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Inflation and Monetary Reform

Author(s):
Pierre-Richard Agénor, and Anna Lennblad
Published Date:
August 1992
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I. Introduction

The introduction of a new currency has occurred in a variety of economic and historical circumstances. Newly independent countries view the creation of a national monetary unit as a symbol of political and economic independence. Following periods of high inflation--at the end of which the value of the “old” currency becomes considerably depreciated--some countries have introduced a new currency as a “pure” change in numeraire. In a large number of cases, however, monetary reforms of this type were part of a comprehensive program aimed at fighting hyperinflation by an inital reduction in the money stock, followed by restraint of liquidity expansion. Early cases of monetary reform occurring in such circumstances are the introduction of the rentenmark in Germany in 1923 and the Zloty in Poland in 1924, while the introduction of the Austral in Argentina and the Cruzado in Brazil in the mid-eighties provide more recent examples (see Dornbusch and Fischer, 1986). After the Second World War, new currencies were introduced in several European countries as a measure to eliminate a “liquidity overhang”, particularly in countries where inflation had remained “repressed” by controls imposed during the war and where rationing and/or hoarding were creating large disequilibria between the existing money stock and available supply of goods. The 1948 reform in Germany is probably the best known example of this motivation for monetary reform (Dornbusch and Wolf, 1990).

The macroeconomic dynamics associated with the introduction of a new currency have not, however, been thoroughly examined in the existing literature. 1/ A possible reason for this might be the well-known neutrality associated with a pure change in numeraire. Clearly, if private agents adopt prices--including exchange rates, in an open economy--in terms of the new currency by applying the same conversion factor as the government, a change in numeraire would be “neutral”, that is, would have no effect on the real money stock. In practice, however, governments have often used non-uniform conversion rates for various categories of assets and liabilities as a mechanism to effect a “forced” redistribution of wealth, or as a measure to eliminate a perceived “excess” of liquidity. 2/ In such conditions, the introduction of a new currency is likely to exert a variety of real and financial effects on the economy, depending in particular on the state of expectations.

This paper examines the anticipatory dynamics associated with non-uniform monetary reforms in a small open economy with optimizing and forward-looking agents. Section II describes the model. Section III studies the effect of alternative reform strategies on the path of inflation and the behavior of foreign currency holdings. The analysis is then extended in Section IV to consider uncertainty over the length of the transition period between announcement and implementation. Section V summarizes the main results of the paper, examines its policy implications, and discusses some possible extensions of the analysis.

II. Structure of the Model

Consider a small, open economy in which the official exchange rate is fixed by the central bank. Due to lack of foreign exchange reserves, however, agents cannot obtain foreign exchange through the official market. All foreign currency operations are conducted through a parallel market, at a more depreciated exchange rate. There are no surrender requirements on exports, and official reserves therefore remain constant. 1/ Private agents in the economy possess three categories of assets: domestic money, domestic government bonds, and foreign currency. Government bonds pay a fixed real rate of interest per period. Domestic output consists of a single exportable good sold abroad, while total consumption is imported, with all transactions--as a result of foreign exchange rationing by the central bank--going through the parallel market. There are no capital flows between the domestic economy and the rest of the world. Finally, agents are endowed with perfect foresight.

The domestic price of the imported good Pt is given by

where P* denotes the foreign price level, and St the parallel exchange rate (that is, the price of foreign exchange in domestic currency units). The foreign price is taken as constant, so that setting P* = 1 yields Pt = St. The domestic price level is therefore identical to the parallel exchange rate, which measures the (marginal) cost of foreign exchange.

The representative consumer’s problem consists in maximizing utility subject to a budget constraint. Let At denote nominal financial wealth, defined as

where Mt denotes domestic money balances, Bt holdings of government bonds, and Ft the foreign currency value of the stock of foreign exchange, which is valued at the parallel exchange rate.

Changes in nominal financial wealth are determined by

where Θ(St/Q) denotes the consumer’s endowment--consisting of output of the domestic good--Q the official (fixed) exchange rate, ct the real consumption level, ¿t the nominal interest rate on government bonds, gt real transfers from the government, and tFt capital gains on foreign currency holdings associated with changes in the parallel exchange rate. Output of the export good is assumed to depend positively on (one plus) the parallel market premium, St/Q. 1/

Equation (3) relates changes in nominal financial wealth to the unofficial current account (measured by the difference between parallel market exports and consumption imports), net transfers and interest payments from the government, and valuation changes on the stock of foreign currency holdings.

