Yugoslav inflation unfolded as a classic wage-price-exchange rate spiral through the 1970s and 1980s, exploding into hyperinflation in the last quarter of 1989. Monetary accommodation of inflation, the behavior of demand for money, and the interaction between the two in Yugoslavia are examined. The asset-liability structure of the central bank, together with the policy stance on exchange and interest rates, led to a significant feedback from inflation to money supply. Despite their explosive and seasonal nature, real money balances were cointegrated with other economic variables, and hence, in long-run equilibrium relationship.


Yugoslav inflation unfolded as a classic wage-price-exchange rate spiral through the 1970s and 1980s, exploding into hyperinflation in the last quarter of 1989. Monetary accommodation of inflation, the behavior of demand for money, and the interaction between the two in Yugoslavia are examined. The asset-liability structure of the central bank, together with the policy stance on exchange and interest rates, led to a significant feedback from inflation to money supply. Despite their explosive and seasonal nature, real money balances were cointegrated with other economic variables, and hence, in long-run equilibrium relationship.

A widely accepted tenet of monetary theory is that persistent inflation, irrespective of its root cause, is a monetary phenomenon. This paper examines the process of monetary accommodation of inflation, the behavior of the demand for money, and the interaction between the two in Yugoslavia in the two decades prior to November 1989. A major conclusion is that the temptation to fine-tune should be resisted and that Yugoslavia needs a steady and tenacious monetary policy along with the structural measures that make it possible.

Yugoslav inflation, which was at double-digit levels throughout the 1970s and 1980s, unfolded as a classic wage-price-exchange rate spiral and exploded into hyperinflation in the last quarter of 1989. A stabilization program launched by the authorities on December 18, 1989 achieved quick successes, and inflation was brought down from above 50 percent a month at the end of 1989 to almost zero in the second quarter of 1990.1

In the economic literature, explanations of inflation run along two distinct, if sometimes intertwined, lines. The first, called “structuralist,” delves into the political economy of a country, its ownership structure, the efficiency of investment and industry, and competition between different groups.2 The second, termed “monetarist.” explains inflation in terms of the interaction between money and prices. Monetarists have been called “structuralists in a hurry,” because their explanation of monetary accommodation of inflation seldom goes beyond the proximate or mechanical determinants of money supply to elaborate the fundamental structural forces driving the process. Although this paper is more in the monetarist tradition, it is recognized that a full explanation of inflation has to address what lay behind the decisions by the monetary authorities to increase the money stock in order to accommodate inflation.3 However, such an explanation would go beyond the scope of this paper.4,5

Apart from examining the demand for money, this paper also investigates the proximate determinants of base money in Yugoslavia—that is, the supply of money. The asset-liability structure of the National Bank of Yugoslavia (NBY), especially the foreign currency liabilities to domestic banks and subsidized loans, complicated the conduct of monetary policy and, in an inflationary environment, led to large increases in high-powered money, thereby reinforcing inflation.

The plan of the paper is as follows. Section I describes some salient features of Yugoslav inflation and proximate determinants of base money growth. The seasonal properties and orders of integration of the variables relating to the demand for money are investigated in Section II. The demand for money in the long and the short run are estimated in Section III. Section IV analyzes some of the implications of the findings and draws conclusions. Appendices I and II contain econometric details.

I. Yugoslav Inflation and Base Money Creation

Consumer prices grew at an annual average rate of 38 percent between 1965 and 1988, while base money rose by 50 percent (Figure 1A).6,7 The annual average rate of retail price inflation increased from 12.5 percent in the 1960s to 17.5 percent in the 1970s and 75 percent in the 1980s (to 1988). There was also a deterioration in the external trade deficit, which was financed by workers' remittances, tourism earnings, and capital inflows from abroad until 1979. With the jump in the trade deficit from $3.8 billion in 1978 to $6.0 billion in 1979 (Figure 1B) and the emergence of financing difficulties, the focus of policies shifted in 1980 from accelerated development through increased investment and imports to external adjustment.8 The dinar was devalued by almost 30 percent in 1980, and throughout the 1980s there were successive devaluations in line with inflation, aimed at maintaining the real effective exchange rate at the new lower level. The average trade deficit in the 1980s was $700 million lower than in the 1970s, but growth faltered to an annual average of 0.7 percent from 6.1 percent in the previous decade, and the rate of inflation more than quadrupled.

The proximate determinants of base money growth and, hence, the mechanism through which inflation was accommodated are examined against this background. First, the linkages are examined in an inflationary context between base money growth, on the one hand, and reserve flows and external sector policy and public sector deficit, on the other. The last part of the section considers the appropriate definition of base money in Yugoslavia in the context of the specific characteristics of the asset and liability structure of the NBY.

Figure 1.

Inflation and Money: Key Indicators

Citation: IMF Staff Papers 1991, 003; 10.5089/9781451930801.024.A004

Source: International Financial Statistics, various years.a Foreign currency deposits as a percentage of M2.b GMP at current prices/average (M2).

Base Money Growth: Quantitative Overview

Base money is the main component of the liabilities of the central bank. Its assets consist mainly of credits to the private sector and banks, the government, and foreign assets (mostly foreign exchange reserves). It is therefore possible to describe the proximate determinants of the growth of base money in terms of the growth of central bank credit and foreign assets. The relevant factors for Yugoslavia are set out here.

From the balance sheet identity of the NBY:


the sources of base money growth can be described in terms of


where BM is base money liability, NCPB is net outstanding credit to the private sector and banks, NCG is net credit to the government, NFA is net foreign assets of the NBY, OI is other items (net), or the residual liability, Δxt, = xtxt − 1, and subscript t refers to year t. Table 1 presents the relevant Yugoslav data for the period 1965–88.9

Direct loans by the NBY to the nongovernment sector and commercial banks rose at an average annual rate of 36 percent and thereby contributed 21 percentage points to the overall average annual growth rate of 50 percent in base money. The corresponding average contributions of credit to government and of net foreign inflows to base money growth were 5 and −8 percentage points, respectively. As can be seen in the table, the growth of total credit and net foreign assets contributed less than 20 perentage points of the average growth in base money between 1965 and 1988, leaving 32 percentage points to be accounted for by movements in the residual.

The rapid growth in the residual item—other items (net)—in the NBYs balance sheet mainly reflects the heavy losses suffered by the bank. Consolidated losses are classified as other assets. They broadly correspond to the difference between consolidated liabilities and assets and provide a rough indicator of the negative net worth of the NBY. These losses arose mainly from the NBY's underwriting of the exchange losses on the foreign currency deposits held by the commercial banks at the NBY. In addition, the provision of cheap credit to the private sector and banks greatly reduced the NBY's revenues below their potential.

Table 1.

Yugoslavia: Inflation and Base Money Growth

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Note: All rates of growth refer to end of period.

