The monetary dynamics in the Yugoslav hyperinflation of 1991–1993: The Cagan money demand

EuropeanJournalof POLITICAL European Journal of PoliticalEconomy Vol. 12 (1996) 467-483

ELSEVIER

ECONOMY

The monetary dynamics in the Yugoslav hyperinflation of 1991-1993: The Cagan money demand Pavle Petrovid a,b,*, Zorica Vujo~evid a,b a University of Belgrade Kameni~ka 6, 11000 Belgrade, Yugoslavia b CES MECON, Belgrade, Yugoslavia

Accepted I September 1995

Abstract

The Yugoslav hyperinflation of 1991-93 is one of the highest and the longest episodes ever recorded. The monetary dynamics of the hyperinflation is well characterized by the Cagan model. With revealed cointegration between real money and inflation, the model is accepted irrespective of the underlying expectations formation process and it implies stationary velocity shocks. Employing cointegrated VAR, the exact rational expectations Cagan model is rejected and an informal test within the same framework shows that the Yugoslav public exhibited a lower degree of forward-looking behavior relative to that in other classical hyperinflations. This enabled the government to extract non-decreasing seigniorage by increasing money growth and inflation above expected rates and suggests an explanation for the ever-increasing money growth in spite of the resulting monetary chaos. JEL classification: E31; E41; E51 Keywords: Hyperinflation;The Cagan model; Seigniorage;Cointegration;Expectations

1. I n t r o d u c t i o n

The 1991-93 hyperinflation in Yugoslavia (Serbia and Montenegro) was one of the most extreme in economic history. It was the second highest after the

* Corresponding author

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Hungarian inflation of 1946-47 and the second longest to the Russian in 1921-24. The episode belongs to classical hyperinflations. The cause was monetization of the large fiscal deficit (Bogeti~ et al., 1994). While covering the deficit, the government succeeded in collecting approximately constant seigniorage throughout the hyperinflationary period. This was, however, accompanied by unstable and accelerating inflation and sharply decreasing real money balances, rather than steady-state inflation that maximizes seigniorage. The dynamics could be explained by the Cagan (1956) model of hyperinflation extended to include a money-financed budget deficit and adaptive expectations (Evans and Yarrow, 1981). Adaptive expectations imply that the government succeeds in fooling the people by increasing the money supply and hence inflation above the expected one, which allows higher seigniorage than a maximum of a steady state. We suggest this as an explanation for the Yugoslav government's pushing inflation beyond the steady state and causing monetary chaos. If the assumption of adaptive expectations seems implausible, one may pose rational expectations and add lagged adjustment in Cagan money demand to obtain hyperinflationary dynamics (see for example Kiguel, 1989). In this paper, we test whether the monetary dynamics of the Yugoslav hyperinflation can be explained by the Cagan (1956) money demand model. We explore the role of expectations expressed in the extent of forward-looking behavior by the public while deciding on real money holdings, to address the question why the government resorted to ever-increasing inflation, and hence monetary chaos, while collecting seigniorage. We also examine the differences, if any, in money demand schedules for the two consecutive Yugoslav hyperinflations, that of the late 1980s and the early 1990s. Having been successively exposed to two different types of hyperinflations - the slowly building and short lived one in the 1980s and the extremely high and long lasting one in the 1990s one might expect the public to react differently. Following Taylor (1991), the validity of the Cagan model can be tested without specifying the expectations formation process. If real money balances and inflation rate are cointegrated, then the forecasting error is stationary, and the model holds for any relevant expectations formation process including adaptive and rational. Thus we test the validity of the Cagan model by investigating whether real money and inflation rate have one unit root each, and whether they cointegrate. This procedure has been used to obtain the results for classical hyperinflations (Taylor, 1991), Latin American (Phylaktis and Taylor, 1993) and for former Yugoslavia's hyperinflation in the 1980s (Frenkel and Taylor, 1993). We compare our results for the new Yugoslav hyperinflation with these studies. Under rational expectations, the Cagan model implies the existence of an additional cointegrating relation, that between real money balances and money growth (Engsted, 1993). If this relation is revealed, cross-equation parameter restrictions can be tested on the corresponding VAR model implied by exact rational expectations. Engsted (1994) found that in four out of six classical

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hyperinflations, the hypothesis of exact rational expectations did not hold. Since rejection of the Cagan model under rational expectations may be due to transitory deviations rather than the hypothesis being wrong, Engsted (1994) proposed an additional informal test that measures forward-looking behavior in money demand, which he applied to six classical hyperinflations. We use the same procedure in testing how expectations were formed in the Yugoslav hyperinflation. Our results are compared with those of classical hyperinflations to assess the extent of forward-looking behavior in Yugoslav hyperinflation. The paper proceeds as follows. Section 2 describes the background and monetary dynamics of Yugoslav hyperinflation. Section 3 examines the validity of the Cagan model irrespective of expectations formation scheme. The Cagan model under rational expectations and the extent of forward-looking behavior are investigated in Section 4. A comparison with money demand in the previous Yugoslav hyperinflation is undertaken in Section 5. The final section contains concluding remarks.

