The “Vicious Circle” Hypothesis

JOHN F. O. BILSON

doi:10.5089/9781451956528.024.A001

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The “Vicious Circle” Hypothesis

Author: JOHN F. O. BILSON

Publication Date:: 01 Jan 1979

eISBN:: 9781451956528

ISBN:: 9781451956528

Language:: English

Keywords:: SP; money supply; output gap; open economy; monetary policy; balance of payments; price elasticity of demand; price level; Inflation; Wages; Demand for money; interest rate

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One of the most obvious characteristics of the 1970s is the increase in the size and diversity of the inflation rates of the major industrial countries. The average rate of inflation of the seven largest industrial countries has risen from 5.3 per cent in 1970 to 10.0 per cent in 1976. During the same period, the standard deviation around the average increased from 1.5 per cent to 4.9 per cent. This increase in the size and dispersion of the inflation rate reflects, in large part, a division of the industrial world into high- and low-inflation groups. In 1976, the rate of inflation in the United States and the Federal Republic of Germany was not significantly greater than in 1970, but the rate of inflation in Italy and the United Kingdom had increased to over 16 per cent per annum. Between these extremes lie a group of smaller countries—Belgium, the Netherlands, Austria, and the Scandinavian countries—who are attempting to resist falling into the high-inflation bloc by fixing their exchange rates to the strong currencies. A fear that is often expressed is that the greater diversity of inflation rates, which is associated with the widespread adoption of flexible exchange rates, will threaten the spirit of international cooperation that fostered the growth of trade and prosperity in the postwar era.

Abstract

The potential for international discord has been increased by differences of opinion over the cause of the diversity in rates of inflation. Defenders of the flexible exchange rate system argue that the inflation rate is primarily determined by domestic monetary and fiscal policies and that the exchange rate plays only a passive role in the adjustment process. Former U. S. Treasury Secretary William Simon took this view in his address to the 1976 Annual Meeting of the Board of Governors of the Fund:

Influenced heavily by the imperatives of experience, we have come to realize that exchange stability cannot be imposed or forced on nations by the establishment of fixed exchange rates. We have embraced the concept that stability will result only from responsible management of underlying economic and financial policies in our countries. We see more clearly that market forces must not be treated as enemies to be resisted at all costs, but as the necessary and helpful reflections of changing conditions in a highly integrated world economy with wide freedom for international trade and capital flows. We recognize—as proved by events in many countries in recent years—that without stable underlying economic and financial conditions, no amount of exchange market intervention will assure stability, but that with stable conditions, little or no such market intervention would be needed. ¹

On the other hand, critics have far less faith in the ability of financial management to control the rate and in the efficacy of the exchange rate as an adjustment instrument. This view, which stresses that an unmanaged exchange rate is an independent source of inflationary pressure, was cogently expressed by Bernard Clappier, the Governor for France, at the Fund’s 1976 Annual Meeting:

These erratic fluctuations [in exchange rates] have adverse effects. A fall in the exchange rate on the market is reflected, even before the slightest impact is felt on export volume, in an immediate rise in the cost of imports. Thus, in the first phase, the external depreciation of the currency aggravates the internal inflation rate. These two phenomena follow and reinforce each other, setting in motion a cumulative process at the end of which the currency’s exchange value continues to fall. As experience has shown, such excessive, disorderly movements distort the conditions of trade and could, if we do not watch out, jeopardize the growth of world trade. It is therefore justified for the Fund’s new Articles of Agreement to require the member countries to ‘promote a stable system of exchange rates.’²

A similar view has also been expressed in the 1976 annual report of the National Bank of Belgium:

… it was obvious … that depreciation of the franc, reflected immediately in an increase in the prices, expressed in the national currency, of imported products, would have quickly set in motion again the rise in domestic prices and costs. For although it is true that, generally speaking, the degree of propagation of this type of imported inflation depends at one and the same time on the import content of total expenditure, on the possibilities of substituting domestic resources for these foreign products and on the rigidity of the links, whether formal or implicit, between prices and incomes, there was a particularly great danger of the Belgian economy’s being afflicted by this malignant fever and drawn into the vicious circle of foreign exchange rates and prices.³

These statements are characteristic of the vicious circle view of the international monetary system. As they illustrate, the vicious circle view is based upon the belief that flexible exchange rate systems have a significant propensity toward dynamic instability and that exchange rate changes constitute an independent source of inflationary pressure. This belief is reflected in the attempt by Falchi and Michelangeli (1977) to test the hypothesis by applying the Sims-Granger causality tests to the exchange rate-price level relationship. ⁴ These authors find statistical evidence that exchange rates lead prices in Italy, although not in the other industrial countries, and suggest, on the basis of this evidence, that Italy has experienced a vicious circle during their sample period. However, there are at least two major objections that can be raised against this test of the vicious circle hypothesis. First, the approach ignores the fact that the exchange rate is an endogenous variable. The causality tests may indicate that exchange rates ‘cause’ prices when the correct explanation is simply that exchange rates respond more rapidly than prices to changes in underlying economic conditions. The Bank for International Settlements supports this interpretation in its Forty-Seventh Annual Report (1977) when it argues that the depreciation-inflation spirals in the United Kingdom and Italy were owing to overly expansionary monetary policies.

The first striking fact … is that both the United Kingdom and Italy got into the vicious circle because of domestic developments. In the case of the United Kingdom the responsibility lies principally with monetary policy: one need not be an orthodox monetarist to regard the 30 per cent rise in the money supply (M₃) in 1973 as the main factor behind the sharp decline in the value of sterling during the same year. However, the situation was seriously aggravated for a time by the ‘threshold’ system of wage indexation that came into operation in the spring of 1974 but was terminated in the course of 1975. In Italy the money supply (M₂) was already expanding at an excessive rate in 1973 (and more so in early 1974), but thé wage explosion during the same year also played an important rôle in weakening the lira on the foreign exchanges.⁵

It is consequently not possible to evaluate the vicious circle argument by simply looking at the relationship between prices and exchange rates.

The second objection that may be raised against the conventional statement of the vicious circle hypothesis is that the implicit economic model underlying the discussion neglects the expenditure-reducing role of the exchange rate in the adjustment process. If prices adjust instantly to exchange rates, it is true that there will be little or no expenditure switching between domestically-produced and imported goods. However, rapid price adjustment increases the effectiveness of the exchange rate as an expenditure-reducing mechanism. A depreciation of the exchange rate that is accompanied by an immediate increase in prices and costs will immediately lower the real value of assets denominated in the domestic currency. This reduction in real wealth will induce an increase in desired saving and a decrease in desired expenditure on both domestically-produced and imported goods. The current account will improve, both because of the reduction in the demand for imports and because of the increase in the supply of domestic goods that are available for export.

The neglect of the expenditure-reducing role of the exchange rate is only justified if the central bank follows a completely accommodating monetary policy. In this case, any reduction in real wealth owing to price inflation will be offset by an increase in the supply of money and bonds. The potential for dynamic instability under these conditions is recognized by even the most fervent advocates of flexible exchange rates. Friedman (1953, p. 181), for example, recognized the possibility in his important paper, “The Case for Flexible Exchange Rates.” He wrote:

The rise in the prices of foreign goods [owing to the depreciation of the currency] may add to the always plentiful list of excuses for wage increases; it does not in and of itself provide the economic conditions for a wage rise—or, at any rate, for a wage rise without unemployment. A general wage rise—or a general rise in domestic prices—becomes possible only if the monetary authorities create the additional money to finance the higher level of prices. But if the monetary authorities are ready to do so to validate any rise in particular prices or wages, then the situation is fundamentally unstable without a change in the exchange rate, since a wage rise for any other excuse would lead to similar consequences. The assumption is that to him who asks will be given, and there is never a shortage of willingness to ask under such circumstances.

