vector, |upsilon~, since there may be more than one equilibrium relationship among three or more variables. The Johansen-Juselius approach is especially relevant for money demand functions in which income, interest rates, and expected inflation appear as arguments. In such a case, interest rates and expected inflation may be cointegrated through a Fisher relation, while money, income, and interest rates may be cointegrated through a long-run money-demand relation.

In our model, real balances and inflation are the two primary variables; the variance of inflation ||sigma~.sup.2~ is a non-linear transformation of inflation. Furthermore, expected inflation is the forecast of inflation from a random walk process. Hence, the natural cointegration relation to look for is the one relating real balances to expected inflation and the variance of inflation. However, we test for the number of cointegration vectors using the Johansen and Juselius procedure, for supporting evidence.(10) The results, discussed below, appear in Appendix Table I.

The use of the GARCH variable ||sigma~.sup.2~ as an argument in a cointegration test poses econometric issues recently analyzed by Nelson |1990~. Since the GARCH process for the conditional variance is a non-linear transformation, it is not subject to unit-root tests designed for linear stochastic processes. However, Nelson proposed a test for stationarity based on the logarithm of the sum of coefficient estimates of equation (2), ||gamma~.sub.i~, i = 1,2, for the case of ||gamma~.sub.0~ |is greater than~ 0. If this logarithmic value is greater than zero, then stationarity is rejected. We apply the Nelson criterion for the stationarity of our estimated ||sigma~.sup.2~.(11)

For short-run demand for money, we estimate the following short-run error-correction model initially under the assumption of constant parameters and then with the Kalman filtering:(12)

|Mathematical Expression Omitted~.

Error-correction models encompass more complex dynamics than partial adjustment models, which model adjustment simply as a function of excess demand or supply. In a partial-adjustment version, only ||delta~.sub.0~ and ||delta~.sub.4~ would matter. Similarly, the error-correction model encompasses a three-variable vector-autoregressive representation (VAR), in which cash-balance accumulation depends on its own lags, as well as the lags of the stationary first-differences of expected inflation and inflation uncertainty. By ignoring the cointegrating relationship ||upsilon~.sub.t-1~, VAR models may miss important channels of causality.(13)

In equation (4), inflation and inflation variance affect short-term money demand through their levels as well as lagged first-differences. The error-correction term ||upsilon~.sub.t-1~ is the difference between actual and optimal real balances (m - p)*, and thus registers the effect of the levels of expected inflation and inflation uncertainty on money demand. The feedback effects of the lagged first-differences of real balances, as well as the effects of the current and lagged first-differences of expected inflation and inflation uncertainty, on current real balance accumulation may extend back beyond one period. We have no a priori reasons to expect one particular lag pattern over another to emerge from our estimation, nor for the signs of the current or past first-differences. However, as actual real balances converge to optimal real balances, all dynamics vanish.

By allowing the coefficients to change through time with Kalman filtering, we pay close attention to the relationship between the time-varying error-correction coefficient ||delta~.sub.4~ and inflation, |delta~p, as agents change their beliefs about future government actions during stabilization and thus alter their speed of cash-balance accumulation in reaction to disequilibrium cash-balances.

In times of rapid inflation and rapidly changing rates of inflation, we thus expect two effects. First, the equilibrium demand for money might shift. Greater variance of inflation could reduce the demand for financial assets because it would make them relatively more risky. Secondly, the risk of being seriously out of equilibrium is greater when inflation is very variable, so money-holders will tend to switch to adjustment strategies which allow more rapid movement to equilibria.

We thus expect ||delta~.sub.4~ would be higher (in absolute value) during high and variable inflation, when agents have pessimistic expectations of future policy, than in periods of low inflation. Similarly, following a credible stabilization with optimistic expectations of future policy, there are lower risks to holding excess real balances, so we expect ||delta~.sub.4~ to be lower in absolute value than before the stabilization.

The specification of a time-varying error-correction coefficient estimated with Kalman filtering in equation (4) is an alternative to a non-linear mechanism specified by Hendry and Ericsson |1991~, who introduced the lagged level, square and cube of the cointegration vector ||upsilon~.sub.t-1~ in their short-run demand-for-money function in order to allow the speed of adjustment of money balances to vary with the extent of disequilibrium.(14) Rather than imposing a non-linear mechanism, we allow the data themselves to determine how the speed of adjustment varies with the extent of disequilibrium, via a recursive Kalman-filter estimation of ||delta~.sub.4~ for generating the best one-period forward predictors of |delta~(m - p).

The procedure for Kalman filter estimation of the coefficients of equation (4) is described by Hansen and Sargent |1991, 152-59~ as a special case of a state-space model. Kalman filtering, as opposed to simple recursive coefficient estimation, discounts past data with an optimal weighting scheme at each period in order to generate best one-period forward predictors.(15)

Equations (1) through (4) thus combine unit-root models of real balances and GARCH estimates of conditional variance, with cointegration and error-correction approaches of short-run money demand and Kalman-filter estimation of time-varying parameters. The payoff of combining these methods is enhanced predictability of real balances during periods of high turbulence and stabilization.

III. EMPIRICAL RESULTS

Money supply and price data for our analysis come from the Central Bank of Bolivia.(16) We do not have a priori reasons for selecting one monetary aggregate over another in our study. Of the three monetary aggregates, base money, M1, and M2, we shall let the data determine which aggregates are the more appropriate. Our price series is the consumer price index.

