Money demand and inflation in Yugoslavia 1980–1989

JACOB A. Ff+EML Bank Jerusalem, of lsrael lsrael hAARK I? TAYLOR lnternutional Money Demand and En Yugoslavia, /shl#)- 1989 Monetary Fund Washington, D.C. n in After discussing the relevant historical and institutional background to Yugoslav monetary and inflationary experiences, lQ8Q-1989, Cagan’s hyperintlation model is tested using an econometric technique which is unrestrictive with respect to assumptions concerning expectations formation. We also examine the hypothesis that the expected return to holding foreign assets was an important determinant of domestic money holding; test alternative hypotheses of expectations formation; and test a buffer-stock version of the Cagan model. Ibe results support the Cagan model (especially but not exclusively when coupled with an adaptive-regressive expectations mechanism) as a description of the salient features of the data. 1. Introduction Notwithstanding the severe political crisis which now appears to have split Yugoslavia irreversibly, the Yugoslav economy wasat least prior to lWO-of considerable interest to monetary economists and macroeconomists, for a number of reasons. Ever since the virtual abandonment of central planning at the natiunal level in the 1950s and its replacement with a system of worker self-management, Yugoslavia was in the forefront of economic innovation in Eastern Europe. At the same time, the economy experienced endemic inflation for much of the postwar period; indeed, the proneness of the Yugoslav economy towards high inflation might be viewed as one of its overriding economic problems, particularly during the last decade.’ Unlike many other Eastern European economies which are currently undergoing a period of rapid change, where the liberalization of prices in markets hitherto characterized by repressed inflation has quite suddenly unleashed a large monetary overhang, *Any views expressed are those of the authors and are not the International Monetary Fund or of the Bank of Israel. The to two anonymous referees for helpful comments on a previous disclaimer applies. ‘See, for example, OECD (1990) and earlier issues. Journal of Macroeconomics, Summer Copyright 0 1993 by Louisiana State 0164-0704/93/$1.50 1993, Vol. University 15, No. Press 3, pp. necessarily those of authors are grateful version; the usual 455-481 455 Jacob A. Frenkel and Mark P. Taylor the experience of Yugoslavia during the 1980s is characterized by substantial rises in both the money stock and inflation (Table 1). The commitment of the Yugoslav authorities to reform the economy’s structural weaknesses has also, until very recently, been a unique trait among communist-ruled countries. In the 1980s alone, Yugoslavia negotiated five stand-by arrangements and one enhanced surveillance procedure with the International Monetary Fund, one structural adjustment loan with the World Bank and several rescheduling arrangements with official creditors and commercial banks. Despite this willingness of the authorities to introduce structural reforms, however, Yugoslav inflation remained high and chronic (Figure 1) and, in 1988-1989, assumed the proportions of a fullblown hyperinflation with prices growing at a monthly rate in excess of 50% by the end of 1989. While some authors have used structuralist arguments to link the worker cooperative system to inflation proneness (for example, Mates 1987; Mencinger 1987; Bradley and Smith 1988), in this paper we wish to examine the link between monetary accommodation T------ II Monthly 456 Figure 1. Rate of Inflation (a) Money Demand and Inflation in Yugoslavia, 1980-1989 and inflation.2 In particular, we apply and test Cagan’s (1956) hyperinflation model of money demand, according to which the demand for real money balances is largely explained by expected inflation. The hyperinflation model has been studied extensively in monetary economics but, until recently, its application has been limited to the European-particularly German-hyperinflations of the interwar and immediate post-second world war periods (Cagan 1956; Frenkel 1977, 1979, 1980; Barro 1970; Sargent 1977; Taylor 199Ia) and, to a lesser extent, high inflation episodes in Latin America (Phylaktis and Taylor 1993). The experience of Yugoslavia thus provides a rare example of a recent hyperinflation which is therefore worthy of study. An interesting feature of our analysis of the Cagan model is that we estimate and test it using a technique which is not contingent on any particular assumption concerning expectations formation except that agents’ errors in forecasting inflation are stationary. We then use these estimates to examine a number of auxiliary topics such as how important foreign currency asset holding was as a determinant of domestic money holdings; whether aggregate behavior accords to one of the alternative hypotheses of rational, adaptive or adaptive-regressive (Frenkel 1975) expectations; and whether a buffer-stock version of the Cagan model, in which unanticipated money is temporarily held by private agents (Cuthbertson and Taylor 1987a) is capable of explaining the data. 2. Inflation in Yugoslavia The Yugoslav economy was for many years in the forefront of change among the socialist countries of Eastern Europe. The central planning of the immediate postwar period was largely abandoned during the 1950s and replaced with a system of worker cooperatives. This strategy was apparently responsible for the steady rise in per capita incomes for the following two decades. Beginning in the 1970s however, a number of major economic problems became apparent. During the 197Os, Yugoslav macroeconomic policy was largely characterized