This discussion points to one of the crucial assumptions in the vicious circle debate—the degree of central bank autonomy. Opponents of the vicious circle view, particularly those from the United States, point to the theoretical impossibility of a wage-price-exchange rate spiral in the absence of an accommodating monetary policy. On the other hand, the proponents argue that it is politically and socially impossible to curb the circle through monetary contraction, since a tight monetary policy results in unacceptable levels of unemployment. The proponents see the vicious circle as a social malaise that is most likely to occur in countries with strong unions, a weak central bank, and an open and large foreign trade sector. Flexible exchange rates contribute to the dynamic instability of the economy by removing the ‘discipline’ that is imposed upon the central bank by a fixed exchange rate regime. ⁶ The discipline argument is that central banks recognize that expansionary monetary policies lead to balance of payments deficits under fixed exchange rates, and that a persistent deficit will finally require a devaluation of the currency. Since a devaluation is generally recognized as an indicator of the failure of the government’s economic policies, which may be followed by a loss of its political support, ⁷ the fear of a devaluation is assumed to counterbalance the inflationary tendencies of the union sector by decreasing the willingness of the monetary authorities to accommodate wage increases. The discipline argument concludes that the move to a flexible exchange rate regime removes the balance of payments constraint on the money supply mechanism and hence eliminates the last barrier to an inflationary spiral. For the first time in history, the central banks of the major industrial countries do not face any external constraint on their ability to increase the stock of high-powered money.⁸

Since the institutional arrangements allow for greater possibilities for monetary creation, it should not be surprising that participants in the private sector have also adopted contractual arrangements that allow for rapid adjustment to inflation. The most obvious example of these arrangements are the price and wage indexation agreements that have been established in most of the industrial countries. ⁹ The vicious circle is then completed by the recognition that these agreements introduce rigidities into the response of wages and prices to real, as opposed to monetary, disturbances, so that the central bank must adopt a more active monetary policy in order to compensate for the greater real-wage rigidity of the private sector.¹⁰

An alternative theory of the vicious circle may be constructed on the basis of the interaction between asset markets, on the one hand, and commodity and labor markets, on the other. The important difference between the two types of market is that asset markets are typically auction markets in which the prices adjust instantaneously to equate supply and demand, while prices in commodity and labor markets are often contractually determined in the short run, so that equilibrium is maintained through quantity adjustment. The other important difference is that asset prices are strongly influenced by expectations and speculation; a successful foreign exchange speculator must anticipate the future behavior of both the private and public sectors. Through this speculative activity, anticipated increases in wages, prices, and monetary aggregates are immediately discounted into the current exchange rate. The circle will be completed if the movement in the exchange rate justifies the expectations of foreign exchange market speculators. For example, an expected increase in nominal wages is likely to decrease the demand for the currency and depreciate the exchange rate. In turn, the depreciation of the exchange rate is likely to create pressure for higher nominal wages. While it is true that this circle will be short-lived in the absence of an accommodating monetary policy, it may not be possible or desirable for the central bank to create a period of prolonged unemployment in order to break the cycle.

As the preceding discussion has emphasized, a complete analysis of the vicious circle hypothesis requires a theory of the behavior of unions, firms, central banks, and foreign exchange speculators. One attempt at such a model is presented in the remainder of this paper. Although dependent upon a number of simplifying assumptions, it does offer a plausible account of the dynamic response of prices, wages, and exchange rates to domestic and foreign disturbances, and presents a clear specification of the factors that determine the effectiveness of monetary and fiscal policies during a period of managed floating.

I. Theoretical Foundations

The theoretical model is based upon two countries, two currencies, two goods, and a single, internationally traded bond. The domestic country is assumed to be small, in the sense that the foreign country (the world) is not influenced by domestic developments. The domestic country produces a single homogeneous good—”domestic output”—that is not a perfect substitute for “world output.”

The demand for the domestic currency is of the following specific functional form:¹¹

\begin{matrix} \frac{M}{P_{m}} = K Y^{η} \exp (- ϵ i) & (1) \end{matrix}

This particular money demand function is characterized by the assumption that the income elasticity of the demand for money is constant, while the interest elasticity is proportional to the nominal rate of interest. The price deflator P_m is assumed to be a geometrically-weighted average of the domestic price of world output, EP^*, and the price of domestic goods, P,

\begin{matrix} P_{m} = P^{α} {({E P}^{*})}^{1 - α} & (2) \end{matrix}

The weight α is equal to the share of domestic goods in total expenditure and is one of the important measures of the openness of the economy that will be considered in the analysis. For most purposes, it is useful to express the model in logarithms in order to linearize the equations. The log-linear version of the money market equilibrium condition can be written as

\begin{matrix} α ρ + (1 - α) (e + ρ^{*}) = m - η y + ϵ i & (3) \end{matrix}

where the lower case letter is used to denote the logarithm of a variable (i.e., m = ln(M)). The shift factor K has been eliminated to reduce the notational burden, but any increase in the demand for money may be analyzed through considering the effect of a decrease in the supply of money.

The nominal interest rate has an important role to play in the model since, under two assumptions, the difference between the domestic and the world interest rate may be interpreted as a market estimate of the expected rate of depreciation. The speculative influence on the exchange rate then enters the model through the speculative influence on the demand for money: an increase in the expected rate of depreciation will increase nominal interest rates, decrease the demand for money, and depreciate (increase) the exchange rate in the absence of price adjustment. The two assumptions are that covered interest arbitrage eliminates any differences between the covered yields on assets denominated in different currencies, so that the interest rate differential is equal to the forward premium on the currency, and, second, that well-informed, profit-maximizing speculators set the forward premium equal to the expected rate of depreciation. It is important to note that the assumption of perfect capital mobility, and hence of the continuous maintenance of interest rate parity, is one of the crucial assumptions of the theoretical model. This assumption permits the government to borrow and lend in the capital market without influencing the rate of interest, the rate of inflation, or the exchange rate. It also permits an analysis of a “pure” fiscal policy—an expansion of government expenditure financed by borrowing—and a “pure” monetary policy—an open market purchase of government bonds—to be carried out independently of the influence of the policy on the stock of interest-bearing assets. The assumption may be invalidated by the presence of capital controls, restrictions on forward exchange market activity, and risk aversity. In defense of the assumption, two arguments may be presented. First, in a choice between the simple extremes of perfect capital mobility and no capital mobility, the former assumption appears to be a better characterization of the countries considered in the vicious circle analysis, and the intermediate case of imperfect substitutability introduces a great deal of additional complexity into the model. Second, the assumption that international financial markets are unconstrained and efficient allows for a very direct specification of the role of speculation in the determination of the exchange rate.

Under the perfect capital mobility assumption, covered interest arbitrage will equate the yields on domestic and foreign bonds. In units of domestic currency, the yield on an investment of X units after t periods is

Y i e l d = X \exp (i)

The yield on an investment of X units of domestic currency in the foreign bond is

Y i e l d = \frac{F}{E} X \exp (i^{*})

where F is the forward exchange rate for period t + τ. Equating the yields and expressing the result in logarithms yields

i = i^{*} + f - e

The equation is completed by imposing the assumption that f is a weighted average of the equilibrium exchange rate ē and the current spot rate e.¹²

f = λ \bar{e} + (1 - λ) e

Combining these equations yields the following expression for the nominal interest rate:

\begin{matrix} i = i^{*} + λ (\bar{e} - e) & (4) \end{matrix}

If the actual rate is below the equilibrium rate, speculators anticipate a depreciation of the actual rate, and they will sell the domestic currency in the forward exchange market until the forward rate depreciates to a level that is equal to the expected future spot rate. Through the interest rate parity condition, a depreciation of the forward rate, for a given value of the spot rate, will cause nominal interest rates to rise. It should be clear, however, that it is not possible to discuss the determination of the spot rate and the forward rate independently, since their equilibrium values will be the result of the simultaneous solution of the entire economic model. Finally, while the forecasts provided by equation (4) will not be exactly equal to the actual rate of depreciation, the equation may be considered a first-order linear approximation to the optimal forecasting equation.

Since monetary accommodation is at the heart of the vicious circle debate, it is necessary to consider specifically the endogenous determination of the money supply. In equation (5), it is assumed that the monetary authority adjusts the money supply around a target level m in response to the deviation of both the exchange rate and real output from their equilibrium levels.

\begin{matrix} m - \bar{m} = ρ_{1} (\bar{e} - e) - ρ_{2} (y - \bar{y}) & (5) \end{matrix}

In the long run, the monetary authority may set either the target money supply m or the target exchange rate ē. Consequently, no loss of generality is associated with definition of the target exchange rate as the equilibrium rate in equation (5). This is not the case, however, with respect to the target level of real income, since a conflict may arise between the level that is consistent with wage and price stability (and hence with the “natural” rate of unemployment) and the level that is consistent with the policy preferences of the authorities. The possibility of a wage-price spiral under these conditions has been discussed and agreed upon by domestic macroeconomists in the period following Friedman’s statement of the problem. ¹³ The introduction of floating exchange rates would not add to this discussion, since the participants typically ignored any complications that would arise if the exchange rate were fixed and thus, by default, assumed either a closed economy or an economy operating under a flexible exchange rate. The discussion in this paper will avoid the obvious possibility of a wage-price-exchange rate spiral because of inconsistent policy goals by assuming that the target level of output is also the level that is consistent with wage and price stability.