The nominal interest rate is defined by

where ח denotes the (constant) real interest rate on government bonds and πtt/Pt the inflation rate--or, equivalently here, the rate of depreciation of the parallel exchange rate.

The consumer maximizes the discounted sum of future utility over an infinite horizon, with instantaneous utility being a function of consumption and real holdings of domestic and foreign currencies: 1/

in which mtMt/Pt denotes real domestic money balances, and δ the subjective discount rate. The functions u(.) and v(. , .) are assumed to be strictly concave and twice continuously differentiable.

Assuming that the discount rate is equal to the real interest rate on government bonds and that the function v(. , .) is of the constant elasticity of substitution variety, maximization of (5) subject to (1)-(4) yields 2/

and c = c, ∀t, so that consumption remains constant over time.

Equation (6) indicates that the ratio of domestic to foreign currency holdings is inversely related to the inflation rate, which measures the opportunity cost of holding the domestic currency.

To close the model requires specifying the government budget constraint. In general, this constraint can be written as

or, with the real stock of bonds equal to btBt/Pt,

To simplify the analysis, assume that the government does not finance the budget deficit by money creation or bond issuance (so that t = Ḃt = 0) but rather varies net transfers so as to maintain fiscal equilibrium (gt = - ¿tbt). 1/ Under this assumption, combining equation (7) with equation (3)--expressed in real terms--yields

which indicates that the real rate of accumulation of financial assets is equal to the rate of accumulation of foreign exchange through the parallel market, which in turn equals exports minus consumption of imported goods.

The dynamics of the model are determined by equations (6) and (8). Taking a log-linear approximation of this system--and dropping constant terms--yields

where zt = logZt, and Z = M, F, S, Q. Since there is rationing in the official market for foreign exchange, reserves are exogenous.

Assuming, in addition, that domestic credit is constant implies, that the nominal money stock--or, rather, its logarithm--remains constant at m. To maintain portfolio equilibrium, therefore, private agents can only alter their holdings of foreign currency.

The structure of the model developed above can be briefly summarized as follows. Private agents are rationed in the official market for foreign exchange and conduct all trade transactions (exports as well as imports) through a (quasi-legal) parallel market. The domestic price level (that is, the price of the imported good) reflects therefore the behavior of the marginal cost of foreign exchange--the parallel exchange rate. The optimal decision rule for private agents is to maintain real consumption constant over time, and to vary the composition of their currency holdings inversely with the inflation rate. The government maintains fiscal equilibrium by varying net transfers to households. Nominal wages are indexed on the official and parallel market prices of imported goods. Export supply is thus a function of the exchange rate differential which, as a result of the constant consumption path, determines the evolution over time of foreign currency holdings. Because nominal holdings of domestic currency are fixed by the budget financing rule followed by the authorities, private agents must adjust their stock of foreign currency to maintain portfolio equilibrium. However, this can only occur gradually and would typically require the parallel market exchange rate to “jump” initially in response to anticipated or unanticipated shocks. An examination of the conditions that determine the direction of such jumps in the context of a monetary reform is the focus of the following sections.

III. Solution and Dynamics

We now describe the solution of the model presented above under alternative assumptions about the nature and timing of monetary reform. The case in which no reform is ever expected to take place is examined first. The analysis then focuses on the case in which the monetary reform is announced well before being implemented, allowing agents to adjust their portfolios gradually. Finally, we examine the case in which the reform occurs “overnight”, and is consequently unanticipated by agents.

1. The pre-reform steady state

Equations (9a) and (9b) can be written as

The system described by (10) is saddle-point stable. 1/ Let λ1, denote the negative root and λ2 the positive root, given by

After solving for the particular solutions, the complete solution of (10) can be shown to be

where C1 and C2 are as yet undetermined coefficients.

Suppose that the existing economic regime is expected to last forever. Stability would then require setting C2 = 0 in the solutions (11a) and (11b). Using an initial condition on the stock of foreign currency holdings would thus allow the determination of C1. The saddle path solution would therefore be given by

where f = m - q ≥ 0.

