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Korean inflation during the U.S. military administration of 1945-48.

I. Introduction

The role of fiscal deficits in the inflationary environment that occurred in Korea during the U.S. military administration of 1945-48 resembles more commonly studied episodes of hyperinflation [9; 12; 13; 16; 17; 24; 25; 26; 27; 29]. For example, the effort to secure some fixed amount of real expenditures leads the government to increase the nominal money supply thereby creating inflation.

In Korea the general state of impoverishment created income levels too low to collect sufficient tax revenues to support the government's spending goal. Thus the U.S. military administration was forced to rely on printing substantial quantities of money to finance its real expenditure gap, thereby creating a high rate of inflation.

While fiscal pressure was similar, there was significant difference in the magnitude of the inflation. For example, the monthly average inflation rate reached a peak of 11 percent in Korea compared to a monthly peak of 322 percent in Germany. This comparatively moderate rate of inflation may have allowed the Korean experience to go relatively unnoticed by academics,(1) yet it affords an opportunity to examine the dynamic process of inflation during a period with circumstances similar to those that produced the more frequently studied episodes of hyperinflation.

Section II of the paper briefly describes the post World War II Korean economy. Section III will employ a structural vector autoregression (SVAR) to model the dynamic process of inflation and discusses the long-run and contemporaneous restrictions employed to identify the structural parameters. The data and subsequent econometric results are reported in section IV.

The results will indicate that the moderately high rate of inflation during the U.S. military administration can be largely explained by velocity shocks to money demand, suggesting that a successful disinflation policy should include measures to increase the demand for money. The final section presents the conclusions from the analysis.

II. The Korean Economy: 1945-48

During the U.S. military administration, Korea experienced a high rate of inflation, reaching at times more than 30 percent per month. According to Cagan [9], the episode is not defined as hyperinflation, though it shares some similar economic environments to those of hyperinflation. Table I shows that the rise in price is much faster compared to the increase in the notes issued. The price rose 4,370 percent while the notes issued increased 376 percent during the period 1945-1948. Furthermore, as argued by Campbell and Tullock [10], there had been noticeable changes in the rate of velocity of money. From the beginning of the administration in August 1945 to the end of 1946, the rate of velocity increased remarkably; from January 1947 through 1948 velocity declined compared to the changes in the previous years.
Table I. Monetary Characteristics of Korean Inflation (August
1945-August 1948)

1 Ratio of prices at the end of final month to prices at the
 beginning of first month 43.70

2 Ratio of quantity of notes issued at the end of final
month to quantity at the beginning of first month 3.76

3 Ratio of (1) to (2) 11.62

4 Monthly average rate of inflation (%) 11.10

5 Monthly average increase in notes issued (%) 3.75

6 Ratio of (4) to (5) 2.93

In contrast to the remarkable changes in the monetary sector, real production did not change significantly. For example, rice production increased by about 20 percent throughout the period, while other agricultural production (such as cotton and corn) decreased by a comparable magnitude. Output of the manufacturing sector increased only 5.6 percent during the period 1946-48.(2) These figures show that the level of physical production remained fairly stable. Therefore, the changes in real income are minor compared to the changes in money and price, which corresponds to the Cagan's [9] argument.

III. The Model

We use a three-variable SVAR system to model the process of inflation in Korea during the period 1945-48. The endogenous variables are: the logarithm of the nominal government budget deficits (G), the growth rate in the nominal money supply ([Delta] M) and the inflation rate ([Delta] P). The SVAR model we use is based on the following illustrative structural model, which is a variant of hyperinflation models:

(1) G = [Epsilon] G

(2) [Delta] M = [Alpha] G + [[Epsilon]]

(3) [Delta] P = [Delta] M + [Beta] ([E.sub.t] [Delta][P.sub.t+1] - [E.sub.t-1] [Delta][P.sub.t]) + [[Epsilon]].sup.(3)]

where [Delta] M is (log [M.sub.t] - log [M.sub.t-1]), [Delta] P is (log [P.sub.t] - log [P.sub.t-1]), and E is the expectations operator.

While it might be desirable to include real income in the system, our model excludes it primarily due to a lack of monthly data. However, since the change in real income is very likely to be dominated by the changes in money and price during a period of high inflation, excluding income will not significantly alter the empirical results. Thus the Korean episode offers an opportunity to study the relations between money and price isolated from real income.

