Stabilizing inflation in the open economy.

Jansen, Dennis W.

1. Introduction

Optimal monetary policy in the open economy continues to be of interest to the profession, as in Benavie and Froyen [1], and price level stabilization has been investigated by Bradley and Jansen [4], Marquis and Cunningham [13], and Fischer [6], among many others. Price level stabilization has also been investigated in the monetary policy literature by, for example, Black [2] or Black and Gavin [3]. The academic literature has included analysis of price level stabilization in a variety of macroeconomic frameworks ranging from overlapping generations models to equilibrium business cycle models and Keynesian contracting models. What has been lacking, however, is a rigorous analysis of price level stabilization in the open economy. This apparent omission is interesting because the most famous historical application of price level targeting occurred in the 1930s in Sweden -- a small open economy.[1]

In this paper we carefully examine the effectiveness of price level or inflation stabilization in the small open economy.[2] Employing an equilibrium business cycle model with differentially informed agents, we find that when shocks to the economy exhibit some persistence, inflation stabilization has favorable output stabilization properties relative to alternative monetary policies. Further, these beneficial aspects of inflation stabilization exist whether or not agents contemporaneously observe the money stock. The only instance in which inflation stabilization policy is not preferred is when all shocks to the economy are strictly temporary shocks and when uninformed agents can not observe the money stock contemporaneously. Finally, in all instances we find that price level stabilization is preferred, from a macroeconomic stabilization perspective, to exchange rate stabilization. This last result is of some historical and policy making interest because the Swedish government pursued an explicit policy of price level stabilization in the 1930s.

II. The Small Open Economy Model

We employ an aggregate open economy equilibrium business cycle model. The model combines elements of the open-economy models of Kimbrough [8; 9] and the closed economy model of Dotsey and King [5). Agents in the small open economy produce and consume two goods, only one of which is traded on world markets. Purchasing power parity governs the price of that traded good. Aggregate output is a function of the ex ante real rate of interest, which measures the relative price of goods between today and tomorrow and thereby captures intertemporal substitution possibilities. The division of aggregate output between traded and nontraded goods depends on the relative price of the two goods.

There is also a money market and a credit market. We postulate a money demand function that depends on real output, the domestic price level, and the domestic interest rate. Domestic and foreign bonds are perfect substitutes, so uncovered interest rate parity holds. Domestic money, however, is only held by domestic residents.

Economic agents are of two types, which are distinguished by their endowment of information. A fraction [Lambda] A are labeled "informed" agents, and at every time t these know the contemporaneous value of all variables and all stochastic disturbances. The remaining fraction 1 -- [Lambda] are labeled "uninformed" agents, and at every time t these agents know the contemporaneous value of only a subset of the variables and disturbances in the economy. King [11] has stressed that differentially informed agents with common access to an economy-wide price is necessary for monetary policy to have an effect on the informational content of prices. Our informational structure satisfies this necessary condition. However, while policy effectiveness results do depend on differentially informed agents, they do not depend on the explicit structure of the differential information assumed here. The assumption of two classes of agents, one "informed" and one "uninformed", is for analytical convenience. Moreover, the implications of variations in the information set of uninformed agents forms an important part of the analysis in this paper.[3]

The model is described by equations (1)-(6) below:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Here:

[Lambda] = fraction of agents who are informed, [Y.sub.t] = log of real output of traded and nontraded goods at time t, [Y.sub.N,t] = log of real output of nontraded goods at time t, [R.sub.t] = nominal interest rate at time t, [P.sub.t] = log of the price level at time t, [r.sub.t.] = real interest rate at time t = [R.sub.t] -- [EP.sub.t+1] +[P.sub.t.] [P.sub.N,t] = log of the price of nontraded goods at time t, [P.sub.T,t] =log of the price of traded goods at time t, [P.sub.N,t] = [P.sub.N,t] -- [P.sub.T,t] the relative price of traded goods, [g.sub.t] = stochastic disturbance to productivity at time t, [M.sub.t] = log of the nominal money stock at time t, [v.sub.t] = stochastic disturbance to money demand at time t, [Epsilon.sub.t] = stochastic disturbance to demand or supply of total output, [Epsilon.sub.N,t] = stochastic disturbance to demand or supply of nontraded goods, [k.sub.i] = a measure of persistence for disturbance i, 0 [less than or equal to] [k.sub.i] [less than or equal to] 1, [U.sub.t] = information set of uninformed agents at time t, [I.sub.t] = information set of informed agents at time t, [R.sub.t.sup.*] = nominal rest of world interest rate at time t, [P.sub.t.sup.*] = log of the rest of world price level at time t, [S.sub.t] = log of the nominal exchange rate at time t, E = mathematical expectation operator.

