The Dornbusch “overshooting”

model

See O&R Ch. 2.5.2, Ch 9.2

“The standard” open economy model

• Perfect foresight/dynamic extension of the static Keynesian Mundell-Flemming model of exchange rates

• Demonstrates how sticky goods prices induce “overshooting behaviour” of the nominal exchange rate.

• Ill-equipped to capture current account dynamics as it does not have intertemporal budget constraints.

• Lacks micro-foundations

Model structure – 1 • Output is fixed at a constant exogenous level

• Demand for domestic output depends– Positively on the ration of foreign to domestic output

prices expressed in a common currency unit– Positively on government expenditure– Negatively on the real interest rate

Model structure – 2

• If demand exceeds supply, suppose that prices increase in proportion to excess demand, i.e according to a “Phillips curve”

• Assume a “LM” schedule which relates the demand for real balances to – Income– The nominal interest rate

Model structure – 3

• Finally, the interest rate differential between domestic and foreign bonds is just enough to offset the depreciation of the domestic currency (UIP)

Model solution: the steady state

• In the steady state,

• So

• which allows us to re-write (4) to get the steady state price level

Steady state (cont)

• In the steady state, aggregate demand = supply, and we can use this in (2) to get an expression for the steady state exchange rate

Model solution: dynamics

• The system can be reduced to 2 equations in p and s that summarises the behaviour of goods and asset markets

• From (4), we can solve for R to get

Dynamics (cont)

• Plug into the UIP relation to get a dynamic equation for the exchange rate, s:

Dynamics (cont)

• Now bring aggregate demand and Phillips curve together

• And make use of (9) to write:

Dynamics (cont)

Phase diagram – 1

Phase diagram – 2

System in matrix form

• Expressing p and s in terms of deviations from the steady state, we can represent in matrix form as

Unanticipated increase in money supply

• Starting from the steady state, the exchange rate adjusts instantly. The impact effect is an immediate depreciation of the currency, with a fixed price level

• The currency appreciates slowly as goods prices gradually adjust upwards along the saddlepath trajectory

• When prices are fixed, monetary expansion reduces interest rates, leading to anticipation of a depreciation of the currency in the long run, and so to the expectation of a depreciation– The reduced attractiveness of domestic assets

leads to an instant depreciation

• The extent of the depreciation is just enough to give rise to an anticipation of appreciation at a rate that just offsets the reduced domestic interest rate

• So monetary expansion induces an immediate depreciation which exceeds the long run depreciation– This must be the case for investors to be

compensated for lower interest rates on domestic assets.

– Full burden of adjustment in the economy falls on the exchange rate

• Instantaneous depreciation produces a disequilibrium in the goods market. This is gradually eliminated as prices slowly adjust– Excess demand for goods due to lower

interest rates and depreciation– As prices rise slowly, real money

balances fall, interest rates rise and exchange rate appreciates.

• Extent of the overshoot depends on slope of the saddlepath, which in turn, depends on – the interest elasticity of demand for

money balances and – the speed of adjustment of goods prices

• Lots of models in economics have a family resemblance to the Dornbusch model.– Tobin’s Q model in Ch 2 of O&R (time to

build means capital is sluggish)– Krugman (AER, 1989): J Curve and the

hard landing in the US (see Cecil) (lags in trade adjustment)