The models of the previous section assume unit roots for inflation |delta~p and expected inflation |pi~, proxied by ||delta~p.sub.t-1~, real balances (m - p), and inflation uncertainty, proxied by the conditional variance |Mathematical Expression Omitted~, as well as cointegration of these three variables. The stationarity or unit root tests for these variables appear in Table I, Panel A. The logarithmic values of all three monetary aggregates, deflated by the CPI, have unit roots. Our tests are based on augmented Dickey-Fuller |1979; 1981~ statistics, using the MacKinnon |1990~ critical values, for six lags with constant and trend terms.(17) One cannot reject the unit-root hypothesis for the rate of inflation, by the same statistical criterion.

Panel B in Table I gives the estimates of the GARCH process for expected inflation. The results show significant GARCH coefficients for the conditional variance for inflation. For the stationarity of the conditional variance series ||sigma~.sup.2~, generated by the coefficients given in Panel B and an initial starting value, Panel A in Table I shows a significant augmented Dickey-Fuller statistic. Since the Dickey-Fuller test is only appropriate for a linear process, and a GARCH process is by definition non-linear, stationarity of ||sigma~.sup.2~ is rejected by the Nelson criterion. As the note in Table I shows, the logarithmic value of the sum of the two coefficients is greater than zero.

The long-run relationship among (m - p), |pi~, and ||sigma~.sup.2~, three non-stationary series, is given by the cointegration vector, estimated as the difference between a linear combination of (|pi~, ||sigma~.sup.2~), plus a constant and time trend, and the actual (m - p). The coefficients come from an OLS regression of (m - p) on |pi~ and ||sigma~.sup.2~ as well as a constant and time trend. Panel C in Table I shows the coefficients for calculating the cointegration vectors for all three monetary aggregates.

The results of the Johansen and Juselius |1990~ procedure for the existence of more than one vector of cointegration for the three money supply definitions appear in the appendix table. The results do not reject at most one cointegration vector for base money and the M1 and M2 monetary aggregates.(18)

The Dickey-Fuller statistics for the cointegration vectors based on our regressions appear in Panel D of Table I. The results allow rejection of the unit-root hypothesis at the 5% level for M2 and at the 10 percent for M1. However, for base money, we cannot reject a unit root in the residuals. Panel D thus indicates that M1 and M2 are more appropriate monetary aggregates for examining money demand during the hyperinflation and stabilization period, since both of these aggregates are more likely to be cointegrated with inflation and inflation variance. For this reason, only these two aggregates appear in the rest of our analysis.

Panel E contains the estimates for the error-correction model for short-run demand for money. The results show that the first-differences of expected inflation and inflation uncertainty, as well as the lagged cointegration vector, are significant determinants of real balance accumulation for both monetary series. A monthly dummy variable appears in each equation for December of each year. This dummy, |d.sub.12~, captures the annual bonus payment, or aguinaldo, given to employees in Latin American countries at the start of the summer vacation period at the end of the year. While the coefficient of this dummy is significant, its exclusion does not affect the sign or significance of the other coefficients. Lagged first-differences of inflation and inflation variance, as well as the lagged first-difference of real balances and the constant term, turned out to be insignificant and were eliminated from the error-correction model.

Panel E shows that the first-differences of expected inflation and inflation uncertainty have opposite effects on short-run money demand, while the levels of both expected inflation and uncertainty have the expected negative effects on long-run money demand. The positive effect of the change in uncertainty may reflect the effect of an increase in inflation variance at the time of the stabilization, when inflation fell dramatically and unexpectedly while cash balance accumulation started to increase as a result of the credible stabilization. As a result, the increase in inflation variance or squared forecast-error is associated with an increase in cash-balance accumulation.

Figure 1 pictures the time-varying error-correction coefficient, ||delta~.sub.4t~, as well as the actual inflation rate, for the short-run money demand equation using the M1 monetary aggregate. This figure shows that the speed of cash balance accumulation varies with the rate of inflation. During the period of high inflation between 1983 and late 1985, the speed of cash balance accumulation reached a level almost 50 percent above its level following stabilization. A similar pattern is true for the time-varying coefficient estimated for the equation with the M2 monetary aggregate. Figure 2 shows the behavior of both coefficients.

The change in the speed of cash balance adjustment, before and after stabilization, is consistent with the more complex dynamic process underlying short-run money demand, involving changing expectations of private agents about future government actions. The fast upward shift of the adjustment coefficients indicates a significant change in 1985 characteristic of a credible stabilization.

V. CONCLUSION

The results of our analysis of cash-balance and inflationary adjustment in Bolivia during the 1980s are consistent with a more complex dynamic adjustment process, indicating changing beliefs of private-sector agents regarding future government actions and the incorporation of inflation variance as well as expected inflation in the demand for money. The payoff has been enhanced estimation of real balance accumulation, for both M1 and M2.