by an overvalued domestic currency, negative real in‘As noted by Lahiri (1991), this does not, however, preclude the possibility the central bank’s accommodative stance may in some way have been due worker self-management system. that to the 457 Jacob A. Frenkel and Mark P. Taylor terest rates and domestic markets distorted by various forms of controls and regulations. By the beginning of the 198Os, a number of major economic imbalances were apparent as the legacy of this strategy coupled with the effects of the second OPEC oil shock. Chief among these were a current account deficit and external debt position with the convertible currency area of some 5% of Gross Social Product (GSP) and U.S. $18 billion respectively, compared to current account balance and debt of less than U.S. $6 billion some five years earlier. In an attempt to correct these imbalances, a number of adjustment policies- including a flexible exchange rate policy-were enacted in the 1980-1985 period. Although this led to some improvement in the external position-current account balance was achieved in 1983-improvements on the domestic side remained disappointing. The annual inflation rate rose from an already high level of about 40% in 1980 to approaching 80% in 1985, while GSP growth stagnated at some 1% per annum over the same period. Domestic structural reforms aimed at improving the operation of markets remained modest while a stop-go cycle of price controls undermined policy credibility. The Economic Resolution for 1985 aimed at improving GSP growth through an expansionary fiscal policy. However, the main effects were a resurgence in import demand and inflationary pressures: in the first half of 1986 the current account swung back into deficit while, on an annualized basis, average earnings rose by more than 100%. Meanwhile, the financial discipline of banks and enterprises continued to be weak and real interest rates negative. By the end of 1987, the year-on-year inflation rate was in excess of 200% and a partial and largely unsuccessful price freeze was imposed. Supported by a stand-by arrangement with the IMF and agreements on external financing with official creditors and commercial banks, the authorities announced in May 1988 a package of restrictive monetary, fiscal and incomes policies coupled with a program of price, import and foreign exchange liberalization. The package had the intention of containing inflation through a stimulation of the supply side concomitant with downward pressure on domestic demand. In the event, the ending of the partial price freeze in mid 1988 combined with a 25% devaluation of the currency unleashed a powerful inflationary impulse. The decision at the beginning of 1989 to allow wages to be freely determined, in turn, allowed a wage-price-exchange rate inflationary spiral to develop and a full-blown hyperinflation ensued. During the first quarter of 1989 458 Money Demand and Inflation in Yugoslavia, 1980-1989 consumer prices rose by 500% on an annualized basis and by the end of the fourth quarter their annualized growth had reached some 13OOO%-thereby qualifying as hyperinflation according to Cagan’s (1956) definition of inflation of 50% or more per month. At the end of 1989, the authorities announced a stabilization program comprising wage-price controls as well as restrictive monetary and fiscal measures. An interesting feature of the package was the attempt to import West German low inflation credibility by introducing a new convertible dinar pegged to the deutschemark and guaranteed during six months of the wage freeze, thereby effectively freezing wages in mark terms. By mid 1990, this heterodox plan was apparently successful in that monthly inflation had fallen to single digit levels. The political situation during the past year has now, of course, overtaken the course of events and it is impossible to say whether or not this initial success would have been sustained especially in the light of the relative failure of similar heterodox plans undertaken in Latin America during the 1980s (Taylor 1987; Solimano 1990). In this paper we address the question of the relationship between inflation and money in Yugoslavia. As Table 1 indicates, whatever the stated policy intentions of the authorities, monetary policy during the 1980s has, de facto, been largely accommodative with respect to inflation. As a number of commentators have indicated,3 the consistent overshooting of the Yugoslav monetary targets can be largely traced to the failure of the National Bank of Yugoslavia (NBY) to exert any significant degree of control over commercial bank lending, so that clients’ credit demands were normally satisfied with little regard to NBY directives and were eventually accommodated by the NBY itself. In 1989 the official M2 target was exceeded by a factor of seventeen. During the same period, the commercial banks’ obligatory reserve ratio declined, despite the stated aim of the NBY to raise it by 2%. 3. The Cagan Model In his seminal paper on the demand for money during hyperinflation, Cagan (1956) argues that, under extreme inflationary conditions, the overwhelming determinant of desired real money holdings will be expected inflation. Denoting the logarithm of nom- ‘See, for example, OECD, 1990 459 Jacob A. Frenkel and Mark P. Taylor Inflation TABLE 1. 1989:xii and Money Creation 198O:i- Average Monthly Increase in the Money Average Monthly Inflation Rate (%) 198O:i-1989:&i 1985:i-1989:xii in Yugoslavia SUPPlY @) 7F l-h 7.34 11.83 6.21 10.57 T/h 1.18. 