2. The Yugoslav hyperinflation: Background and some facts Much as the classical hyperinflations in the 1920s, Yugoslav hyperinflation was driven by monetization of the large fiscal deficit. The origins of the fiscal deficit are deeply rooted in the disintegration of the former Yugoslavia, which started in 1991 (Bogetid et al., 1994). The disintegration of the former federal republic, the war and the international embargo sharply decreased output and fiscal revenues. There was at the same time substantial pressure on government expenditures. Transfers were for example made to the Serbian population in the Krajinas. The general security situation obliged military and security expenditures. This was in addition to fiscal problems of transition that would in any event have placed pressures on government finances (see Bogetid and Hillman, 1995). No attempt was made to adjust expenditures because of the priorities of the government. Rather than confront the fiscal problem, the government proceeded with monetization of the fiscal deficit, with the justification of more substantive issues at stake. The fiscal situation in particular deteriorated with introduction of the United Nations embargo in May 1992. There was no adjustments made and the international community was blamed for the further acceleration of inflation. The problem of controlling the fiscal deficit was aggravated by the distribution, observed also in other high inflations (Paldam, 1994), of the deficit among the Federal government, the governments of Serbia and Montenegro, and municipal governments. The Federal government was weak. Political power rested in Serbia, which accounted for about 95 percent of the new federation in all relevant indicators. Public expenditures were allocated such that the federal government spent only 20 percent, mainly for the army. Republics spent 70 percent and municipal governments 10 percent. As to fiscal expenditures in the republics, the budgets accounted for 30 percent and public pension and health care funds for the

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remaining 40 percent. Additionally, the republics were in charge of the main public enterprises that incurred losses. Apart from weakening control over fiscal deficits, the above circumstances also affected their location: the republics transferred part of their deficits to the weak Federal government by postponing and decreasing their contributions to its budget. Deficits in the republics were mainly in pension and health care funds but not in government budgets. The distribution of deficits influenced the manner of monetization. The federal deficit was transparently financed by Central Bank credits, while deficits in the social funds and the losses of public enterprises were mainly covered by commercial bank credits which were partly refinanced by the Central Bank. Consequently, seigniorage on both the base money issued by the Central Bank and on the MI should be looked at while analyzing the monetization of fiscal deficits. The economic background of the Yugoslav hyperinflation is well described by the widespread presence of soft budget constraints which affected monetary dynamics. The former Yugoslavia practised a form of market socialism, reflected in a labor-managed economy which gave a prominent role to the market. The private sector was limited practically to agriculture, while all other firms and banks were socially owned and labor-managed. In this system soft budget constraints were built-in. The transition of Serbia and Montenegro towards a full-scale market economy started in 1989 when a private sector was allowed and privatization was promoted. The transition basically halted with disintegration of the former Yugoslavia and subsequent political crises. The private sector managed to encompass a considerable part of services and trade, but the vast majority of banks and industrial firms remained socially owned. The banks were in fact controlled by the firms which were, at the same time, their largest creditors. The dominance of social ownership affected the monetary dynamics of the Yugoslav hyperinflation. The escalating losses of the socially owned sector caused by disintegration of the former Yugoslav market and the UN embargo were mostly covered by low-cost bank credits extended at very negative real interest rates. These credits were partly refinanced by the Central Bank, so leading to additional printing of money, to monetize the quasi-fiscal deficit. The other part of credits was extended out of the banks' sources and, as hyperinflation exploded, the result was the complete cancellation of firms' debts and the corresponding capital of the socially owned banks. An additional reason for the government's opting to use the money supply to cover the deficits is success in capturing non-decreasing seigniorage throughout the hyperinflationary period. This is clear from Fig. 1 which shows that monthly seigniorage on MI oscillated around a constant; 2 the same result is obtained for

i See Bogeti~et al. (1994). 2 In fact, the unit root test shows that the seigniorageseries is stationary around its mean value.

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In 6 i

4

i -2

-4 234567891011121 91

!

234567691011121 92

I

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9,4

Fig. 1. Real moneybalances(M 1/P).

base money. In 1993 seigniorage on M1 amounted to approximately 25 percent of GDP and 12 percent of base money, while tax revenues were only 13 percent. In January 1994 when hyperinflation peaked, tax revenues dropped to the annual equivalent of around 3 percent of GDP, thus indicating the enormous size of the Tanzi effect. This vividly demonstrates the extent of inflationary financing compared to tax revenues. A consequence of the approximately constant seigniorage over three years was accelerating inflation, as shown in Fig. 2. In February 1992 monthly inflation reached the 50 percent Cagan bench mark, while in 1993 it increased from 100 percent in January to almost 2,000 percent in August and finally 20,000 percent in

5V

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91

I

92

I

93

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Fig. 2. Ratio between inflation and exchangerate depreciation(dp/dex).