The results show a sharp change in 1985 in the speed of cash balance accumulation, indicating a fundamental change in the beliefs of private-sector agents about future government actions, and thus a credible stabilization. How did this credible stabilization take place? According to Morales |1988~, the total fiscal deficit was not quickly reduced at the time the stabilization plan was announced in August 1985. In fact, deficit reduction problems persisted for some time after 1985. In succeeding years the government suffered two major fiscal setbacks: a collapse by more than 50 percent in the international price of tin less than six months after the stabilization, and thus a loss in the revenues of COMIBOL, the state mining corporation, and a default by Argentina for more than two years in payments on natural gas pipeline shipments, causing major losses to YPFB, the state gas and oil company. In addition, Morales |1990~ has shown that the exchange rate remained considerably overvalued in the years following the New Economic Policy of August 1985. This persistent overvaluation has caused export performance as well as government revenue to suffer. However, a strong signal of reform was given by one major policy action at the time of stabilization, which prevented these later fiscal setbacks from undermining the success of the stabilization program. The government simply front loaded its stabilization effort with a drastic reduction of the government payroll and public sector salaries.(19) COMIBOL, for example, was quickly cut from over 30,000 employees to less than 7,000, with once and for all severance payments given to the dismissed workers. The staff of the Central Bank was also drastically reduced. This action of government payroll reduction appears to be the key which changed once-and-for-all both the expectations about future inflation, the speed with which agents accumulated cash balances, and the inflation path of the economy.

The methods we have employed in our analysis may not be appropriate for all cases. However, when there are sharp changes in inflation and inflation variance, as in the case of Bolivia, the combination of Kalman filtering methods, error-correction models, and the incorporation of inflation variance with expected inflation in money demand, may enhance significantly the predictability of money demand.

TABULAR DATA OMITTED

1. Hendry and Ericsson |1991~ cite parameter stability as well as homogeneity in prices as the key tests of money demand specification. See Boughton and Talvas |1990~ for a comparison of the buffer-stock and error-correction models.

2. Dornbusch and Fischer |1986~ emphasize the "need to print money" after stabilization, calling this the "most overlooked lesson of stabilization." They state that any policy package that makes a "fetish" out of lower monetary growth is "headed for trouble" in the form of high real interest rates. See Dornbusch and Fischer |1986, 42-43~. In the case of the Bolivian stabilization, Morales |1990, 11~ states that remonetization has been very slow, since "no provision was made for the step increase in the demand for money after the stabilization."

3. For more information on the Bolivian stabilization, see Morales |1988; 1990~.

4. Baba, Hendry and Start |1992~ explore the impact of interest rate uncertainty on the demand for money in the United States.

5. See Bollerslev |1986~ for a description of the GARCH model and an application to the United States' inflation process.

6. Two maximum-likelihood programs were used to estimate the GARCH parameters. One was written by Jon Breslaw |1991~ for GAUSSX, version 2.1, a sub-program for GAUSS. The other, written in MATLAB |1990~, was written by the third author. Both are available upon request.

7. Bollerslev did not impose a unit root on the inflation process, but simultaneously estimated autoregressive coefficients.

8. It may be objected that inflation uncertainty is not appropriate for long-run money demand. However, we define the long-run money demand as the optimal money demand rather than the steady-state money demand. What is optimal today may not be optimal next period, depending on what happens. Thus uncertainty plays a role in the determination of optimal cash balances.

9. See Engle and Granger |1987~ for a description of error-correction representation, estimation, and testing. The cointegration vector is thus the difference between actual and optimal real balances.

10. A good explanation of the Johansen-Juselius method is given in Dolado, Jenkinson, and Sosvilla-Rivero |1990~. The method is a likelihood test based on the eigenvalues of the canonical correlations of three or more variables. The test is for the maximum number of possible cointegrating relationships.

11. Peter Phillips made this suggestion in private conversation.

12. The error correction model is consistent with optimal cash-balance accumulation from minimization of an intertemporal loss function. See Salmon |1982~ and Nickell |1985~ for explicit derivation of an error-correction model from optimization.

13. This point was recently made by Miller |1991~.

14. See Hendry and Ericsson |1991, 25~.

15. A MATLAB |1990~ Kalman filter program, written for Hansen-Sargent |1991~, was used to estimate the time-varying coefficients.

16. Since there were several currency changes during the sample period, the data were put in consistent units of measurement by Juan Antonio Morales.

17. See MacKinnon |1990~ for more information for calculating the critical values for the Dickey-Fuller and Augmented Dickey-Fuller tests.

18. A copy of a MATLAB program for estimating the eigenvalues of the canonical correlations in the Johansen-Juselius method is available upon request.

19. Dornbusch |1991~ analyzes the incentives to front load adjustment in two-period models. He also points out that Bolivia's suspension of external debt service "amounted to a self-administered loan" at the time of the stabilization.

REFERENCES

Baba, Yoshihisa, David F. Hendry, and Ross M. Starr. "U.S. Money Demand 1960-1988." Review of Economic Studies, January 1992, 25-61.

Bollerslev, Tim. "Generalized Autoregressive Heteroskedasticity." Journal of Econometrics, April 1986, 307-27.

Boonekamp, C. F. J. "Inflation, Hedging, and the Demand for Money." American Economic Review, December 1978, 821-33.

Boughton, James M., and George S. Talvas. "Modeling Money Demand in Large Industrial Countries: Buffer Stock and Error-Correction Approaches." Journal of Policy Modeling, Summer 1990, 433-61.