Equation (1) states that nominal budget deficits arise solely due to a government expenditure shock. It may depend on the lagged budget deficits. Equations (2) and (3) are derived from the money demand equation used by Cagan [9] and extended in Sargent and Wallace [26] and Sargent [25]. In particular, equation (3) is obtained simply by taking the first-difference of Cagan's money demand equation, assuming the money market is always in equilibrium. The inflation rate is a function of the money growth rate, changes in the expected future rate of inflation, and a money demand shock. Accordingly, price movements are influenced by the structural shocks in the system. Equation (2) specifies the money growth process shown in equation (3). It states that the growth in the money supply depends on the budget deficits and a money supply shock. This reflects the government's attempts to finance its nominal expenditure through money creation. Here, G embraces the effects of price increase on budget deficits.

The model described above is "illustrative" in that it may ignore various interactions among the variables. As Sims [28] argued, it is not easy to find a general consensus among economists upon the specific nature of me economy. Therefore, we specify a more general unconstrained dynamic model to minimize a priori restrictions on the structure of the economy.

Now let the structure of an inflationary economy be represented by the following joint stationary process:

(4) X = A(L) [Epsilon]

where X= (G [Delta] M [Delta] P)' is a vector of endogenous variables, [Epsilon] = ([[Epsilon].sub.G][[Epsilon]][[Epsilon]])' is a vector of "primitive" structural disturbances with cov([Epsilon]) = I where I is an identity matrix. The assumption that cov(e) = I implies these shocks are, with a convenient normalization, serially and mutually uncorrelated. A(L), where L is the lag operator, is the 3 x 3 matrix which is to be estimated.

The Wold moving average representation of X is given by:

(5) X = B(L)e

where B(L) is assumed to be an invertible 3 x 3 matrix with B(0) = I and e is the vector of innovations with cov(e) = [Omega]. Further, we assume that the innovations e are linear combinations of the structural disturbances [Epsilon] such that

(6) e = D[Epsilon]

where D is 3 X 3 decomposition matrix with full rank. Equations (4), (5), and (6) can be manipulated to yield

(7) A(L) = B(L)D.

From (6) we derive

(8) DD' = [Omega]

in which there are six independent elements in [Omega] and nine unknowns in D. Consequently, we need to impose three restrictions on D to identify the structural parameters. Once D is determined, we can obtain A(L) from (7).

The identifying restrictions emerge from the specific nature of the Korean economy described above. There are two general types of restrictions, contemporaneous [5; 6] and long-run [1,7,18]. Gali [15] applied a combination of these restrictions to postwar U.S. data. We follow a similar strategy and identify the structural parameters by imposing a combination of one long-run and two contemporaneous restrictions.

The long-run restriction reflects the standard long-run neutrality of money. In particular, the money supply shock will lead to equiproportionate changes in money supply and price. (Further explanation will be given for the long-run restriction in section IV.) In terms of our notation, it implies:

[B.sub.21](1)[D.sub.12] + [B.sub.22](1)[D.sub.22] + [B.sub.23](1)[D.sub.32] = [B.sub.31](1)[D.sub.12] + [B.sub.32](1)[D.sub.22] + [B.sub.33](1)[D.sub.32]

where [B.sub.ij](1) is sum of the related moving average coefficients.

The two contemporaneous restrictions are based on the assumption that government budget deficits are independent of contemporaneous shocks to the money supply and money demand. This should be plausible if the government was unable to identify the current changes in money market conditions. In terms of our notation, the restrictions are:

[D.sub.12] = [D.sub.13] = 0.

IV. Econometric Results

A standard two-step procedure is employed to estimate the model. First, we estimate and invert the vector autoregressive model of X to obtain equation (5). Next, we obtain the decomposition matrix, D, by imposing the identifying restrictions and then recover the equation (4) which is our objective.

In vector autoregression, in addition to a constant, a seasonal dummy variable with the value 1 assigned to November was added to the system to capture the government's purchase of newly produced rice. Finally, a lag length of 6 was chosen based on the Sims [28] likelihood ratio test.

