A note on the specification of the demand for money in open economies.

• Author: Auernheimer, Leonardo

1. Introduction

   Open economy models which make a distinction between traded and non-traded goods have been widely used to analyze a variety of issues. For simplicity, in many cases the real money stock is defined by using as the relevant deflator the price of either of those goods. Moreover, this is true both for the case of models in which the demand for money is derived via explicit utility maximization, as in [6; 7] and for models with an "ad-hoc" demand for money [3; 4; 5].

   The purpose of this brief note is to show the extent to which the choice of the deflator can alter the adjustment of a monetary economy to various shocks in a qualitative, and hence important, way. As it is shown below, while the qualitative response to monetary innovations will in general not depend on the choice of the numeraire, the same is not true for the response to changes that modify the relative price between traded and non-traded goods (i.e., the "real exchange rate"). For the latter type of changes, different choices of the deflator can mean the difference between monetary accumulation and a temporary balance of trade surplus, and a fall in the real money stock and a temporary balance of trade deficit, both as a response to the same exogenous change.

   In sections II and III we present a very simple model and provide examples. In section IV we discuss the implications and justify the importance of the issue.

2. The Model

   The main points can be demonstrated in a small open economy model with traded and non-traded goods.(1) Normalizing the exogenous foreign price of the traded good to unity, the domestic traded good price is equal to the nominal exchange rate, E. The deflator used in defining the demand for real money balances is given by the index

   [Mathematical Expression Omitted],

   where 0 [less than or equal to] [Sigma] [less than or equal to] 1 and [P.sub.H] is the domestic currency price of the non-traded good. This index can also be expressed as P = [[Epsilon].sup.[Sigma]][P.sub.H], where [Epsilon] is the relative price of the traded good in terms of the non-traded good and is defined as the real exchange rate. The price of the non-traded good is perfectly flexible so the market clearing condition,

   [x.sub.H] = [c.sub.H], (2)

   is always satisfied, where [x.sub.H] is non-traded good output and [c.sub.H] is non-traded good consumption.

   Individuals are identical and infinitely lived, and the representative individual maximizes the functional

   [integral of] U([c.sub.T],[c.sub.H],m)[e.sup.-[Delta]t] dt between limits of [infinity] and 0, (3)

   where [Delta] is the constant rate of discount, [c.sub.T] is traded good consumption, and m is the stock of real money balances, defined as the nominal money stock deflated by the price index (1). It is assumed that the utility function is strictly concave and, for simplicity, separable in real money balances and both consumption goods.

   The...