The two terms in the money supply function reflect the internal and external policy concerns of the central bank. The first term captures the desire to stabilize the exchange rate: if the actual rate is below ē, the central bank expands the money supply, thereby speeding the depreciation of the spot rate toward the position of sustainable equilibrium. The polar extremes are systems of free floating—ρ₁ = 0—and fixed exchange rates—ρ₁→∞. In the latter case, the money supply is always set equal to the level at which the actual exchange rate is equal to the target exchange rate. In effect, the central bank stands willing to exchange domestic currency for foreign currency at a fixed price and, hence, abdicates its control over the domestic money supply. That there is a loss of monetary independence under fixed exchange rates is the main conclusion to be drawn from the extensive literature on the monetary approach to the balance of payments. ¹⁴ The second term reflects the internal countercyclical role of the central bank. Through this term, the central bank expands the money supply when output is below capacity. A policy of complete monetary accommodation—ρ₂→∞—implies that the central bank is always willing to expand the money supply to the level that will ensure full employment. The two parameters of the central bank reaction function are crucial variables in the vicious circle analysis, because most observers agree that the probability of an inflationary spiral is positively related to the size of ρ₂ and negatively related to the size of ρ₁.

In the commodity markets, it is assumed that domestic and foreign goods are imperfect substitutes, so that an increase in the price of domestic goods will decrease, but not eliminate, the demand for them. The demand function is assumed to be of the form

\begin{matrix} y = {\bar{y}}^{d} - γ (ρ - e - ρ^{*}) & (6) \end{matrix}

where ${\bar{y}}^{d}$ = the exogenous level of demand for domestic goods, and γ = the price elasticity of demand, which will reflect the openness of the economy, the degree of substitutability between domestic and foreign goods, and the income elasticity of demand. ¹⁵

On the supply side, it is assumed that the typical firm produces domestic goods through the utilization of a fixed stock of real capital in conjunction with variable inputs of labor and imported goods. In the short run, the firm offers an infinitely elastic supply of goods to the market at a set price. If the volume of goods purchased at that price exceeds the profit-maximizing volume, the firm increases prices in proportion to the excess. This theory of aggregate supply implies the following equation for the rate of inflation if the underlying production functions are Cobb-Douglas:¹⁶

\begin{matrix} \dot{p} = θ_{p} [y - {\bar{y}}^{s} + δ_{1} (w - p) - δ_{2} (p - e - p^{*})] & (7) \end{matrix}

In this equation, θ_p is the speed of price adjustment, and δ₁ and δ₂ are related to the shares of labor and imported inputs in total costs.

In the labor market, it is assumed that the nominal wage is set by unions or other labor organizations at a level that ensures an infinitely elastic supply of labor to the firm in the short run. The firm may decide how many members of the labor force to employ, but it must employ them at the nominal wage rate specified in the existing labor contract. The union adjusts the nominal wage in order to maintain the real wage of its members in the long run. This description is embodied in the following equation, which determines the rate of wage inflation:

\begin{matrix} \dot{w} = - θ_{w} [w - α p - (1 - α) (e + p^{*})] & (8) \end{matrix}

In equation (8), θ_w is the indexation parameter that measures the speed with which increases in prices are passed through into wages. If θ_w were infinite, as would be the case with complete indexation, the real wage would be constant. It would be possible to allow for real wages to grow with the rate of growth in real labor productivity, but this complication is peripheral to the topics under study.

The wage equation completes the formal specification of the model. In the next section, the long-run solution will be presented and, in the following section, the path by which the endogenous variables approach the steady state will be studied. A knowledge of this path will permit an analysis of the influence of the structural parameters on the dynamic stability of the model and on the effectiveness of monetary and fiscal policies as demand management instruments. In this regard, the key parameters are

II. The Steady-State Solution

The steady state is reached when the rate of wage and price inflation is zero. ¹⁷ Subject to the condition that $\dot{p} = \dot{w} = 0,$ the model specified in the preceding section may be solved for the equilibrium values of output, prices, exchange rates, wages and interest rates as functions of the exogenous levels of aggregate demand and supply, the exogenous component of the money supply, and the levels of foreign prices and interest rates. Denoting the equilibrium values by an upper bar, the solution is contained in the following five equations:

\bar{y} = \frac{δ_{1} (1 - α) + δ_{2}}{γ + δ_{1} (1 - α) + δ_{2}} {\bar{y}}^{d} + \frac{γ}{γ + δ_{1} (1 - α) + δ_{2}} {\bar{y}}^{s} (9)

\begin{matrix} \bar{e} = \bar{m} - η \bar{y} + {ϵ i}^{*} - p^{*} - \frac{1 - α}{γ + δ_{1} (1 - α) + δ_{2}} ({\bar{y}}^{d} - {\bar{y}}^{s}) & (10) \end{matrix}

\begin{matrix} \bar{p} = \bar{m} - η \bar{y} + {ϵ i}^{*} + \frac{1 - α}{γ + δ_{1} (1 - α) + δ_{2}} ({\bar{y}}^{d} - {\bar{y}}^{s}) & (11) \end{matrix}

\begin{matrix} \bar{w} = \bar{m} - η \bar{y} + {ϵ i}^{*} & (12) \end{matrix}

\begin{matrix} \bar{i} = i^{*} & (13) \end{matrix}

Equation (9) states that the equilibrium level of real output will be a weighted average of the exogenous components of demand and supply. This result differs from most macroeconomic models of closed economies where the equilibrium level of real output is purely supply-determined. The reason for this result is specified in equations (10) and (11). An expansion in aggregate demand owing, for example, to an increase in government expenditure on domestic goods will result in an increase in the price of domestically-produced goods relative to both the price of imported goods and wages. Consequently, the expansion in demand lowers the cost of both labor and imported inputs in terms of domestic output and hence increases the profit-maximizing level of output. The size of the increase in output is strongly related to the price elasticity of demand, γ. If domestic and foreign goods are perfect substitutes (γ = ∞), then the expansion in government demand will be exactly offset by a decrease in private demand, and no expansion in real output will be forthcoming.

A related point is that no attempt is made to impose the purchasing-power-parity condition as a long-run equilibrium condition. Instead, the relative price of domestic goods in terms of foreign goods is determined by

\begin{matrix} \bar{p} - \bar{e} - p^{*} = \frac{1}{γ + δ_{1} (1 - α) + δ_{2}} ({\bar{y}}^{d} - {\bar{y}}^{s}) & (14) \end{matrix}

The left-hand side of this equation, which is often called the “real exchange rate,” is determined by the exogenous levels of demand and supply. The model does retain the property of degree one homogeneity in money and prices, however, since an increase in the money supply will result in a proportional increase in the price level, the exchange rate, and the wage rate, while leaving the real side of the model unaffected.

III. Short-Run Dynamics

In the short run, the levels of wages and domestic goods prices are predetermined variables, so that the brunt of the adjustment is placed upon the exchange rate and the level of real output and employment. With exchange rates and output adjusting to maintain short-term equilibrium, the rate of price and wage inflation is determined so as to bring the system toward a position of long-run equilibrium.

The short-run equilibrium conditions in the money market and the commodity market are presented in equations (15) and (16)

\begin{matrix} (1 - α + ρ_{1} + ϵ λ) (e - \bar{e}) & = - α (p - \bar{p}) \\ + (ρ_{2} + η) (y - \bar{y}) (15) \end{matrix}

\begin{matrix} (y - \bar{y}) = - γ (ρ - \bar{p}) + γ (e - \bar{e}) & (16) \end{matrix}

The coefficient in front of the exchange rate term in equation (15) defines the three direct channels through which a depreciation of the exchange rate clears the money market: (i) an increase in the exchange rate increases the price of imported goods and decreases the supply of real money balances; (ii) an increase in the exchange rate above the target level induces central bank intervention, which decreases the supply of nominal balances; and (iii) an increase in the exchange rate above its equilibrium level causes speculators to anticipate an appreciation of the rate, thereby lowering the nominal rate of interest and increasing the demand for money.

A depreciation also clears the money market through its effect on real income; a depreciation shifts demand toward domestic goods. The increase in demand both increases the demand for money and, through the central bank reaction function, induces a tightening of the money supply. By substituting equation (16) into equation (15), the reduced-form solution for the exchange rate may be found to be

\begin{matrix} (e - \bar{e}) = Ω (p - \bar{p}) & (17) \end{matrix}

where $Ω \frac{(ρ_{2} + η) γ - α}{1 - α + ρ_{1} + ϵ λ + (ρ_{2} + η) γ} .$ The sign of Ω determines whether the exchange rate overshoots its equilibrium value in response to a monetary expansion. The sign reflects the two conflicting roles of the price level in the money market: through the term (ρ₂ + η)γ in the numerator, an increase in the price level decreases the demand for domestic goods and creates an excess supply of money, both by directly decreasing the demand for money and by prompting an increase in the money supply in order to mitigate the impact of the price rise on the levels of output and employment. Through the second term, −α, an increase in the price level increases the aggregate price index and creates an excess demand for money. If the second factor dominates, the exchange rate will initially overshoot its equilibrium value and will then appreciate during the period of price adjustment, as suggested by Dornbusch (1976). However, it is likely that the first term will dominate in the type of economy considered in the vicious circle analysis. In the first place, the share of foreign goods in total expenditure is likely to be relatively high in the open economies considered in the analysis, so that α will be relatively small. Second, it is also likely that the price elasticity of demand for domestic goods will be relatively high, so that the first term will be large.