Equation (1) models economy-wide supply. The coefficient [Lambda] (0 < [Lambda] < 1) is the exogenously determined fraction of the population which is informed. Economy-wide supply consists of supply by [Lambda] informed and (1 - [Lambda]) uninformed agents. Uninformed and informed agents both react with elasticity [alpha.sup.s] to the ex ante real interest rate [r.sub.t], but their expectation of the real interest rate are based on different information sets. For instance, an increase in the real interest rate signals high returns to supplying output in the present, thereby inducing an increase in supply. Supply also depends on a productivity shock [g.sub.t] which has two effects. The first effect is a wealth effect. The productivity shock is wealth enhancing, and both informed and uninformed agents respond to the expected value of this increase in wealth with elasticity -[Beta.sup.s]. Again, however, informed agents know the value of [g.sub.t] since E([g.sub.t]\[I.sub.t]t) = [g.sub.t], while uninformed agents form E([g.sub.t]\[U.sub.t]). The second effect of the productivity shock is to directly increase supply. This effect is the same for all agents, and has elasticity [Theta.sup.s]. Note, too, the disturbance [Epsilon].sup.s.sub.t] which affects supply.

In equation (1) (and also in equations (2)-(5)) the disturbances are modeled as first order moving average processes of the form [k.[Chi][Chi.sub.t] + (1 - [k.sub.[Chi])[Chi].sub.t]-1. This modeling strategy incorporates both persistent shocks (when [k.sub.[Chi] [is not equal to] 1) and temporary shocks (when [k.sub.[Chi] = 1).(4) Because disturbances have this moving average form, a lagged value of [g.sub.t] enters equation (1). The lagged value of [g.sub.t] has coefficient ([Theta.sup.s] - [Beta.sup.s]) due to the two effects of the productivity shock. Similarly, a lagged value of [Epsilon.sup.s.sub.t] enters equation (1).

Economy-wide demand is given by equation (2). Like supply, demand depends on the ex ante real interest rate, [r.sub.t], which measures the intertemporal substitution possibilities available to private agents. Changes in the ex ante real interest rate will initiate an intertemporal reallocation of consumption. Demanders will reduce demand when the real interest rate is high, indicated by the elasticity -[Alpha.sup.d]. The productivity shock has a positive wealth effect on demand with elasticity [Beta.sup.d], and a positive direct demand effect with elasticity [Theta.sup.d].(5) Finally, both demand and supply are subject to the disturbances [Epsilon.sup.i.sub.t].

Equations (3) and (4) model the supply and demand for nontraded goods. These make up only part of the supply and demand for all goods given in equations (1) and (2). Hence equations (3) and (4) contain all of the general features of equations (1) and (2), but with different coefficients.(6) Equations (3) and (4) also contain the relative price of traded goods, as this relative price determines the split of output between these two components. This relative price does not enter equations (1) and (2), because aggregate supply and demand are assumed independent of relative price changes.

Equations (5) and (6) represent money demand and money supply. The money demand equation is standard, with real money demand a function of real output and the nominal interest rate. There is a stochastic disturbance [v.sub.t], to money demand. The money supply rule has a deterministic trend, and allows a contemporaneous response to variations in the exchange rate, [S.sub.t], and the price level, [P.sub.t]. This specification is general enough to embody a strict money rule, an exchange rate stabilization policy, or an inflation stabilization policy, depending on the choice of parameters [Psi.sup.s] and [Psi.sup.p]. The relevant target levels for [S.sub.t] and [P.sub.t] are simply their expected values formed by all agents (including the monetary authority) in the previous period. This type of policy target precludes the indeterminacy problem sometimes associated with this class of policy formulation.

Equations (7)-(9) are ancillary equations defining the price level and the various arbitrage conditions. Equation (7) defines the price level [P.sub.t] as a weighted average of the price of traded goods [P.sub.T,t] and nontraded goods [P.sub.N,t]. Equation (8) is the uncovered interest rate parity condition, which states that the domestic nominal interest rate [R.sub.t] is equal to the world nominal interest rate [R.sup.*.sub.t] plus the expected rate of exchange rate depreciation between t and t + 1. Finally, equation (9) is the law of one price for traded goodys.(7)

The world nominal interest rate [R.sup.*.sub.t] and the world price level [P.sup.*.sub.T,t] are exogenous to the small open economy. These variables are determined in the rest of the world according to equations (10) and (11).