The economy’s equilibrium path is the unique non-explosive path SS (that passes through the stationary point E) depicted in Figure 1. If the parallel exchange rate is sufficiently depreciated (appreciated) foreign currency holdings are rising (falling), as indicated by the arrows pointing east (west) in the Figure. Along the saddlepath, the parallel exchange rate and foreign currency holdings evolve according to

Figure 1.Steady State Equilibrium in the Pre-Reform Regime

which indicates that SS has a negative slope. 1/

However, if the authorities announce today their intention to introduce a new currency in the future, agents will anticipate the abandonment of the “old” regime. In this context, the coefficient C2 need not be zero. Instead, as shown below, agents will set coefficients C1 and C2 at values that satisfy constraints imposed by a perfectly anticipated transition to the post-reform regime.

2. Pre-announced monetary reform

Consider first the case in which the authorities announce at t = 0 the conversion rate as well as the new exchange rate that will be used at period T. 2/ The behavior of prices and the parallel exchange rate in the transition period will depend not only on the structure of the economy in the pre-reform regime, but also--with forward-looking agents--on the nature of the post-reform regime.

The monetary reform is here defined as consisting of the replacement of the currency currently used in domestic transactions with a new numeraire. Holders of cash balances in the “old” currency are assumed to obtain from the central bank new banknotes by presenting the old ones at a rate of exchange equal to the rate of conversion. All outstanding nominal assets and liabilities are also re-written in the new currency. However, a non-uniform structure of conversion rates applies to different categories of assets and liabilities, thereby leading to “confiscation” of some assets.

Formally, let T > 0 represent the future transition date announced at period t = 0--that is, the initial instant at which the authorities intend to introduce the new currency, and let a ‘~’ denote the post-reform values of the variables in the system for t ≥ T. Let ρ denote the (logarithm of the) rate of conversion of the old currency into the new one, and let ε → 0+. If the reform is on a one-to-one basis (that is, a pure change in numeraire), we have

implying that the real money stock does not change an instant after the reform, compared to its value an instant before. The introduction of the new currency is therefore “neutral.” Suppose, however, that the authorities adopt a non-uniform structure of conversion rates--perhaps as an anti-inflationary measure, as discussed earlier--that is such that some components of the nominal stock of money are converted at a lower rate than the one used by traders in the parallel foreign exchange market, ρ. Then, we have

where α ≥ 1 can be defined as the “expropriation” or “confiscation” factor. Defining mTm¯+ρ(1α), and comparing (14) and (15) shows that a non-uniform conversion rate, as defined here, is equivalent to a permanent fall in the nominal money stock. 1/

Solving the model as before yields a saddle-path solution that is similar to the solution given in equations (12) with mT+ replacing m that is, for t ≥ T, 2/

where C is a (as yet undetermined) parameter and κ1 is as given above.

Under perfect foresight, the time paths for the variables of the system are continuous for t > 0. In particular, no variable can jump at t = T. An anticipated jump in prices and the parallel exchange rate, for instance, would provide an opportunity to realize a capital gain on foreign currency holdings which would be arbitraged away by competition among agents. The complete solution of the model must therefore satisfy three conditions, that “connect” the pre- and post-reform regimes: an initial condition on foreign currency holdings, and two conditions on the solutions at t = T, that prevent a jump in the parallel exchange rate and foreign currency holdings at the moment the new currency is introduced:

These conditions allow us to determine the 3 unknown parameters, C, C1, and C2. Using equations (11), (16) and (17) yields 1/

where Δ=κ1e(λ1+λ2)T(κ2κ1)<0.

Substituting equations (18a) and (18b) in equations (11) yields the complete solution for the parallel exchange rate and foreign currency holdings during the transition period. Assume that initially, the system is in a steady state, so that f0 = f. This implies that C, C1 < 0. The transition solution is thus given by

for 0 ≤ tr.

Equations (12) characterize the path of reserves and the parallel rate prior to the announcement of the future reform. From the first equation, and since f0 = f, we have s0 - = q. Equations (19) therefore indicate that, since mT+ < m, an announcement at t = 0 of a future monetary reform at T leads to an immediate appreciation of the domestic currency in the parallel market for foreign exchange, with no change in foreign currency holdings.