Base Money and the External Sector

The analysis of the impact of the external sector on base money growth can start from changes in net foreign assets. Changes in net foreign assets occur because of both reserve flows and revaluation of past stocks when the exchange rate changes. Net foreign assets made a positive contribution to reserve money creation during 1965–78 because of reserve inflows, increasing from a net liability position of $80 million in 1965 to more than $1 billion in 1978. The adverse balance of payments development in 1979 reduced net foreign assets to a net liability position of almost $1 billion. Between 1979 and 1984 both reserve flows and revaluations had a contractionary impact on reserve money developments, while during 1984–88 the two affected base money in opposite directions. Although reserves flowed in and net foreign assets increased by almost $3 billion on this account between 1984 and 1988, the revaluation of past net foreign liabilities in domestic currency terms more than neutralized the positive impact of the reserve flows on base money. Over the whole 1965–88 period, reserve flows alone accounted for a relatively insignificant part of base money expansion (2 percentage points out of 50), whereas the revaluation effect accounted for -10 percentage points. The counterpart of this latter effect is a +10 percentage point component of the residual item attributable to the accumulated exchange losses as net foreign assets.

The relatively modest amount of reserve inflows until 1988, however, does not justify the conclusion that the external sector and relevant policy (especially exchange rate policy) did not have a significant effect on base money growth. It is necessary also to take account of the effects of changes in the exchange rate on base money itself, since base money in Yugoslavia includes not only a dinar component (H) consisting of currency in circulation and bank reserves (plus small amounts of other dinar liabilities), but also foreign currency liabilities of the NBY to resident commercial banks (FCLB):


where E is the exchange rate. The foreign currency component, E.FCLB, accounted for more than 80 percent of reserve money at end-1989.

The origin of the foreign currency component of base money in the NBY's balance sheet was the system, in force from 1978 to October 15, 1988, under which the NBY underwrote the exchange losses on the principal of foreign currency deposits redeposited by commercial banks with the NBY.10 Dinars, equivalent to the foreign currency redeposited at the prevailing exchange rate, were extended as NBY credit to the banks to augment liquidity in the domestic market.11 The credit was cheap to give the banks an incentive to mobilize these deposits.12 To avoid creating losses whenever the dinar was devalued, the NBY should have charged the banks an interest rate on such credits that exceeded the rate paid by the NBY to the banks on their foreign currency deposits. The failure to achieve ex post uncovered interest rate parity and the pursuit of international competitiveness through devaluations led to increases in the dinar value of the foreign currency component of base money without a corresponding offset through increased interest receipts on the dinar credit counterparts of such liabilities. On the asset side—that is, the right-hand side of equation (2)—the increase was reflected in the “residual” or “other items net,” as in Table 1, and contributed to the mounting losses and negative net worth of the NBY. The system of reserve requirements, which offered interest rates that were severely negative in real terms, provided only partial offset to the losses.

It could, of course, have been possible for the NBY to avoid this situation with countervailing measures while continuing with the policy of underwriting the exchange losses of redeposited foreign currency deposits. One way would have been to have raised interest rates on dinar credits to the banks as mentioned above. Another could have been to have made a regular transfer to the NBY from the public sector budgets. Either means would have avoided the impact on base money growth of the policies for foreign currency deposits and the exchange rate, though the former would have reduced the appeal of foreign currency deposits.

In the absence of these alternatives, the NBY was left with a situation in which exchange rate depreciation had a feedback effect on the available liquidity in the economy, which in turn accommodated inflation.13 In addition, the currency depreciation played its more familiar role of adding to import price rises.

Public Sector Deficit and Seigniorage

Traditionally, the existence of a public sector deficit has been a necessary condition for inflation in most models of price behavior (see Fischer and Easterly (1990, p. 138)).14 On first reading, Yugoslavia provides a rare example of an economy in which inflation was not associated with a sizable public sector deficit, monetized or otherwise. As will be shown, the deterioration of the NBY's net worth can be viewed as a deficit of the consolidated public sector, thus providing an explanation consistent with the fiscal view of inflation. It will also be shown why the NBY's net worth deteriorated while real resources continued to be captured through seigniorage.

The public sector in Yugoslavia has traditionally matched current expenditures by current revenues. Consequently, the contribution of the public sector deficit to money growth has been small.15 The NBY has had direct dealings only with the federal government and not with other segments of the public sector, and except for 1972, 1975, and 1987, NBY credit to the federal government accounted for only a marginal part of the growth in base money. As detailed in Table 1, on average, net credit to the government accounted for only 5 percentage points of the 50 percent nominal growth in base money a year between 1965 and 1988, and its contribution to base money growth remained marginal throughout the 1980s when inflation accelerated. The figures in Table 1, however, do not make a distinction between “dinar” and “foreign currency” components of base money—that is, H and E · FCLB, and are therefore not appropriate for isolating the importance of government finance in money printing in Yugoslavia during the reference period. Furthermore, Table 1 takes too narrow a view of the impact of the finances of the government—in the widest sense—on base money growth.

The analysis begins with a decomposition of the counterparts of seigniorage, ΔHt/Pt, in the NBY's balance sheet:


One can keep track of the evolution of real dinar base money, Δ(H/P)t, as a result of the interaction between seigniorage, ΔHt/Pt, and inflation tax, ΔPt/Pt(H/P)t − 1, with the familiar expression


For the years 1979–88, each of the components involved in equations (4) and (5) have been calculated on a monthly basis, and the yearly totals as percentages of gross material product (GMP) are presented in Table 2.

Table 2 shows that during 1979–88, on average, the NBY captured resources through seigniorage at the rate of 2.8 percent of GMP a year. These resources were made available to the private sector and banks in the form of loans at an annual rate of 4.4 percent of GMP, while loans to the government absorbed only a marginal 0.2 percent of GMP. Net foreign assets, other items net, and foreign currency components of base money changed at the rates of −3.7, −11.1, and 9.2 percent of GMP a year, respectively. Dinar base money in real terms decreased at the rate of 1 percent of GMP a year, while inflation tax accrued to the NBY at 3.8 percent of GMP a year.

Two important questions arise from the above analysis. First, given the government's limited need for financing, why did the NBY resort to high seigniorage? Second, with inflation tax accruing to the NBY at the rate of 3.8 percent of GMP a year and the conventional public sector in balance, why were the profits of the NBY not greater than they were after taking account of the exchange losses on foreign currency deposits?

Table 2.

Seigniorage and Its Uses

(As percent of gross material product)

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Note: The following identities hold: (1) = (2) + (3) + (4) − (5) − (6); (8) = (1) − (7).