The data used were monthly observations recorded during the period of U.S. military administration. Although the administration began in August, 1945, our sample includes the period from October 1945 to August, 1948 since budget deficit data are not available for the first two months. It may be argued that low frequency data and more observations should be used since we exploit a long-run restriction. However, if the movements of the variables are fast enough to reveal their interactions within a short period of time, it is legitimate to use long-run restrictions in order to characterize the long-run properties of an economic system. This is very likely for a period of high inflation.(4)

The money supply is measured using notes issued by Chosun Bank, the central bank of Korea at that time. The price index is wholesale price of Seoul indexed to 1936 = 100. All data are obtained from Annual Economic Review of Korea, 1948 and 1949.

Prior to estimation, we apply the unit root tests developed in Phillips and Perron [22] and Perron [21] to examine the stationarity of the variables. The tests, which are based on a first-order autoregressive non-zero drift model, are summarized in Table II.(5) We reject the null hypothesis of a unit root in all three variables. The null hypothesis is rejected at the 1% level for G and at the 5% level for [Delta] M and [Delta] P.
Table II. Unit Root Test Results

Variables Z(a) Z([t.sub.a]) Z([[Phi].sub.3])

G -39.98(**) -7.44(**) 30.74(**)
[Delta] M -19.76(*) -3.61(*) 7.30(*)
[Delta] P -20.82(*) -3.70(*) 7.71(*)

Notes: With sample size 25, the critical values at 5% (1%) level are, -17.9(-22.5) for Z(a), -3.60(- 4.38) for Z([t.sub.a]) and 7.24(10.61) for Z([[Phi].sub.3]). (*) and (**) denote, respectively, significance at 5% and 1% levels. See Dickey and Fuller [11,1063] and Fuller [14,371,373].

The next two subsections detail the dynamic characteristics of structural disturbances on the endogenous variables using the results from the impulse response and variance decomposition analysis.(6) Although our analysis is based on the first-differenced series of money and price, the dynamic effects of structural shocks on levels can be examined without any qualitative changes. Notice that impulses with levels are simply the cumulated sum of the impulses with first-differenced series of the variables. Since the variance decompositions are based on the impulses, there should be no qualitative change in variance decompositions.(7)

Impulse Response

Table III reports the impulse responses to a one standard deviation shock in the level of each endogenous variable. Those pertaining to the money supply and the price are also plotted in Figures 1 and 2.

Table III. Impulse Responses to One Standard Deviation Shock

Variables M/A Shock

 Panel A

Government Budget Deficits 1 0.066
 2 -0.013 (0.011)
 4 0.022 (0.012)
 8 0.002 (0.020)
 16 0.001 (0.031)
 24 0.001 (0.095)

 Panel B

Money Supply 1 0.007
 2 0.014 (0.002)
 4 0.021 (0.006)
 8 0.025 (0.015)
 16 0.022 (0.024)
 24 0.026 (0.035)

 Panel C

Price 1 0.004
 2 0.009 (0.003)
 4 0.013 (0.008)
 8 0.030 (0.019)
 16 0.030 (0.037)
 24 0.037 (0.054)

Variables Shock

Government Budget Deficits 0.00
 0.009 (0.005)
 0.000 (0.004)
 0.003 (0.004)
 0.001 (0.006)
 -0.001 (0.011)

Money Supply 0.013
 0.016 (0.001)
 0.014 (0.002)
 0.011 (0.004)
 0.012 (0.007)
 0.013 (0.009)

Price 0.004
 0.008 (0.001)
 0.011 (0.006)
 0.009 (0.006)
 0.013 (0.011)
 0.012 (0.016)

Variables Shock

Government Budget Deficits 0.00
 -0.005 (0.012)
 -0 002 (0.012)
 -0.004 (0.011)
 0.001 (0.017)
 0.001 (0.044)

Money Supply 0.000
 -0.006 (0.003)
 -0.009 (0.007)
 0.005 (0.013)
 -0.009 (0.019)
 -0.005 (0.026)

Price -0.020
 -0.025 (0.005)
 -0.034 (0.011)
 -0.025 (0.018)
 -0.039 (0.028)
 -0.032 (0.040)

Numbers in parentheses are standard errors

M/A = Month(s) Ahead

The impulse responses of budget deficits are shown in Panel A of Table III.(8) As we expected, budget deficits are mainly driven by the government expenditure shock. While the money supply shock has some effect at 2 months ahead, the overall effects of money supply and money demand shocks are negligible. This suggests that the government budget deficit may be exogenous.