Finally, one might refer to the informal discussions of the vicious circle, which invariably stress that an increase in domestic prices leads to a depreciation of the exchange rate, thus implying that the aggregate demand effects dominate the reduction in real money balances owing to the higher prices. On these grounds, Ω is assumed to be positive. Although higher prices depreciate the exchange rate under this assumption, it is clear from the definition of Ω that this elasticity will always be less than unity, so that it is impossible for an increase in prices to create a proportionally larger depreciation of the exchange rate. In part, this result follows from the greater number of channels through which a depreciation of the exchange rate increases the demand for the domestic currency: a depreciation will reduce the supply of money because of the defensive intervention by the central bank and will increase the demand for the currency by reducing the expected rate of depreciation. In addition, it is important to recognize that an equal increase in domestic and foreign prices will create an excess demand for money by decreasing the real value of the available supply. This is the important expenditure-reducing role of the exchange rate that guarantees that the elasticity is less than unity, or, less formally, that the economic system will reach a stable equilibrium in time.

Equation (17) is represented in Chart 1 by the EE curve in the lower half. As suggested by the preceding discussion, the slope of the EE curve is positive but less than unity. The curve may be used to find the value of the exchange rate for any given level of prices. The position of the curve will change in response to changes in both the equilibrium exchange rate and the equilibrium price level.

Substituting equation (17) into (16) yields:

\begin{matrix} (y - \bar{y}) = - ψ (p - \bar{p}) & (18) \end{matrix}

where ψ = γ (1 – Ω). Equation (18) is a reduced-form aggregate demand curve that takes account of the induced movements in exchange rates, interest rates, and the supply of money in the relation between output and prices. The equation is represented in the lower half of Chart 1 as the YY curve. Since Ω is less than unity, the YY curve has a negative slope, which implies that an increase in the price of domestic goods will reduce the demand for them.

Through equations (7), (17), and (18), the rate of price inflation may be expressed as a function of the deviation of wages and prices from their equilibrium values in the following way:

\begin{matrix} \dot{p} = π_{w} (w - \bar{w}) - π_{p} (p - \bar{p}) & (19) \end{matrix}

where $π_{w} = θ_{p} δ_{1} and π_{p} = θ_{p} [(γ + δ_{2}) (1 - Ω) + δ_{1}] .$ As one would expect, an increase in nominal wages increases the rate of inflation by decreasing the profit-maximizing level of output.

An increase in the price of domestic goods reduces the rate of inflation by both decreasing the demand for these goods and increasing the supply of them. The ṗ = 0 line in the upper half of Chart 1 traces those combinations of wages and prices that are compatible with zero inflation of domestic prices. The slope of the line is greater than unity because an equal increase in wages and prices would not result in any increase in labor cost pressure on prices, but it would actually reduce the cost pressure from imported inputs. The decrease in demand, combined with this increase in desired supply, would bring the economy into an area of price deflation. It is therefore necessary that the increase in wages exceed the increase in prices in order to prevent prices from falling, which implies that the ṗ = 0 line must have a slope that is greater than unity.

In a similar way, equations (8) and (17) may be solved for the rate of wage inflation

\begin{matrix} w = - χ_{w} (w - \bar{w}) + χ_{p} (p - \bar{p}) & (20) \end{matrix}

where $χ_{w} = θ_{w} and χ_{p} = θ_{w} [1 - (1 - α) (1 - Ω)] .$ The ẇ = 0 line the upper half of Chart 1 traces those combinations of wages and prices that are consistent with zero wage inflation. In this case, the slope of the line is less than unity because an equal increase in wages and prices would bring the economy into an area of wage deflation. The reason for this result is again based on the result that the elasticity of the exchange rate with respect to prices is less than unity, so that an increase in wages and prices by the same proportion increases the real wage paid to labor suppliers.

Chart 1 may be used to analyze the impact of changes in the exogenous variables on prices, wages, the exchange rate, and the level of real output. Since monetary expansion is often considered to be the root cause of a vicious circle, the response of the economy to an expansion in the money supply will be analyzed first.

An increase in the money supply causes a proportional increase in the equilibrium level of prices, wages, and the exchange rate while leaving the equilibrium level of output unchanged. In Chart 1, the policy change is represented by the increase in prices from ${\bar{p}}_{0}$ to ${\bar{p}}_{1}$ , in wages from ${\bar{w}}_{0}$ to ${\bar{w}}_{1}$ , and in the exchange rate from ${\bar{e}}_{0}$ to ${\bar{e}}_{1}$ All of the reference lines in Chart 1 are drawn with respect to the new equilibrium values. At the instant at which the increase in the money supply occurs, prices and wages will be fixed at ${\bar{p}}_{0}$ and ${\bar{w}}_{0}$ , respectively. However, in the lower half, the exchange rate immediately depreciates to the point on the EE curve, and output immediately increases to the point on the YY curve. The depreciation is required to induce private wealth holders to hold the additional quantity of money; a depreciation increases the demand for the domestic currency by decreasing its purchasing power over imported goods and by lowering domestic interest rates. It is important to note that domestic interest rates will increase in the first instance, because speculators will be anticipating a further depreciation of the currency during the adjustment period. However, it is also true that the increase in interest rates will be smaller, the greater is the initial depreciation of the exchange rate. The short-run increase in real output is owing to the classical relative price mechanism; with prices and wages fixed, a depreciation of the exchange rate increases the price of imported goods and thus shifts demand toward domestically-produced goods.

Returning to the upper half of Chart 1, one notes that the monetary expansion has placed the economy in a position of both wage and price inflation. In the first instance, the rate of wage inflation becomes positive because the depreciation has lowered the real wage by increasing the cost of imported goods. As time passes, nominal wages will also increase in response to increases in the prices of domestically-produced goods. This price inflation will be owing to both demand-pull and cost-push factors. On the demand side, the increase in the demand for domestic goods will prompt an increase in the rate of price inflation as a rationing device, while, on the cost side, the higher cost of imported inputs will also be passed on in higher final goods prices. As this process of wage and price adjustment develops, the economy will move up along the arrowed line from point A to the point of sustainable equilibrium at the intersection of the ṗ = 0 and ẇ = 0 loci at point B. At the same time, the exchange rate will continue to depreciate, and aggregate demand will gradually decline toward its equilibrium level.

It is easy to see how an observer of this pattern of dynamic adjustment would reach the conclusion that the inflation of wages and prices is “caused” by the depreciation of the exchange rate. The process begins with an immediate jump in the exchange rate and is followed by a period of adjustment in which the exchange rate continues to depreciate, as suggested by most of the descriptions of the vicious circle. Indeed, if the shocks to the economy were predominantly monetary, a causality analysis of the type undertaken by Falchi and Michelangeli would reach the conclusion that the exchange rate causes inflation in the Sims-Granger sense. The only real difference between the description derived from the theoretical model and the description given in published versions of the vicious circle is that the theoretical model recognizes the stabilizing role of the general inflation of prices, wages, and exchange rates. By lowering the real value of the outstanding money stock, this inflation removes the root cause of the inflationary spiral and brings the economy to a point of sustainable equilibrium. This analysis consequently supports the view, taken by the Bank for International Settlements, that the type of price-wage-exchange rate interaction described in the vicious circle literature is most likely to occur in a situation of excessive monetary expansion. It also supports the view taken by critics of the vicious circle hypothesis that a continuing spiral can result only from a persistent policy of excessive monetary growth.

A more specific description of the dynamic response of the economy may be obtained by stipulating values for the structural parameters and simulating the paths of the endogenous variables in the time following an increase in the money supply. In Table 1, two sets of parameter values are presented. These parameter sets represent two hypothetical economies that differ in their degree of openness. Openness is defined in terms of the following parameters:

Table 1.

Determinants of Policy Effectiveness

^¹The elasticity reported in the table is defined as the percentage change in the measure of policy effectiveness owing to a 1 per cent increase in the structural parameter, given that the policy considered is a 10 per cent increase in: the money supply (column 1), aggregate demand (column 2), and aggregate supply (column 3).

Table 1.