Breslaw, Jon. Gaussx, version 2.1. Kent, Washington: Aptech Systems Inc, 1991.

Cagan, Phillip. "The Monetary Dynamics of Hyperinflation, " in Studies in the Quantity Theory of Money, edited by Milton Friedman. Chicago: University of Chicago Press, 1956, 25-117.

Dickey, David, and Wayne A. Fuller. "Distribution of the Estimators for Autoregressive Time Series with a Unit Root." Journal of the American Statistical Association, 74, June 1979, 427-31.

-----. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root." Econometrica, July 1981, 1057-72.

Dolado, Juan J., Tim Jenkinson and Simon Sosvilla-Rivero. "Cointegration and Unit Roots." Journal of Economic Surveys, 3, April 1990, 249-73.

Dornbusch, Rudiger. "Credibility and Stabilization," Quarterly Journal of Economics, November 1991, 837-50.

Dornbusch, Rudiger, and Stanley Fischer. "Stopping Hyperinflations Past and Present." Weltwirt-schaftliches Archiv, 1, 1986, 1-47.

Engle, Robert F. "Autoregressive Conditional Heteroscedasticity With Estimates of the Variance of United Kingdom Inflations." Econometrica, July 1982, 987-1008.

Engle, Robert F., and Clive W. J. Granger. "Cointegration and Error-Correction: Representation, Estimation, and Testing." Econometrica, March 1987, 251-76.

Evans, Martin. "Discovering the Link Between Inflation Rates and Inflation Uncertainty." Journal of Money, Credit, and Banking, May 1991, 169-84.

Hansen, Lars P., and Thomas J. Sargent. Linear Recursive Models of Dynamic Economies, Princeton, N.J.: Princeton University Press, 1991.

Hendry, David, and Neil Ericsson. "An Econometric Analysis of U.K. Money Demand in Monetary Trends in the United States and the United Kingdom by Milton Friedman and Anna J. Schwartz." American Economic Review, March 1991, 8-38.

Johansen, Soren, and Katarina Juselius. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money." Oxford Bulletin of Economics and Statistics, May 1990, 169-210.

Khan, Moshin S. "The Variability of Expectations in Hyperinflations." Journal of Political Economy, August 1977, 817-27.

Klein, Benjamin. "The Demand for Quality-adjusted Cash Balances: Price Uncertainty in the U.S. Demand for Money Function," Journal of Political Economy, August 1977, 691-715.

MacKinnon, James. "Critical Values for Cointegration." Working paper, University of California, San Diego, 1990.

MATLAB. 386-Matlab. South Natick, Mass.: The Math-Works, Inc., 1990.

Miller, Stephen M. "Monetary Dynamics: An Application of Cointegration and Error-Correction Modeling." Journal of Money, Credit, and Banking, May 1991, 139-54.

Morales, Juan Antonio. "Inflation Stabilization in Bolivia," in Inflation Stabilization: The Experience of Israel, Argentina, Brazil, Bolivia, and Mexico, edited by M. Bruno, G. DiTella, R. Dornbusch, and S. Fischer. Cambridge: MIT Press, 1988, 307-46.

-----. "The Transition from Stabilization to Sustained Growth in Bolivia." Working paper, Catholic University of Bolivia, La Paz, 1990.

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Sweeney, Richard J. "Inflation Risk and the Speed of Adjustment in Short-Run Money Demand Functions." Economics Letters, 3, May 1988, 271-76.

The stability of demand-for-money equations has been at issue in both econometric research and policy analysis. The academic debates about the relative merits of the traditional, buffer-stock, and the error-correction models of demand for money have centered on parameter stability.(1) In policy discussion, the scope for remonetization following stabilization depends on the upward shift in the demand for money and the consequent predictability of higher money demand with lower rates of inflation.(2) Only an increased demand for money would make further credit expansion non-inflationary.

Inflation uncertainty has a pervasive effect in the money-price nexus. High inflation uncertainty makes money a riskier asset, depressing the demand for money on a long-term and possibly short-term basis. This impact on the demand for money means that policies influencing inflation will have an additional effect through their impact on inflation uncertainty, as well as on expected inflation.

This paper examines the role of inflation uncertainty in a dramatic case study: Bolivia during the 1980s. This was a decade of extreme macroeconomic instability. Annual inflation rates reached over 20,000 percent, motivating a subsequent stabilization which drove annual inflation rates down to less than 25 percent, where they have remained for more than five years. Perhaps more than any other country in recent history, Bolivia has undergone a dramatic structural shift in its macroeconomic policy regime. To what extent did the demand for money shift during this period in its sensitivity to expected inflation, inflation uncertainty, and to underlying monetary disequilibria? As the inflation stabilization progressed, how fast did the money-demand parameters react to this new regime change? Was there scope for remonetization in Bolivia following the now famous stabilization plan of August 1985, the New Economic Plan introduced by President Victor Paz Estenssoro?(3)

Previous literature on the demand for money has explored the role of inflation uncertainty with ambiguous results.(4) Klein |1977~ observed that inflation-rate uncertainty reduced the average and marginal productivity of real cash balances in providing monetary services. Effectively, a greater volume of real cash balances is required to obtain the same "quality-adjusted" level of cash balances. While the impact on the demand for money is theoretically uncertain because the income and substitution effects work in opposite directions, Klein provided empirical evidence that inflation uncertainty (measured by a moving five-year variance around a moving ten-year trend, with data from 1880 to 1972) actually increased the demand for money in the United States. Around the same time, Boonekamp |1978~ presented a two-period mean-variance model of money and bond demand, highlighting the potential importance of a hedging role in the demand for money in the face of inflation uncertainty.

