Real exchange rate in forward-looking Rules : advantages and pitfalls

Abstract

In a small open economy model, we assess the advantages and cost of a systematic policy response to the real exchange rate. In particular, in the context of the Gali and Monacelli (2005) model, we use the method of undetermined coe cients to derive closed form solutions for the evolution of all the variables under an augmented Taylor rule that, besides reacting to domestic in ation and output gap, also respond to expected real exchange rate uctuations. We perform this exercise for three orthogonal innovations: demand, supply and country risk premium shocks. We also consider alternative information sets available to the central bank. Our main ndings are as follows. First, when the central bank observes the natural rate of interest, an aggressive policy response to expected exchange rate has the potential of inducing a decline in the volatility of domestic in ation and the output gap in the face of all shocks. This equilibrium, however, is in general not unique: it induces instability due to self-ful lling expectations. In other words, an aggressive policy response to exchange rate induces indeterminacy, pretty much in line with Uribe (2003) and Woodford (2000). The only exception is the potential decline in domestic in ation volatility. In this case, we derive the conditions under which a positive response to expected exchange rate can reduce the volatility of domestic in ation and induce determinacy. This response will lead, however, and increase in output gap variance. Second, when the central bank is not able to observe the natural rate of interest, reacting to expected exchange rate depreciation can be an e cient response in the face of demand shocks. In particular, we show that there is a unique exchange rate reaction coe cient that can mimic the optimal policy response under full information and also induces determinacy. This coe cient is directly linked to the degree of openness in the economy: as the economy becomes more open, the response to expected exchange rate uctuations increase. This optimal exchange rate response generates a zero domestic in ation and output gap. Alternative policy responses, in which this policy coe cient is set to zero are unable to induce the optimal allocation.