Stabilizing inflation in the open economy.

• Author: Bradley, Michael D.

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.

2. 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...