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P. Petrovi(, Z. VujogeviC/ European Journal of Political Economy 12 (1996) 467-483 In

i

8.5~

6.8

~ ~ \

i

4.51¸

l [

123456789101112123456789101112 I 91 92

[

234567891011121 93 914

Fig. 3. Real money balances ( M I / P ) .

November. Inflation exploded further in December and J a n u a r y 1994, but the published price indices are completely unreliable. 3 Ever-increasing inflation together with approximately constant seigniorage implies a sharp decline in real money balances, as displayed in Fig. 3. A closer inspection of inflation dynamics, shown in Fig. 2, indicates that, after reaching a peak of 1900 percent in August 1993, inflation decreased to 700 percent in September and then exploded again towards 20,000 percent in November. The slow-down of inflation in September was a direct consequence of a price freeze introduced at the end of August, which was, however, accompanied by severe shortages. These shortages indicate that the inflation was repressed and hence the actual rate in September was in fact higher than the 'controlled' one that was recorded. The attempted price freeze in September and subsequent increase in inflation rate by a factor of 20 through November, makes this sub-period somewhat different from the rest of the sample. The monetary dynamics of the hyperinflation can be considered within the Cagan (1956) model. The model assumes that real money balances decrease with a rise in the expected rate of inflation. It has a steady-state solution where expected and actual inflation rates are equal, and there is a stable inflation rate that maximizes seigniorage. Thus a government should not increase money growth and hence inflation above that rate. However, hyperinflations, including Yugoslavia's, often exhibit an unstable and accelerating inflation rate rather than a stable one. An explanation for this is that

3 In December 180,000 percent and in January 300,000,000 percent. Compared to black market exchange rate depreciation and money growth, the inflation rate in December was about twenty times lower, while in January five times higher. The authors' discussions in the Statistical Office also confirmed that these official inflation rates are unreliable•

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the government can collect even larger seigniorage than in the steady state one, if it systematically succeeds in misleading the people by pushing the actual inflation rate above the expected one. This can occur when expectations are formed adaptively and the public makes systematic mistakes. Or the same dynamics of inflation and seigniorage can stem from rational expectations and a lagged adjustment in the money market (Kiguel, 1989). We first test whether the Cagan demand for money is a valid description of monetary dynamics in Yugoslav hyperinflation irrespective of the way expectations are formed. Then we look at how expectations are formed to explain non-decreasing seigniorage in the face of exploding inflation.

3. Estimating the cagan demand for money The Cagan money demand in hyperinflation states that real money balances decline with the rise in expected inflation: m,-p,

= ~ o - c~dp~+, + u,

(1)

where m t and Pt are natural logarithms of the money stock and the price level, respectively, and dp~+j is expected rate of inflation in the next period; u t is a stochastic disturbance and the coefficient c~ is the semi-elasticity of money demand to be estimated. Taylor (1991) showed that under certain conditions the Cagan model (1) can be estimated without having to assume a particular expectations formation process. That is, if money (m) and prices ( p ) are integrated of order two, I(2), and real balances (m - p ) of order one, I(1), then the cointegration between real balances ( m - p) and inflation rate (dp) implies that forecasting errors are stationary. The stationarity of forecasting errors indicates that a wide range of expectations formation schemes may hold, including adaptive and rational. Thus, one need not specify in advance the expectations formation process while estimating the model. Consequently, the existence of cointegration between real money balances and inflation rate proves the validity of the Cagan model irrespective of the way in which the expectations are formed. The estimating procedure consists of two steps: first, a test of order of integration of the variables considered and, second, the existence of cointegration between real money holdings and inflation. Monthly data for M1 and retail prices are used for the period January 1991 through August and November 1993. The results on unit root testing are reported in Table 1. Let us first consider the period January 1991-August 1993, for which the results obtained are unambiguous. As can be seen, the hypothesis that money (m) and prices ( p ) have three unit roots each is clearly rejected. The values of ADF and PP test statistics for money are - 7 . 1 4 and - 7 . 4 3 and they are greater in absolute value than the 5 percent critical value -3.56. The corresponding values

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Table 1 Tests for unit roots " AugmentedDickey-Fuller

Phillips-Perton

Pt

mt

mt - Pt

Pt

mt

mt - Pt

-7.14 - 1.32

-8.33 --5.62 -2.62

-3.23 1.42

-7.43 1.06

-7.77 --6.50 -3.16

--6.75 -4.37 - 1.62

-4.49 1.96

--2.35 2.47

--8.87 5.53 - 1.84

Period: January 1991-August 1993 Ho:I(3); Hi:I(2) Ho:I(2); Hl:I(l) Hod(l); HI:I(0)