The dynamic effects of structural disturbances on [Delta] M and [Delta] P show somewhat erratic behavior in that the paths do not reveal smooth patterns. However, the results support the hypotheses we posited. Panel B reports the results for the money supply. The government expenditure shock positively affects the money supply; in fact, it exerts a greater impact than the money supply shock itself. This reflects the fact that the administration relied heavily on money creation to finance the budget deficits. In addition, the money demand shock hardly affects money supply. This implies that the monetary authority was not accommodative to a change in the demand for money.

Panel C presents the impulse responses of the price level corresponding to each structural disturbance. A positive money demand shock has a negative impact on the price. Yet, while the impact is larger, in absolute value, than the other two innovations in both the short-run and inter- mediate-run, over the long-run its impact is similar to the government expenditure shock.(9) The permanent effect is a 0.032 percent decrease in price. The money supply shock exerts a positive impact, but its impacts are much smaller relative to the other shocks. Finally the long-run effects of an innovation in money supply on money supply and price are similar due to the long-run restriction imposed as shown in Figures 1 and 2.

Variance Decomposition

Variance decompositions convey information on the relative contribution of each structural disturbance to the variance of the forecast error for the endogenous variables. Table IV summarizes three main findings.
Table IV. Variance Decomposition of Forecast Error

 Government Money
 Expenditure Supply
Variables M/A Shock Shock

Government Budget Deficits 1 100 0.0
 2 97.5 (92.6,98.1) 1.9 (1.4,3.4)
 4 94.3 (87.6,95.7) 1.6 (1.2,3.0)
 8 88.5 (79.6,90.3) 2.0 (1.6,3.6)
 16 87.2 (77.1,89.1) 2.0 (1.6,3.5)
 24 86.6 (75.2,88.8) 2.0 (1.6,3.5)

Money Supply 1 23.1 76.5
 2 34.5 (30.7,38.2) 59.3 (55.4,63.4)
 4 51.8 (44.4,57.7) 39.1 (33.9,44.3)
 8 72.3 (61.1,77.0) 21.9 (17.6,27.0)
 16 74.3 (63.7,79.6) 19.6 (15.2,24.3)
 24 77.3 (66.4,81.8) 18.3 (14.1,23.1)

Price 1 3.9 4.0
 2 7.7 (6.1,11.2) 6.3 (5.5,7.5)
 4 8.8 (6.5,15.7) 7.8 (6.3,9.7)
 8 26.4 (18.9,39.5) 6.1 (4.7,8.1)
 16 42.2 (31.8,58.0) 5.9 (4.5,8.1)
 24 45.5 (33.6,58.0) 5.7 (4.3,8.0)

Variables Shock

Government Budget Deficits 0.0
 0.6 (0.5,5.1)
 4.0 (3.0,10.8)
 9.5 (7.6, 18.2)
 10.9 (8.7,20.7)
 11.4 (9.0,22.5)

Money Supply 0.4
 6.2 (4.5,9.8)
 9.1 (6.5, 18.0)
 5.8 (4.5,16.8)
 6.1 (4.7,17.7)
 4.5 (3.5,16.1)

Price 92.1
 86.0 (82.8,87.9)
 83.4 (76.0,86.8)
 67.5 (53.8,75.9)
 51.9 (39.2,63.9)
 48.8 (36.2,61.8)

Numbers in parentheses are estimated one standard deviation band.

M/A = Month(s) Ahead

First, the government expenditure shock explains most of the fluctuation in the budget deficits at all forecasting horizons. It is solely responsible for the one month ahead forecast error variance because of the contemporaneous restrictions imposed. Nevertheless, it still dominates the other shocks at longer horizons. In fact, over 85 percent of the forecast error variance of budget deficits are allocated to the government expenditure shock. This, together with the results in Panel A of Table III, implies that the government budget deficit is exogenous.

Second, in the short-run the money supply is largely driven by innovations in money supply. However, after 4 months it becomes dominated by the government expenditure shock, accounting for as much as 77 percent of the fluctuations at 24 months ahead. This is the evidence of the government's efforts at creating money to finance the budget deficit.