Determinants of Policy Effectiveness

		Elasticity¹
Structural Parameter	Value	1. Money Supply	2. Aggregate Demand	3. Aggregate Supply
	Open Economy
α	0.50	0.221	0.221	0.221
η	1.00	0.000	0.000	0.000
ϵ	20.00	0.000	0.000	0.000
λ	0.04	0.000	0.000	0.000
ρ₁	0.10	0.000	0.000	0.000
ρ₂	0.10	0.000	0.000	0.000
γ	1.50	0.663	0.663	0.663
θ_ρ	0.05	−0.331	−0.292	−0.398
θ_w	0.05	−0.663	−0.702	−0.579
δ₁	2.00	0.442	0.481	0.375
δ₂	2.00	−0.442	−0.442	−0.442
Gain		2.000	−1.200	−0.741
	Less Open Economy
a	0.80	1.137	1.137	1.137
η	1.00	0.000	0.000	0.000
ϵ	20.00	0.000	0.000	0.000
λ	0.04	0.000	0.000	0.000
ρ₁	0.10	0.000	0.000	0.000
ρ₂	0.10	0.000	0.000	0.000
γ	0.50	0.758	0.758	0.758
θ_p	0.05	−0.248	−0.216	−0.306
θ_w	0.05	−0.746	−0.778	−0.688
δ₁	3.00	0.461	0.494	0.404
δ₂	1.00	−0.473	−0.473	−0.473
Gain		1.904	−1.217	−0.687

Table 1.

Determinants of Policy Effectiveness

		Elasticity¹
Structural Parameter	Value	1. Money Supply	2. Aggregate Demand	3. Aggregate Supply
	Open Economy
α	0.50	0.221	0.221	0.221
η	1.00	0.000	0.000	0.000
ϵ	20.00	0.000	0.000	0.000
λ	0.04	0.000	0.000	0.000
ρ₁	0.10	0.000	0.000	0.000
ρ₂	0.10	0.000	0.000	0.000
γ	1.50	0.663	0.663	0.663
θ_ρ	0.05	−0.331	−0.292	−0.398
θ_w	0.05	−0.663	−0.702	−0.579
δ₁	2.00	0.442	0.481	0.375
δ₂	2.00	−0.442	−0.442	−0.442
Gain		2.000	−1.200	−0.741
	Less Open Economy
a	0.80	1.137	1.137	1.137
η	1.00	0.000	0.000	0.000
ϵ	20.00	0.000	0.000	0.000
λ	0.04	0.000	0.000	0.000
ρ₁	0.10	0.000	0.000	0.000
ρ₂	0.10	0.000	0.000	0.000
γ	0.50	0.758	0.758	0.758
θ_p	0.05	−0.248	−0.216	−0.306
θ_w	0.05	−0.746	−0.778	−0.688
δ₁	3.00	0.461	0.494	0.404
δ₂	1.00	−0.473	−0.473	−0.473
Gain		1.904	−1.217	−0.687

(i) α, the share of domestic goods in total expenditure, which is assumed to be 50 per cent in the open economy and 80 per cent in the less open economy;

(ii) γ, the price elasticity of demand for domestic goods, which is assumed to be 1.5 in the open economy and 0.5 in the less open economy;

(iii) δ₂, the share of imported input costs in total costs, which is assumed to be 40 per cent in the open economy and 20 per cent in the less open economy. Variable costs are assumed to be 80 per cent of total costs.

In addition, the economies share the following set of parameter values:

(i) η, the income elasticity of the demand for money, which is equal to unity;

(ii) ϵ, the interest rate semielasticity of the demand for money, which is equal to 20. If the annual rate of interest is 12 per cent and the unit of time is a month, this value implies an interest elasticity of the demand for money of −0.2;

(iii) λ, the fraction of the difference between the actual and equilibrium exchange rates that is expected to be made up in one month, which is equal to 4 per cent per month;

(iv) ρ₁, the central bank intervention parameter, which is equal to 0.1. This value implies that a depreciation of the exchange rate of 10 per cent induces a 1 per cent reduction in the money supply;

(v) ρ₂, the central bank’s domestic policy parameter, which is equal to 0.1. A reduction in real output of 10 per cent will, through this parameter, result in a 1 per cent increase in the money supply;

(vi) θ_p, the price adjustment parameter, which is set equal to 5 per cent per month;

(vii) θ_W, the wage adjustment parameter, which is equal to 5 per cent per month.

The open economy variants of these values are used in Chart 2 to describe the reaction of the economy to a 10 per cent increase in the money supply in the fifth period. The exchange rate immediately depreciates by 6 per cent, and the demand for domestic goods immediately increases by 9 per cent, owing to the fall in their relative price. The persistence of the competitive advantage, and hence of the increase in demand, depends crucially on the speed of price and wage adjustment. The proponents of the vicious circle viewpoint often argue that the exchange rate or, more correctly, monetary policy is ineffective as a policy instrument because the competitive advantage is rapidly eroded by inflation. This effect is evident in Chart 2, where, as prices and wages increase, the level of output declines toward its steady-state level.

This issue may be examined more formally by introducing an indicator of policy effectiveness. One measure that takes account of the dynamic aspects of the problem is the integral of the deviation of output from its steady-state value over the interval from the point at which the policy is implemented to the infinite horizon. Formally, the index is defined as¹⁸

\begin{matrix} G (z) = \int_{0}^{\infty} [y (t) - \bar{y}] d t & (21) \end{matrix}

Intuitively, G (z) may be interpreted as the increase in the stock of domestic goods produced as a result of the policy z. Since the deviation of output from trend is related to the relative price of domestic goods, G(z) is also an indicator of the overall competitive advantage resulting from the policy.

The index is determined by the size of the initial increase in the money supply and by all of the underlying structural parameters. In principle, it should be possible to derive the relationship between the index and the structural parameters and to show how changes in these parameters influence the effectiveness of monetary policy. In practice, the relationship is nonlinear and complex, and it is virtually impossible to derive any qualitative conclusions. However, the elasticities reported in Table 1 do give the percentage change in G(z) resulting from a 1 per cent change in each of the structural parameters. These elasticities are calculated from the postulated parameter sets for the open and less open economies.

The most obvious conclusion to be drawn from the money supply elasticities in Table 1 is that the money market parameters, including both the demand elasticities of the private sector and the supply elasticities of the central bank, have a negligible impact on the effectiveness of monetary policy. Although it is difficult to locate the reason for this result, there apparently is a tradeoff between the initial response and the speed of adjustment. For example, if the demand for money becomes more sensitive to the interest rate, the size of the initial depreciation will increase and so, consequently, will the initial stimulus to aggregate demand. However, this change will also increase the speed of adjustment, so that the expansion in aggregate demand will be eroded more rapidly. If these two factors offset each other, the elasticities will be zero. It is also interesting to note that the elasticities are zero in both the open and less open economy examples.

The second conclusion to be drawn from Table 1 is that the stimulus to aggregate demand from a monetary expansion is negatively related to the openness of the economy. In particular, effectiveness declines as the share of imported goods in final expenditure increases, and as the share of imported input costs in total costs increases. The measure of effectiveness is far more sensitive to the share of imports in total costs than it is to the share of imports in final demand in the open economy example, but this result is reversed in the less open economy example. The one aspect of openness that does not reduce the expansionary impact of an increase in the money supply is the price elasticity of demand for domestic goods. The reason for this result may be clearly seen by considering the case in which domestically-produced and imported goods are perfect substitutes, so that their relative price is always constant. In this case, the monetary expansion cannot have any immediate impact on the exchange rate, since this would alter the relative price. Instead, all of the increase in the money supply is absorbed by the increase in money demand owing to the increase in real income. Since the exchange rate does not depreciate, the price of imported inputs does not increase, nor is there any immediate pressure for increases in nominal wages. Both of these factors will stimulate aggregate supply relative to a situation in which the demand elasticity is less than infinite. An increase in the elasticity of demand therefore increases the immediate demand stimulus and also increases the supply response during the adjustment phase.

Finally, the results state that increases in the speed of price and wage adjustment reduce the effectiveness of monetary policy. The elasticity with respect to wage adjustment is over twice the size of the elasticity with respect to price adjustment, in both the open and less open economy cases. The reason is that while rapid price adjustment reduces the stimulus to aggregate demand, it increases the supply stimulus by inducing a larger and more prolonged decline in real wages. In contrast, rapid wage adjustment decreases the supply response without providing any offsetting stimulus to demand.

In one sense, these conclusions support the contention that the key to a successful monetary expansion lies in the ability to control the subsequent pressure on nominal wages. However, it is also necessary to recognize that labor suppliers will respond to inflationary policies by adopting contractual arrangements that allow for rapid adjustment of nominal wages to price increases. It is therefore likely that only unanticipated increases in the money supply will have the real effects described in this paper, because anticipated changes in the money supply will be immediately reflected in wages, prices, and the exchange rate.

Typically, vicious circle arguments arise when the inflationary tendencies of the economy are fully anticipated by the private sector. At this time, the authorities are left with rapid rates of inflation and depreciation, while real output and employment are stagnating. An attempt to reduce the rate of inflation by reducing the rate of monetary growth would result in politically unacceptable levels of unemployment, and so the authorities feel caught in a cycle from which it appears to be impossible to escape. Fortunately, the model does suggest a solution to the problem, which will be described in the next section of the paper.