Figure 2 illustrates the transitional dynamics associated with an anticipated monetary reform. The position of the economy before the reform announcement is at point E. The steady-state equilibrium in the post-reform regime is E', corresponding to a stock of foreign currency holdings equal to mT+q˜ and a parallel exchange rate equal to q. 1/ At the moment the future introduction of the new currency is announced, the parallel exchange rate jumps downward to a point such as A and keeps appreciating thereafter until it reaches--without further jumps--the new saddle-path S'S' (point B) at the moment the reform is implemented, T. From then on, the parallel exchange rate starts depreciating and converges to point E'. Foreign currency holdings fall continuously during the transition period and in the post-reform regime, until the (lower) steady-state value is reached at point E'.

Figure 2Dynamics in Anticipation of Reform

The temporal behavior of the parallel exchange rate and foreign currency holdings before and after the introduction of the new currency is also illustrated in Figure 3. The Figure assumes that, initially, f0 < f, so that the parallel market premium is, an instant before the reform announcement, positive. 2/ In the first panel of the Figure, the trajectory of the price level before the future introduction of the new currency is announced corresponds to the saddlepath SS shown in Figure 2. At t = 0, the parallel exchange rate jumps downward and keeps appreciating thereafter--relative to its previously anticipated path--at an accelerating pace until it reaches its post-reform path at T. At that point, it starts depreciating and converges smoothly towards its (unchanged) steady-state value, q. The path of foreign currency holdings is illustrated in the second panel of Figure 3. No jump in the level of foreign currency holdings occurs at t = 0 but its rate of decumulation accelerates over time--until period T--towards its post-reform steady-state value (mT+ - q), obtained by setting t → ∞ in equation (16). 1/

Figure 3Temporal Behavior of Prices and Foreign Currency Holdings

Intuitively, the reason for the initial downward jump in the parallel exchange rate upon announcement of the reform and the subsequent appreciation is as follows. Under perfect foresight, agents know that the future reform will imply a fall in the domestic money stock, and therefore disturb the composition of their portfolios. Consequently, they will immediately begin to reduce their holdings of foreign currency, so as to maintain portfolio equilibrium at the moment the discrete change in the domestic money stock takes place. For this to occur, the parallel exchange rate must appreciate to a point where it is expected to depreciate. The appreciation occurs in two steps, on impact following the announcement, and during the transition period. The size of the initial jump is determined by two factors: the length of the transition period, and the requirement that the rate of decumulation of foreign currency holdings must be on the (unique) stable trajectory in the post-reform regime.

3. “Overnight” monetary reform

Consider now the case where the introduction of the new currency occurs “overnight”, and is therefore unanticipated by private agents. 2/ Formally, this case can be analyzed by setting T → 0 in the solution equations (19). 1/ As shown in Figure 2, the parallel exchange rate jumps downward upon announcement to point A' on the new saddle path S'S', with no change in the initial stock of foreign currency holdings. Thereafter it depreciates steadily towards its post-reform steady state. The important difference with the previous case is therefore that the economy does not, at any moment, follow a divergent transitory path. The implication of this result is that if there is no explicit “cost” associated with a non-zero transition period, a pre-announced reform is more desirable than an overnight reform because it gives agents the possibility to work off gradually “excess” foreign currency balances.

Finally, we can briefly indicate how the model may be used to account for a temporary reduction of the money stock. As indicated in the introduction, monetary reforms have often been accompanied by a temporary freeze on some categories of monetary assets. A typical example is a decision, by the authorities, to maintain bank deposits above a certain level in blocked accounts for, say, 6 months. Formally, a temporary freeze of this type can be modeled as a reduction, at t = 0, of the nominal money stock from m to m0+, followed by an increase at t+T, that takes the money stock back to its original level. The phase diagram shown in Figure 2 can be used to analyze this case under the assumption that the date at which deposits are unfrozen is known with certainty. As before, the parallel rate will on impact appreciate somewhere between point E and A'. From then on, the system will follow an unstable path, in such a way that it reaches the stable trajectory SS associated with the original money stock at t+T. The parallel exchange rate therefore appreciates instantaneously to a point like A, and then starts depreciating along the path AC as agents increase their holdings of foreign currency. After reaching point C at t+T, the system moves along the saddlepath SS--with rising prices, a depreciating exchange rate, and a continuous fall in holdings of foreign exchange--back to the initial steady-state equilibrium, point E.