Related to aspects of both of these two approaches, and working with a capital-asset pricing model (CAPM), Sweeney |1988~ drew on University of Michigan survey data on inflationary expectations to resolve the theoretical ambiguity of the impact Of inflation uncertainty. His results, based on post-war quarterly U.S. data, contrasted with those of Klein by showing a negative impact of inflation uncertainty on money demand.

In his study of the demand for money in the six hyperinflations originally examined by Cagan |1956~, Khan |1977~ measured inflation uncertainty by the absolute value of the change in inflation. His model assumed that inflation uncertainty would affect the demand for money not directly, but by altering the adaptive expectations parameter in the adjustment of inflation expectations. His empirical estimates implied a negative impact of inflation uncertainty on the demand for money during accelerating inflation.

Engle |1982~ introduced the concept of ARCH (autoregressive conditional heteroskedastic) models with a specific application to inflation expectations. Using United Kingdom data, he argued that such models provided a better measure of inflation uncertainty than the approaches of Klein and Khan. Evans |1991~ recently suggested that Engle's approach should be augmented by allowing for time-varying parameters in the model for inflation.

Our approach draws on all of this literature. Like Baba, Hendry and Starr |1992~, we model the demand for money as an error-correction process. Like Klein |1977~ and Sweeney |1988~, we allow inflation uncertainty to enter the demand for money directly, following Engle |1982~ as well as Bollerslev |1986~ in using a generalized ARCH (GARCH) model of inflation to generate the estimate of inflation uncertainty. In the spirit of Khan |1977~ and Evans |1991~, we allow the possibility of time-varying adjustment coefficients, estimated with Kalman filtering. While these elements are thus not new individually, the combination of all three has not hitherto been applied to the demand for money in the context of high inflation and subsequent stabilization.

Our results show that both expected inflation and inflation uncertainty influence the demand for money. The time-varying parameter analysis shows that the reaction to monetary disequilibria was significantly more rapid during hyperinflation.

Section II describes our empirical methodology and section III contains the results of our analysis. The last section is the conclusion.

II. A GARCH MODEL WITH ERROR CORRECTION

Our method of empirical analysis combines three approaches: first, a generalized autoregressive conditional heteroskedastic (GARCH) estimation of inflation variance variable, ||sigma~.sup.2~; second, an error-correction model of money demand; and third, estimation of time-varying coefficients of the error-correction model with Kalman filtering.

To obtain a proxy for inflation uncertainty we estimate a GARCH random walk model for inflation. Tests appearing in Table I, Panel A, discussed below, confirm that the rate of inflation has a unit root. We assume that our GARCH estimate of the conditional variance is correlated with inflation uncertainty. We also assume that this has both a short-term and a long-term effect on money demand. The following equations represent our GARCH model:(5)

|Mathematical Expression Omitted~,

|Mathematical Expression Omitted~

where p represents the logarithm of the price level, |delta~|p.sub.t~ period t inflation, ||epsilon~.sub.t~ the random error term, and |Mathematical Expression Omitted~ the squared error at time t-1 and ||sigma~.sup.2~ the conditional variance of inflation. Given an initial specification for ||sigma~.sup.2~ at time t = 0, equations (1) and (2) are estimated by a maximum-likelihood process to obtain the conditional variance parameters {||gamma~.sub.i~}.(6) Given these parameters and an initial starting value, inflation uncertainty, proxied by ||sigma~.sup.2~, is generated for each period by forward recursion. The GARCH process for the inflation uncertainty is similar to the one estimated by Bollerslev |1986~.(7)

The long-run equilibrium or optimal demand for money (m - p)* depends on the expected rate of inflation |pi~ and on inflation uncertainty, ||sigma~.sup.2~.(8) The long-run model is an extension of Cagan |1956~, with the inclusion of the uncertainty variable. Since the inflation uncertainty term is estimated from a random-walk model of inflation, for consistency with this measure of inflation variance, expected inflation |pi~ for time (t + 1) is set equal to |delta~p. The long-run money demand is given by the following expression:

|Mathematical Expression Omitted~.

We test this specification of equilibrium for the cointegration of real balances (m - p) with |pi~, and ||sigma~.sup.2~, plus a time trend, tr. Cointegration implies the existence of a stationary vector |upsilon~ which is a linear combination TABULAR DATA OMITTED of (m - p), |pi~, and ||sigma~.sup.2~ as well as a constant and trend term. We obtain this vector |upsilon~ by a regression of (m - p) on |pi~ and ||sigma~.sup.2~, and setting |upsilon~ = (m - p) - (m - p)*, where (m - p)* is the optimal level of real balances, generated by a least squares estimation of the parameters of equation (3).(9)

In our study, we do not use a "scale variable" (representing transactions) in the money demand model, nor an "opportunity cost" variable other than the rate of inflation. We ignore the scale variable since we wish to work with monthly data during the hyperinflation episodes, when adjustment becomes rapid, and data for income are not available as monthly series in Bolivia. Similarly, variables for interest rates or other rates of return were severely distorted during the hyperinflation, so that the expected rate of inflation is the only available indicator of the costs of holding money.