Third, in both the short-run and intermediate-run, the fluctuation in the price is primarily induced by the money demand shock. Even though its effect diminishes as the forecasting horizon increases this is indeed a most striking result. Although Campbell and Tullock's [10] study on the problem of inflation in Korea for the period 1945-54, did not suggest that the inflation was a result of a rapid increase in velocity of money, they pointed out noticeable changes in the velocity of money, as mentioned in section II. In particular, they noticed that there has been a remarkable increase in the velocity of money in the first 9 months of 1946, and then it declined during the last 3 months of the year so that the wholesale price actually fell.

However, according to our investigation of the wholesale price index of Seoul, the price did not fall during the last 3 months of 1946; rather it rose by 57 percent. This implies that the velocity might not decline enough to cause the price to fall. Yet, it is true that, as argued in Campbell and Tullock [10], the velocity of circulation was much lower in the period 1947-48 than in the previous years. From January 1947 to August 1948, notes issued increased by 70 percent while the wholesale price rose by 199 percent. On the other hand, from the beginning of the administration to the end of 1946, notes issued increased by 122 percent while the wholesale price rose by 1,359 percent. Both the different sample period and different information on the data set may be responsible for our findings which differ from the analysis of Campbell and Tullock.

Our empirical finding corresponds to the implications drawn from the stabilization process of inflation. In particular, Bomberger and Makinen [8], who examined the stabilization program of Hungarian hyperinflation of 1945-46, found that it was the reform of fiscal system together with various measures designed to increase the general acceptability of money that ended the hyperinflation. The price stabilization was achieved while the money supply increased significantly. In addition, in their study of stabilization in Taiwan, Makinen and Woodward [19] found that the introduction of bank deposits offering high real interest rates helped the movements of real money demand.

V. Concluding Remarks

This paper uses a structural VAR (SVAR) model to investigate the dynamic process of Korean inflation under the U.S. military administration. A combination of one long-run and two contemporaneous restrictions is imposed to identify the structural parameters. The empirical results show that shocks to money demand are the dominant factor in explaining price movements during this episode of inflation.

The previous study for example, Bomberger and Makinen [8] suggests that a regime change breaks market participants' expectations for the future inflation thereby producing a subsequent increase in the demand for money. Thus, the innovations in money demand are eventually responsible for the abrupt end of inflation. However, this study also suggests that these regime breaks are not limited to occasions of hyperinflation. Rather, episodes of both hyperinflation and more tempered inflation can be ended by the measures to increase the demand for money. Thus, this study provides a very important disinflation policy implication, which prioritizes the establishment of the measures to increase the demand for money. (*) The authors would like to thank Dr. Yoonbae Kim and an anonymous referee for helpful comments and suggestions. We would also like to thank Dr. William Keating, Dr. Braxton Hinchey, and Dr. Irwin Shapiro for their helpful suggestions in the early stage of the paper. Early draft was written when Dr. Young-Yong Kim was a visiting scholar at University of Kentucky.

(1.) Campbell and Tullock [10] studied the problem of inflation in Korea for the period 1945-54. They discussed the nature of the inflationary process focusing on the interactions between the roles of government and the private sector.

(2) Detailed production figures are available from Annual Economic Review of Korea, 1948 and 1949 [2] and Annual Report of Agricultural Economy of Korea, 1949 [3].

(3.) Cagan's money demand relationship is given as in (A) below.

(A) [M.sub.t] - [P.sub.t] = [a.sub.0] - [a.sub.1] ([E.sub.t][P.sub.t+1] - [P.sub.t]),

and then

(B) [M.sub.t-1] - [P.sub.t-1] = [a.sub.0] - [a.sub.1] ([E.sub.t-1][P.sub.t] - [P.sub.t-1]).

Subtracting (B) from (A) yields the equation (3) with [a.sub.1] = [Beta]. (4.) Taylor [29] and Engstead [12] applied cointegration analysis to some of European hyperinflation episodes, of which the monthly observations range from 20 to 42, and found support for the Cagan model. Phylatkis and Taylor [23] also applied cointegration analysis to Taiwanese inflation of 1945-49. In addition, Hu [16] found that any gap between the desired and actual level of real cash balances was almost instantaneously closed during the hyperinflation in China. This supports present authors' argument that the movements of the variables are fast enough to reveal their long-run properties during a period of high inflation.

