Innovation Accounting with Incomplete Identification of a Structural VAR – An Application to Exchange Rates

Abstract

Two main objectives of Structural Vector AutoRegression (SVAR) modeling are recovering structural shocks from reduced form shocks and Impulse-Response Analysis and Forecast error variance decomposition. As is well known, the first of these is possible only if the number of structural shocks is less than or equal to the number of endogenous VAR variables. The main goal of this paper is to highlight that the second objective can be accomplished even if the number of structural shocks is greater than the number of VAR variables. As an illustration, a bivariate SVAR is developed to relate the joint dynamics of real and nominal exchange rates to three structural shocks, namely, demand, supply and nominal shocks. Variance decomposition results suggest that demand shocks are the dominant source of movements in both the real and nominal exchange rates. However, nominal shocks also appear to play a smaller but still important role. Interestingly, the persistence of exchange rates appears to be related mainly to nominal and supply shocks.