VAR (SVAR) representation:
K (L)Yt = C* Dt + et (4)
p
K(L)=A + Ai*Li (5)
i=1
The contemporaneous relations between the variables are now directly explained in
A, which is a lower triangular matrix with all elements of the main diagonal being
1. The innovations et are by construction uncorrelated since E(ete't) = AΣA-1 =
APP' A = DP-1PP'P 1D = DD. Similarly, the Cholesky decomposition is used
to construct orthogonal innovations from the moving average representation of the
system which is the cornerstone of the impulse response analysis and the forecast
error variance decomposition carried out later. Furthermore, the use of the Cholesky
decomposition implies a recursive identification scheme which involves restrictions
about the contemporaneous relations between the variables. These are given by the
(Cholesky) ordering of the variables and might considerably influence the results of
our analysis. Therefore, different orderings are used to evaluate the robustness of
the results.
To compute standard errors for the impulse responses and the forecast error
variance decomposition which are not relying on any specific assumptions, in partic-
ular concerning the distribution of the coefficients, Monte Carlo techniques are an
appropriate way to construct the desired confidence intervals.11 Thus, this method
will be used in the subsequent analysis.
Since the macroeconomic variables included in the analysis are likely to be non-
stationary, the question arises whether one should take differences of the variables
in order to eliminate the stochastic trend. Here, we follow Sims, Stock and Watson
(1990) and estimate the VAR model in levels which, due to its simplicity, might be
the more appropriate technique, too.
11See Enders (2003), p. 277-278.
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