IV. Stochastic Transition Date

We now extend the model to consider the case in which agents are certain that a monetary reform will eventually take place. They also know what the structure of conversion rates will be (that is, the parameter α) but are uncertain about the actual date at which the reform will be implemented. However, they form a probability distribution over possible reform dates and make their portfolio decisions on the basis of the perceived course of events. 1/

Since agents do not know precisely the moment at which the new currency will be introduced, prices and the exchange rate will typically experience a jump (upward or downward) when the reform actually takes place--thus creating a capital loss (or gain) on domestic money holdings. The expected rate of depreciation of the parallel exchange rate will in general account for this potential loss. Assume that the instantaneous probability of reform--given that none has occurred to date--is exogenous and constant at ν. The (percentage) capital loss on holdings of domestic currency is given by υ(s˜tst), where s˜t denotes, as before, the level to which the parallel exchange rate jumps at the instant the reform takes place. Consequently, equation (9a) is replaced by 2/

while equation (9b) remains unchanged.

To determine the solution of the model in the transition period is now slightly more involved but conceptually straightforward. Before the reform announcement, the equations driving the parallel exchange rate and foreign currency holdings are given by equations (12), obtained by setting C2 = 0 in equations (11) and solving for C1 with the initial condition f0 = f0. Upon announcement, the system jumps to a new saddlepath--with foreign currency holdings unchanged--determined by solving the system formed by equations (9a') and (9b), with ν > 0. Once the reform is implemented, ν = 0 and the system must jump again to the post-reform saddlepath. The parallel exchange rate that obtains after the reform takes place must satisfy--assuming the reform occurs at t--an equation similar to (13):

where m+m + ρ(1 - α). Substituting equation (20) for s˜t in equation (9a') and solving the system (9a') and (9b) as before yields the required solution for the period between announcement and the (unknown) implementation date.

Figure 4 provides a graphical illustration of the transitional dynamics associated with a monetary reform that is expected to take place at an unknown date in the future. The announcement at t = 0 of the future reform at an uncertain date does not affect the slope of the [t = 0] curve, but does affect the position of the curve [t = 0], which moves to [t = 0]'. The new curve is flatter than the previous one. 1/ The equation of the new saddlepath QQ is given by

Figure 4Dynamics with a Stochastic Transition Date

where μ1 denotes the negative root of the system formed by (9a'), (9b) and (20). f* denotes the steady-state level of foreign currency holdings in the transition regime, and is given by

so that f* < f = mq. Since agents anticipate an appreciation of the domestic currency (that is, a capital gain on domestic money holdings), their long-run equilibrium position requires a lower stock of foreign currency holdings. It can also be shown that |μ1| > |λ1|, implying that the new saddlepath QQ is steeper than SS.

Assume again that the economy is initially in a steady-state equilibrium, at point E in Figure 4. Upon announcement, the parallel exchange rate appreciates from E to A on QQ and starts depreciating towards point P, which can be defined as a point of “temporary” or “quasi-” equilibrium, since it is associated with expectations of a reform that has not yet taken place. If the reform does not actually occur, and the economy reaches point P, it will remain there--as long as ν remains constant. When the reform is actually implemented, the curve [t = 0] shifts leftward. The slope of the post-reform saddlepath S'S' is the same as the slope of SS if no further reform is anticipated, implying that ν = 0. At that moment, the parallel market exchange rate experiences a second (downward) jump, from (say) point B to C, and starts depreciating thereafter towards the post-reform steady state, point E'. 1/ Equivalently, the domestic price level falls on impact, begins to rise towards a quasi- equilibrium point during the transition period, falls again upon implementation of the reform, and resumes its upward course towards its post-reform equilibrium value.

Assume now that the initial position of the economy is at a point such as D--corresponding to a positive premium--located on the saddlepath SS. Then, upon announcement of the reform (or, more generally, following an exogenous increase in the probability of reform), prices will jump upwards--to a point such as F on QQ--and start falling towards the quasi-equilibrium point P. When the reform is actually implemented, prices will jump downwards, as before, to a point located on S'S', and will begin converging towards the new steady state E'.

