Extract monetary policy shocks via Kalman filter

Extracts structural shocks from reduced-form residuals using the Kalman filter formula. Given the impact matrix Psi and the covariance matrices of residuals on event and control days, the function recovers the latent shocks for each observation. Optionally rescales shocks to unit variance.

Usage

kfpredict(Sig, SigR, Psi, et, tol = sqrt(.Machine$double.eps), scale = TRUE)

Arguments

Sig: Numeric matrix (N x N). Covariance matrix of reduced-form residuals on policy event days (e.g. et from hetiv()).
SigR: Numeric matrix (N x N). Covariance matrix of reduced-form residuals on control (non-event) days. Used to back out the implied shock variances when scale = TRUE.
Psi: Numeric matrix (N x E). Impact matrix, i.e. the contemporaneous responses of all N variables to the E structural shocks (e.g. Psi from hetiv()).
et: Numeric matrix or data frame (T x N). Reduced-form residuals on event days (e.g. et from hetiv()). Rows correspond to time periods, columns to variables.
tol: Numeric scalar. Tolerance for the generalized inverse (MASS::ginv()). Clipped from below at sqrt(.Machine$double.eps).
scale: Logical. If TRUE (default), shocks are rescaled to unit variance using the implied shock variances recovered from Sig and SigR. This scaling assumes that structural shock variances are diagonal, so that Sig - SigR = sum_i sigma_i Psi_i Psi_i'. If FALSE, the raw Kalman filter projection is returned.

Value

A numeric matrix (T x E) of extracted structural shocks, with the same number of rows as et and one column per shock dimension.

References

Burri, M. and Kaufmann, D. (2026a). Measuring monetary policy shocks. IRENE Working Papers 24-03, IRENE Institute of Economic Research, University of Neuchatel.

Examples

Sig <- diag(2)
SigR <- diag(c(0.5, 0.5))
Psi <- matrix(c(1, 0.5), nrow = 2)
et <- matrix(rnorm(20), ncol = 2)
kfpredict(Sig = Sig, SigR = SigR, Psi = Psi, et = et)
#>              [,1]
#>  [1,] -0.53121758
#>  [2,]  0.29646687
#>  [3,]  1.11203917
#>  [4,] -0.74216125
#>  [5,]  0.87744535
#>  [6,]  0.38718522
#>  [7,]  0.26866947
#>  [8,] -0.37366525
#>  [9,] -0.15323607
#> [10,]  0.01922568