Measuring the Effects of a Shock to Monetary Policy - Humboldt ...

32 Bayesian FAVARs with Agnostic Identification
where ¯ Λi = ¯ M −1
i ( F ′ T (i) F i T ) ˆ Λi and ¯ M −1
i ( F ′ T (i) F i T ).
The next Gibbs block requires to draw vec(Φ) and Q conditional on the most cur-
rent draws of the factors, the R ′ iis and Λ ′ is and the data. As the FAVAR equation has a
standard VAR form one can likewise estimate vec( ˆ Φ) and ˆ Q via equation by equation OLS.
BBE impose a diffuse conjugate Normal-Wishart prior :
Posterior Q is drawn from:
vec(Φ) | Q ∼ N(0, Q ⊗ Ω0), Q ∼ iW (Q0, K + M + 2)
iW ( ¯ Q, T + K + M + 2);
In order to assume a prior in the vein of the Minnesota prior that expresses more
distant lags to have less impact, hence be more likely zero, they follow Kadiyala and
Karlsson [1997] 31 . First we draw Q from the Inverse-Wishart, iW ( ¯ Q, T + K + M + 2),
where ¯ Q = Q0 + ˆ V ′ ˆ V + ˆ Φ ′ [Ω0 + ( ˜ F ′ T −1 ˜ FT −1) −1 ] −1 ˆ Φ and ˆ V the matrix of OLS residuals.
The conditional on the drawn Q we draw vec(Φ) from the conditional normal according
to
vec(Φ) ∼ N(vec( ¯ Φ), Q ⊗ ¯ Ω)
Here ¯ Φ = ¯ Ω( ˜ F ′ T −1 ˜ FT −1) ˆ Φ and ¯ Ω = (Ω −1
0 + ( ˜ F ′ T −1 ˜ FT −1)) −1 . It is straight forward that
we truncate the draws to only acceptable values for Φ less than one in absolute values in
order to ensure stationarity. This block on Kalman filter and smoother and the block on
drawing the parameter space are iterated until convergence is achieved.
31 for a detailed description please refer to BBE [2005]