1.12 NOTE: 71 and GI were constructed MT = M,(l + Iil/loo)T, + n/loo)‘, level and nominal narrow allowing for monthly compounding: PT = P,(l where Pi and M, denote the consumer price stock in period i and T is the sample size. money inal money balances and prices by m and p respectively, can be written, ignoring the constant term: (m - ~)t = c&G+,, + the model (.t , (1) where it is a stationary disturbance term which we assume to be serially uncorrelated. Replacing expected with actual inflation in (1): (m - ~)t = (YAP,+, + l t+1 (2) 9 where l t+1 = [L - GP,+I - AP~+JI. During the 198Os, it is not unreasonable to conjecture that Yugoslav inflation and real money balances will each be non-stationary processes which need to be differenced at least once in order to achieve stationarity. In the terminology of Engle and Granger (1987), if (m - P)~ and Ap, need to be differenced d and e times respectively in order to achieve stationarity, they would be integrated of orders d and e, respectively: h Subtracting - ph - I(d) An , - cwAp, from both sides of (2) we have Cm - PL - aApt = aA2p,+l If we assume that expectational 460 d,erl. Z(e) , + l t+1 . errors are stationary, (3) regard- Money Demand and Inflation in Yugoslavia, 1980-1989 less of the particular method used to form expectations,4 then since is stationary, Equation (3) implies that the linear combination %+1 Km - PL - C&AI must be integrated of order (e - 1). Now, an interesting case arises where d = e = 1. In this case, is, it is Km - PL - 4~1 must be integrated of order zero-that stationary-even though (m - pJt and Ap, are individually non-stationary. Hence, real money balances and inflation are cointegrated (Engle and Granger 1987) with a cointegrating parameter (after normalization on real balances) just equal to the parameter of interest in the Cagan model (that is, the semi-elasticity of real money demand with respect to expected inflation).5 Thus, when inflation and the logarithm of real-mmeybalances are integrated processes of order one, a simple test of the applicability of the hyperinflation model lies in testing whether or not real money balances and inflation are cointegrated. If they are, then a highly efficient (“super consistent”-Stock 1987) estimate of its major parameter of interest can be obtained which is robust to a wide range of assumptions concerning expectations formation (Taylor 1991a). 4. Empirical Results Monthly data on consumer prices and narrow money for Yugoslavia, for the period January 1980 through December 1989, were obtained from the International Monetary Fund’s International Financial Statistics (IFS) data tape.6 The narrow money series was deflated by the consumer price index to obtain a real money stock series (which was then put into logarithmic form) and the first difference in the logarithm of consumer prices was taken as the monthly inflation rate. Table 2 lists the results of tests for one or more unit roots in “Taylor (1991a) investigates the plausibility of the assumption of stationary forecasting errors when the variable being forecast is I(1) for a range of alternative assumptions concerning expectations formation. Wnder the additionuZ assumption of rational expectations, this implication of the hyperinflation model is a particular case of a general result for present value models discussed by Campbell and Shiller (1987). A main purpose of the present analysis, however is to derive a test of the hyperinflation model which is non-specific with respect to expectations formation. The importance of considering alternative forms of expectations formation in the context of testing present value models is demonstrated by Chow (1969). ‘IFS line 64 and line 34, respectively. 461 Jamb A. FrenJcel and Mark P. Taylor TABLE 2. Unit Root Tests AZ cm - -5.92 -6.03 A”Pt -7.83 -8.11 P)t Ah - -3.08 -3.53 A”P~ -2.99 -3.74 PL Cm - PL 0.64 -2.27 Apt 3.79 2.79 NOTE: The null hypothesis is that the series in question contains a unit root in its univariate autoregressive representation. 7, is the regression t-ratio for the autoregressive co&cients to sum to unity-the augmented Dickey-Fuller statistic. Seasonal dummies were included in the auxiliary regressions. T, is computed similarly but after including a time trend in the autoregression. Seventh-order autoregressions in&ding seasonal dummies were used in each case. The rejection regions, for a nominal test size of 58, are {T, E RI?,, < -2.89) and {r, E il+, < -3.45) (Fuller 1976). the real money balance and Mation rate series. Following the suggestion of Dickey and Pantula (1987), we tested sequentially for two, ‘one and zero unit roots, using the augmented Dickey-Fuller test both with and without an allowance for trend in mean (Fuller 1976). Our conjecture that Yugoslav real money balances and inflation are each I(1) series during the 1980s appears to be borne out: the I(1) hypothesis can only be rejected at the 5% level when the inflation and real money series are first or second differenced. The results reported in Table 3 reveal strong evidence of cointegration of current inflation and real money balances. Applying the likelihood ratio test for cointegration due to Johansen (WB), the hypothesis of at most one cointegrating vector (H,:r z I) cannot be rejected at the 5% significance level, whilst the hypothesis of zero cointegrating vectors (Ha: r = 0) is easily rejected in every case.’ This constitutes evidence in favor of the Cagan model as applied to the Yugoslav erxmamy during the 198Os..’ ‘See Cuthbertson, Hall, and Taykrr (1992) for an introductory discussion of the Johansen technique, or MacDonahl and Taylor (1991) for a brief discussion. *lt is now well known that the power of unit root tests is an increasing function of the length of the sample period, rather ~tban the frequency of observation (SbiWer and perron 1985), and this is also likely to be the case for tests of cointegration. Since, however, we are able to reject the hypothesis of non-cointegration with only ten years of data (when the power may be expected to be low), this implies that our results hold a fortiori. 