-3.24 1.07

Period: January 1991-November1993 Ho:I(3); Hi:I(2) --4.47 2.06 Ho:I(2); HI:I(I) 1.05 2.30 Ho:I(l ); H i :I(0)

a The number of corrections is equal to 0 in all AugmentedDickey-Fuller (ADF) test-statistics (see Fuller, 1976), except it is 1 for p in the period: January 1991-November 1993. The Newey and West (1987) lag window of order 1 is used while the Phillips and Perron (1988) (PP) test statistic is computed. The critical value for ADF and PP tests that are calculated in the regression with constant and trend is equal to -3.56 (-3.21) and -3.55 (-3.20) at the 5 percent (10 percent) significance level for 32 and 35 observations,respectively(MacKinnon,1991)

for prices: - 3 . 2 4 and - 3 . 2 3 respectively, are greater than the 10 percent critical value - 3 . 2 1 . The existence of two unit roots, however, cannot be refuted. The statistics obtained are equal to - 1.32 and - 1.06 for money and 1.07 and 1.42 for prices, and so are lower than the 10 percent critical value. Hence, as expected these variables are integrated of order two, and consequently their first differences, i.e. growth rates, d m and d p are integrated of order one. In the case of real money balances (m - p ) , two unit roots are rejected as - 5 . 6 2 and - 6 . 5 0 are larger than the 5 percent critical value, while the presence of one unit root cannot be refuted since - 2 . 6 2 and - 3 . 1 6 are lower than the 10 percent critical value. Thus I(2) processes money (m) and prices (p), cointegrate into the I ( l ) real money process (m - p ) . When the period is extended through November 1993, the tests suggest that money now might have three unit roots, since the values of test statistics ( - 2.35 for PP and - 2 . 0 6 for ADF) are below the 5 percent critical value - 3 . 5 5 . Prices remain an I(2) process, since the values of ADF and PP test-statistics - 4 . 4 7 and - 4 . 4 9 are greater than - 3 . 5 5 . However, real money balances are still an I(1) process as - 1 . 6 2 and - 1 . 8 4 are lower than the 10 percent critical value, implying that p and m cointegrate and hence both should be I(2) processes. Having obtained that real money balances (m - p ) and inflation rate (dp) have one unit root each, one may proceed and test for cointegration between them, thus examining the validity of the Cagan model. The procedure usad is that of Johansen (1988), and the results are reported in Table 2. As can be seen, cointegration is present in both periods. The values of trace test

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Table 2 Test for cointegration between (m - p) and dp and estimation of cointegration vectors a Rank

Eigenvalue

Trace test

Cointegration vector mt - Pt

dPt

1

1

3.736

- 6.412

1

1.055

- 11.4429

Period: January 1991-August 1993 r=0 r<1

0.394 0.207

21.260 6.716

Period: January 1991-November 1993 r=0 r _<1

0.584 0.223

35.039 7.829

~ A constant term is restricted to entering the cointegration vector. The number of lags in VAR models are three. The 5 percent critical values for trace test are: 20.17 for r = 0 and 9.09 for r _<1 (Johansen and Juselius, 1990).

statistics 21.26 and 35.04 are greater than the 5 percent critical value 20.17, while values 6.72 and 7.83 are less than the 5 percent critical value 9.09. However, the estimated semi-elasticity of money demand decreases nearly four times, from 3.74 to 1.06, when the period is extended from August to November, indicating instability of the relationship. Having that in mind, we also tested for cointegration through September and October, but it did not show up. Thus a clear cut result is obtained only through August 1993. The break-up of Cagan money demand in the last three months may be, as explained earlier, due to the attempted price freeze in September and the subsequent enormous increase in the inflation rate throughout November. At the same time, despite inflation explosion, real money balances had been rising (see Fig. 3). All this makes these three months somewhat different from the rest of the sample. A similar phenomenon, growing real balances in spite of increasing inflation, was observed at the end of the German hyperinflation and the explanation usually advanced has been that the public expected a coming monetary reform and hence raised their money holdings. This was not the case in Yugoslavia, especially as early as August through November 1993, for it was widely believed that under the extensive UN embargo inflation stabilization was not feasible. One should therefore consider the monetary dynamics through the end of hyperinflation (January 1994), in order to asses whether the last period of extreme hyperinflation can be explained within the Cagan framework. This is not feasible within the standard framework as data on inflation in December 1993 and January 1994 are unreliable although promising results have been obtained with a modified version of the Cagan model, where inflation rate is replaced by exchange rate depreciation (Petrovi6 and Vujo~evir, 1995). Thus, apart from the last few months, the Cagan money demand is accepted as a valid description of the monetary dynamics of Yugoslav hyperinflation. Further-