III. The Small Open Economy: Basic Solution

Given the structure of the rest of the world's economy, we analyze the small open economy. We begin by looking at the conditions that the market for nontraded goods and the money market must clear domestically. These conditions yield two equilibrium relationships for the macroeconomic variables:

[Y.sup.s.sub.N,t] - [Y.sup.d.sub.N,t'] (12)

and

[M.sup.d.sub.t] = [M.sup.s.sub.t] (13)

There are also two arbitrage conditions that constrain die behavior of the macroeconomic variables in the economy, the interest rate parity condition given by equation (8), and the purchasing power parity condition for traded goods given by equation (9). Equations (8), (9), (12), and (13) are thus four constraints on the behavior of macroeconomic variables in the small open economy; they are the four constraints that aid uninformed agents in their signal extraction problem for determining the state of the economy.

To demonstrate the information content of the market clearing conditions, we substitute equations (3) and (4) into equation (12), obtaining the equation describing equilibrium in the market for nontraded goods:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Here we have defined several composite variables. In addition to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] we have [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. We have also defined the composite disturbance term [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

We also impose equilibrium in the money market. We write this expression by substituting equations (5) and (6) into equation (13), making use of the aggregate income equation (1), to obtain the equation describing money market equilibrium as:(8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

For convenience, we also rewrite the interest rate parity and purchasing power parity arbitrage conditions:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

To solve for the relative price of nontraded goods and the exchange rate, we postulate the following undetermined coefficients solutions for these variables. Note the inclusion of the foreign disturbance terms. These are included to capture the ability of foreign disturbances to affect the small open economy via relative price and exchange rate movements. The foreign variables included are those that enter the solutions for the foreign price level and foreign interest rate, as given in the appendix:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The solution for the undetermined coefficients on the predetermined right hand side variables is given by:

[Phi.sub.0] = 0 [Phi.sub.1] = 0 [Phi.sub.2] = 0 [Phi.sub.3] = ([Beta.sub.n] + [Theta.sub.N]) (1 - [k.sub.g]/([Theta] + [Alpha.sub.n][Sigma.sub.n] [Phi.sub.4] = (1 - [k.sub.n)/ ([Theta.sub.n][Sigma.sub.n] [Phi.sub.5] - 0 [Phi.sub.6] = 0 [Phi.sub.12] = [Alpha.sub.n](1 - k.sup.*.sub.R])/([Theta] + [Alpha.sub.n][Sigma.sub.n]) [Phi.sub.13] = [Alpha.sub.n](1 - [k.sup.*.sub.p])/ ([Theta + [Alpha.sub.n][Sigma.sub.n]) [II.sub.0] = (Mo + [Gamma]n) - (Mo + [Gamma]*n*) [II.sub.1] = n - n* [II.sub.2] = [Tau.sub.2] - [k.sub.v]))/(1 + [Gamma]) [II.sub.3] = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [II.sub.4] = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [II.sub.5] = [Tau.sub.5]/(1 + [Gamma]) [II.sub.6] = [[Tau.sub.6] - [Sigma](1 - [k.sub.s])]/(1 + [Gamma] [II.sub.12] = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [II.sub.13] = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The solutions for the other undetermined coefficients are considerably more complicated, and vary with the information structure of the model and the policy rule in force. As an alternative to explicitly solving for these coefficients, we employ a strategy proposed by Hercowitz [7], and solve for the signals recoverable by uninformed agents. We describe this technique in the following section of the paper, where we use it to analyze the effects of inflation stabilization in the small open economy.

IV. Full Information Output

The model is solved in two steps. First, we solve for the level of output when all agents are fully informed. The full information solution for the level of output of nontraded goods, [Y.sup.#.sub.N,t], is obtained by setting the fraction of informed agents to unity and solving equations (3) and (4). This yields full information output of nontraded goods,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [Alpha.sub.N] = [Alpha.sup.s.sub.N] + [Alpha.sup.d.sub.N]

Note that full information output of nontraded goods depends on the stochastic disturbances [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and the relative price of traded and nontraded goods. Thus full information output varies with the stochastic state of the economy.