The implications of the above analysis are twofold. First, the announcement of a monetary reform with an uncertain implementation date will lead to a jump in the parallel exchange rate and the price level, even if agents foresee with certainty that a discrete jump--of a known magnitude--will indeed occur upon implementation. The direction of the jump cannot be determined a priori, and depends on the initial position of the economy. Nevertheless, the possibility remains that an increase in the probability of reform (or, equivalently, an increase in the likelihood of a fall in the nominal money stock) may raise prices, in comparison with a situation in which agents are perfectly informed of the policymaker’s intentions. 2/ More generally, fluctuations in the perceived probability of reform will generate fluctuations in inflation and portfolio decisions, as a result of changes in the expected rate of return on foreign currency holdings. It may also exacerbate inflationary pressures in the presence of inertial forces in wage and price setting mechanisms. Consider, for instance, an economy in which nontradables prices are set as a mark-up over wages and imported input costs, while tradable goods prices are determined--as previously postulated--by a purchasing power parity condition holding at the prevailing parallel exchange rate. Assume, in addition, that nominal wages exhibit downward rigidity. In such conditions, an increase in the probability of monetary reform may not only raise the overall price level, but also fuel inflation. 1/

V. Summary, Policy Implications, and Extensions

The purpose of this paper has been to examine the anticipatory dynamics associated with non-uniform monetary reforms in a small open economy with optimizing and forward-looking agents. Although the analytical framework developed above is highly simplified, the model offers some general implications that are likely to remain valid in a variety of alternative settings. 2/ The analysis suggests that a monetary reform that incorporates a once-and-for-all confiscatory element has a deflationary effect upon announcement as well as during the transition period, and leads ultimately to a “de-dollarization” of the economy. When the monetary reform occurs “overnight”, the fall in prices is more pronounced, but there is no change in foreign currency holdings. Under uncertainty about the reform date, a monetary reform leads to a downward jump in the price level at the moment the reform is implemented--in addition to the jump that occurs upon announcement--even if the behavior of prices in the post-reform regime is perfectly known by agents. Moreover, an increase in the probability of a future reform--or, equivalently, a greater likelihood of a future fall in the domestic money stock--may actually lead to a rise in domestic prices.

The key policy issue on which the model is able to shed some light relates to whether a monetary reform should be pre-announced or implemented by “surprise.” The analysis indicates that, if there are no substantive costs incurred by delaying the introduction of a new currency, pre-announcement may be preferable--provided the official statement is credible enough--since it leads to an immediate fall in prices and at the same time allows agents to work off gradually excess balances in foreign currency. 1/ Once a pre-announcement strategy is chosen, however, uncertainty about the actual reform date should be avoided. Keeping agents guessing about the likely date of reform may have an adverse effect on prices and may distort portfolio decisions by private agents.

The analysis developed in this paper can be extended in a variety of directions. One area that could be of considerable interest relates to the problem of determining the “optimal” length of the transition period between reform announcement and implementation, taking into account the costs and benefits faced by the authorities when deciding on the appropriate timing of a reform. Another important issue that needs to be addressed is the link between monetary reforms and changes in macroeconomic policy regimes, such as monetary and exchange rate policy. Countries that introduce a new currency often simultaneously alter the exchange rate arrangement that was previously in place: they may decide to move from a fixed to a floating exchange rate regime, or to change the currency to which the domestic monetary unit is pegged. A particularly interesting case relates to the situation in which a country decides to peg its currency to that of a low and stable inflation country. Such a switch would generate two types of effects. First, it would lower the expected opportunity cost of holding foreign currency assets, and provide an additional source of anticipatory dynamics. Second, it would generate a short-term “credibility gain” which could enhance the degree of confidence that agents attach to the new currency. Finally, the existence of a confiscatory element attached to monetary reforms is likely to have distributional effects that would alter the path of aggregate consumption or, more generally, the evolution of “real” variables. While some of these issues can be discussed in relatively straightforward extensions of the model developed above, 1/ others might require more substantial changes.

APPENDIX Solution to the Consumer Optimization Problem

Dividing equation (2) by Pt yields real wealth at as

where btBt/Pt denotes the real stock of bonds. Similarly, using (3) and (A1), changes in real financial wealth can be written as:

Assume that the utility function v(.,.) is of the CES variety:

Using (5), (A1), (A2) and (A3), the Hamiltonian can be written as

where λ denotes the co-state variable. Defining Λ = λeδt, first-order conditions are given by, with k = 1, 1/

Assuming that δ = ח implies from (A5d) that the marginal utility of wealth is constant so that, from (A5a), consumption is also constant, at c = u'−1(Λ). Equations (A5b) and (A5c) yield

which is equation (6) in the text, with κ = [ω/(1 − ω)]σ.