462 Money TABLE 3. Demand Cointegration Ql QZ 12.40 (0.13) 15.33 (0.053) and Znflation in Yugoslavia, 1980-1989 Tests and Estimates Johansen Statistics H,,: r I 1 H,,: r = 0 0.45 36.23 B -21.96 NOTE: If r denotes the number of significant cointegrating vectors, then the Johansen statistics test the hypotheses of at most one and zero cointegrating vectors, respectively. Seasonal dummies were included in the vector autoregressions. The 5% critical value for H,: r 5 1 is 9.094 and for Ho: r = 0 it is 20.168 (Johansen and Juselius 1989). Q,, and Qz denote Ljung-Box statistics applied to the residuals from the real money and inflation regressions respectively, computed at eighteen autocorrelations; they are distributed as chi-square with eight degrees of freedom under the null hypothesis of white noise residuals. Figures in parentheses denote marginal significance levels. Cagan (1956) sh ows that the percentage rate of increase of prices and money which maximizes the revenue accruing to the authorities from the inflation tax is equal to -(100/a)% per month in the hyperinflation money demand model. Given an average rate of inflation of 7.34% per month for Yugoslavia over the sample period, an “optimal” value of cx of - 13.63 (= - 100/a) is thus implied. A likelihood ratio test of the hypothesis Ho: = -13.63 yielded: x2(1) = 4.89, which has a marginal significance level of 2.7%.’ Thus, the hypothesis of inflation tax revenue maximization appears to be rejected at the 5% level. However, Frenkel (1975, 1976) notes that Cagan’s analysis of the inflation tax is in terms of the steady state when expectations are fully realized. He observes that, in the short run, the authorities may be able to raise both the marginal tax ratethe inflation rate-and the size of the tax base-the level of private sector real money holdings. lo Thus, the proper objective for optimization is the discounted flow of inflation tax revenue over time, and this may differ from that suggested by steady-state analysis. ‘Using the higher average rate of inflation for the 1985-1989 period (Table 1) would have resulted in an even stronger rejection. “‘This argument relies on a stylized fact concerning hyperinflations that nominal and real money balances are highly correlated in the short term. This is, in fact, inconsistent with both rational and adaptive expectations. This issue is discussed further in Section 8 below. 463 Jacob A. Frenkel and Mark P. Taylor 5. Rational Expectations The observed positive correlation between the rate of money growth and the level of real balances (Figure 2) provides at least prima facie evidence of the failure of rational expectations in the context of the Cagan model for this period, since, under. rational expectations, increased monetary growth would be expected to feed into higher prices (and hence Zozoer real balances) with a very short lag. A more formal test of the rational expectations hypothesis can be developed as follows. Rearranging (l), we have AP:++~ = a-‘t(m so that agents’ forecasting - PL - &I , (4) errors can be inferred: IJ++I = AP,+I - ~-‘[(m - oh - 5J . (5) According to the rational expectations hypothesis, agents’ forecasting errors should be orthogonal to information available at time t, I, say (see for example, Cuthbertson and Taylor 1987b): 40 “~“““~“~‘~““‘~” Real 198(1 Money Balances mo and Figure Monthly 2. Nominal Money Growth (8) Money Demand and Znf lation in Yugoslavia, 1980-1989 Eh+llL) = 0 . 63) If, following Sargent (1977), we assume that E&11,) = 0, then (5) and (6) imply the orthogonality condition: E(St+1IZ*) =0 (7) St+1= [Apt+1- a-’ (m - p),l . (8) for A simple way of testing (7) is to test for zero coefficients in a least squares projection of st+l onto lagged values of itself.” The parameter cx can be estimated by cointegration analysis and, because of the super-consistency of such an estimate when the variables are cointegrated (Stock 1987), treated as known in testing (7). A series for &+i was constructed for Yugoslavia using (8) and the point estimate of (Y of -21.96 (Table 3). This series was then regressed onto four lags of itself (and a constant) by ordinary least squares and the slope coefficients tested against the null vector. This yielded an F-statistic of F(4,llO) = 1896.694, which has a marginal significance level of virtually zero. This indicates a very strong rejection of the rational expectations hypothesis. l2 6. Comparison with Results for Other High Inflation Episodes Taylor (1991a) applies the methods outlined above to the classic interwar hyperinflations studied by Cagan (1956), while Phylaktis and Taylor (1992, 1993) h ave examined high inflation episodes in a number of Latin American countries during the 1970s and 19SOs, and in Taiwan in the immediate post World War II period. Table 4 lists the estimates 01 reported in those studies, as well as the average monthly inflation rate during the period of investigation, for purposes of comparison. “Taylor (19Qla) demonstrates that this is equivalent equation rational expectations restrictions on the vector tion of [A$, (tn - p), - aAp,)]‘. “Subject to the maintained assumption E(i$,) = 0. to testing autoregressive a set of crossrepresenta- 465 Jacob A. Frenkel TABLE 4. Country Yugoslavia Austria* Germany*’ Hungary * Poland * Argentina** Bolivia** Brazil** Chile** Peru** Taiwan*** and Mark Comparison P. Taylor- of Results across Countries Sample Period Estimate of ci Average Monthly Inflation Rate 1980-1989 1921-1922 1920-1923 1922-1924 1922-1923 1971-1989 1971-1987 1971-1986 1971-1985 1971-1989 1945-1949 -21.96 -3.77 -0.43 -8.29 -3.44 -12.68 -7.39 -11.25 -16.87 -11.77 -4.68 7.34 47 322 46 81 10.30 6.58 4.67 5.44 6.30 21.79 NOTE: Column 5 is column 3 multiplied by column * Source: Taylor (1991a). ** Source: Phylaktis and Taylor (1993). *** Source: Phylaktis and Taylor (1992). + Allowance made for foreign asset substitution. 