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more, the cointegration obtained between real money and inflation implies that money velocity shocks are stationary. This is in accordance with the results obtained by Taylor (1991) and Engsted (1994) for other hyperinflations, and contrary to the previously employed assumption that these shocks follow a random walk. A steady-state solution of the Cagan model, when actual and expected inflation are equal and stable, gives a corresponding relationship between seigniorage and inflation with the properties of the Laffer curve. Maximum steady-state seigniorage is reached for the monthly steady-state rate of inflation equal to the inverse of money demand semi-elasticity. The estimate of the latter obtained for Yugoslavia is 3.74, hence suggesting that a 27 percent monthly inflation rate maximizes steady-state seigniorage. This inflation rate is, however, far below actual monthly rates. This indicates that the government did not attempt to maintain stable inflation in order to collect maximum steady state seigniorage. On the contrary, it opted for ever-increasing inflation, succeeding in pushing the actual inflation rate above the expected one, thus collecting higher seigniorage than the maximum steady-state one. When the actual inflation rate is greater than expected, households tend to keep larger real money holdings than in a steady state, and hence the government can collect greater seigniorage for any given inflation rate, compared to a steady state one. 4 As inflationary expectations tend to adjust upwards, although with a lag, the actual inflation rate needs to further increase if the same amount of seigniorage is to be captured. Thus we have an explanation for the constant seigniorage combined with explosive inflation observed in Yugoslavia. 5 The Cagan money demand is sometimes extended to include currency substitution by adding exchange rate depreciation to the model (for example Abel et al., 1979). Taylor (1991) provided some support in the case of German hyperinflation, Phylaktis and Taylor (1993) found insignificant influence of exchange rate depreciation on real money balances in five Latin American high inflations, while Choudhry (1995) supported the inclusion of exchange rate depreciation. 6 All used cointegration analysis such as ours. As these studies gave mixed outcomes, we now explore whether the extended version of the Cagan model holds for the Yugoslav hyperinflation. Upon testing we found that the black market exchange rate series is integrated

4 Cf. Sachs and Larrain (1993, pp. 740-743). 5 This does not imply that the steady-state Laffer curve in Yugoslavia did not bend backwards despite the enormous rate of inflation. Rather it means that Yugoslav inflation was out of the steady-state and hence its relation with seigniorage cannot be explained by employing the former steady-state relationship. The same remark applies to steady-state analysis which includes currency substitution as in Bufman and Leiderman (1992). 6 Phylaktis and Taylor (1993) analyzed Argentina, Bolivia, Brazil, Chile and Peru, while Choudhry (1995) looked at Argentina, Israel and Mexico.

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of order two, and hence its rate of change has one unit root. Cointegration between real money holdings, inflation and exchange rate depreciation was then tested and the cointegrating vector estimated. The estimates obtained gave the wrong sign on exchange rate depreciation, implying that domestic real balances increased with currency depreciation. 7 This called for further testing which showed that the coefficient on real money holdings, in the former cointegrating vector, is not significantly different from zero, which then reduces the cointegrating relation to that between inflation and exchange rate depreciation. 8 This refutes the validity of the extended Cagan model for the Yugoslav hyperinflation, and points to the standard one. Of course, this does not imply that currency substitution was absent during this hyperinflation, but rather that it could not be captured by the above extension of the Cagan model.

4. Testing the Cagan model under rational expectations The Cagan model is valid irrespective of the expectations formation process. One may now proceed further and make stricter assumptions concerning expectations - rational expectations and no bubbles. Then, as Engsted (1993) has shown, an additional cointegrating relation between real money balances ( m - p ) and money growth (dm) holds in the Cagan model. In the long-run, expected inflation equals to money growth, hence the cointegrating factor in the former relation is again the semi-elasticity coefficient a from (1). Also, testable restrictions may be imposed on a VAR model that includes the former cointegrating relation. As has been shown, both real money balances and money growth have one unit root each, hence one may look for cointegration between them. The results obtained, employing the Johansen (1988) procedure are reported in Table 3. Cointegration is present in both periods. The values of trace test-statistics 29.70 and 29.28 are greater than the 5 percent critical value 20.17. The existence of one cointegration vector is confirmed by the values of trace test-statistics 7.70 and 8.45, being less than the 5 percent critical value 9.09. As expected, the estimated semi-elasticity of money demand through August 1993, 3.65, is very close to the

7 Employing Johansen's procedure through August 1993, the cointegration vector obtained is: 0 . 5 5 ( m - p ) + 1 5 . 6 9 d p - 1 7 . 6 8 d e x , and when normalized on real money holdings the following relation is reached: ( m - p ) = - 2 8 . 5 3 d p + 3 2 . 1 5 d e x , where ex is the logarithm of black market exchange rate, and dex its first difference, that is depreciation. Similar results are obtained through November 1993. 8 The testing is done using the Johansen (1988) procedure and the null hypothesis, that the coefficient on real money holdings is zero, cannot be refuted as test statistics chi square (1) = 0.39 is less than the 10 percent critical value 2.71. This is expected from the above estimate of the cointegrated vector, where the coefficient on real money (0.55) is far below that on inflation (15.69) and currency deprecation ( - 17.68). In fact, we have already obtained cointegration between inflation and exchange rate depreciation (Petrovi6 and Vujo~evir, 1995).