The answers to both questions lie in the credit activities of the NBY. The expansion of credit to the private sector and banks needs to be seen in the context of an institutional setup where the NBY was committed to support socially owned enterprises and to pursue an activist policy with the aim of preventing systemic disruptions induced by liquidity problems.16 NBY credit to the private sector and banks more or less kept pace with inflation through the period. The credit was subsidized and the subsidy increased with inflation, because the nominal interest rate was not adjusted fully when inflation rose.17 Given this interest rate policy, the interest earned on these credits was insufficient to compensate for the erosion of their real value. The NBY's income from domestic lending was well below what it could have been with a proper interest rate policy.18 To put the point in terms of the inflation tax, the full revenue from this source was not obtained by the NBY because it was partly offset by an inflation subsidy on the NBY's assets.19

The apparent puzzle of the absence of any significant public sector deficit during the course of Yugoslav inflation is therefore resolved when the accumulating losses and deteriorating net worth of the NBY are taken into account. As already explained, these losses occurred because of the valuation effects on foreign currency deposits and the subsidization of credits to banks and the private sector. Although most inflationary episodes have traditionally been associated with substantial deficits in the public sector, in Yugoslavia the association was with the quasi-fiscal operations carried out by the central bank. The expansion of base money could have been avoided if revenues had been transferred from the budgets to meet the policy commitment. By their very nature, the quasi-fiscal operations are not always transparent and are difficult to gauge, but a significant characteristic of these operations is their departure from sound banking principles. The departures made by the NB Y from appropriate interest rate policy, both with regard to its foreign currency redeposit scheme and subsidized credits, argue in favor of regarding the losses of the NBY as part of the consolidated public sector deficit.20 Such a view leads to the resolution of the missing public sector deficit puzzle.21

Appropriate Definition of Base Money

As already noted, base money in Yugoslavia is defined to include foreign currency liabilities of the NBY to resident commercial banks (E · FCLB), which were the fastest growing component of base money between 1978 and 1989. The question is: is it appropriate to include this component in the definition of base money?

The concept of base money is primarily designed to explain the money stock from the supply side. Thus, the appropriate definition depends on the choice of the monetary aggregate. In a variety of countries the preferred choice of monetary aggregate is the one with the most stable and predictable velocity behavior.

In Yugoslavia, over the years, foreign currency deposits became very close substitutes for dinar liquidity.22,23 Prospects of devaluations induced economic agents to hold a growing proportion of their liquid resources in foreign currency deposits. Furthermore, as can be verified from Figure 1C, apprehensions about impending policy action periodically led to large shifts between the foreign currency and dinar components of liquidity holdings. Admittedly, the appropriate choice of the monetary aggregate is an empirical matter. As shown in the following sections, the fast spread of currency substitution led to difficulties in defining the demand for dinar liquidity independently of the demand for foreign currency-denominated liquid claims in Yugoslavia.24 Although the velocity of all monetary aggregates increased in Yugoslavia in response to accelerating inflation (see Figure 1D and 1E), the faster increase in the velocity of aggregates excluding foreign currency deposits raises serious doubts about the usefulness of the dinar money stock as an intermediate target of monetary policy. The difference in the seasonal unit root properties of monetary aggregates excluding foreign currency deposits and those of macroeconomic variables, such as prices and wages, confirms the limitations of defining the money stock without foreign currency deposits. The most appropriate definition of money stock for Yugoslavia is therefore M2, including foreign currency deposits; this money stock is satisfactorily explained from the supply side only when E · FCLB is included in the definition of base money.25 The results reported in this paper are in line with the findings of others that broad monetary aggregates often have better modeling qualities than narrower ones.26

When the exchange rate was not directly determined by the NBY, it had immediate leverage only over the dinar component (H) of base money, consisting of currency in circulation and bank reserves, and its operational policy had to be formulated in terms of dinar base money. Theoretically, given an inflation objective, it should have been possible to set the level of dinar base money on the basis of projections of the demand for total (dinar and foreign currency) liquidity and the expected path of the exchange rate and its impact on currency substitution. Projecting the demand for dinar liquidity in the face of a flight from dinars induced by volatile inflationary expectations and the relative superiority of foreign currency deposits, combined with the continuous increase in the dinar value of foreign currency deposits through devaluations, turned out to be fairly hazardous. The pursuit of a projected level of base money through periodic variations in the dinar component of base money, taking into account developments in the foreign currency component, would have been a safer operational strategy for monetary policy.

II. Money Demand: Some Preliminaries

Apart from the consideration of its fundamental role in the formulation and implementation of monetary policy, demand for money in Yugoslavia merits particular attention because of its suspected volatile behavior and sharp increases in velocity induced by inflationary expectations in a high-inflation environment.

In previous studies, on Yugoslavia, Tyson (1979) and Payne (1990) used quarterly and annual data to estimate demand for money by, respectively, enterprises and by the economy as a whole.27 Mihaljek (1989) analyzed demand for money by households during 1963–88 using a cash-in-advance optimizing framework and annual and monthly data. Bole and Gaspari (1991) used monthly data to estimate demand for money by households and business firms for the periods June 1986 to December 1987 and January 1988 to June 1989. This paper uses monthly data for June 1970 to November 1989—a 20-year period that includes, perhaps for the first time, the hyperinflationary episode. The use of a long data series reflects the view that Yugoslav inflation was a continuous process, beginning with an initial slow buildup in the 1970s, picking up momentum through the 1980s, and bursting out into galloping price rises in the last few months of 1989. Instead of building on the assumption that the demand function for money changed at the beginning of the high-inflation episode, the data are used to test the hypothesis that the onset of inflation was characterized by a structural break in the behavior of demand for money.

A priori, one may hypothesize that the demand for money in Yugoslavia may depend on retail prices, P, the relative rates of return on alternative assets, and a scale variable measuring income or transactions. Apart from the variable P. the deposit rate of interest, R, is included as an obvious argument in a demand for money function.28 The existence of foreign exchange deposits and the possibility of a large degree of currency substitution in Yugoslavia with a nominally depreciating currency during the sample period argue for the inclusion of the exchange rate (X, in terms of dinar per U.S. dollar) as a relevant rate of return variable in the demand for money function.29 The official rate was used instead of the parallel market rate, because data on the parallel rate were not available. Also, the official rate was used to translate foreign currency deposits into dinar terms. Therefore, insofar as foreign currency deposits and not “money under the mattress” are included in the monetary aggregate analyzed in this paper, the official rate may be more relevant.

Tyson (1979) and Bole and Gaspari (1991), while analyzing demand for money by enterprises, used enterprise transactions or sales as the scale variable. The scale variable chosen by Bole and Gaspari (1991) for explaining demand for money by households was pretax income including wages, transfers, subsidies, and pensions. Because the focus of this paper is on aggregate demand for money, both the nominal monthly wage rate, W, and industrial production, Y, have been included as scale variables.30 In light of the evidence in Bole and Gaspari (1991) that households had a higher propensity to demand money relative to enterprises, inclusion of W simultaneously with Y should capture any change in demand brought about by a wage-induced change in the distribution of income between labor and enterprises.

Four alternative definitions have been considered for the money stock: narrow (M1); broad with the valuation effect (M2); broad without the valuation effect (M2(-V)); and broad dinar money (D). Although the importance of both M1 and M2 is evident, M2(-V) and D were also considered because of the crucial role they played in the formulation of monetary targeting in Yugoslavia. The stock of foreign currency deposits, or at least past stocks of it. was considered a store of value that was immutable in the short run. Accordingly, monetary targeting was often formulated in terms of M2(-V) or D, which is M2 adjusted partially or fully for foreign currency deposits.31

For the purposes of the present analysis, the real rate of interest on deposits was derived as follows: first, the nominal rate, R, which is reported in an annualized form, was used to derive the corresponding monthly rate; second, this monthly rate was adjusted for contemporaneous inflation. Thus, r* is defined as


The two defining characteristics of the variables for Yugoslavia for the period under observation are their pronounced seasonal patterns and dominant trends. To alleviate the problem of trend, all variables have been transformed into logarithmic form and lowercase letters have been used to indicate logarithms of corresponding uppercase variables.