4 divided Average Elasticity -1.61 -1.77 -1.39 -3.81 -2.78 -1.30 -0.48 -0.52 -0.91 -0.74 -1.02 by 100. Although the estimated values of CYdiffer quite widely across the countries, the implied average elasticities show a greater degree of homogeneity-ranging horn -3.81 to -0.48, with an average value of -1.48. It is also noteworthy that, with the exception of Taiwan, the rational expectations hypothesis is generally rejected in these other studies. This suggests that examining other expectations formation schemes in this context may be fruitful, and we examine below an alternative scheme suggested by Frenkel (1975, 1976) which is, in addition, capable of explaining the short-run positive correlation between real and nominal money holdings. In the meantime, however, we turn to the issue of foreign asset substitution during high inflation. 7. Foreign Asset Substitution During the hyperinflation of 1989, there is strong anecdotal evidence that the West German mark increasingly replaced the di466 Money Demand and Znflation in Yugoslavia, 1980-1989 nar in both commercial and personal transactions. I3 This would suggest that the expected rate of depreciation of the dinar relative to the mark should be an important determinant of the holdings of domestic money balances. Following Blejer’s (1978) analysis of highinflation Latin American countries, we assume that the expected rate of foreign inflation will also be a significant determinant of the expected return to holding foreign real and nominal assets. If we denote the return, in domestic terms, to holding foreign real and we have nominal assets as ft+l, then, to a close approximation ft+l = As,+1 + APL, > (9) where an asterisk denotes a foreign variable and s denotes the (natural logarithm of the) exchange rate (domestic price of foreign currency). Including the expected return to foreign asset holding as an additional explanatory variable of the domestic demand for real money balances in (l), we have Cm - PL = HAP;+,, + *f;+l which can be written + 5, , (10) in the form (m - ~1~ - aApt - Wi = ~A’P,+~ + SAfi+l + A,,, , (11) where h,+r is a linear combination of the disturbance term ct, errors made by agents in forecasting inflation and the return to holding foreign assets: At+l = 5t - 4Apt+, - AP;++) - S(L+l - f:+J . (12) From (11) and (12) it is clear that, if f is an I(1) process and, as before, forecasting errors are assumed to be stationary, then cointegration would be expected between current real money balances, current inflation and the current rate of return to holding foreign assets if (10) d oes indeed closely explain variation in the data. Furthermore, this would be expected to hold if substitution between domestic money and foreign assets is significant, regardless of the exact method used to form expectations, again subject only 130ECD 1990 467 Jacob A. Frenkel TABLE 5. and Mark P. Taylor Unit Root Tests for the Return to Holding Foreign Assets 71r 5 NOTE: See note -7.28 -7.46 to Table -3.88 -5.01 2.78 1.07 2. to the weak assumption that forecasting errors are stationary. A test of this model against the simpler Cagan model analyzed above can thus be made by testing for the significance of Aft in this cointegrating relationship (that is, testing the hypothesis 3 = 0 in [lo]). Table 5 contains results of unit root tests applied to the return to holding foreign assets, constructed according to (9), using the West German inflation rate and the exchange rate against the German mark (dinars per mark);r4 the time series for this variable does indeed appear to contain a single unit root in its autoregressive representation. The cointegration analysis of Equation (10) (Table 6) yields a point estimate of the semi-elasticity with respect to the foreign rate of return (6) which is of a plausible magnitude and of the correct sign, suggesting that substitution between domestic money and foreign real and nominal assets does to some extent explain the behavior of real money balances. However, the likelihood ratio statistic for the inclusion of the foreign return is statistically insignificant at the 5% level. Thus, although there is some evidence of the influence of the return to foreign asset holding on the level of real money balances, this effect appears to be dominated by the influence of the domestic rate of Yugoslav inflation.” One possibility for this finding, given the strong anecdotal evidence of currency substitution, is that this effect only became important during the final phases of the 1989 hyperinflation and thus is incapable of explaining “Data for the West German consumer price index was taken from the International Financial statistics data tape (IFS line 64); data on the German mark-U.S. dollar and Yugoslav dinar-U.S. dollar rates were also taken from this source (IFS line ae) and the dinar-mark rate constructed by assuming a triangular arbitrage condition. “It should be noted, however, that these statistical results may to some extent be confounded by collinearity between inflation and exchange rate depreciation. 