IV. How to Escape from a Vicious Circle

Although the ultimate solution to an inflationary spiral must involve a reduction in the rate of monetary growth, any realistic assessment of the social and economic costs of prolonged unemployment would eliminate from consideration a policy involving a rapid decline in the monetary growth rate. The reduction in the rate of monetary growth must be gradual and anticipated in order to minimize the decline in output and employment.

This does not imply, however, that an extended period of time is required to break the inflationary spiral. The model suggests that expansionary demand and supply policies will both maintain output and employment while reducing the pressure on prices, wages, and the exchange rate. Further, the structural characteristics of the economy that limit the effectiveness of monetary policy actually increase the effectiveness of demand and supply policies.

The first policy that will be considered is an exogenous increase in the demand for domestic goods. This increase may be the result of an increase in public expenditure on domestic goods; or it may be the result of increases in private expenditure brought about by tax cuts, transfer payments, or import restrictions. The only necessary restriction on the policy is that the increase in demand must not be financed, either directly or indirectly, by an expansion in the money supply. An exogenous increase in aggregate demand will have the following effects on the equilibrium values of the dependent variables:

\begin{matrix} d \bar{p} = - η d \bar{y} + \frac{1 - α}{γ + δ_{1} (1 - α) + δ_{2}} d {\bar{y}}^{d} & (22) \end{matrix}

\begin{matrix} d \bar{e} = - η d \bar{y} + \frac{α}{γ + δ_{1} (1 - α) + δ_{2}} d {\bar{y}}^{d} & (23) \end{matrix}

\begin{matrix} d \bar{w} = - η d \bar{y} & (24) \end{matrix}

\begin{matrix} d \bar{y} = \frac{δ_{1} (1 - α) + δ_{2}}{γ + δ_{1} (1 - α) + δ_{2}} d {\bar{y}}^{d} & (25) \end{matrix}

As long as the price elasticity of demand for domestic goods is less than infinite, the expansion in aggregate demand will increase the equilibrium level of real income, as described in equation (25). The increase in real income will increase the demand for money and will result in a general deflation of prices, wages, and exchange rates. This income effect is represented by the first terms in equations (22) to (24). In addition, the price of domestic goods will decrease by less than the decrease in the exchange rate. This substitution effect is captured in the second terms in equations (22) and (23). The fact that the prices of domestically-produced goods increase relative to wages and imported goods prices explains why the profit-maximizing level of output increases.

The paths that the endogenous variables take after there has been a 10 per cent increase in aggregate demand are depicted in Chart 3. Surprisingly, the increase has a relatively small impact on the level of output in the short run. This is because the increase in demand sharply appreciates the exchange rate and thereby shifts demands toward imports. The combination of a small initial demand response and the appreciation of the exchange rate results in downward pressure on prices; the decrease in the cost of imported inputs overwhelms the inflationary pressure on the demand side. This feature persists during the subsequent adjustment. Although demand continues to rise, the cost of production declines because of the decline in nominal wages and the exchange rate.¹⁹

At first glance, the conclusion that an increase in demand decreases the price of domestic goods appears implausible. However, in a macroeconomic analysis, it is important to distinguish between relative prices and the price level. The increase in demand does cause the price of domestic goods to increase relative to both wages and the price of imports. This result is required in order for the increase in aggregate output to take place. The final link in the chain is the condition for money market equilibrium, which requires that an increase in money demand be offset by a decline in the aggregate price level.

Through the period of adjustment, the level of output lies below the equilibrium level. Consequently, the measure of effectiveness developed for the monetary policy—the integral of the deviation of output from trend—is reversed in the case of an aggregate demand policy. In particular, rapid price and wage adjustment permits the economy to reach the higher equilibrium level of real output more rapidly, and hence increases the gain in output and employment that results from the policy. In addition, the gain in output will be larger and the price deflation more rapid, if the share of imported goods in final expenditure and costs is large. In conclusion, this analysis suggests that an expansionary demand policy may lessen the pressure on prices and wages while providing a stimulus to employment during the time in which an adjustment in the rate of monetary growth is taking place. This policy prescription is likely to be most effective in an open economy that has adjusted to an inflationary environment.

The one structural parameter that limits the effectiveness of an expansionary demand policy is the price elasticity of demand for domestic goods. Obviously, if the elasticity were infinite, the expansion in demand by the government would be completely offset by a reduction in demand by the private sector. In this case, the only consequence of the policy would be a current account deficit that would be financed by the export of debt issued by the authorities to finance the expenditure. Prices, wages, the exchange rate, and the level of output would remain unchanged.

When the price elasticity of demand is high, a policy of stimulating the aggregate supply of domestic goods may be a more effective means of breaking the vicious circle. A supply policy may involve investment tax credits, employment subsidies, incentives to foreign investors, or relaxation of antipollution restrictions. All of these policies should increase the profit-maximizing level of output. In many ways, the response of the economy to an expansionary supply policy is similar to its response to an expansionary demand policy. In both cases, the equilibrium level of real output increases and the general price level falls in response to the increase in the demand for money. The principal difference in the long run is in the behavior of relative prices; an expansionary demand policy increases the relative price of domestic goods, while an expansionary supply policy has the opposite effect. For similar reasons, the policies are also likely to have a different impact on the current account; while the demand policy is certain to induce a current account deficit, the supply policy is more likely to induce a current account surplus because of the improvement in the competitive position of domestic producers.

The two policies do differ in their short-run dynamics, as can be seen by comparing Charts 3 and 4. Whereas the demand policy leads to a large initial appreciation of the exchange rate, and an immediate increase in output and employment, the supply policy has a far more muted impact on these variables in the short run. There is a small appreciation owing to speculation and central bank intervention, and this appreciation does decrease demand in the short run. However, the short-run reaction is rapidly dominated by the deflation of domestic prices caused by the excess supply of domestic goods. This deflation provides a stimulus to demand, leads to a decrease in wages, and is associated with an appreciation of the exchange rate. In contrast to the demand policy, the final increase in output will be positively related to the price elasticity of demand for domestic goods in this case.

Before concluding this section, two possible objections to the analysis will be considered. The first relates to the downward rigidity of prices and wages; many observers would argue that the predictions in this section are implausible because of the empirical fact that nominal wages never fall. This is, however, a fallacious argument. The model in the text is set, for expositional convenience, in a world without steady inflation. In an inflationary environment, the conclusion to be drawn from the analysis is that a fiscal expansion will reduce the rate of wage and price inflation, rather than reducing the absolute level of wages and prices.

The second objection relates to the prediction that an expansion in aggregate demand will cause the exchange rate to appreciate. Since the policy clearly increases the demand for imported goods, and hence leads to a current account deficit, one could argue that a balance of payments analysis leads to the prediction that the exchange rate would depreciate. This argument may be countered on two grounds. First, from a balance of payments viewpoint, it is not at all certain that an expansionary demand policy will result in an overall incipient balance of payments deficit. Since the increase in demand must be financed by borrowing, the policy will also result in an excess supply of assets, which will be reflected in an incipient capital account surplus. Since the demand for domestic goods does increase, the incipient current account deficit should be less than the incipient capital account surplus. The second counterargument is based upon the definition, derived from Walras’ law, that the excess supply of goods and interest-bearing assets is equal to the excess demand for money. Since the policy unambiguously increases the demand for money without influencing the supply, it follows that the policy must induce an incipient balance of payments surplus, which will be eliminated by an appreciation of the exchange rate. Finally, the view that an expansionary fiscal policy appreciates the exchange rate in a world of complete capital mobility has a long history in international economics. The first formal statements of the argument are contained in Mundell (1968, chapters 11, 17, and 18) and Fleming (1962).

The preceding discussion is not meant to understate the difficulty of escaping from a vicious circle. Both the aggregate demand and aggregate supply policies rely on the assumption that the increase in the quantity of debt required to finance the policies does not influence the domestic real rate of interest. If international capital markets are not perfectly integrated or if the domestic debt instruments bear a risk premium that is related to the outstanding stock of debt, then the policies will increase real interest rates, and the conclusions reached in this section will have to be modified to account for the effect of the higher real interest rates. In addition, it may be very difficult to increase the government’s budget deficit without inducing some increase in the supply of money. Both of the policies discussed in this section lead to situations of tight money, and there is a tendency for both commercial banks and central banks to respond to increases in the demand for money by increasing the supply. Finally, it may be an extended period of time before the policies have their postulated effects upon the levels of output and employment. In particular, firms will require evidence that the policy changes are permanent before they will be willing to adjust their production and capital budgeting decisions in response to the policies. All of these considerations imply that theory can provide only a guide to policy; implementation of particular proposals requires a detailed knowledge of the institutional and historical characteristics of the economy in question.

