Bidian (3) notes the overshooting model will help us understand why: (i.) over the short run, there are deviations from purchasing power parity; (ii.) there is volatility in both the nominal exchange rate and in the real exchange rate. Using the money demand equation1, the UIP condition2 and the PPP condition3, the model uses [where yt is the national income, i* is the international interest rate (exogenous) and p* is the international price level (also exogenous)]:
The crucial ingredient is the assumption that prices pt is sticky in short run (Bidian 3). The following figure on the monthly variability of the US dollar/Deutsch mark exchange rate and the US/German price ratio illustrates this point:
Benigno (5-7) cites the following outcomes of monetary expansion in the Dornbusch model and the items must be noted in order to determine the long-run effect of the monetary expansion: 1) we know that aggregate demand has to be equal to the long run level of output given by y. Thus, we can conclude that long-run equilibrium will be on the vertical aggregate supply curve; 2) since i* (international/foreign interest rate) did not change, we know that in the long run equilibrium, I (local interest rate) = i*: our IS and LM curve need to return to the original equilibrium. Particularly, the increase in money supply translates into a proportional increase in the price level.3) Since the IS curve depends only on the real exchange rate, this means that the real exchange rate must return to the initial equilibrium. To determine its impact effect (keep in mind that goods market adjust slowly while financial markets adjust instantaneously), note that an increase in money supply determines a decrease in the domestic interest rates (the liquidity effect) in order to cushion the excess supply of real money balances (the excess supply brought about by sticky prices).Also, the UIP condition in the Dornbusch model holds which implies that the decline in the domestic interest rate is compatible only if there is an equilibrating change in the nominal exchange rate. In order to keep domestic assets in their portfolio, households must foresee that the nominal exchange rate will appreciate along the path that goes to the long-run equilibrium. Meanwhile, in order to generate expectation of appreciation, the nominal exchange rate overdepreciates (overshoots), so as the domestic currency becomes undervalued that it is expected to appreciate in the future. Given the depreciation of the nominal exchange rate the IS curve then shifts outward.
Suppose an unanticipated permanent increase in money supply m occurs, Bidian (4-5) cites the following outcomes to take place: due to fixed prices (in short run) and exogenous output, this means that the interest rates decrease by m/. Since long run money neutrality means that the change in money supply is (fully) incorporated into the price level, hence pt+1 increases by m. Equation (3) implies that in the absence