468 TABLE 6. Cointegration Tests and Estimates Q1 Q2 43 12.70 (0.12) 12.71 (0.12) 14.55 (0.07) Including the Return to Holding Johansen Statistics Ho: r I 1 Ho: r = 0 Ho: r 5 2 0.43 13.71 53.66 Foreign B -35.94 Assets 4 -9.80 LR(6 = 0) 2.82 (0.09) NOTE: If r denotes the number of significant cointegrating vectors, then the Johansen statistics test the hypotheses of at most two, at most one and zero cointegrating vectors, respectively. A constant was included in the vector autoregressions. The 5% critical value for Ho: r 5 2 is 9.094, for H,: r 5 1 it is 20.168 and for H,: r = 0 it is 35.068 (Johansen and Juselius 1989). The likelihood ratio statistic for H,: 8 = 0 was constructed as in Johansen (1988) and is chi-square with one degree of freedom under the null hypothesis. A tenth-order vector autoregression with seasonal dummies was used. Q,, Qz, and Q3 denote Ljung-Box statistics applied to the residuals from the real money, inflation and return to mark holding regressions, respectively, computed at eighteen autocorrelations; they are distributed as chi-square with eight degrees of freedom under the null hypothesis of white noise residuals. Figures in parentheses denote marginal significance levels, Jacob A. Frenkel and Mark P. Taylor variation in the full data set which inflationary expectations. is not largely accounted for by 8. Explaining the Short-Run Behavior of Real Money Holdings A stylized fact concerning hyperinflations is that accelerations in the growth of money are followed, in the short run, by a rise in the level of real money balances. One possible rationalization of this phenomenon is that agents temporarily hold the extra money balances in a short-run “buffer”, which they later run off as they adjust their portfolios (Carr and Darby 1981; Cuthbertson and Taylor 1987a); thus, agents would be temporarily off the Cagan demand schedule. Another rationalization is that the rise in the growth of money balances leads agents to anticipate higher output so that, if the rise in output is immediate or if money demand is sufficiently forwardlooking (Cuthbertson and Taylor 1987c, 1990), there is a rise in the transactions demand for money. l6 In the extreme conditions of hyper-inflation, however, it seems unlikely that actual or anticipated variations in real output would be of a sufficient magnitude to explain the comparatively large swings in real and nominal money balances, and we do not pursue this argument further.” Frenkel (1975, 1976) proposes an alternative model of expectations formation which yields short-run behavior consistent with the evidence on short-run real money holdings and monetary growth whilst retaining the Cagan money demand schedule and the assumption that this demand function is always satisfied. Frenkel’s model might be termed an “adaptive-regressive” model of expectations formation since inflation expectations are postulated to adjust adaptively to current inflation but to regress towards an expected “normal” level of inflation. In this section, we analyze the buffer-stock and adaptive-regressive expectations rationalizations of the short-run behavior of real money holdings using the Yugoslav data. “To the extent that shocks to the money supply are unanticipated, it is possible that agents combine elements of forward-looking and buffer-stock behavior (Cuthbertson and Taylor 1989). “Variations in real output were of a very small magnitude during the 1980s. See, for example, OECD (1990) and earlier issues. 470 Money Demand and Znflation in Yugoslavia, 1980-1989 Adaptive-Regressive Expectations Here, we provide an analysis of the Frenkel model, adapted to discrete rather than continuous time. The model consists of the Cagan money demand schedule, (l), and the following relations: =t+1 - nt = r@pt - 4 > Y>O, AP:+, - AP; = VT - Apt) + P@P~ - AP;) > 03) s> p > 0) (14) where IT, denotes the expected average or normal rate of inflation at time t. Thus, (13) encapsulates the idea that agents revise their estimate of the normal rate of inflation only slowly and partially in response to deviations between this and the actual current rate of inflation. This, in fact, seems to correspond well to the case where inflation is a non-stationary process and thus has a constantly shifting mean. In (I4), which describes the evolution of inflationary expectations, the first term captures agents’ belief that if inflation was above the normal level in the immediate past, then it will be expected to regress back towards this level in the future. The second term in (14) is a standard adaptive component whereby agents adjust their expectations by a constant proportion of past forecast errors. The assumption that S > p is required to ensure that the model produces behavior consistent with the empirical evidence on the short-run effects of changes in monetary expansion. Using (l), (13) and (14) (an d assuming (Y < 0), we can establish the following: 0-c 2 t = [l - a(6 - p)]-’ < 1 ; aApt+ = -a[1 aAm, - cX(S- p)]-” [yS + p(s - p)] > 0 ; a7Ft+1 = $1 - a(S - p)]-’ > 0; aAm, dAPF+,, = -(S - p) [l - a(6 - @)I-’ < 0. aAm, (15) (16) (17) (18) 471 Jacob A. Frenkel and Mark P. Taylor Thus, (15) implies that an increase in the rate of growth of nominal money will induce a less than proportionate rise in the rate of inflation, thus allowing real money holdings initially to rise. Relations (17) and (18) sh ow that the short-run rise in inflation leads at the same time to an upward revision in the expected path of the price level-and thus the implicit normal rate of inflation-and a downward revision in the expected future short-run rate of inflation, thus ensuring that the real value of money holdings will continue to rise. Expression (16) demonstrates that, following the initial jump, inflation continues initially to accelerate. Using (l), (13) and (14) it is also straightforward to derive