To solve for the level of nontraded goods output when some agents are uninformed, we again equate demand and supply in equations (3) and (4), and solving for output we obtain

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [H.sub.N] = ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII])

Inspection of equation (17) reveals that output in the nontraded goods market deviates from its full information level only when the expectation of the stochastic disturbance [g.sub.t] by uninformed agents deviates from the realized value of [g.sub.t]. This leads immediately to the conclusion that for given [Lambda], monetary policy can be judged by how well it allows uninformed agents to extract information on [g.sub.t] from the knowledge they possess about the state of the economy. Another feature of the model, evident in equation (17), is that uninformed agents are necessary for output to deviate from the full information output level. With only fully informed agents, we have [Lambda] = 1, and not surprisingly the difference between current output and full information output in equation (17) is eliminated.

V. Analyzing Inflation Stabilization

In this section we turn to the main focus of the paper, the analysis of price level stabilization in a small open economy. To facilitate our understanding of the properties of price level stabilization, we compare the macroeconomic performance under this policy with the macroeconomic performance under two other well studied policies, a money growth rule and exchange rate stabilization by, for example, Kimbrough [9; 10] or Lachler [12]. These well known policies can thus serve as benchmarks for measuring the effectiveness of inflation stabilization.

As described above, policy effectiveness is evaluated in terms of deviations of output in the non-traded goods sector from the full information output level.(9) This deviation, in turn, will be minimized by the policy that provides the best information to uninformed agents about the current state of the economy. As the informational environment improves, the uninformed agents' forecast of [g.sub.t] also improves and output deviations are reduced.

In the following subsections we examine the case where the information set of uninformed agents consists of the current nominal interest rate both foreign and domestic, the exchange rate, the money stock, and the price of both traded and nontraded goods. This is formalized as [U.sub.t] = {[R.sub.t],[R.sup.*.sub.t], [S.sub.t], [M.sub.t], [P.sub.T,t], [P.sub.N,t]}

Informational Signals

In this subsection we describe the technique for deriving the informational signals under each type of monetary policy. Because the informational structure of the economy changes with the choice of policy, the exchange rate stabilization policy and an inflation stabilization policy. Once the general solutions for the informational signals are derived, the specific forms are presented and policy rankings can be made.

We first consider a strict money growth rule, so that [[Psi].sup.P] = [[Psi].sup.S]. In this case, there are three potential signals available to uninformed agents: an exchange rate signal, a goods market signal, and a money market signal. Observation of the foreign and domestic interest rates and the exchange rate serves to reveal, from the interest rate parity condition, the expectation of informed agents about the one period ahead exchange rate, E([S.sub.t+1] [vertical bar] [I.sub.t]). This provides uninformed agents with an observation on the linear combination of disturbances which we label [[Omega].sup.M.sub.1,t], given as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

The superscript M denotes that this signal is valid when the monetary authority is pursuing a money aggregate policy. Notice that the signal [[Omega].sup.M.sub.1,t] does not contain the foreign disturbances [[Micro].sup.*.sub.R,t] and [[Micro].sup.*.sub.P,t]. This omission arises because the values for these disturbances are already perfectly revealed to uninformed agents by their knowledge of [R.sup.*.sub.t] and [P.sup.*.sub.t], the latter being obtained from knowledge of [P.sub.t] and [S.sub.t] via the equation for the law of one price.

The second signal is derived from the equilibrium condition in the market for nontraded goods, equation (12'). This condition, and the information set specified above, provides an observation on a second linear combination of variables that are individually unobserved by uninformed agents. We call this the nontraded goods market signal and label it [[Omega].sup.M.sub.2,t]. This signal is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

Finally, the money market provides uninformed agents with a second linear combination of contemporaneous disturbances. From their knowledge of the money market equilibrium condition, equation (13'), and their knowledge of the macroeconomic variables in [U.sub.t], uninformed agents receive the money market signal [[Omega.sup.M.sub.2,t] given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

Equations (18)-(20) represent three linear combinations of the disturbances to the model that uninformed agents receive when the monetary authority follows a strict money rule. Uninformed agents then use these signals to form a prediction of the current [g.sub.t].