With three or more variables in the cointegration equation given by (3), Johansen and Juselius |1990~ have shown that there may be more than one cointegrating vector, |upsilon~, since there may be more than one equilibrium relationship among three or more variables. The Johansen-Juselius approach is especially relevant for money demand functions in which income, interest rates, and expected inflation appear as arguments. In such a case, interest rates and expected inflation may be cointegrated through a Fisher relation, while money, income, and interest rates may be cointegrated through a long-run money-demand relation.

In our model, real balances and inflation are the two primary variables; the variance of inflation ||sigma~.sup.2~ is a non-linear transformation of inflation. Furthermore, expected inflation is the forecast of inflation from a random walk process. Hence, the natural cointegration relation to look for is the one relating real balances to expected inflation and the variance of inflation. However, we test for the number of cointegration vectors using the Johansen and Juselius procedure, for supporting evidence.(10) The results, discussed below, appear in Appendix Table I.

The use of the GARCH variable ||sigma~.sup.2~ as an argument in a cointegration test poses econometric issues recently analyzed by Nelson |1990~. Since the GARCH process for the conditional variance is a non-linear transformation, it is not subject to unit-root tests designed for linear stochastic processes. However, Nelson proposed a test for stationarity based on the logarithm of the sum of coefficient estimates of equation (2), ||gamma~.sub.i~, i = 1,2, for the case of ||gamma~.sub.0~ |is greater than~ 0. If this logarithmic value is greater than zero, then stationarity is rejected. We apply the Nelson criterion for the stationarity of our estimated ||sigma~.sup.2~.(11)

For short-run demand for money, we estimate the following short-run error-correction model initially under the assumption of constant parameters and then with the Kalman filtering:(12)

|Mathematical Expression Omitted~.

Error-correction models encompass more complex dynamics than partial adjustment models, which model adjustment simply as a function of excess demand or supply. In a partial-adjustment version, only ||delta~.sub.0~ and ||delta~.sub.4~ would matter. Similarly, the error-correction model encompasses a three-variable vector-autoregressive representation (VAR), in which cash-balance accumulation depends on its own lags, as well as the lags of the stationary first-differences of expected inflation and inflation uncertainty. By ignoring the cointegrating relationship ||upsilon~.sub.t-1~, VAR models may miss important channels of causality.(13)

In equation (4), inflation and inflation variance affect short-term money demand through their levels as well as lagged first-differences. The error-correction term ||upsilon~.sub.t-1~ is the difference between actual and optimal real balances (m - p)*, and thus registers the effect of the levels of expected inflation and inflation uncertainty on money demand. The feedback effects of the lagged first-differences of real balances, as well as the effects of the current and lagged first-differences of expected inflation and inflation uncertainty, on current real balance accumulation may extend back beyond one period. We have no a priori reasons to expect one particular lag pattern over another to emerge from our estimation, nor for the signs of the current or past first-differences. However, as actual real balances converge to optimal real balances, all dynamics vanish.

By allowing the coefficients to change through time with Kalman filtering, we pay close attention to the relationship between the time-varying error-correction coefficient ||delta~.sub.4~ and inflation, |delta~p, as agents change their beliefs about future government actions during stabilization and thus alter their speed of cash-balance accumulation in reaction to disequilibrium cash-balances.

In times of rapid inflation and rapidly changing rates of inflation, we thus expect two effects. First, the equilibrium demand for money might shift. Greater variance of inflation could reduce the demand for financial assets because it would make them relatively more risky. Secondly, the risk of being seriously out of equilibrium is greater when inflation is very variable, so money-holders will tend to switch to adjustment strategies which allow more rapid movement to equilibria.

We thus expect ||delta~.sub.4~ would be higher (in absolute value) during high and variable inflation, when agents have pessimistic expectations of future policy, than in periods of low inflation. Similarly, following a credible stabilization with optimistic expectations of future policy, there are lower risks to holding excess real balances, so we expect ||delta~.sub.4~ to be lower in absolute value than before the stabilization.

The specification of a time-varying error-correction coefficient estimated with Kalman filtering in equation (4) is an alternative to a non-linear mechanism specified by Hendry and Ericsson |1991~, who introduced the lagged level, square and cube of the cointegration vector ||upsilon~.sub.t-1~ in their short-run demand-for-money function in order to allow the speed of adjustment of money balances to vary with the extent of disequilibrium.(14) Rather than imposing a non-linear mechanism, we allow the data themselves to determine how the speed of adjustment varies with the extent of disequilibrium, via a recursive Kalman-filter estimation of ||delta~.sub.4~ for generating the best one-period forward predictors of |delta~(m - p).

The procedure for Kalman filter estimation of the coefficients of equation (4) is described by Hansen and Sargent |1991, 152-59~ as a special case of a state-space model. Kalman filtering, as opposed to simple recursive coefficient estimation, discounts past data with an optimal weighting scheme at each period in order to generate best one-period forward predictors.(15)

Equations (1) through (4) thus combine unit-root models of real balances and GARCH estimates of conditional variance, with cointegration and error-correction approaches of short-run money demand and Kalman-filter estimation of time-varying parameters. The payoff of combining these methods is enhanced predictability of real balances during periods of high turbulence and stabilization.