an error correction form describing the dynamic evolution of real money balances:r8 A(m - p), = ArA(m - p),ml + X2A2pt + A, (m - p - oAp),-, + 51+ a-1 + h55r-2 > (19) where Al = 0 - PM - Y) A2 = o(B - 6) A4 = (P + Y - 2) A5 = (1 - P)(l - Y). (20) In deriving (19) we have deliberately chosen a parameterization in which each of the variables will be I(0). By the Granger Representation Theorem (Engle and Granger 1987), the fact that such an error correction form exists implies that, in the adaptiveregressive Cagan model (ARCM), real money balances and current inflation are indeed cointegrated with a cointegrating parameter ‘*Error correction representations have proven to be a popular and relatively successful form of estimated money demand functions for a range of countries. See, for example, Gordon (MM), Boughton (1991) and the various money demand studies in Taylor (1991b). 472 Money Demand and Znf lation in Yugoslavia, 1980-1989 (normalized on real money holdings) equal to the semi-elasticity of money demand with respect to expected inflation.” Equation (19) can be contrasted with the error correction form resulting from the Cagan money demand schedule under the assumption of purely adaptive expectations. The purely adaptive model corresponds to setting y = 1 and 6 = 0 in (13) and (14),” yielding the error correction form Ah - dt = dh + Kh - P - c&)~-~ + L + ~~~~~~ , (21) where K2= Kg -p<o = (p - 1) (22) Expressions (19) through (22) thus suggest the following strategy. Equation (19) is estimated empirically and the restrictions Ho:X, = h5 = 0 tested. This constitutes a test of a null hypothesis which includes the Cagan model under adaptive expectations (ACM) against an alternative hypothesis which includes the Cagan model under adaptive-regressive expectations (ARCM).‘r The fit and general econometric performance of the estimated equations also provide an informal guide as to the adequacy of the underlying hypotheses. Estimation of Equations (19) and (21), by maximum likelihood techniques, using the Yugoslav data over the period January 1980 ‘%nce, as we demonstrated in Section 3, cointegration only follows from the Cagan model if forecasting errors are stationary and real money and inflation are Z(l), demonstrating the existence of the error correction form is equivalent to demonstrating the stationarity of forecasting errors generated by Frenkel’s adaptive regressive formulation when inflation is Z(1). 20Note that setting 6 = 0 in (15) yields (aApJ8AmJ > 1, so that in the Cagan model under adaptive expectations, a rise in nominal monetary growth leads to a fall in real money balances. “In principle, if the ACM is not rejected, then tests of the restrictions implied by (22) could be performed and would constitute a test specifically of the ACM; while if it is possible to reject the null hypothesis, then a test of the restrictions implied by (20) constitute a test specifically of the ARCM. In practice, however, estimation of ARMAX models with non-linear restrictions between the parameters is extremely difIlcult, and this was not undertaken. 473 ]acob A. Frenkel and Mark P. Taylor through December 1989, using the cointegration ble 3),22 yielded the following results? estimate of OL(Ta- A(m - p>t = 0.886 A(m - p),-r + 0.713 A2p, (0.071) (0.078) - 0.00472 (m - p + 21.96Ap),-, (0.0010) + it - 0.875 it-l + 0.788 it-2 (0.126) (0.126) R2 = 0.65, @a SER=3.1%. A(m - p)t = -0.341 A’p, - 0.00004 (m - p + 21.96Ap),-, (0.078) (0.0026) + it + 0.159 i,-I , (O.lW > R2 = 0.58, (24) SER = 3.4%. Where R2 denotes the coeffi$ent of determination, SER the standard error of the regression, ct the fitted residuals, and estimated standard errors are given in parentheses. A likelihood ratio test of the restrictions imposed in going from (23) to (24) yielded x”(2) = 22.66 , which has a marginal significance level of virtually zero, implying a very strong rejection of the ACM against the ARCM. Moreover, Equation (23) gives a reasonably good fit to the data and all of the estimated coefficients in that equation are of plausible signs and magnitudes and are statistically well determined. Using the first three coefficient estimates in (23) together with (20) implies a value for both R and y of approximately 0.06 and a =We can again appeal to the super-consistency property estimate to justify this procedure. e3A constant and seasonal dummies were also included but ficients are not reported. 474 of the their cointegration estimated coef- Money Demand and Inflation in Yugoslavia, 1980-1989 value of 6 of around 0.09.24 Although these values do imply quite slow speeds of adjustment, they are at least of the correct sign (positive) and satisfy the restriction 6 > l3, which is necessary in order for the ARCM model to explain the short-run behavior of money holdings following an increase in the growth of money. Overall, therefore, the Cagan model combined with Frenkel’s (1975, 1976) adaptive-regressive model of expectations formation appears to provide a reasonable explanation of the Yugoslav data for the period 1980-1989. Buffer-Stock Money The Carr-Darby (1981) formulation of the buffer-stock approach to money demand suggests that agents will willingly hold a proportion of unanticipated increases in the money supply in a shortrun “buffer,” which is later run off as portfolios are rebalanced (Cuthbertson and Taylor 1987a). Thus, unanticipated rises in the nominal money supply lead to short-run increases in real money holdings. Anticipated increases in the money supply, on the other hand, will be quickly reflected in the price level and so will leave real money holdings unchanged. In the present context, a reformulation of the Cagan demand