Impulse Response Analysis

The impulse response function traces the effect of a one standard deviation shock to one of the variables on current and future values of all the endogenous variables. A shock to any variable in the system does not only affect that variable directly but is also transmitted to all of the endogenous variables through the dynamic structure of the VAR. This function thus measures the time profile of the effect of shocks on the future states of a dynamical system.

The innovations are, however, usually correlated, so that they have a common component, which cannot be associated with a specific variable. A common method of dealing with this issue is to attribute all of the effect of any common component to the variable that comes first in the VAR system (Sims 1980, 1981; Lutkepohl 1991). In this approach, the underlying shocks to the VAR model are orthogo- nalized using the Cholesky decomposition of the variance-covariance matrix of the errors. The drawback is that the orthogonalized impulse responses, in general, depend on the order of the variables in the VAR.

This problem of dependence on the ordering of the variables in the VAR is overcome in the generalized impulse response method (see Koop et al. 1996; Pesaran and Pesaran 1997; Pesaran and Shin 1998). The generalized impulse responses are uniquely determined and take into account the historical pattern of correlations observed amongst the different shocks. We therefore use the generalized impulse response method for our analysis.

Once the impulse response of a variable to one standard error shock in another variable is computed, it is important to analyse whether the response is statistically significant or not. In order to test the statistical significance of the impulse response functions, bootstrapped confidence intervals are computed. The impulse response function along with the upper and the lower percentiles indicate the significance of the impulse response functions. In this study the upper 90% and the lower 10% percentiles are used to test for the significance of the impulse response functions.

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