III. EMPIRICAL RESULTS

Money supply and price data for our analysis come from the Central Bank of Bolivia.(16) We do not have a priori reasons for selecting one monetary aggregate over another in our study. Of the three monetary aggregates, base money, M1, and M2, we shall let the data determine which aggregates are the more appropriate. Our price series is the consumer price index.

The models of the previous section assume unit roots for inflation |delta~p and expected inflation |pi~, proxied by ||delta~p.sub.t-1~, real balances (m - p), and inflation uncertainty, proxied by the conditional variance |Mathematical Expression Omitted~, as well as cointegration of these three variables. The stationarity or unit root tests for these variables appear in Table I, Panel A. The logarithmic values of all three monetary aggregates, deflated by the CPI, have unit roots. Our tests are based on augmented Dickey-Fuller |1979; 1981~ statistics, using the MacKinnon |1990~ critical values, for six lags with constant and trend terms.(17) One cannot reject the unit-root hypothesis for the rate of inflation, by the same statistical criterion.

Panel B in Table I gives the estimates of the GARCH process for expected inflation. The results show significant GARCH coefficients for the conditional variance for inflation. For the stationarity of the conditional variance series ||sigma~.sup.2~, generated by the coefficients given in Panel B and an initial starting value, Panel A in Table I shows a significant augmented Dickey-Fuller statistic. Since the Dickey-Fuller test is only appropriate for a linear process, and a GARCH process is by definition non-linear, stationarity of ||sigma~.sup.2~ is rejected by the Nelson criterion. As the note in Table I shows, the logarithmic value of the sum of the two coefficients is greater than zero.

The long-run relationship among (m - p), |pi~, and ||sigma~.sup.2~, three non-stationary series, is given by the cointegration vector, estimated as the difference between a linear combination of (|pi~, ||sigma~.sup.2~), plus a constant and time trend, and the actual (m - p). The coefficients come from an OLS regression of (m - p) on |pi~ and ||sigma~.sup.2~ as well as a constant and time trend. Panel C in Table I shows the coefficients for calculating the cointegration vectors for all three monetary aggregates.

The results of the Johansen and Juselius |1990~ procedure for the existence of more than one vector of cointegration for the three money supply definitions appear in the appendix table. The results do not reject at most one cointegration vector for base money and the M1 and M2 monetary aggregates.(18)

The Dickey-Fuller statistics for the cointegration vectors based on our regressions appear in Panel D of Table I. The results allow rejection of the unit-root hypothesis at the 5% level for M2 and at the 10 percent for M1. However, for base money, we cannot reject a unit root in the residuals. Panel D thus indicates that M1 and M2 are more appropriate monetary aggregates for examining money demand during the hyperinflation and stabilization period, since both of these aggregates are more likely to be cointegrated with inflation and inflation variance. For this reason, only these two aggregates appear in the rest of our analysis.

Panel E contains the estimates for the error-correction model for short-run demand for money. The results show that the first-differences of expected inflation and inflation uncertainty, as well as the lagged cointegration vector, are significant determinants of real balance accumulation for both monetary series. A monthly dummy variable appears in each equation for December of each year. This dummy, |d.sub.12~, captures the annual bonus payment, or aguinaldo, given to employees in Latin American countries at the start of the summer vacation period at the end of the year. While the coefficient of this dummy is significant, its exclusion does not affect the sign or significance of the other coefficients. Lagged first-differences of inflation and inflation variance, as well as the lagged first-difference of real balances and the constant term, turned out to be insignificant and were eliminated from the error-correction model.

Panel E shows that the first-differences of expected inflation and inflation uncertainty have opposite effects on short-run money demand, while the levels of both expected inflation and uncertainty have the expected negative effects on long-run money demand. The positive effect of the change in uncertainty may reflect the effect of an increase in inflation variance at the time of the stabilization, when inflation fell dramatically and unexpectedly while cash balance accumulation started to increase as a result of the credible stabilization. As a result, the increase in inflation variance or squared forecast-error is associated with an increase in cash-balance accumulation.

Figure 1 pictures the time-varying error-correction coefficient, ||delta~.sub.4t~, as well as the actual inflation rate, for the short-run money demand equation using the M1 monetary aggregate. This figure shows that the speed of cash balance accumulation varies with the rate of inflation. During the period of high inflation between 1983 and late 1985, the speed of cash balance accumulation reached a level almost 50 percent above its level following stabilization. A similar pattern is true for the time-varying coefficient estimated for the equation with the M2 monetary aggregate. Figure 2 shows the behavior of both coefficients.

The change in the speed of cash balance adjustment, before and after stabilization, is consistent with the more complex dynamic process underlying short-run money demand, involving changing expectations of private agents about future government actions. The fast upward shift of the adjustment coefficients indicates a significant change in 1985 characteristic of a credible stabilization.

V. CONCLUSION

The results of our analysis of cash-balance and inflationary adjustment in Bolivia during the 1980s are consistent with a more complex dynamic adjustment process, indicating changing beliefs of private-sector agents regarding future government actions and the incorporation of inflation variance as well as expected inflation in the demand for money. The payoff has been enhanced estimation of real balance accumulation, for both M1 and M2.