On the other hand, suppose that the monetary authority stabilizes the exchange rate. If so, [[Psi].sup.s.[right arrow] [infinity]] and the exchange rate is pegged to E([S.sub.t][vertical bar][I.sub.t-1]). This expected exchange rate target is general enough to involve feedback elements, so that the rule governing the exchange rate is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)

With this policy in place, the money stock becomes endogenous. Although this renders the money market equilibrium condition irrelevant, the money demand equation continues to hold. Stabilizing the exchange rate also restricts variation in the aggregate price level [P.sub.t]. The aggregate price level is the weighted average of the traded goods price [P.sub.T,t] and the nontraded goods price [P.sub.N,t]. The traded goods price is restricted by the law of one price to equal [S.sub.t] + [P.sup.*.sub.t]. Substituting the law of one price into the price level definition and then substituting the resultant expression into the money demand equation yields the following equation which uninformed agents use to extract the information from the money market:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (22)

Given this new informational structure, what are the signals available to uninformed agents? The answer will determine which policy is preferred because the ability of uninformed agents to identify the productivity shock influences the size of the deviation of output from the full information level of output. To determine agents' forecast accuracy, we must consider each of the three signals now available to uninformed agents. First, the interest rate parity condition reveals a linear combination of disturbances that aid uninformed agents in forecasting next period's exchange rate. Under an exchange rate rule, this forecast of the exchange rate is without error, and reveals to uninformed agents the signal [[Omega].sup.S.sub.1,t], where the superscript S indicates that the signal is valid under an exchange rate rule:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (23)

Note that equation (23) does not contain the foreign sector disturbances because, as before, these disturbances are revealed to uninformed agents directly from their knowledge of the foreign sector interest rate and price level.

As for the goods market signal, inspection of equation (12') indicates that exchange rate stabilization, by setting the value of [S.sub.t+1], also changes the nontraded goods market signal. The new signal, labeled [[Omega].sup.S.sub.2,t], is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (24)

Conditional on the respective information sets from the interest rate parity condition, [[omega].sup.S.sub.2,t] is the same as [[Omega].sup.M.sub.2,t]. These two signals differ only in the linear combination of disturbances that are used in predicting next period's exchange rate.

Turning finally to the money market, an exchange rate peg requires the money supply to adjust to maintain the exchange rate. Since the money stock is observable, uninformed agents can still observe the money demand equation itself, written as equation (22) above. Observing [M.sub.t], [R.sub.t], and [P.sub.t] thus allows observation of the linear combination of shocks represented by [Y.sub.t] plus the money demand shock [v.sub.t]. This is the same signal that we labeled [[Omega].sup.M.sub.3,t] in equation (20) above. Thus the information content of the money market is not influenced by the choice between a money rule and an exchange rate peg.

Finally, what if the monetary authority decides to stabilize the inflation rate, so that [[Psi].sup.P] [right arrow] [infinity]? Again, since the money stock is observable, inflation stabilization does not destroy the information available from the money market despite making the money stock endogenous. Pegging the price level at E([P.sub.t] [vertical bar] [I.sub.t-1]) could involve feedback elements, so that the rule governing the price level is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (25)

With predetermined growth in the price level, the money demand equation is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (26)

Substituting equation (25) into equation (26), we can derive the equation which provides uninformed agents with information from the money market.

Examining each signal in turn, we first look at the information available from the interest rate parity condition:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (27)

Examining next the nontraded goods market equilibrium condition, the signal obtained by uninformed agents is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (28)

Notice that this goods market signal, conditional on the signal from the interest rate arbitrage condition, consists only of a linear combination of [g.sub.t] [[Epsilon].sub.N,t].

Finally, we present the signal from the money market. This signal is available from the money demand equation, derived from substituting the price level equation into equation (24). The signal uninformed agents thus observe is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (29)

This is exactly the same signal that is available from the money market under a money stock rule, [[Omega].sup.M.sub.3,t]. In the money market, the signal is the same for a price rule as for a money rule.

Policy Effectiveness

Having derived the signals that arise under each of the policies, we can now compare them for ability to provide uninformed agents with a clear signal about [g.sub.t]. These results are presented in Table I. Note that Table I also includes the results that are obtained when the shocks to the economy do not persist. Because this lack of persistence is simply a special case of the general result in which all of the "k" parameters are set to one, it is easily obtainable from the general results obtained above.(10)

Table I lists the three signals that arise from each of the three markets under each of the three types of policies. The first noticeable result is that the interest rate parity condition provides a signal to uninformed agents under either a money growth policy or an inflation stabilization policy, but not under exchange rate stabilization. Moreover, the quality of the signal differs under the money stock policy and the inflation control policy.