A purely deterministic trend or seasonality does not complicate the problems of statistical inference as much as unit roots do in the time-series behavior of variables.32 The problem of statistical inference in the presence of unit roots has generated a growing literature on cointegration (see, for example, Granger (1986), Hendry (1986). and Engle and Granger (1987)). More recently, Hylleberg and others (1990), Beaulieu and Miron (1990), and Lee (1990) have investigated the problems associated with seasonal unit roots. One of the important implications of the recent literature is that if two series do not have unit roots at corresponding frequencies, they cannot be “fully” cointegrated, ruling out the possibility of a long-run relationship between them in the sense of finding a linear combination of the two that is stationary. Hence, in what follows, the possibility of the existence of seasonal unit roots in the variables is investigated. Then the series is examined for multiplicity of unit roots or order of integration.33

Testing for Seasonal Unit Roots

Following Hylleberg and others (1990), for monthly data a general class of linear time-series models that exhibit potentially complex forms of seasonality can be written as


where Sjt's are monthly dummy variables, t is trend, ϕ(B) is a polynomial in the backward-shift operator B with the property Bj ωt = ωtj, and ϵ is a white-noise process. If θ is a root of the characteristic polynomial, ϕ(·), the frequency associated with it is the value of α in eαi, the polar representation of θ. For monthly data, a root will be seasonal if α = 2πj/ = 1, 2, …., 11. Furthermore, as shown by Beaulieu and Miron (1990), for such data the seasonal unit roots are


with these roots corresponding to 6, 3, 9, 8, 4, 2, 10, 7, 5, 1, and 11 cycles a year, respectively. If the ωt process has a unit root at a particular seasonal frequency, then it is said to be integrated at the same frequency.

Hylleberg and others (1990) developed procedures for testing whether a process is integrated at only some, not necessarily all, of the seasonal frequencies. The details of the methodology and the finite sample critical values of the associated test statistics provided by Hylleberg and others, however, were restricted to the case of quarterly data. Beaulieu and Miron (1990) presented the corresponding results for the case of monthly data. A brief summary of the Beaulieu and Miron test procedure is presented in Appendix I. The evidence on all variables, except m1, m2(-v), and d, strongly rejects the hypothesis of a unit root at any seasonal frequency other than zero.34,35

Narrowly defined money, m1, valuation-adjusted money. m2(-v), and dinar money, d, displayed some fairly complicated patterns of stochastic seasonality. The existence of unit roots could not be rejected at frequencies π/2 and 2π/3, which correspond to 3 and 9, and 8 and 4 cycles a year, for m1. Similarly, there is evidence that m2(-v) and d have unit roots at frequencies zero and 5π/6. The existence of unit roots at frequencies other than zero in m1, /m2(-v), and d rules out the possibility of full cointegration between any of these three variables, on the one hand, and p, w, x, r*, and y, on the other, and has two interesting interpretations. First, over the years, foreign currency deposits became a dominant component of liquid assets in Yugoslavia, and perhaps exclusion of their total impact in any form from the monetary aggregate leads to an artificial concept that does not correlate in the long run with variables such as prices, wages, and income.36 The existence of an elaborate system, with additional variables and properly defined constraints, that allows for the estimation of separate demand functions for domestic and foreign currencies and deposits has not been ruled out by this investigation. The evidence from the available data, however, does not indicate any obvious representation of such functions. Second, m1, m2(-v), and d have close relationships with dinar base money. In Yugoslavia monetary policy has often been carried out by expanding dinar base money, through NBY credit to agriculture, exporters, and banks, based on a simple rule, such as so many percents over some past period. Pursuit of such a rule tends to perpetuate the effect of a random shock on dinar base money, and, hence, on m1, m2(-v), and d, and changes their seasonal patterns forever.

With the finding that m2, p, w, x, r*, and y do not have unit roots at different seasonal frequencies, a necessary condition for the existence of full cointegration or an equilibrium relationship among the variables is satisfied. In the next subsection, the order of integration of the variables is tested for—that is, the multiplicity of unit roots at frequency zero—in order to find the degree of differencing required to reduce each variable to stationarity.

Testing for Order of Integration

To test for the order of integration for any variable z, augmented Dickey-Fuller (ADF) tests are carried out. Appendix II contains the test procedure followed and the detailed findings.

The order of integration was tested for m2, p, w, x, and y, as well as real balance. m2p, the real wage, wp, the “real exchange rate,” xp,37 and the (ex post) real rate of interest per month on deposits, r*.

As shown in Appendix II, the variables fall into two separate groups: (i) m2, p, w, and x are I(2); and (ii) y, m2p, wp, xp, and r* are I(1). The highly integrated nature of the variables should not be surprising, in view of the policies pursued in Yugoslavia. A simple three-equation model of the money market can be used to give a stylized representation to the structure of the variable. Consider38


as a three-equation system incorporating the dependence of money demand on expected inflation and money supply on past inflation.39

Taking logarithms and approximating log(1 + z) by z, one obtains from equations (7)(9)




which can be solved to yield


Furthermore, if it is assumed that yt is I(1)—that is


where μt is a white-noise process and monetary policy is sufficiently responsive to inflation with b = 1, one obtains


which implies a price path integrated of order two. It is easy to verify that m is also I(2). The high response of money supply to inflation—that is, a value of b close to unity—is the primary reason for the high order of integration of the variables.

III. Demand for Money in the Long and the Short Run

The demand for money in Yugoslavia is estimated in two stages: the first stage consists of a test for cointegration and a search for a long-run relationship among the variables m2 p, w, x, r*, and y; in the second stage, a dynamic equation is estimated to explain the short-run behavior of the demand for money.40 The question of stability of the estimated relationship and the dynamic multipliers associated with inflation, the real wage, the real exchange, and the real interest rate is taken up at the end of the section.

Testing for Cointegration

Cointegration of variables with different orders of integration has to be tested in multiple stages.41 First, variables with the highest speed have to be tested for their cointegration property through an examination of the residual, μ, from the cointegrating relationship. If μ is integrated of a lower order than the variables themselves, then the variables at the first step can be considered to be cointegrated. In the second stage, μ has to be tested for cointegration with the variables of the next lower order of integration, and so on until the lowest order is reached.

Accordingly, since m2, p, w, and x are I(2) variables with the highest speed of all. a static regression was run with m2 as the left-hand-side variable. ADF tests on the residual of this regression and the critical values for such tests provided by Engle and Yoo (1987) suggested the strong likelihood of the residual being I(1) rather than I(2).

