Dornbusch’s Overshooting Model

Dornbusch’s Overshooting Model
As we have already seen, the sticky-price rational expectations models put
forward by Fischer (1977) and Phelps and Taylor (1977) analyse the role of
monetary policy in the context of a closed economy. Before considering the
importance of real rigidities in new Keynesian analysis we briefly examine
Dornbusch’s (1976) sticky-price rational expectations model of a small open
economy. This exchange rate ‘overshooting’ model has been described by
Kenneth Rogoff (2002) ‘as one of the most influential papers written in the
field of International Economics since World War II’, a paper which Rogoff
suggests ‘marks the birth of modern international macroeconomics’.
Before discussing the main predictions of Dornbusch’s model it is helpful
to place the model in the context of earlier discussion of aspects of international
macroeconomics. In Chapter 3, section 3.5.4 we discussed how in the
fixed price (IS–LM–BP) Mundell–Fleming model of an open economy operating
under a regime of flexible exchange rates monetary expansion results in
an increase in income, with the effects of monetary expansion on aggregate
demand and income being reinforced by exchange rate depreciation. Furthermore,
in the limiting case of perfect capital mobility monetary policy becomes
‘all-powerful’. In contrast, in Chapter 4, section 4.4.3 we considered how in
the monetary approach to exchange rate determination, where real income is
exogenously given at its natural level, monetary expansion leads to a depreciation
in the exchange rate and an increase in the domestic price level. In
what follows we outline the essence of Dornbusch’s (1976) sticky-price
rational expectations model in which monetary expansion causes the exchange
rate to depreciate (with short-run overshooting) with no change in
real output.
In his model Dornbusch made a number of assumptions, the most important
of which are that:
1. goods markets are slow to adjust compared to asset markets and exchange
rates; that is, goods prices are sticky;
2. movements in the exchange rate are consistent with rational expectations;
3. with perfect capital mobility, the domestic rate of interest of a small open
economy must equal the world interest rate (which is given exogenously),
plus the expected rate of depreciation of the domestic currency; that is,
expected exchange rate changes have to be compensated by the interest
rate differential between domestic and foreign assets; and
4. the demand for real money balances depends on the domestic interest
rate (determined where equilibrium occurs in the domestic money market)
and real income, which is fixed.
Given these assumptions, what effect will monetary expansion have on the
exchange rate? In the short run with fixed prices and a given level of real
income an increase in the (real) money supply results in a fall in the domestic
interest rate, thereby maintaining equilibrium in the domestic money market.
The fall in the domestic interest rate means that, with the foreign interest rate
fixed exogenously (due to the small-country assumption), the domestic currency
must be expected to appreciate. While short-run equilibrium requires
an expected appreciation of the domestic currency, long-run equilibrium
requires a depreciation of the exchange rate. In other words, since long-run
equilibrium requires a depreciation of the domestic currency (compared to its
initial level), the exchange rate depreciates too far (that is, in the short run it
overshoots), so that it can be expected to appreciate back to its long-run
equilibrium level. Such short-run exchange rate overshooting is fully consistent
with rational expectations because the exchange rate follows the path it is
expected to follow.
A number of points are worth noting with respect to the above analysis.
First, the source of exchange rate overshooting in the Dornbusch model lies
in goods prices being relatively sticky in the short run. In other words, the
crucial assumption made in the model is that asset markets and exchange
rates adjust more quickly than do goods markets. Second, the rate at which
the exchange rate adjusts back to its long-run equilibrium level depends on
the speed at which the price level adjusts to the increase in the money stock.
Finally, in the long run, monetary expansion results in an equi-proportionate
increase in prices and depreciation in the exchange rate.