V. Conclusion

This paper has demonstrated that the pattern of price, wage, and exchange rate dynamics described by proponents of the vicious circle hypothesis may be derived from a general equilibrium model of an economy operating under a regime of managed flexible exchange rates. Although it appears that the exchange rate causes subsequent movements in prices and wages, the paper has demonstrated that the probable cause of both the depreciation of the exchange rate and the inflation of domestic prices is an expansionary money supply. When asset prices—exchange rates and interest rates—are determined in auction markets, while wages and commodity prices are set by contract, changes in underlying economic conditions are first reflected in the auction prices, so that the impression is created that these prices cause changes in the contractual prices. However, the paper has demonstrated that it is necessary to go back to the underlying economic conditions in order to provide a complete analysis of the sources of inflation and depreciation. In this analysis, monetary expansion results in a pattern of dynamic adjustment in prices, wages, and exchange rates that is consistent with the published descriptions of the vicious circle hypothesis. The theoretical model consequently supports the view that the wage-price-exchange rate spiral in the United Kingdom and Italy between 1973 and 1976 was primarily the result of excessive money creation.

The paper has also presented an analysis of the effectiveness of monetary and fiscal policy under a system of managed flexible exchange rates. Effectiveness was defined as the increase in the stock of goods produced as a result of the implementation of a monetary or fiscal policy. This analysis generally supports the view, expressed by proponents of the vicious circle hypothesis, that rapid adjustment in prices and wages limits the effectiveness of monetary policy, and that monetary policy is likely to be less effective in more open economies. However, the opposite conclusion was reached in regard to policies that attempted directly to increase the demand for, or the supply of, domestically-produced goods. In these cases, rapid price and wage adjustment not only result in a greater stimulus to output and employment but also serve to lessen the inflationary pressure on prices and costs.

This conclusion forms the basis for policies designed to permit countries to escape from a vicious circle. Although the ultimate solution must involve a reduction in the rate of monetary growth, the paper has recognized that a tight monetary policy, by itself, may be infeasible because of the resulting increase in unemployment. As an alternative, an expansionary demand or supply policy was found to both stimulate output and employment and reduce the inflation of prices and costs. The only necessary restriction on the policy is that the increase in demand must not be financed, either directly or indirectly, by an expansion in the money supply. This conclusion was based upon the following considerations. First, an expansion in demand that is financed by borrowing will not result in higher interest rates if capital is perfectly mobile internationally. In other words, an increase in the supply of bonds, ceteris paribus, will not be inflationary because the world capital market is assumed to be capable of absorbing the additional supply without changing interest rates. Second, the increase in real income will increase the demand for money. This increase in the demand for money will lead to an incipient balance of payments surplus, which will be eliminated by an appreciation of the exchange rate. Finally, the appreciation of the exchange rate will lessen the inflation of wages and prices by lowering the cost of imported final and intermediate goods. This conclusion should not be interpreted as an advocation of a persistent policy of deficit financing. The benefits of the higher level of real income must be weighed against the increase in the level of international indebtedness in the assessment of the longer-run impact of the policy.

APPENDIX

This appendix provides a derivation of the index of policy effectiveness employed in the text. This index is defined as

\begin{matrix} G (z) = \int_{0}^{\infty} (y (t) - \bar{y}) d t & (26) \end{matrix}

In order to derive the index, it is necessary to solve the dynamic model for the time path of the price level. The first step in this solution involves the solution of equations (19) and (20) for the following second-order differential equation:

\begin{matrix} \dot{p} + (π_{p} + χ_{w}) \dot{p} - (π_{w} χ_{p} - χ_{w} π_{p}) (p - \bar{p}) = 0 & (27) \end{matrix}

The solution to equation (27) is of the form

\begin{matrix} p (t) = \bar{p} + A_{1} e^{r_{1} t} + A_{2} e^{r_{2} t} & (28) \end{matrix}

where r₁ and r₂ are the solution to the quadratic equation

\begin{matrix} r_{1}, r_{2} = - {(π_{p} + χ_{w}) \pm \sqrt{{(π_{p} - χ_{w})}^{2} + 4 π_{w} χ_{p}}} / 2. & (29) \end{matrix}

and the constants, A₁ and A₂, may be found from the initial conditions to be

\begin{matrix} A_{1} = \frac{π_{p} + r_{2}}{r_{2} - r_{1}} (p (0) - \bar{p}) - \frac{π_{w}}{r_{2} - r_{1}} (w (0) - \bar{w}) & (30) \end{matrix}

\begin{matrix} A_{2} = \frac{π_{p} + r_{1}}{r_{2} - r_{1}} (p (0) - \bar{p}) - \frac{π_{w}}{r_{2} - r_{1}} (w (0) - \bar{w}) & (31) \end{matrix}

Since the discriminant in equation (29) is positive, the roots are both real and distinct, which implies that the adjustment of prices toward the equilibrium level will be monotonic. With equation (28) in hand, the path of the level of output follows immediately from equation (18)

\begin{matrix} y (t) - \bar{y} = - ψ (p (t) - \bar{p}) & (32) \end{matrix}

\begin{matrix} = - ψ A_{1} e^{r_{1} t} - ψ A_{2} e^{r_{2} t} & (33) \end{matrix}

The index of policy effectiveness may therefore be expressed as

\begin{matrix} G (z) = - ψ A_{1} \int_{0}^{\infty} e^{r_{1} t} d t - ψ A_{2} \int_{0}^{\infty} e^{r_{2} t} d t & (34) \end{matrix}

\begin{matrix} = - ψ A_{1} / r_{1} - ψ A_{2} / r_{2} & (35) \end{matrix}

All of the coefficients in equation (35) may be related to the structural parameters through the preceding definitions. As mentioned in the text, it is extremely difficult to derive any qualitative conclusions about the direction of influence between the structural parameters and the index of effectiveness, but it is a simple matter to find the direction of influence through numerical calculations based upon postulated values.

Finally, consider the case in which the authorities exhibit a preference for current output over future output, as expressed in a rate of time preference, ζ. The present value of the increase in output owing to the policy change, evaluated using this rate of time preference, is

\begin{matrix} G^{'} (a) = \int_{0}^{\infty} ((t) - \bar{y}) e^{- ζ t} d t & (36) \end{matrix}

Following the same procedure as outlined above,G ’(z) may be expressed as

\begin{matrix} G^{'} (z) = - ψ A_{1} / (r_{1} - ζ) - ψ A_{2} / (r_{2} - ζ) & (37) \end{matrix}

The index defined in equation (37) penalizes future output relative to current output to a degree determined by the rate of time preference.

REFERENCES

Argy, Victor, and Joanne Salop, “Price and Output Effects of Monetary and Fiscal Policies Under Flexible Exchange Rates” (unpublished, International Monetary Fund, November 21, 1978).
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Bank for International Settlements, Forty-Seventh Annual Report (Basel, 1977).
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Belgium, National Bank of, Report on the Activities of the Year 1976 (Brussels, 1977).
Braun, Anne R., “Indexation of Wages and Salaries in Developed Economies,” Staff Papers, Vol. 23 (March 1976), pp. 226–71.
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Braun, Anne R., “Incomes Policies in Industrial Countries Since 1973,” (unpublished, International Monetary Fund, January 31, 1978).
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Brillembourg, Arturo, “Purchasing Power Parity Tests of Causality and Equilibrium” (unpublished, International Monetary Fund, December 27, 1976).
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Cooper, Richard N., “An Analysis of Currency Devaluation in Developing Countries,” in International Trade and Money, ed. by Michael B. Connolly and Alexander K. Swoboda (London, 1973), pp. 167–96.
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Crockett, Andrew D., and Morris Goldstein, “Inflation Under Fixed and Flexible Exchange Rates,” Staff Papers, Vol. 23 (November 1976), pp. 509–44.
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Dornbusch, Rudiger, “Expectations and Exchange Rate Dynamics,” Journal of Political Economy, Vol. 84 (December 1976), pp. 1161–76.
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Falchi, Giannandrea, and Mauro Michelangeli, “IMF Surveillance of Exchange Rates and the Problem of the Vicious Circle” (unpublished, Bank of Italy, Research Office, April 5, 1977).
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Fischer, Stanley, “Wage Indexation and Macroeconomic Stability,” Journal of Monetary Economics, Vol. 5, Supplementary Series (1977), pp. 107–47.
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Frenkel, Jacob A., and Harry G. Johnson, eds., The Monetary Approach to the Balance of Payments (London, 1976).
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Friedman, Milton, “The Case for Flexible Exchange Rates,” in his Essays in Positive Economics (University of Chicago Press, 1953), pp. 157–203.
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Friedman, Milton, “The Role of Monetary Policy,” American Economic Review, Vol. 58 (March 1968), pp. 1–17.
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Fleming, J. Marcus, “Domestic Financial Policies Under Fixed and Under Floating Exchange Rates,” Staff Papers, Vol. 9 (November 1962), pp. 369–79.
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Grey, Jo Anna, “Wage Indexation: A Macroeconomic Approach,” Journal of Monetary Economics, Vol. 2 (April 1976), pp. 220–35.
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Grey, Jo Anna, “On Indexation and Contract Length,” Journal of Political Economy, Vol. 86 (February 1978), pp. 1–18.
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International Monetary Fund, Summary Proceedings of the Thirty-First Annual Meeting of the Board of Governors (Washington, 1976).
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International Monetary Fund, The Monetary Approach to the Balance of Payments (Washington, 1977).
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Mundell, Robert A., International Economics (New York, 1968).
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Niehans, Jürg, “Some Doubts about the Efficacy of Monetary Policy Under Flexible Exchange Rates,” Journal of International Economics, Vol. 5 (August 1975), pp. 275–81.
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Phelps, Edmund S., Inflation Policy and Unemployment Theory: The Cost-Benefit Approach to Monetary Planning (New York, 1972).
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Sims, Christopher A., “Money, Income, and Causality,” American Economic Review, Vol. 62 (September 1972), pp. 540–52.
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Mr. Bilson is Assistant Professor of International Economics in the Graduate School of Business at the University of Chicago. He was formerly an economist in the External Adjustment Division of the Fund’s Research Department and an Assistant Professor in the Department of Economics at Northwestern University. He is a graduate of Monash University, Melbourne, and the University of Chicago.