Given that Δp, y, and r* are I(1), the next step was to determine whether the residual from the first step was cointegrated with these three variables.42 A regression was run with the residual of the first stage on the left-hand side, and Δp, y, and r* on the right-hand side. Values of ADF test statistics for the residual of the second stage again suggested the likelihood of its being 7(0) rather than I(1).

Having proved the cointegrating properties of m1, p, w, x, Δp, y, and r* sequentially as above, a static regression of 2 was estimated on all the other variables simultaneously, to obtain


The ADF test statistic for testing unit roots in the residual ¯u; indicated the existence of no such roots. Note that the coefficients of p. w, and x add up to 0.992, which conforms to the earlier finding that m2, w. and x are individually cointegrated with p with cointegrating vector (1, -1), and suggests the estimation of


The cointegration technique was first developed to make the concept of long-run equilibrium operational, and so equation (18) may be thought of as a description of the long-run relationship resulting from the interaction between money demand and supply. However, the accordance of the estimated parameters with priors on money demand elasticities and the history of large discretionary changes in monetary policy implicit in Table 1 suggest that equation (18) should be interpreted as a money demand equation.

The estimated relationship involves only I(1) variables and has interesting properties. First, it is homogeneous of degree zero in levels of nominal variables. Second, an increase in the real wage increases the demand for real balances for reasons already discussed above, while an increase in the real exchange rate (a real devaluation) decreases it. It appears that the decrease in the demand for real dinar balances exceeds the increase in the demand for foreign currency deposits following a real devaluation and results in a net decrease in the demand for real balances.43 Third, the semi-elasticity of demand for real balance with respect to inflation is -0.65.44 It is important to note that a mechanical inversion of this semi-elasticity to derive the rate of inflation that maximizes revenue from the inflation tax is inappropriate, because much of M2 consisted of foreign currency deposits, which, with the pursuit of the real exchange rate rule, were virtually indexed to inflation and yielded no inflation tax. It is a well-known property of inflation to increase the velocity of money and to accommodate itself in part. In Yugoslavia, according to equation (18), almost four fifths of the inflation was accommodated by the resulting increase in velocity of money. Fourth, the elasticity of real balance with respect to the index of industrial production is 0.7. This estimate, as a proxy for income elasticity of demand for real balances, indicates that liquidity was not a luxury good in Yugoslavia with its history of high and volatile inflation.45 Fifth, demand for real balances goes down by -0.15 percent for every 1 percent increase in the real rate of interest on deposits. It appears that the decrease in demand for the non-interest-bearing component of M2 exceeds the increase in demand for the interest-bearing component in response to an increase in the real rate of interest and results in a slight decrease in aggregate demand for money.

The Dynamics

The dynamics of demand for real balances is specified as an error-correction model:


where ̂u′ is the residual from equation (18).46 Note that all the variables in the equation are I(0). A simplification search was conducted, and in the process these hypotheses could not be rejected:


by standard F-tests.47 The estimated equation is given by


where Δ2ptpt−Δpt−1 is the acceleration in the rate of inflation over the last two months, and Δ3(w − p)t = (w − p)t − (w − p)t-3 is the rate of growth of real wage during the last quarter. Equation (20) is interpreted as the short-run demand for real balances. Note that a significant feedback mechanism is captured by the coefficient of u^t1 the rate of growth of real balances is sensitive to the departure of real balances from their equilibrium value in the preceding month, and real balances change over time to adjust to their equilibrium long-run value.

By explaining 65 percent of the variation in the acceleration of the rate of growth of real balances, equation (20) does a satisfactory job of modeling the short-run demand for real balances. The complicated dynamics reflect, perhaps, the inherent problem of modeling dynamic behavior in a situation of highly volatile inflation and discrete policy shifts.


Typically, for analyzing the behavior of demand for money during high inflation, a demand function is estimated only for the period of high inflation as in the study by Bole and Gaspari (1991). This approach is equivalent to assuming a structural change in the behavior of demand for money at the onset of high inflation. The estimated money demand function reported in this paper maintains the assumption that there was no structural break in liquidity preference in Yugoslavia over the 20-year period (June 1970 to November 1989), during which inflation accelerated from 1–3 percent a month to over 50 percent a month. The validity of this assumption was examined by tests of stability.

The residual from a cointegrating relationship is required to be of a lower order of integration than that of the variables involved in the relationship. Any instability in the relationship characterized by systemic departures of the coefficient of one or more variables in a subsample results in a contribution to the residual of a term with the same order of integration as the variables themselves. Thus, there cannot be cointegration if there is a structural break in the relationship. The acceptance of the cointegration property of equation (18) is equivalent to the acceptance of stability in the long-run behavior of demand for real balances. Hence, the analysis concentrated on testing the stability properties of the short-run demand for real balances—that is, equation (20)—through recursive regressions.

Starting with an initial set of regression estimates based on data for September 1970 to February 1973, subsequent observations for the period March 1973 to November 1989 were added one at a time to obtain the recursive error terms and point estimates of the parameters. Figure 2 depicts the sequence of estimated standard errors of the equation and one-step-ahead forecast errors. In the absence of any structural break, the forecast errors should be close to zero, and 95 percent of such errors should lie within the band delineated by two estimated standard errors. As can be seen from Figure 2. the confidence band is penetrated only 15 times in 201 months, and 92.5 percent of the recursive residuals lie within the confidence band. There is no indication of any major instability problem in the behavior of demand for real M2 balances in Yugoslavia, especially when the history of incessant price “freezes and unfreezes” is taken into account.4849

Figure 2.
Figure 2.

Stability of Money Demand

Citation: IMF Staff Papers 1991, 003; 10.5089/9781451930801.024.A004

Dynamic Multipliers

Figure 3 portrays the dynamic multipliers associated with inflation, the real wage, the real exchange rate, and the real interest rate. As can be verified from the diagram, convergence to the final multiplier is neither monotonic nor fast. For example, in response to a permanent 1 percent increase in the inflation rate, real balances decline by more than 1 percent in the first three months and then slowly increase over time, settling down in the long run at a level 0.8 percent lower than that prevailing before the inflationary shock. The nature of the dynamic response of real balances to exogenous shocks underscores Friedman's warning about “the long and variable lags” associated with monetary adjustment and the need for caution in interpreting the short-run response of real balances.

IV. Some Policy Implications and Conclusions

As demonstrated here, the asset-liability structure of the NBY, together with the policy stance on exchange and interest rates, led to inflation with large concomitant increases in base money, specifically since 1980. Real money balances were also shown to be cointegrated with the relevant economic variables, despite their highly explosive and seasonal nature, and in long-run equilibrium relationship, as economic theory would suggest.

Over the long haul, money growth is a necessary condition for sustained inflation, and inflation itself sometimes leads to increases in the velocity of money and money supply. In Yugoslavia inflation generated considerable increases in the velocity of money, and such increases accommodated 80 percent of the inflation. The NBY's commitment to support economic activity through the prevention of systemic disruptions caused by liquidity problems and the existence of foreign currency deposits and successive devaluations in the absence of supporting policies produced a significant feedback from inflation to money supply. The simultaneous increases in the velocity of money and money supply induced by inflation perpetuated and accelerated inflation in Yugoslavia.