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*The authors would like to thank, without implication, Charles Adams, Donal Donovan, Allan Drazen, Robert Flood, Alexander Hoffmaister, Malcolm Knight, Timothy Lane, and Kent Osband for helpful discussions and comments on a previous draft.
1/Cagan (1956) briefly discussed the effect of an anticipated currency reform on money demand in his study of the German hyperinflation of the early 1920s (see also Siklos, 1990). A more formal discussion of this episode, that applies a stochastic “process switching” model to money supply behavior, was provided by Flood and Garber (1980) and Lahaye (1985). These authors did not, however, examine the macroeconomic implications of such reforms.
2/In the case of the 1948 German monetary reform mentioned above, money balances exceeding a given limit were converted at a lower rate, while in the 1979 reform in Ghana, currency was exchanged at a lower rate than deposits. In these reforms--as well as in (cont’d from page 1) Belgium in 1944, or Vietnam in 1975--bank deposits above a specified limit were also temporarily frozen by the government or confiscated. Note that structural rigidities--such as sticky prices or nominal wage contracts--could also lead to non-neutrality of a monetary reform, even with a uniform conversion rate.
1/For a model with a similar rationing rule, see Kharas and Pinto (1989). Alternatively, it could be assumed that the central bank resells its export proceeds in the parallel market.
1/A simple model that highlights this relationship is as follows. Suppose that the nominal wage in the economy is fixed and fully indexed on the official price of the imported good. Since total output is smuggled out, profits of the representative exporter--in domestic currency terms--are given by StΘt - QLt, where Lt denotes the quantity of labor used. Let Lt=L0Θtη, where η > 1. The first-order condition for profit maximization yields St-Q¯ηL0Θtη -1=0, so that
Note that a similar result would obtain if the nominal wage were indexed on a weighted average of the official and parallel market (cont’d from page 3) exchange rates, instead of depending only on the former rate. Neither assumption is, however, entirely satisfactory here, since no transactions take place at the official exchange rate. Extending the model in this regard would considerably complicate the analysis, without adding much insight.
1/For a model in which individual preferences are similarly defined, see Rogers (1990). The introduction of each currency separately in the consumer utility function--instead of entering aggregate money balances--assumes implicitly that domestic and foreign currencies are imperfect substitutes. This may occur, for instance, as a result of legal restrictions which require payments of certain transactions to be conducted in the domestic currency.
2/See the Appendix for a description of the solution procedure. The equality between the discount rate and the real rate of interest is necessary to obtain a stationary level of consumption. For δ < ח consumption would tend to zero, while for δ > ח it would grow indefinitely, regardless of the behavior of the inflation rate.
1/This assumption is not, of course, very realistic. It allows us, however, to focus on foreign currency holdings as the principal source of wealth dynamics.
1/The determinant of the system is -ψ/σ, implying that the two roots are of opposite sign.
1/Note that, from the definition of λ11/ψ| < 1. An increase in the inflation elasticity σ has no effect on the curve [ṡt = 0] and rotates SS clockwise. A rise in the elasticity of foreign currency holdings with respect to the premium ψ translates into a clockwise rotation of the saddlepath SS. Finally, a devaluation of the official exchange rate leads to an upward shift of the [t = 0] curve. A devaluation leads, in the steady-state, to an equi-proportional depreciation of the parallel exchange rate and a fall in foreign currency holdings.
2/In general, the choice of a conversion rate will reflect various considerations, including simplification of the operation--particularly the calculation of new prices by agents--and an attempt to bolster the credibility of the new currency as well as the new monetary policy (the public must be induced to think that the parity will be maintained). A full discussion of these issues is, however, outside the scope of the present paper (see Giovannini, 1992).
1/Implicit in the above formulation is the assumption that expropriation occurs at random, and that each individual agent faces only a small probability of being expropriated. Otherwise, the shift from domestic to foreign currency assets discussed below would occur abruptly, as soon as agents become aware of the future monetary change, or at the moment the reform announcement is made.
2/The official exchange rate is also assumed to be redefined in terms of the new currency. As a result, the premium is not affected and (9b) does not change.
1/Setting t = 0 in equation (11b), t = T in equations (11a)-(11b) and using (16) yields
olving this system yields equations (18).