[TABULAR DATA NOT REPRODUCIBLE IN ASCII]

The signal from the nontraded goods market is operative under all three policies but is different in each case. Conditional on the signal from the interest rate parity condition though, the nontraded goods market signal is the same for the money stock policy and the exchange rate policy. Finally, the money market signal is the same for all three policies.

In terms of ranking the alternative policies, the inflation stabilization policy leads to the lowest variance of output around its full information level. In fact, in terms of the criteria of this model, the inflation stabilization policy is "perfectly" stabilizing. As can be seen by inspection of Table I, this result arises under the inflation control policy because the signals from the nontraded goods market and the interest rate parity condition are sufficient to fully reveal [g.sub.t], and uninformed agents can accurately extract the contemporaneous value of that shock.(11) Thus, an inflation stabilization policy dominates the other two policy approaches.

When the effects of shocks to the economy do not persist, the three types of monetary policy can be investigated directly. In the model, a lack of persistence is generated by setting all the "k" parameters equal to one. Inspection of Table I reveals that this changes the informational signals and the results are presented in part B of that table.

Without persistence the intertemporal exchange rate signal is not operative and provides no information under any of the policies. The signals from the other two markets, in addition, are identical. The three classes of policies are equivalent and our criteria of minimizing the variance of real output around its full information value provides no basis for ranking the policies.

VI. Price Stabilization with an Alternative Information Set

We next investigate an information set including the nominal interest rate, exchange rate, and the price of traded and nontraded goods, but not the money stock. This case corresponds most closely to the information assumptions used by previous authors of new classical models, including Kimbrough [9]. We formally identify this information set as [U.su.t] = {[R.sub.t],[R.sup.*.sub.t], [S.sub.t],[P.sub.T,t], [P.sub.N,t]}.

To analyze the policy choice under this information set, we again look at each policy in turn. We start with strict money growth, under which [[Psi].sup.P] = [[Psi].sup.S = 0. The interest rate parity condition still furnishes the signal [[Omega.sup.M.sub.1,t] to uninformed agents. Inspection of the nontraded goods market equilibrium condition, equation (12'), indicates that the signal [[Omega].sup.M.sub.3,t] can again be obtained from the goods market equilibrium condition. In the money market, the money stock is unobserved by uninformed agents, but under a strict money rule the otherwise unobservable money stock is pegged at a predetermined value by the monetary authority. This act of following a deterministic money rule allows uninformed agents to extract the signal [[Omega].sub.3,t] from the money market. In this case, the monetary authority, by following a money growth rule improves the informational environment by providing uninformed agents with a signal they would not otherwise have available.

What of an exchange rate policy, under which [[Psi].sup.S] [right arrow] [infinity]? The interest rate parity condition still furnishes the signal [[omega].supS.sub.1,t] and the nontraded goods equilibrium condition still provides the signal [[Omega].sup.S.sub.2,t]. In the money market, however, the fact that [M.sub.t] is unobserved means that pegging [S.sub.t] destroys the ability of uninformed agents to extract an additional signal from the money market. That is, the money demand equation no longer provides an observation on a linear combination of disturbances to uninformed agents, because the contemporaneous money stock is not observed. The inability to observe [M.sub.t] makes the money demand equation uninformative about the value of [g.sub.t.] In sum, uninformed agents are still able to observe the linear combination of disturbances labeled [[Omega].sup.S.sub.1,t], and [[Omega].sup.S.sub.2,t], but lose the signal [[Omega].sup.S.sub.3,t] when the monetary authority follows an exchange rate peg instead of a money growth rule.

Finally, we consider an inflation stabilization policy, under which [[Psi].sup.P] [right arrow] [infinity]. For simplicity, suppose that the price level is pegged such that [P.sub.t] = 0. This means that [P.sub.T,t] + [[Delta].sub.NPN,t] = 0, or that [P.sup.*.sub.T,t] + [S.sub.t] + [[Delta].sub.NPN,t] = 0. This last condition can be rewritten as [S.sub.t] = - ([P.sup.*.sub.T,t] + [[delta].sub.NPN,t] = which clearly shows that inflation stabilization implies a particular type of exchange rate rule.(12) As in the case of an exchange rate policy, however, pegging [P.sub.t] while [M.sub.t] is not observable destroys the information in the money market signal. The goods market signal remains [[Omega].sup.P.sub.2,t] and the interest rate parity condition continues to provide the signal [[Omega].sup.P.sub.1,t]. As a result, price level stabilization does not aid in recovering the signal [[Omega].sup.P.sub.3,t] from the money market.