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Table 3 Test for cointegration between (m - p) and dm and estimation of cointegration vectors Rank

Eigenvalue

Trace test

a

Cointegration vector mt - Pt

dmt

1

1

3.650

- 7.001

1

6.849

- 2.929

Period: January 1991-August 1993 r=0 r< 1

0.557 0.248

29.704 7.705

Period: January 1991-November 1993 r=0 r< 1

0.489 0.238

29.280 8.445

a A constant term is restricted to entering cointegration vector. The number of lags in VAR models are four in the first part of the table and three in the second part.

e s t i m a t e o b t a i n e d in c o i n t e g r a t i n g r e l a t i o n b e t w e e n real m o n e y a n d inflation, 3.74. T h i s is not, h o w e v e r , the case w h e n the p e r i o d is e x t e n d e d t h r o u g h N o v e m b e r 1993; the e s t i m a t e s are 6.85 as a g a i n s t 1.06. T h i s also p o i n t s to the i n s t a b i l i t y o f the e s t i m a t e s w h e n the last t h r e e m o n t h s are added, a n d t h e r e f o r e w e a g a i n opt for the p e r i o d t h r o u g h A u g u s t 1993. T h e s e m i - e l a s t i c i t y e s t i m a t e f r o m the c o i n t e g r a t i n g relation, 3.65, is a s u p e r c o n sistent one, a n d c a n b e u s e d in the s e c o n d step w h i l e e s t i m a t i n g a V A R for the t w o s t a t i o n a r y v a r i a b l e s ( E n g s t e d , 1993): S t = ( m t - P t ) + 3 . 6 5 d m t - 7 a n d d2m. T h e results are r e p o r t e d in T a b l e 4. A s c a n b e seen f r o m T a b l e 4, m o n e y is e n d o g e n o u s , that is S t G r a n g e r - c a u s e s m o n e y (dZm), w h i l e S t is e x o g e n o u s . T h u s f e e d - b a c k f r o m prices to m o n e y is o b t a i n e d as o n e w o u l d e x p e c t w h e n h y p e r i n f l a t i o n is the c o n s e q u e n c e o f a large fiscal deficit w h i c h is m o n e t i z e d ( S a r g e n t a n d W a l l a c e , 1973). T h e e n d o g e n e i t y o f

Table 4 Summary statistics from the VAR model a Sample: January 1991-August 1993 d2mt equation: ~ 2 = 0.47. F test for the hypothesis that S t Granger-causes d 2mr: F(4, 17) = 5. l 1 (0.01) S t equation: ~2 = 0.63.

F test for the hypothesis that d2m, Granger-causes St: F(4, 17) = 1.24 (0.33) F test of parameter restrictions: F(8, 17) = 32.06 (0.00) Correlation (St, St* ) = 0.74 Slope coefficient in regression of St* on St: 0.80 (0.05) a There are four lags in the VAR model. The number of lags was chosen by inspection of the residual auto-correlations.

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506070 40 f

479

. . . . .

30 201 i 10~ /

_1o ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 I 91 92 I 93 [914 S

--S*

Fig. 4. Plot of S t and St*

money was also obtained for Austrian, German, Hungarian, Polish and Russian hyperinflations, and suggests forward-looking behavior. 9 However, the parameter restrictions on the estimated VAR system, implied by the exact rational expectations Cagan model are clearly rejected. The corresponding value of test statistic F(8, 17) = 32.06 (0.00) shows that the null hypothesis, stating that the restrictions hold, cannot be accepted. 10 The same result is obtained in four (Austria, Germany, Greece and Russia) out of six hyperinflations considered by Engsted (1994). Estimated VAR, nevertheless, can also be used for an additional informal test based on the result that, under exact rational expectations, S t is the optimal predictor of St*, that is, the present value of future changes in money growth rate (dZmt) (Engsted, 1993). The latter has been generated by employing the semi-elasticity parameter from cointegration analysis (3.65), and the estimates of unrestricted V A R parameters. If the two are very close to each other, the Cagan model under rational expectations has empirical content, and the former rejection of the model may be due to transitory deviations from it. In any case, the correlation between S t and St* gives a measure of the public's forward-looking behavior while deciding on real money holdings, The two series, S t and St*, are depicted in Fig. 4. The correlation coefficient between them, equal to 0.74, is low compared to that in most other hyperinflations

9 See Engsted (1994). 10The parameter restrictions lead to a variable X t - S t -(1 + a ) ~ - I S t 1-(1 + ot)d2mt, that is innovation when velocity shocks are negligible, which should be uncorrelated with lagged variables from the former VAR model. Hence, the testing was performed by regressing Xt, with a equal to 3.65, on lagged values of St and dZmt. As the F-statistic has shown, the correlation emerged and therefore the null hypothesis was refuted.

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- Austria (0.83), Germany (0.98), Greece (0.93) and Hungary (0.998). It is close to the coefficient in Russian hyperinflation (0.76) and higher than in the Polish (0.55) (see Engsted, 1994). Thus, this informal test indicates that the elements of forward-looking behavior in Yugoslav hyperinflation are not that strong compared to others.