The results show a sharp change in 1985 in the speed of cash balance accumulation, indicating a fundamental change in the beliefs of private-sector agents about future government actions, and thus a credible stabilization. How did this credible stabilization take place? According to Morales |1988~, the total fiscal deficit was not quickly reduced at the time the stabilization plan was announced in August 1985. In fact, deficit reduction problems persisted for some time after 1985. In succeeding years the government suffered two major fiscal setbacks: a collapse by more than 50 percent in the international price of tin less than six months after the stabilization, and thus a loss in the revenues of COMIBOL, the state mining corporation, and a default by Argentina for more than two years in payments on natural gas pipeline shipments, causing major losses to YPFB, the state gas and oil company. In addition, Morales |1990~ has shown that the exchange rate remained considerably overvalued in the years following the New Economic Policy of August 1985. This persistent overvaluation has caused export performance as well as government revenue to suffer. However, a strong signal of reform was given by one major policy action at the time of stabilization, which prevented these later fiscal setbacks from undermining the success of the stabilization program. The government simply front loaded its stabilization effort with a drastic reduction of the government payroll and public sector salaries.(19) COMIBOL, for example, was quickly cut from over 30,000 employees to less than 7,000, with once and for all severance payments given to the dismissed workers. The staff of the Central Bank was also drastically reduced. This action of government payroll reduction appears to be the key which changed once-and-for-all both the expectations about future inflation, the speed with which agents accumulated cash balances, and the inflation path of the economy.

The methods we have employed in our analysis may not be appropriate for all cases. However, when there are sharp changes in inflation and inflation variance, as in the case of Bolivia, the combination of Kalman filtering methods, error-correction models, and the incorporation of inflation variance with expected inflation in money demand, may enhance significantly the predictability of money demand.

TABULAR DATA OMITTED

1. Hendry and Ericsson |1991~ cite parameter stability as well as homogeneity in prices as the key tests of money demand specification. See Boughton and Talvas |1990~ for a comparison of the buffer-stock and error-correction models.

2. Dornbusch and Fischer |1986~ emphasize the "need to print money" after stabilization, calling this the "most overlooked lesson of stabilization." They state that any policy package that makes a "fetish" out of lower monetary growth is "headed for trouble" in the form of high real interest rates. See Dornbusch and Fischer |1986, 42-43~. In the case of the Bolivian stabilization, Morales |1990, 11~ states that remonetization has been very slow, since "no provision was made for the step increase in the demand for money after the stabilization."

3. For more information on the Bolivian stabilization, see Morales |1988; 1990~.

4. Baba, Hendry and Start |1992~ explore the impact of interest rate uncertainty on the demand for money in the United States.

5. See Bollerslev |1986~ for a description of the GARCH model and an application to the United States' inflation process.

6. Two maximum-likelihood programs were used to estimate the GARCH parameters. One was written by Jon Breslaw |1991~ for GAUSSX, version 2.1, a sub-program for GAUSS. The other, written in MATLAB |1990~, was written by the third author. Both are available upon request.

7. Bollerslev did not impose a unit root on the inflation process, but simultaneously estimated autoregressive coefficients.

8. It may be objected that inflation uncertainty is not appropriate for long-run money demand. However, we define the long-run money demand as the optimal money demand rather than the steady-state money demand. What is optimal today may not be optimal next period, depending on what happens. Thus uncertainty plays a role in the determination of optimal cash balances.

9. See Engle and Granger |1987~ for a description of error-correction representation, estimation, and testing. The cointegration vector is thus the difference between actual and optimal real balances.

10. A good explanation of the Johansen-Juselius method is given in Dolado, Jenkinson, and Sosvilla-Rivero |1990~. The method is a likelihood test based on the eigenvalues of the canonical correlations of three or more variables. The test is for the maximum number of possible cointegrating relationships.

11. Peter Phillips made this suggestion in private conversation.

12. The error correction model is consistent with optimal cash-balance accumulation from minimization of an intertemporal loss function. See Salmon |1982~ and Nickell |1985~ for explicit derivation of an error-correction model from optimization.

13. This point was recently made by Miller |1991~.

14. See Hendry and Ericsson |1991, 25~.

15. A MATLAB |1990~ Kalman filter program, written for Hansen-Sargent |1991~, was used to estimate the time-varying coefficients.

16. Since there were several currency changes during the sample period, the data were put in consistent units of measurement by Juan Antonio Morales.

17. See MacKinnon |1990~ for more information for calculating the critical values for the Dickey-Fuller and Augmented Dickey-Fuller tests.

18. A copy of a MATLAB program for estimating the eigenvalues of the canonical correlations in the Johansen-Juselius method is available upon request.

19. Dornbusch |1991~ analyzes the incentives to front load adjustment in two-period models. He also points out that Bolivia's suspension of external debt service "amounted to a self-administered loan" at the time of the stabilization.

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-----. "The Transition from Stabilization to Sustained Growth in Bolivia." Working paper, Catholic University of Bolivia, La Paz, 1990.

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Author: | Asilis, Carlos M.; Honohan, Patrick; McNelis, Paul D. |
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Publication: | Economic Inquiry |

Date: | Apr 1, 1993 |

Words: | 4778 |

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