Question

Suppose that a monetary model describes the long-run behavior of the nominal exchange rate well, but fails to describe the short-run behavior; specifically, in the short run large deviations from purchasing power parity are observed due to nominal rigidities in goods’ prices and overshooting of the nominal exchange rate in response to monetary shocks occurs as a result.

a) What are the three key modeling assumptions used to derive the monetary model of exchange rates? What is the only one of these modeling assumptions which is different in the Dornbusch over-shooting model?

b) Write down an equation that reflects the nominal exchange rate solution provided by the monetary model i.e. expresses the nominal exchange rate as a function of monetary and real fundamentals and expectations of the future exchange rate and explain each term.

c) Use diagrams and words to describe the impact of a (relative) home money supply shock for

i) the nominal exchange rate

ii) the home interest rate, and

iii) the home price level

in the short run (according to the Dornbusch overshooting model) and in the long run (according to the monetary model). Explain carefully why the differences in prediction arise in each case.

d) What do each of these two models imply about the ability of monetary policy to influence interest rates and aggregate demand/output in an open economy?

Answer 1

economists generally believed that markets should, ideally, arrive at equilibrium, and stay there. Some economists had argued that volatility was purely the result of speculators and inefficiencies in the foreign exchange market, like asymmetric information, or adjustment obstacles. Dornbusch rejected this view. Instead, he argued that volatility was more fundamental to the market than this, much closer to inherent in the market than to being simply and exclusively the result of inefficiencies. More basically, Dornbusch was arguing that in the short-un, equilibrium is reached in the financial markets, and in the long run, the price of goods responds to these changes in the financial markets.

Suppose an economy is disturbed by an unanticipated exogenous change, which we call a shock. This might be a change in monetary or fiscal policy, but it need not be policy related. We say the endogenous variable exhibits overshooting in response to this shock if its short-run movement exceeds the change in its steady-state value. For example, given the long-run neutrality of money, a one-time, permanent increase in the money supply will eventually lead to a proportional depreciation of the steady-state value of the currency. If the short-run depreciation is more than proportional, then the short-run depreciation of the spot rate is greater than the depreciation of its steady-state value. We say such an economy exhibits exchange-rate overshooting in response to money-supply shocks.

According to the model, when a change in monetary policy occurs (e.g., an unanticipated permanent increase in the money supply), the market will adjust to a new equilibrium between prices and quantities. Initially, because of the "stickiness" of prices of goods, the new short run equilibrium level will first be achieved through shifts in financial market prices. Then, gradually, as prices of goods "unstick" and shift to the new equilibrium, the foreign exchange market continuously reprices, approaching its new long-term equilibrium level. Only after this process has run its course will a new long-run equilibrium be attained in the domestic money market, the currency exchange market, and the goods market.

As a result, the foreign exchange market will initially overreact to a monetary change, achieving a new short run equilibrium. Over time, goods prices will eventually respond, allowing the foreign exchange market to dissipate its overreaction, and the economy to reach the new long run equilibrium in all markets.

Popular models of such exchange rate overshooting have three key ingredients: covered interest parity, regressive expectations, and a liquidity effect of money supply changes. You are already familiar with the covered interest parity relationship: it is just the requirement that domestic assets bear the same rate of return as fully hedged foreign assets. This means that i = i ? + fd. If we decompose the forward discount on the domestic currency into expected depreciation and a “risk premium,” then we can write this as i = i ? + ?s e + rp

Since this lecture is aimed at a broad audience, it is not my intention to invoke too many mathematical formulas, though there will be a few. A small number of equations is necessary if only to impress upon the reader how simple the concept really is. The reader can easily skip over them.

Two relationships lie at the heart of the overshooting result. The first, equation (1) below, is the "uncovered interest parity" condition. It says that the home interest rate on bonds, i, must equal the foreign interest rate i*, plus the expected rate of depreciation of the exchange rate, Et (et+1 - et), where e is the logarithm of the exchange rate (home currency price of foreign currency)4, and Et denotes market expectations based on time t information. That is, if home and foreign bonds are perfect substitutes, and international capital is fully mobile, the two bonds can only pay different interest rates if agents expect there will be compensating movement in the exchange rate. Throughout, we will assume that the home country is small in world capital markets, so that we may take the foreign interest rate i* as exogenous.5

Uncovered interest rate parity

(1)

____

nominal
interest rate

expected rate of
charge of exchange rate

Let t s denote the log of the exchange rate, measured as the log of the domestic currency price of foreign currency. Thus, depreciation of the currency implies an increase in . Consider models of the exchange rate that relate the value of the currency to economic fundamentals, and to the expected future exchange rate: t s (1) = ? + 2 + + (1 ) ' ' t s b a x 1 t ba xt bEt t 1 s , 0 1 < b < . t x is a vector of economic “fundamentals” that ultimately drive exchange-rate behavior. Many familiar exchange-rate models based on macroeconomic fundamentals take this general form, as subsequent examples will demonstrate. To illustrate the theorem, suppose is a scalar 1 t a 'x t x , and that is identically zero. As shown below, this is a special case of the monetary model. Suppose further that 2 t a 'x t x has a unit root, but is not a random walk. Assume 1 1 2 ( ) t t t t t x x ? x x ? ? = ? ? ? ? + i.i.d t , ? ? . Then the solution for the change in the exchange rate is given by: 1 1 2 (1 ) 1 ( ) 1 1 t t t t b s s x x b b t ? ? ? ? ? ? ? ? ? = ? + ? ? . It is clear from this example that the change in the exchange rate is predictable from the lagged change in the fundamental t x . But as , the coefficient on the lagged money supply goes to zero, and the exchange rate approaches a random walk.

Monetary policy is referred to as being either expansionary or contractionary. Expansionary policy is when a monetary authority uses its tools to stimulate the economy. An expansionary policy maintains short-term interest rates at a lower than usual rate or increases the total supply of money in the economy more rapidly than usual. It is traditionally used to try to combat unemployment in a recession by lowering interest rates in the hope that less expensive credit will entice businesses into expanding. This increases aggregate demand(the overall demand for all goods and services in an economy), which boosts short-term growth as measured by gross domestic product(GDP) growth. Expansionary monetary policy usually diminishes the value of the currency relative to other currencies (the exchange rate).[5]