5. Money demand: The two Yugoslav hyperinflations compared Serbia and Montenegro have experienced two consecutive hyperinflations, one within the former Yugoslavia in the 1980s and the other in the first half of the 1990s, and it would be interesting to explore the differences, if any, in money demand schedules in the two hyperinflations. Inflation in the former Yugoslavia started to build up in the first half of the 1980s following a stop-and-go-pattern, and then took off towards hyperinflation after May 1988. In the last quarter of 1989 monthly rates reached 50 percent, indicating the existence of hyperinflation which lasted just few months. 11 Thus, it was quite similar to most Latin American high inflations as opposed to classical European hyperinflations in the 1920s. Frenkel and Taylor (1993) estimated the Cagan model in order to explain the monetary dynamics of Yugoslavia's high inflation in the 1980s. Having obtained cointegration between real money holdings and inflation rate, they accepted Cagan's model with semi-elasticity of money demand equal to 22. In this paper we have found that the Cagan model holds for the hyperinflation of the 1990s, however with a semi-elasticity of 3.74, that widely differs (is more then five times lower) than the one obtained for the 1980s. This is an unexpected result, implying that real money holders, experiencing hyperinflation for the second time and which was more violent, were less sensitive to changes in the inflation rate. Clearly, the elasticity of money demand, being the product of inflation rate and semi-elasticity, did not vary much across the two inflationary episodes, but still this does not support the use of the same specification, that is the Cagan model, in both episodes. A large variation in semi-elasticity is also obtained when comparisons are made across different hyperinflationary episodes: the huge classical hyperinflations in the 1920s recorded low semi-elasticities, while they were much higher in the less extreme episodes of Latin America. 12 Evidence in Petrovi6 and Vujo~evi6 (1996) questions the validity of the Cagan model in explaining money demand in Yugoslavia's high inflation in the 1980s. This concurs with the acceptance of the constant elasticity of money demand,

11Inflationreached 48 percent in September1989, then decreasedto 45 percent and 43 percent in the next two months, reaching a maximumof 58 percent in December. 12See Table 4 in Frenkel and Taylor (1993).

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where real money cointegrates with price level and real exchange rate (Petrovi6, 1995). On the other hand, the Cagan model is accepted for the hyperinfiation in the 1990s. These results explain, in the case of Yugoslavia, why a recorded difference in semi-elasticity estimates has emerged. However, they also suggest that the same may be true for most Latin American high inflations as opposed to classical hyperinflations: namely, a conjecture to be tested is that the Cagan model, while valid for hyperinflation, does not hold in high inflation.

6. Conclusions We have shown that, in common with other classical hyperinflations (Taylor, 1991), the Cagan (1956) money demand model is an adequate representation of monetary dynamics in Yugoslav hyperinflation, apart from the last few months. This result is not contingent on any particular assumption concerning expectations formation. The model was tested and accepted because real money and inflation, each having one unit root, cointegrate. The presence of cointegration further implies that velocity shocks in Yugoslav hyperinflation are stationary. This is in line with the findings of Taylor (1991) and Engsted (1994) for classical hyperinflations, and contrary to the often-made assumption that velocity shocks follow a random walk (Sargent and Wallace, 1973). The corresponding cointegrated VAR model allows for feed-back from prices to money, as one would expect in hyperinfiation (Sargent and Wallace, 1973), and upon testing this conjecture is accepted. The obtained endogeneity of money is consistent with the results for other classical hyperinflations (Engsted, 1994) and points to forward-looking behavior. In spite of the above and the cointegration found between real money and money growth, the Cagan model under exact rational expectations was formally rejected for Yugoslav hyperinflation. As rejection of the model could be due to transitory deviations from it, an additional informal test was applied. The results obtained, compared with those for classical hyperinflations (Engsted, 1994), indicate that refutation of rational expectations is not due to transitory deviations from the model. Thus, in Yugoslav hyperinflation, the public demonstrated a lower degree of forward-looking behavior compared to that in Austrian, German, Greek and Hungarian hyperinflations. This attitude of the public enabled the government to fool them and collect non-decreasing seigniorage throughout the hyperinflation, by pushing money growth and infation above expected rates. Consequently, the hyperinflation lasted longer, and it was brought to a halt only when tax revenues almost disappeared. The estimates obtained do not cover the last five months of hyperinflation September 1993 through January 1994, when the inflation rate reached a maximum. This is due to measurement errors of price levels in the last two months and