(5.) Since the Z([Multiplied by])-statistics reported in Table II reject the null hypothesis of a unit root, there is no need for further examination [21]. The augmented Dickey-Fuller t-test gave the same results as in Table II; the consistent estimator of variance, [s.sup.2] = lim [T.sup.-1] E ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) used for evaluation of Z(Multiplied by])-statistics was constructed using the window of Newey and West [20] with a truncation lag 1 = 2.

(6.) We obtained standard errors of impulse response and variance decomposition using a Monte Carlo simulation of normal random drawings from the distribution of reduced form VAR coefficients. Initial decomposition matrix "D" was used to generate impulses based on randomly drawn coefficients.

(7.) We did conduct our analysis with the changes in the variables. The results show very little changes. The only noticeable exception is the money demand shock which accounts for the fluctuations of the price. It explained more than the figures reported in Table IV at all forecasting horizons. For instance, it explains more from 48.8% to 63.3% at 24 months ahead.

(8.) Using the real government budget deficits did not alter the empirical results with nominal value of the deficits.

(9.) The finding that, over the long-run, the government expenditure shock exerts a strong effect on the price thereby on the nominal income is consistent with the finding of Atesoglu and Tillman [4]. Though the sample period (1960:1- 1974:4) differs from ours, they found a causal relationship from nominal autonomous expenditures (e.g., government spending) to nominal income. This explanation also applies to the results of variance decomposition.


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[8.] Bomberger, William A. and Gail E. Makinen, "The Hungarian Inflation and Stabilization of 1945-46." Journal of Political Economy, October 1983, 801-24.

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[12.] Engsted, Tom, "Cointegration and Cagan's Model of Hyperinflation under Rational Expectations." Journal of Money, Credit and Banking, August 1993, Part 1, 350-60.

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[14.] Fuller, Wayne A. Introduction to Statistical Time Series. New York: Wiley, 1976.

[15.] Gali, Jordi, "How well does the IS-LM Model Fit Postwar US. Data?" Quarterly Journal of Economics, May 1992, 709-38.

[16.] Hu, Teh-wei, "Hyperinflation and the Dynamics of the Demand for Money in China." Journal of Political Economy, January/February 1971, 186-95.

[17.] Kiguel, Miguel A., "Budget Deficits, Stability, and the Monetary Dynamics of Hyperinflation." Journal of Money, Credit and Banking, May 1989, 148-57.

18. King, Robert G., Charles I. Plosser, James H. Stock, and Mark Watson, "Stochastic Trends and Economic Fluctuations." American Economic Review, September 1991, 819-40.

[19.] Makinen, Gail E. and G. Thomas Woodward, "The Taiwanese Hyperinflation and Stabilization of 1945-1952." Journal of Money, Credit and Banking, February 1989, 90-105.

[20.] Newey, Whitney K. and Kenneth D. West, "A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix." Econometrica, May 1987, 703-708.

[21.] Perron, Perrie, "Trends and Random Walks in Macroeconomic Time Series: Further Evidence from a New Approach." Journal of Economic Dynamics and Control, June-September 1988, 297-332.

[22.] Phillips, Peter C. and Pierre Perron, "Testing for a Unit Root in Time Series Regression." Biometrika, June 1988, 335-46.

[23.] Phylaktis, Kate and Mark P. Taylor, "The Monetary Dynamics of Sustained High Inflation: Taiwan, 1945-1949." Southern Economic Journal, January 1992, 610-22.

24. Salemi, Michael K., "Adaptive Expectations, Rational Expectations, and Money Demand in Hyperinflation Germany." Journal of Monetary Economics, October 1979, 593-604.

[25.] Sargent, Thomas J., "The Demand for Money during Hyperinflation under Rational Expectations." International Economic Review, February 1977, 59-82.

[26.] -- and Neil Wallace, "Rational Expectations and the Dynamics of Hyperinflation." International Economic Review, June 1973, 328-50.

[27.] Siklos, Pierre L., "Hyperinflation: Their Origins, Development and Termination." Journal of Economic Surveys, vol. 4 no. 3, 1990, 225-48.

[28.] Sims, Christopher A., "Macroeconomics and Reality." Econometrica, January 1980, 1-48.

[29.] Taylor, Mark P., "The Hyperinflation Model of Money Demand Revisited." Journal of Money, Credit and Banking, August 1991 part 1, 327-51.
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