The money supply accommodated inflation through the NBY's effort to maintain credit growth in line with inflation. Furthermore, the interest rate policy of the NBY both with regard to selective credit and the foreign currency redeposit scheme was inappropriate, leading to losses and a deteriorating net worth. These losses were exacerbated by the NBY's underwriting of exchange losses on commercial banks' foreign currency redeposits in the face of repeated devaluations during the 1980s.

Figure 3.
Figure 3.

Dynamic Response of Real Balances

Citation: IMF Staff Papers 1991, 003; 10.5089/9781451930801.024.A004

a Real rate of interest held constant.

These losses can be seen as part of the consolidated public sector deficit on an accrued basis, and this mounting deficit generated excessive money growth. In its formulation of monetary policy, the NBY took the view that the losses, being “accrued.” and not “realized,” were not relevant, The obvious political advantage of this argument was that it left more room for domestic credit and discretionary monetary expansion. With hindsight, however, it appears that the NBY overestimated the lags with which accrued losses exert pressure on monetization.

Foreign currency deposits over the years became the dominant component of liquid assets in Yugoslavia. Monetary targeting was variously formulated in terms of narrow money (Ml), broad money without the valuation effect (M2(—V)), or dinar money (D). These aggregates either partially or fully excluded the dinar value of foreign currency deposits. On a priori grounds it is difficult to argue for or against the inclusion of a particular variable in the monetary target. It appears, however, that over the years foreign currency deposits became an integral part of the liquidity stock in Yugoslavia and were extremely close substitutes for dinar money. The prospect of devaluation induced economic agents to hold increasing proportions of their liquidity in foreign currency deposits, while devaluation per se directly increased the dinar equivalent of foreign currency deposits. The increased money supply measured in dinars, together with diminished demand for dinars, sustained the Yugoslav inflationary process. The seasonal unit root properties of Ml, M2(-V), and D, which are found to have been out of line with other variables in the economy such as wages, prices, and the exchange rate, confirm the inappropriateness of formulating monetary targets that exclude foreign currency deposits. Does all this imply that the introduction of foreign currency deposits in Yugoslavia was a mistake to begin with? It is fair to say that in the absence of other policy corrections and structural reform, Yugoslavia would have been in difficulty, with or without foreign currency deposits. Without them, capital flight would have been higher and savings lower: with them, inflation had a direct and robust feedback effect on the available liquidity in the economy.50

M2 was found to be cointegrated with prices, wages, the exchange rate, inflation, the index of industrial production, and the real rate of interest, permitting the estimation of a long-run relationship for the demand for real balances with standard properties. The short-run dynamics, however, proved to be predictable but complicated. The convergence of real balances to equilibrium in response to a shock in exogenous variables was far from rapid or monotonic. Thus, the temptation to fine-tune should be resisted, and the best policy for Yugoslavia appears to be to pursue a steady and tenacious monetary policy without any effort to accommodate or neutralize short-run fluctuations. This will require interest rates closely in line with those prevailing in international markets and an exchange rate policy that avoids a continuously rising dinar value of foreign currency deposits.

Needless to say. the feasibility of pursuing such a robust policy opens up the “whys” of monetary policy and points to the necessity of addressing structural issues. A comprehensive explanation of Yugoslav inflation has to go beyond simply delineating how a steady supply of liquidity sustained the inflationary process. It first has to find out why inflation started in the first place and why monetary policy accommodated inflation, and then address the fundamental structural forces driving the process.


Testing for Seasonal Unit Roots in Monthly Data

For monthly data, the Beaulieu and Miron (1990) test procedure consists of estimating


where t is trend, Ss–s are seasonal dummies, and51


According to Beaulieu and Miron (p. 5): “for frequencies 0 and π, one simply examines the relevant t-statistic. For the other roots, one tests πk = 0. where k is even, with a two-sided test. If one fails to reject, then one tests πk-1 = 0. Another strategy is to test πk-1 = πk = 0 by calculating an F-statistic.” The relevant critical values are contained in Beaulieu and Miron (1990). In this paper. the order of lag for the dependent variable has been chosen to minimize the Schwartz information criterion (SC), The relevant estimates, along with t-values and F-statistics for m2 m2(-v), d,p, w, x, r*, and y, are reported in Table 3.

The evidence on all variables except m1, m2v), and d strongly rejects the hypothesis of a unit root at any seasonal frequency other than zero. However, for m1,. apart from at frequency zero, the existence of unit roots cannot be rejected at frequencies π/2 and 2π/3, which correspond to 3 and 9, and 8 and 4 cycles a year. Similarly, there is evidence that m2(-v) and d have unit roots at frequencies zero and 5π/6.52

Table 3.

Money Demand in Yugoslavia: Testing for Seasonal Unit Roots with Constam, Trend, and Seasonal Dummies

article image
Note: For all variables, the sample period ends in November 1989; for m1p, and w, it begins July 1971; for d and m2(-v), it begins January 1981; and for m2, x, r*. and y, it begins June 1971, Sample periods vary for m1, m1, p, w, x, r*, and y, depending on whether the value of “q” in equation (21) maximizing SC is 0 or 1; (*) indicates significance at 10 percent; (**), at 5 percent; (***), at 2.5 percent; and (****), at 1 percent level of significance.


Testing for Order of Integration

For any variable z, to test for the order of integration, the augmented Dickey-Fuller (ADF) tests are carried out. whereby


and the following regressions are set up:


For testing the hypothesis that zt has j unit roots at frequency zero—that is, zt is I(j)—against the alternative hypothesis that zt is I(j-1), Ho: β = 0 is tested against H1: β < 0. For each variable the test was carried out for j = 1,2, and 3 under three alternative specifications:


The tests can be carried out by estimating equation (23) and comparing t-values of β with critical values provided by Fuller (1976).53 The relevant t-statistics are reported in Table 4.54

The variables fall into two separate categories: m2, p. w, and x are I(2); and y, m2p, wp, xp. and r* are I(1) variables.

Table 4.

Money Demand in Yugoslavia: Testing for Order of Integration and Augmented Dickey-Fuller Test Statistics

article image
Note: (*) indicates significance at 10 percent; (**) at 5 percent; (****) at 2.5 percent; and (****) at 1 percent level of significance. For all variables, the sample period ends in November 1989. For the hypothesis of I(1). the sample begins in September 1971, except for m2 and m2p. for which it starts from February 1972; and r*, for which it starts from October 1971. One observation at the beginning of the sample is lost when moving from the test of hypothesis Z ~ I(j) to Z ~ I(j + 1).


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Ashok Kumar Lahiri, an Economist in the European Department, is a graduate of Calcutta University, and the Delhi School of Economics, University of Delhi. The author thanks Devjyoti Ghosh, Daniel Hardy, Leif Hansen, Mohsin Khan, Hahn Shik Lee, John Odling-Smee, Hans Schmitt, Jan van Houten, and Harilaos Vittas for comments and suggestions, and Mirko Novaković for valuable research assistance.