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an attempted price freeze in September. Nonetheless, it may well be that with the sharp increase of inflation in the last few months, the public switched towards more forward-looking behavior. Some preliminary results support this conjecture (Petrovi6 and Vujo~eviE, 1995). A comparison of the two Yugoslav hyperinflations - in the 1980s and the 1990s - shows that the semi-elasticity in the Cagan money demand sharply differ. Surprisingly, there was a decrease from 22 (Frenkel and Taylor, 1993) to 3.74, implying that the public, experiencing for the second time hyperinflation which was much higher and longer, reacted less sensitively. However, the same pattern emerges when comparisons are made across inflationary episodes: the Latin American hypefinflations that built up slowly and lasted briefly, have much larger semi-elasticities compared to those of the vehement classical European hypefinflations (Frenkel and Taylor, 1993). An answer to the above puzzle in the case of Yugoslav hyperinflations is that the pattern of money demand schedule changed. While valid for the fierce hyperinflation in the 1990s, the Cagan model does not hold for the short-lived one in the 1980s (Petrovi6 and VujogeviE, 1996). The latter hyperinflation is better characterized by an alternative - constant elasticity specification of money demand (Petrovir, 1995). This suggests a possible line for further research of money demand in Latin American high inflations.

Acknowledgements We thank two anonymous referees, Tom Engsted and Arye Hillman for valuable comments. Responsibility for any remaining errors rests with the authors.

References Abel A., R. Dornbusch, J. Huizinga and A. Marcus, 1979, Money demand during hyperinflation, Journal of Monetary Economics 5, 97-104. Bogetir, Z. and A.L. Hillman, eds., 1995, Financing government in transitions, Bulgaria: The political economy of tax policies, tax bases, and tax evasion (The World Bank, Washington, DC). Bogetir, Z., D. Dragutinovi6 and P. Petrovir, 1994, Anatomy of hyperinflation and the beginning of stabilization in Yugoslavia 1992-1994, Working paper (CES MECON, Belgrade) Sep. Bufman, G. and U Leiderman, 1992, Simulating an optimizing model of currency substitution, Revista de Analisis Economico 7, 109-124. Cagan, P., 1956, The monetary dynamics of hyperinflation, In: M. Friedman, ed., Studies in the quantity theory of money (Chicago University Press, Chicago, IL) Choudhry, T., 1995, High infation rates and the long-run money demand function: Evidence from cointegration tests, Journal of Macroeconomics 17, 77-91. Engsted, T., 1993, Cointegration and Cagan's model of hyperinflations under rational expectations, Journal of Money, Credit and Banking 25, 350-360. Engsted, T., 1994, The classic European hyperinflations revised: Testing the Cagan model using a coiutegrated VAR approach, Economica 61, 331-343.

P. Petrovi(, Z Vujo~evi(/ European Journal of Political Economy 12 (1996) 467-483

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Evans, I.L. and G.K. Yarrow, 1981, Some implications of alternative expectations hypothesis in the monetary analysis of hyperinflation, Oxford Economic Papers 33, 61-88. Frenkel, J.A. and M.P. Taylor, 1993, Money demand and inflation in Yugoslavia, 1980-1989, Journal of Macroeconomics 15, 455-479. Fuller, W.A., 1976, Introduction to statistical time series (Wiley, New York). Johansen, S., 1988, Statistical analysis of cointegration vectors, Journal of Economic Dynamics and Control 12, 231-254. Johansen S. and K. Juselius, 1990, Maximum likelihood estimation and inference on cointegration with application to the demand for money, Oxford Bulletin of Economics and Statistics 52, 169-210. Kiguel, A.M., 1989, Budget deficits, stability and the monetary dynamics of hyperinflation, Journal of Money, Credit and Banking 21, 148-157. MacKinnon, J., 1991, Critical values for cointegration tests, In: R.F. Engle and C.W.J. Granger, eds., Long run economic relationships: Readings in cointegration (Oxford University Press, Oxford). Newey, W.K. and K.D. West, 1987, A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix, Econometrica 55, 703-708. Paldam, M., 1994, The political economy of stopping high inflation, European Journal of Political Economy 10, 135-168. Petrovi~, P., 1995, Quasi-fiscal deficit and money demand in Yugoslavia's high inflation: Some econometric evidence, Journal of Comparative Economics 20, 32-48. Petrovi~, P. and Z. Vujo~evir, 1995, Demand for money and exchange rate determination in Hyperinflation: Conceptual issues and evidence from Yugoslavia, Working paper (CES MECON, Belgrade) May. Petrovir, P. and Z. Vujo~evir, 1996, Comment on Frenkel and Taylor's money demand and inflation in Yugoslavia, 1980-1989, Journal of Macroeconomics 18, 177-185. Phillips, P.C.B. and P. Perton, 1988, Testing for a unit root in time series regression, Biometrica 75, 335-346. Phylaktis, K. and M.P. Taylor, 1993, Money demand, the Cagan model, and the inflation tax: Some Latin American evidence, The Review of Economics and Statistics 75, 32-37. Sachs, J.D. and F. Larrain, 1993, Macroeconomics in the global economy (Harvester-WheatsheaL Hemel Hempstead). Sargent, T.J. and N. Wallace, 1973, Rational expectations and the dynamics of hyperinflation. International Economic Review 14, 328-350. Taylor, M.P., 1991, The hyperinflation model of money demand revisited, Journal of Money, Credit and Banking 23, 327-351.