schedule, (l), to incorporate bufferstock holdings would be Cm- PL = ~AP:+~+ 4m, - 4) + L , O<v<l. (25) Carr and Darby (1981) use an autoregressive equation for m, to obtain estimates of (m, - m?) as the fitted residuals-that is, they assume expectations are “weakly rational” (Feige and Pierce 1976). In the present context, since m, is an I(2) process,25 it would seem more appropriate to estimate an autoregressive representation These figures are approximate only, since they are subject to sampling errors. In developing a quadratic in p from the coefficient estimates in (23) and expressions for A, and A3 in (ZO), we have p” - 0.118728 This, in fact, has no real solutions. is sufficient to allow us to make = 0.018, then the equation has %Given that real money, (tn we have A(m - p)* - Z(0) which that is, m, - Z(2). + 0.00472 = 0 If, however, we assume that the sampling error the approximations (0.11872)’ = 0.014 = 4(0.00472) a unique solution of I3 = 0.059. - p),, and inflation, An,, are each Z(1) processes, implies Am, = Ap, + (Z(0) process) = (Z[l] process); 475 Jacob A. Frenkel and Mark P. Taylor for A2q and use (mt - rn?) = (A”% - A’rna in (25). Thus, a framework for testing the buffer-stock version of the Cagan model (BSCM) might be ” (m - P)~= crApt+i + Y A2m, - 2 i=l 87 A2m,-r + E, , (26) n A2m, = 2 61A2rn-1 + qt . (27) i=l Where l t = [ct .- o(Ap,+r - ApT+r)].” Carr and Darby (1981), by using the residuals from their autoregressive equation, implicitly impose cross-equation restrictions on their system. In the present context, this would amount to imposing the restrictions in (26) and (27). Cuthbertson and Taylor (1986, 1988), show that such cross-equation restrictions are often rejected for the bufferstock model. Accordingly, we follow the procedure suggested by Cuthbertson and Taylor (1986) and estimate the system (26)-(27) jointly, in order to allow the restrictions (28) to be tested rather than arbitrarily imposed (Mishkin 1983). At least two points are worth noting in this connection. First, the system (26), (27) requires certain identifying restrictions to be imposed before it can be estimated, in particular cov (et, qt) = 0. Second, the system (26), (27) m akes clear that the Carr-Darby bufkerstock model only makes sense if, at the aggregate level, (25) is interpreted as a price equation, since otherwise we would have two equations with only one dependent variable. It might still be argued, however, that individual agents attempt to set the level of their money holdings according to an equation such as (26) (Carr, Darby, and Thornton 1985). Examination of the time series for A2m, suggested that a second-order autoregression was an adequate univariate representation of the data in terms of generating adequate diagnostics and the statistical significance of the estimated coefficients. Joint estimation of (26)-(27) by full 1‘nf ormation maximum likelihood, using the coin“There seems no a priori reason to suppose that the inflation forecasting errors for period t + 1 and the money forecasting errors for period t are correlated. In fact, if forecasts of inflation are conditioned on past money, then although inflation and money forecasting errors may he contemporaneously correlated, current inflation expectations errors must be orthogonal to past money expectations errors. 476 Money Demand and Znflation in Yugoslavia, 1980-1989 tegration estimate of (Y (Table 3),27 with n = 2, and with (28) imposed, yielded. za (m - P)~ = -21.96 AP,+~ - 4.859 [A2mt - (-0.667 A2mt-1 (2.367) (0.082) + 0.471 A2m, -211 + 6 . (0.079) And a likelihood ratio test of the restrictions (29) (28) yielded x”(2) = 4.55 , which has a marginal significance level of 10.28%. However, although it is difficult to reject the cross-equation restrictions and although all of the estimated coefficients in (29) are statistically welldetermined, the estimated value of the buffer-stock coefficient, v in (26), is negative, implying that unanticipated money supply rises lead in the short run to a fall in real money holdings, contrary to the buffer-stock hypothesis and the observed short-run behavior of real money holdings. Thus, the buffer-stock approach fails to provide a convincing explanation of the data. 9. Concluding Remarks The research presented in this paper suggests that Cagan’s (1956) model of money demand under hyperinflation does indeed provide an adequate characterization of the salient features of the ir&tionary and monetary experiences of Yugoslavia during the 1980s. We also found some weak support for the hypothesis that the expected rate of return to holding West German assets was a significant determinant of domestic money holding. For the 1980s as a whole, however, this factor is dominated by the effect of domestic inflationary expectations. Further empirical analysis rejected the hypothesis that expectations were formed rationally or adaptively but gave some support to Frenkel’s (1975, 1976) adaptive-regressive model of expectations *‘This was necessary because Ap t+l is not exogenous to ensure stationarity of the dependent variable. We consistency result (Stock 1987). =A constant intercept term and seasonal dummies equation and their coefficients estimated freely. with respect again appeal were also to E,, and also to the super- included in each 477 Jacob A. Frenkel and Mark P. Taylor formation when coupled with the Cagan model. A major advantage of the adaptive-regressive framework is that it is capable of explaining the stylized fact that, during periods of high inflation, accelerations in nominal monetary growth tend to lead to short-run increases in real money holdings. 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