The author is grateful to Jacob A. Frenkel, Robert J. Gordon, and to members of the International Trade Workshop at the University of Chicago for comments on an early draft of this paper. The views expressed are solely the responsibility of the author.

International Monetary Fund (1976), p. 93.

Ibid., p. 74.

Belgium, National Bank of (1977), pp. XI–XII.

See Sims (1972). Brillembourg (1976) also examines the causal relationship between prices and exchange rates by means of the Sims-Granger tests.

Bank for International Settlements (1977), pp. 38, 40.

See Crockett and Goldstein (1976, pp. 531–37), for an evaluation of the discipline argument.

Cooper (1973) concluded, on the basis of a study of 23 devaluations that occurred between 1953 and 1966, that a devaluation roughly doubles the probability that the government will be removed from power.

Under the gold standard system, the central bank was constrained by the possibility of running out of gold; under fixed exchange rates, the constraint was the possibility of running out of reserves and credit lines; only flexible exchange rates offer the possibility of unlimited monetary expansion.

See Braun (1976, 1978) for a useful survey of wage-setting behavior in the major industrial countries.

The argument that indexation exacerbates the real effect of real disturbances is developed in Fischer (1977) and Grey (1976, 1978).

Specific functional forms will be used throughout the paper in order to reduce the complexity of the notation and to aid in the interpretation of the results.

This specification is also employed by Niehans (1975) and Dornbusch (1976). Dornbusch derives conditions under which the forecasts provided by the equation are equal to the actual rate of depreciation.

See Friedman (1968). Phelps (1972, p. 35) summarizes the argument in his statement that “A change in inflation policy can bring ‘only’ a temporary variation of output and employment, and, further, the prolonged maintenance of an unemployment rate away from the natural level must eventually bring either rising inflation or growing deflation in an explosive fashion.”

See Frenkel and Johnson, eds. (1976) and International Monetary Fund (1977) for collections of papers on the monetary approach to the balance of payments.

The last factor enters because of the influence of real income on aggregate demand. Assume that the complete specification of the demand function is $y = {\bar{y}}^{d} + γ_{1} (y - {\bar{y}}^{d}) - γ_{2} (p - e - p^{*})$ This formulation is equivalent to equation (6) with $γ = γ_{2} / (1 - γ_{1}) .$

In logarithmic form, the Cobb-Douglas production function can be written as $y = y^{\circ} + α_{1} x_{1} + α_{2} x_{2}$ where x₁ = the number of units of the labor input; x₂ = the number of units of the imported input; y^∘ = a constant related to the technical characteristics of the production process and the capital stock; and α₁ and α₂ are, respectively, the shares of labor costs and imported input costs in total costs. Profit maximization requires that the marginal product of the input be equal to the marginal cost. These first-order conditions, in logarithmic form, are $\begin{matrix} \ln (a_{1}) + y - x_{1} = w - ρ \\ \ln (a_{2}) + y - x_{2} = e + p^{*} - p \end{matrix}$ The profit-maximizing level of output may be found from these conditions to be $\bar{y} = {\bar{y}}^{s} - δ_{1} (w - p) + δ_{2} (p - e - p^{*})$ where $\begin{matrix} {\bar{y}}^{s} = [y^{\circ} + a_{1} \ln (a_{1}) + a_{2} \ln (a_{2})] / (1 - a_{1} - a_{2}) \\ δ_{1} = a_{1} / (1 - a_{1} - a_{2}) a n d δ_{2} = a_{2} / (1 - a_{1} - a_{2}) \end{matrix}$ The equation in the text follows immediately from the assumption that $\dot{p} = θ_{p} [y - \bar{y}]$

It would be possible to allow for steady-state inflation through a simple extension of the model. The equilibrium condition would then be that the rate of inflation be equal to the rate of monetary expansion less the rate of growth of real income.

A derivation of G (z) is provided in the Appendix. It would be possible to allow for discounting of future output by incorporating a discount factor into equation (18). This alternative measure would be the present value of the future stream of income from the policy.

This conclusion has also been reached by Argy and Salop (1978) in a static model of output and price level determination under flexible exchange rates.

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IMF Staff papers: Volume 26 No. 1

Author: International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1979: Issue 001

Publisher:: International Monetary Fund

ISBN:: 9781451956528

ISSN:: 1020-7635

Pages:: 232

DOI:: https://doi.org/10.5089/9781451956528.024

Keywords
I. Theoretical Foundations
II. The Steady-State Solution
III. Short-Run Dynamics
IV. How to Escape from a Vicious Circle
V. Conclusion
- APPENDIX
REFERENCES

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The Pattern of Dynamic Adjustment

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Simulation of the Effect of a 10 Per Cent Increase in the Money Supply

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Simulation of the Effect of a 10 Per Cent Increase in Aggregate Demand

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Simulation of the Effect of a 10 Per Cent Increase in Aggregate Supply

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Table 1.

Determinants of Policy Effectiveness

		Elasticity¹
Structural Parameter	Value	1. Money Supply	2. Aggregate Demand	3. Aggregate Supply
	Open Economy
α	0.50	0.221	0.221	0.221
η	1.00	0.000	0.000	0.000
ϵ	20.00	0.000	0.000	0.000
λ	0.04	0.000	0.000	0.000
ρ₁	0.10	0.000	0.000	0.000
ρ₂	0.10	0.000	0.000	0.000
γ	1.50	0.663	0.663	0.663
θ_ρ	0.05	−0.331	−0.292	−0.398
θ_w	0.05	−0.663	−0.702	−0.579
δ₁	2.00	0.442	0.481	0.375
δ₂	2.00	−0.442	−0.442	−0.442
Gain		2.000	−1.200	−0.741
	Less Open Economy
a	0.80	1.137	1.137	1.137
η	1.00	0.000	0.000	0.000
ϵ	20.00	0.000	0.000	0.000
λ	0.04	0.000	0.000	0.000
ρ₁	0.10	0.000	0.000	0.000
ρ₂	0.10	0.000	0.000	0.000
γ	0.50	0.758	0.758	0.758
θ_p	0.05	−0.248	−0.216	−0.306
θ_w	0.05	−0.746	−0.778	−0.688
δ₁	3.00	0.461	0.494	0.404
δ₂	1.00	−0.473	−0.473	−0.473
Gain		1.904	−1.217	−0.687

where M = the number of units of the domestic currency outstanding
	P_m = the price deflator for nominal money balances
	K = a shift factor in the demand for money
	Y = the level of domestic real income
	η = the income elasticity of the demand for money
	exp = the exponential operator
	i = the nominal rate of interest
	ϵ = the interest rate semielasticity of the demand for money

where M = the number of units of the domestic currency outstanding
	P_m = the price deflator for nominal money balances
	K = a shift factor in the demand for money
	Y = the level of domestic real income
	η = the income elasticity of the demand for money
	exp = the exponential operator
	i = the nominal rate of interest
	ϵ = the interest rate semielasticity of the demand for money

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Abstract

I. Theoretical Foundations

II. The Steady-State Solution

III. Short-Run Dynamics

IV. How to Escape from a Vicious Circle

V. Conclusion

APPENDIX

REFERENCES

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