1/Equation (16) implies that, as defined above (see equations 14 and 15) mT+ - m, so that - mT+ - q < f.
2/The assumption of a positive premium before announcement is empirically quite relevant and allows us, in any case, to highlight the nature of the initial jump. For t < 0 the equation driving the parallel rate is (12), while it is (19a) with (18a)-(18b) for 0 ≤ tT, and (16) for t ≥ T.
1/Note also that if the monetary reform is announced to occur in the very distant future--that is, for T → ∞--the announcement effect on the path of the parallel exchange rate and foreign currency holdings in the transition interval is negligible. Setting T → ∞ n equations (16) and (19) indicates that the solutions for st and st coincide with those for and s˜tandf˜t
2/As recently emphasized by Fisher and Turnovsky (1992), the consideration of “unanticipated” shocks in the type of model considered here requires in fact assuming “quasi-perfect foresight”: agents act as if they have perfect foresight, even though they are subject to surprises. Note also that an unanticipated change in the money stock would also affect the marginal utility of wealth, therefore generating real effects.
1/setting T → 0 in equations (19) and using (16) yields s0s0, and f0f0.
1/The analytical technique used here follows Daniel (1989), who examines uncertainty about temporary fiscal policy in an open economy. A more rigorous approach would be to reformulate the consumer’s optimization problem to account for an uncertain transition date, along the lines of Drazen and Helpman (1990), but this would not necessarily provide results that are qualitatively different from those obtained here. Note also that a more general discussion would allow simultaneously for uncertainty on the reform date and the structure of conversion rates.
2/The expected rate of change of the parallel exchange rate is, over an arbitrary interval of length h, given by
where s˜t+h denotes the post-reform value of the exchange rate, if the monetary reform indeed occurs over the interval (t,t+h). Dividing the above formula through by h and taking the limit as h → 0 yields the expression for the expected rate of change of the parallel exchange rate used in (9a').
1/The slope of [st = 0]' is given by
which is lower than unity--in absolute value--since |λ1/ψ| < 1, as noted above.
1/Assuming that the reform occurs at T, the size of the jump from B to C is given by s˜TsT.
2/The derivative of the slope of the [st = 0]' curve--as well as the slope of the saddlepath QQ--with respect to ν is positive since |λ1/ψ| < 1, as noted above. The point of temporary equilibrium P shifts to the left with a rise in ν. Since QQ becomes flatter, the length of the segment DF--the size of the price jump if the economy is initially at D--falls.
1/An extension of the analysis to endogenize the reform probability could follow along the lines of the Bayesian approach developed by Driffill and Miller (1991).
2/The assumption, for instance, of complete rationing in the official market for foreign exchange can easily be relaxed, but would increase the complexity of the analysis and would preclude a graphical representation of the results. Similarly, the assumption of fiscal equilibrium could be dispensed with, at the cost of complicating substantially the algebra without altering the main insights discussed in the text. Finally, it is important to stress that some of the basic assumptions made above--in particular, the existence of parallel market transactions, and the emphasis on currency substitution--are particularly relevant for small open developing economies, as well as most of the former Soviet republics.
1/An “overnight” reform may be preferable to a pre-announced reform if the latter approach is likely to give rise to cross-border currency movements during the transition period, as agents attempt to obtain a capital gain on their currency holdings. This is a particularly relevant issue for the former Soviet republics that are now considering the introduction of a national currency. The above conclusion would, nevertheless, remain valid if the authorities can prevent this type of capital flows, by imposing limits on the amounts to be converted by individuals and at the same time subjecting all transactions to a proof of residency.
1/For instance, the switch from a high-inflation peg to a low-inflation one can be modeled in the framework developed above by assuming that the pre-reform regime is characterized by a constant foreign inflation rate equal to π*, and the post-reform regime by an inflation rate equal to π˜*<π*. Note that this assumption would generate non-trivial dynamics even if the monetary reform implies a uniform conversion rate.
1/In addition to equations (A5), the optimal solution must satisfy the lifetime resource constraint limtδtat0. Using equation (A2), this inequality can be written in a form that restrict*; the present value of consumption and services derived from domestic and foreign currency holdings to the value of real wealth at the beginning of period t.

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