To summarize, this information set corroborates the policy conclusions suggested by Kimbrough [9] with regard to choosing between a money rule and an exchange rate rule. In particular, a money rule is generally preferred to an exchange rate rule because it provides the most information to private uninformed agents. This occurs because the exchange rate policy (as well as the inflation stabilization policy) destroy a source of information. In the case of exchange rate stabilization, the signal extraction task of uninformed agents is unambiguously more difficult relative to a money rule and, thus it increases (or at least does not decrease) the variance of output about full information output.

A clear ranking between a money growth rule and an inflation stabilization policy does not emerge, however. The inflation stabilization rule destroys a source of information but, at the same time, improves the quality of the remaining signals relative to those provided by the money rule. In this situation, the choice between these two rules is ambiguous and a ranking cannot be made without further specification of the stochastic structure of the economy.

When there are persistent shocks to the economy, uninformed agents receive the signals reported in part A of Table II. As discussed above, even when the money stock is not contemporaneously available the money growth rule continues to reveal a signal from the money market. This signal is not available to uninformed agents under the other policies.

As in the case when agents observe the money stock, the interest rate parity condition reveals an informational signal under both the money growth and inflation stabilization policies but not under an exchange rate peg. Finally, the nontraded goods market reveals a signal under each policy, although the signal under an inflation stabilization policy differs from that available under the other two policies.

The ranking of alternative policies is also the same here as when agents observe the money stock. Inspection of Table 11 reveals that the two signals available when the monetary authority is stabilizing inflation again fully reveal g, to uninformed agents. This type of policy thus continues to be perfectly stabilizing. In contrast, stabilization of the exchange rate does not yield the minimum variance of output around its full information value. A money growth rule reveals three signals to uninformed agents but these signals include more than three shocks. Consequently, these signals are not sufficient to reveal [g.sub.t] to uninformed agents except under a most fortuitous combination of parameter values.

Part B of Table II contains the signals available when there is no persistence in the stochastic structure of the economy. As in Table I, the signal from the interest rate parity condition disappears under these conditions and the signal from the nontraded goods market is again identical under the three policy choices. Because the money stock is not observable by uninformed agents, the signal from the money market is destroyed under the exchange rate and inflation stabilization policies. The strict money rule restores this signal, however, and this becomes the preferred policy. As part B of Table II shows, the money growth rule provides an additional signal to uninformed agents that is not available under the two types of policies and thus provided the minimum variance of real output around its target.

VII. Conclusion

We analyze the effect of price level stabilization on the variance of output in an open economy equilibrium business cycle model with uninformed agents. We find that in most cases inflation stabilization is as good as other traditional policies and that when shocks to the economy persist, inflation stabilization is preferred. This result is robust over specifications of the information set available to uninformed agents. We also find that, in all cases, inflation stabilization dominates exchange rate stabilization in terms of its macroeconomic stabilization properties.

References

[1.] Benavie, Arthur and Richard Froyen, "A Note on Optimal Monetary and Wage Indexation Policies in a Small Open Economy." Australian Economic Papers, December 1991, 33440.

[2.] Black, Robert P., "Reflections on the Strategy of Monetary Policy." Economic Review, Federal Reserve Bank of Richmond, July/August 1990, 3-7.

[3.] Black, Susan and William T. Gavin, "Price Stability and the Swedish Monetary Experiment." Economic Commentary, Federal Reserve Bank of Cleveland, December 15, 1990.

[4.] Bradley, Michael D. and Dennis W. Jansen, "Informational Implications of Money, Interest Rate, and Price Rules." Economic Inquiry, July 1988, 437-48.

[5.] Dotsey, Michael and Robert G. King, "Informational Implications of Interest Rate Rules." American Economic Review, March 1986, 33-42.

[6.] Fischer, Stanley, "Monetary Rules and Commodity Money Schemes Under Uncertainty." Journal of Monetary Economics, January 1986, 21-35.

[7.] Hercowitz, Zvi. "Money and the Dispersion of Relative Price." Unpublished doctoral thesis, University of Rochester, 1980.