Growing policy slippages led to a renewed buildup of inflationary pressure in Yugoslavia since midsummer of 1990.


The possible inflationary bias of Yugoslav socialism under workers' self-management has been the subject of a lively discussion along structuralist lines. See, for example, Mates (1987), Mencinger (1987), and Bradley and Smith (1988).


Chowdhury, Grubaugh, and Stollar (1990) found that money supply in Yugoslavia was endogenous between 1964 and 1986. There is similar evidence on how inflation itself caused money to grow in many other countries. For the European experience, see Sargent and Wallace (1973); for Brazil and Chile, see Hanson (1980); for Indonesia, Aghevli and Khan (1977); and for Israel, Brezis, Leiderman, and Melnick (1983).


For a survey of theoretical developments explaining central bank behavior, see Cukierman (1986).


As a possible reason for passivity of money supply in Yugoslavia, Tyson (1979) has argued that in the absence of severe sanctions for payment defaults, enterprises deliberately generated liquidity crises and payments defaults to obtain fixed interest short-term credit with a high subsidy element in an inflationary environment. Coupled with a policy commitment to avoid disruptions in economic activity, this led to money supply increasing with inflation.


Although base money grew faster than prices between 1965 and 1988 and resulted in an overall increase in real base money, there was a dramatic difference in the relative behavior of the two series before and after 1980 (see Figure 1D).


All the data used in this study were taken from the International Monetary Fund's International Financial Statistics (IFS), except for data on deposit rate of interest prior to December 1984 and foreign currency deposits, which came from the Yugoslav Bankers' Association. I am grateful to Mr. Petrović of the NBY for making these data available to me.


The external environment deteriorated sharply in 1979 following the oil price shock and the increase in interest rates in world financial markets.


The survey begins with 1965, because the method of collecting data on components of hase money was revised in that year. For the analyses of base money growth in Table 1, annual data were used, because monthly data would have added little apart from complicating the exercise.


Foreign currency deposits were first introduced in Yugoslavia in 1963 to attract emigrants' savings and residents' transfers from abroad into the domestic banking system and to ease the availability of foreign exchange.


Instead of offering the redeposit facility along with dinar credit, the NBY could have made an outright purchase of the foreign currency from the banks. In this case, however, insofar as the exchange risk associated with foreign currency deposits would have rested with the commercial banks, the banks would have had an incentive to increase the dinar lending rates appropriately and thereby restrain monetary expansion.


The NBY credits were called “interest-free credit,” since in the period until April 1, 1985, no interest was paid by commercial banks on their dinar liabilities. As a reciprocal arrangement, the NBY also did not pay any interest on foreign currency deposits. Although banks and the NBY started paying interest on their corresponding liabilities from April 1, 1985 and August 1, 1986. respectively, interest rate parity was never maintained in the ex post sense.


It is well known that in the long run the authorities can set either the nominal exchange rate or the money supply independently but not both. Furthermore, as shown by Adams and Gros (1986), the pursuit of a target real exchange rate by devaluation in line with inflation leads to unstable prices at worst and, in the long run, lack of monetary control over the inflationary process at best. In an economy integrated with world financial markets, the long-run result extends to the short run through capital flows in the balance of payments. In such an economy, any tightening of domestic credit only leads to an acceleration of such flows. Given the restrictions on external capital transactions in Yugoslavia, however, it appears that there was considerable scope for pursuing an independent anti-inflationary monetary policy in the short run simultaneously with a real exchange rate rule. In this paper it is argued that the existence of foreign currency deposits and the NBYs policies toward these deposits circumscribed the scope for pursuing such an independent monetary policy.


In these models (see, for example, Sargent and Wallace (1973)), financing of the deficit by seigniorage—that is, printing money—leads to inflation, which in turn generates an inflation tax on the public's holding of base money at a rate equal to the rate of inflation. En the absence of foreign inflows or direct credit to the private sector by the central bank, seigniorage equals the monetized public sector deficit. With the public sector deficit constant in real terms, the economy converges to the steady state, with inflation tax equal to seigniorage, leaving the real stock of base money unchanged.


The Yugoslav public sector consists of two types of communities: the sociopolitical communities at the federal, republican, provincial, municipal, and communal levels catering to traditional governmental duties; and the self-managing communities of interest looking after health care, education, child care, pensions, and so on.


For Israel during the 1970s, similar evidence has been found by Litvin, Meridor, and Spivak (1988).


During the hyperinflation in the early 1920s in Austria, Hungary, and Germany, the central banks in these countries made loans and discounts to private agents at very low nominal interest rates. These loans amounted virtually to government transfer payments to the recipients of the loans; see Sargent (1982).


Also note that credit repayments depend on the subsidy element of loans, and as the subsidy element increases, larger monetary injections are necessary to keep the flow of new credit unchanged.


The conventional measure of inflation tax, as reported in Table 2, has obvious limitations in the Yugoslav context. The conventional measure is appropriate only when there is no inflation-induced change in the real rate of interest that applies on the central bank's assets and liabilities apart from base money. Given the NBY's interest rate policy and, hence, the large reduction brought about by inflation in the real rate of interest that it earned on credits to banks and the private sector, only an increase in real fiscal tax revenue could have kept the consolidated public sector revenue constant in real terms with accelerating inflation, In that sense, it could be argued that the NBY did not get an inflation tax from explosive prices, but, rather, it paid an inflation subsidy.


Before launching the stabilization program in December 1989, the Federal Government of Yugoslavia took over the accumulated valuation losses of the NBY as its own public debt. See Mates (1991) for a discussion of the parafiscal operations of the NBY.


Apart from introducing greater transparency, this approach also clarifies the policy choices involved in reducing subsidies and identifying alternative fiscal sources of financing the subsidies. Whether such a consolidation would have led to a change in policies is difficult to speculate in the absence of a comprehensive analysis of the constraints facing the policymaker.


No data exist on foreign notes and coins held by the public in Yugoslavia during the reference period. Such “money under mattresses” is not captured in the measure of foreign currency-denominated liquid claims used in this paper.


Dinars and foreign currency assets may be complements as well, for instance, as a result of a cash-in-advance constraint in a setup with illegal goods markets, where both currencies are used in transactions. In Yugoslavia, however, the substitution effect appears to have dominated the complementary effect.


It may be argued that Yugoslav inflation is in terms of dinars and, hence, the focus of attention should he dinar money. Such reasoning is not correct when close substitutes exist for dinar liquidity. The existence of such substitutes can lead to a highly unstable relationship between dinar liquidity and inflation.


Note that E · FCLB is different from other components of base money insofar as the former cannot be used to support a multiple expansion of credit and deposits: that is, the multiplier is unity. With the growing importance of foreign currency deposits in M2, the money multiplier, defined as M2/BM, does display a tendency to converge to unity during the sample period.


