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Handbook of Exchange Rates by Lucio Sarno, Ian Marsh, Jessica James

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13.2 Basic Monetary Model

The simplest dynamic model of exchange rate determination is the monetary model. We examine the impact of incomplete information within a two-country version of this standard framework. The model is described by the following four equations:

13.1 13.1

13.2 13.2

13.3 13.3

13.4 13.4

Equation (13.1) is a standard money market equilibrium equation, with mt being the log-money supply, pt the log-price level, yt the log-output level, and it the interest rate. Equation (13.2) is the analogous equation for the Foreign country.1 Equation (13.3) is a purchasing power parity equation and Equation (13.4) is an interest rate parity equation. ψt is the deviation from uncovered interest rate parity (UIP).

Substituting Equations (13.1)–(13.3) into Equation (13.4) we obtain a first-order difference equation with a familiar solution

13.5 13.5

where images and λ = α/(1 + α).

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