[8.] Kimbrough, Kent P, An Examination of the Effects of Government Purchases in an Open Economy." Journal of International Money and Finance, 1985, 113-33.

[9.] _____, "Aggregate Information and the Role of Monetary Policy in an Open Economy." Journal of Political Economy, April 1984, 208-85.

[10.] _____, "Price, Output, and Exchange Rate Movements in the Open Economy." Journal of Monetary Economics, January 1983, 25-44.

[11.] King, Robert G., "Monetary Policy and the Information Content of Prices." Journal of Political Economy, April 1982, 247-79.

[12.] Lachler, Ulrich, "Fixed Versus Flexible Exchange Rates in an Equilibrium Business Cycle Model." Journal of Monetary Economics, July 1985, 95-107.

[13.] Marquis, Milton H. and Steven R. Cunningham, "Is There a Role for Commodity Price in the Design of Monetary Policy? Some Empirical Evidence."

(1.) See Black and Gavin [3] and the references cited therein.

(2.) In our model, as in most analyses, aggregate price level stabilization takes place through minimization of deviations of the actual price level from a pre-announced target for the price level which is known by all agents in the economy. Because that pre-announced target for the current price level could embody a non-zero level of expected inflation, price level stabilization is equivalent to inflation stabilization. Only if the pre-announced target level precludes any growth in the aggregate price level would price level stability imply zero inflation. As we do not impose this condition in this paper we will use the terms price level stabilization and inflation stabilization interchangeably.

(3.) In this work the information structure is exogenous. This abstracts from issues regarding informational equilibrium and the endogenous determination of the fraction [Lambda] of informed agents. This interesting avenue for research is beyond the scope of the present paper.

(4.) Clearly the persistence of these moving average shocks is only for two periods, but this is sufficient to yield the qualitatively different results for persistent shocks. An autoregressive specification would result in additional algebraic complexity without yielding any further qualitative results.

(5.) The direct demand effect of [g.sub.t], is included only for completeness. We could "zero out" this demand effect without changing our results.

(6.) The coefficients of equations (1) and (2) are related to the coefficients of equations (3) and (4). For example, the coefficient of the expected real interest rate in aggregate supply, [Alpha.sup.s], is equal to the weighted average of coefficient of the expected interest rate in nontraded goods supply, [Alpha.sup.s.sub.N], and the coefficient of the expected interest rate in traded goods supply.

(7.) It is also true that the market for traded goods clears each period. However, this equilibrium condition is not explicitly examined here. Note that the domestic excess demand for traded goods is equal to the value of net imports. It is not necessary to further analyze this equilibrium condition for two reasons. First, we allow an equilibrium in which net imports are non-zero. That is, we do not analyze a long run equilibrium in which capital flows make net exports zero. Second, we do not give uninformed agents information on current commodity flows such as quantities supplied or demanded. Since net imports is such a measure, we also do not allow uninformed agents to observe net imports. Information on any of these variables would be very useful to uninformed agents, but is assumed to be unavailable contemporaneously. The practical justification for not permitting uninformed agents to observe either output or the trade accounts contemporaneously is that such information is available only with significant lags in the real world. Thus, there is no information available to uninformed agents from the equilibrium condition in the market for traded goods.

(8.) Aggregate supply defines aggregate income. Using equation (1), we substitute in the values of E([r.sub.t]/[I.sub.t]) and E([r.sub.t][U.sub.t]) implied by equilibrium in the nontraded goods market. This gives an equation for aggregate income as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(9.) If the nontraded goods sector is stabilized at the full information level of output, then so is the traded goods sector and aggregate output. However, there may still be non-zero net exports, as discussed in footnote 7.

(10.) We also analyzed the case in which policy makers pursued "feedback" policies in an economy with persistent shocks. We find, like many previous authors, that a complicated feedback rule will be perfectly stabilizing. In this paper we focus on simpler and more feasible policy rules and find that price level stabilization can replicate the "perfect" stabilization of complicated feedback rules in an economy with persistence.

(11.) The result occurs because under an inflation stabilization policy (but not under either of the other two policies) the two signals each contain a linear combination of the two shocks [g.sub.t] and [[Epsilon].sub.N,t], and it is well known that two independent linear combinations of two variables can be solved for the value of each of the two variables.

(12.) This is analogous to the demonstration by Dotsey and King [5), in a closed economy setting, that an interest rate peg is equivalent to a certain