For example. Kremers and Lane (1990) have found that the aggregate monetary demand equation for the countries participating in the exchange rate mechanism of the European Monetary System compares favorably with individual country equations.


Tyson's (1979) period of observation was 1961:4 to 1971:4; Payne's (1990) was 1952–85. Although neither study included the period when inflation accelerated the most, both authors estimated a significant negative impact of inflation on money demand.


Because nominal interest rates were controlled and relatively stable during the sample period, the variable R is not a good indicator of the relative tightness of the money market, which led Tyson (1979) to use the rate of growth of base money as a proxy for the rate of return variable in the demand for money by enterprises. However, since R is the only choice for return on interest-earning money substitutes in Yugoslavia, and it is not desirable to introduce money supply as an explanatory variable in money demand, R is returned here as an explanatory variable.


Bole and Gaspari (1991) used a synthetic single measure of the opportunity cost of holding money constructed from the rates of inflation and currency depreciation. They estimated the structural parameter of a “coefficient of dollarization,” which measured the relative importance of currency substitution. No attempt is made in this paper to retrieve this coefficient.


Barring some seasonal fluctuations, employment grew at almost a constant rate during the sample period, and variations in the growth of the wage rate were the main source of variations in total wage income. Because of lack of availability of data, transfers, subsidies, and pensions could not be taken into account.

Although data on all other variables are available on a monthly basis starting from June 1970, information on foreign currency deposits, F, was available only from January 1980. Thus, Dt, and Mt are defined as
and their behavior is analyzed only for the period January 1980 to November 1989.
Consider, for example, monthly variables
Zt= β′Zt2+ϵt.
For β = β′ = 1, Zt has a unit root corresponding to a peak at frequency zero in the spectrum, while Zt has unit roots at frequencies ±π/2. Notice that the above two equations can be rewritten as
Zt=j=0( β′)jt2j.
It is obvious that for mod(β), mod(β′) < 1, the effect of a random shock, ϵ, on the variables will get diluted with the progress of time. In the case of unit roots. β = β′ = 1, however, the two series will have long memories and shocks will last forever. In particular, for Zt, a random shock may in fact change the seasonal patterns permanently.
To see the relationship between unit roots and order of integration, note that for α = 1
that is, Zt in the first equation in the preceding footnote is the integration of all past shocks. Now consider
which can be rewritten as
with B as the backward shift operator. Clearly, Zt″, which has two unit roots at frequency zero, is I(2) or integrated of order two; in other words, the past shocks have to be cumulated twice to obtain the variable. Since the strength of memory of a variable and the persistence of past shocks depend on the order of integratedness, the order has obvious implications for cointegration or existence of a long-run relationship.
Note that the result that all these variables have unit roots only at frequency zero rules out the transformation
to carry out the analysis. Such a transformation, which roughly corresponds to the rate of growth over the last 12 months, is valid only when z has unit roots at all seasonal frequencies.

The existence of a unit root at zero frequency is perhaps a common feature of many economic variables, and was found by Beaulieu and Miron (1990) to be true for prices, nominal and real interest rates, and nominal and real wages in the United States.


The problem may be akin to trying to relate demand for only golden apples to income and price, when red apples are very close substitutes for golden apples.


Because of the omission of foreign prices, the definition of the real exchange rate is unconventional. The expression is used as shorthand for the term xp, which appears in equation (18) below, as an econometric construct used to simplify equation (17).


I am indebted to Daniel Hardy for drawing my attention to this simple illustration.


The model of demand for money used in the next section is much more general than that used in this illustration. In that model, expected inflation is implicitly assumed to be dependent on past developments in inflation, money supply, and other relevant variables.


Despite the pronounced seasonality in the series, no deseasonalizing filters were applied to the data before the demand functions were estimated, lest important information hidden in the seasonal patterns be lost.


See Yoo (1987, Chap. 2) for a discussion of muiticointegration.


Note that since p is I(2). Δp is I(1).


Note that exchange rate changes, apart from bringing about shifts in the composition of money between dinar balances and foreign currency deposits, also induce shifts between these two categories and deposits held abroad and money under mattresses, which are not part of the monetary aggregates analyzed in this paper.


If the real rate of interest remains unchanged in the face of increasing inflation, the semi-elasticity of demand for real balance with respect to inflation is -0.8 and not -0.65 (= -0.8 + 0.151).


GMP is observed to have had an elasticity of 0.73 with respect to the index of industrial production. When this relationship between GMP and the index of industrial production is taken into account, liquid assets appear to have been unit elastic with respect to income.


Some simple experimentation with longer lags did not indicate the need to increase the lag length beyond two months.


The tests were conducted sequentially.


See Mencinger (1987) for a chronological overview of interventions in price formation in Yugoslavia during 1971–86. Extensive price liberalization was undertaken in multiple stages in the period after May 1988. It is reasonable to assume that interventions in price formation did not alter the long-term trend in inflation but imparted a stop-go pattern to inflation. The resulting volatility of the inflation rate would be reflected in oscillations in real money balances, particularly when price controls and decontrols were unanticipated, and due allowance should be made for this factor in analyzing the stability of demand for real balances.


It is important to note that the test is biased toward accepting the null hypothesis in models with lagged endogenous variables. Furthermore, although there is no evidence to suggest that the sample should be broken up into two or more subsamples to accommodate the possibility of discrete structural breaks at specific points of time, the stability properties of the model are not fully satisfactory. For example, the recursive point estimates of the coefficients do not tend to converge rapidly to their final values, and there are indications of increased instability after 1984. The stability properties of the demand for money function in Yugoslavia merit careful scrutiny, especially in view of the changes in the economic system introduced from time to time. According to Ben-ner and Neuberger (1990), Yugoslavia has had six economic systems in the postwar period, with at least three different systems prevailing during the sample period used here.


See Beckerman (1987) for similar policy conclusions in the Peruvian context.


This representation of zt's, for j = 1,2,12 contained in Beaulieu and Miron (1990) explicitly demonstrates how these transformations are related to particular seasonal frequencies.


Note that the hypothesis of d and m2(-v) having a unit root at frequency 5π/6, which corresponds to 7 and 5 cycles a year, can be rejected only Dy the sequential t-test at the 10 percent level of significance. However, since the F-statistics are better behaved than the sequential t-tests, the balance of evidence is in favor of not rejecting the hypothesis.


See Fuller (1976, p. 373). In general, the value of q was chosen to minimize the SC over the range of q = 0,1,2 … 19. In the case of testing the hypothesis that m2, p, w, and x are I(3) against the alternative of I(2), a monotonic positive relationship was observed between larger values of q and the likelihood of not rejecting the null hypothesis. Furthermore, although the global minima of SC were attained for q = 12 or 13 in the case of m2,p, and w, the SC tended to have local minima at a much lower value of q < 4. For these cases, the values of q chosen correspond to these local minima. The detailed results are available on request from the author.


The t-statistics are reported only until the hypothesis Ho: z ~ Ij) is not rejected.

IMF Staff papers: Volume 38 No. 4
Author: International Monetary Fund. Research Dept.