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transmission

transmission Compute the transmission effect given a transmission condition.

effects = transmission(from, arr1, arr2, q, method) calculates the transmission effect for a given transmission condition q using either the BOmega method or the irf method. If BOmega is used, then transmission effects will be calculated using the systems form x=Bx+Ωε

Arguments

  • from (integer): Index of the shock.
  • arr1 (matrix):
  • If method = "BOmega", this must be B from the systems form.
  • If method = "irf", this must be structural irfs (technically only those of the shock that is being investigates (from)). Has to be a IRF matrix. See toTransmissionIrfs for more information.
  • arr2 (matrix):
  • If method = "BOmega", this must be Omega from the systems form.
  • If method = "irf", this must be irfsOrtho (Cholesky IRFs) following the ordering of the transmission matrix.
  • q (Q): A transmission condition. See also Q.
  • method (string): Specifies the calculation method:
  • "BOmega" uses the systems form.
  • "irf" uses only IRFs and can thus be used with local projections.
  • order (vector, optional): variable ordering as defined by the transmission matrix.

Returns:

  • effects (vector): A vector where entry i corresponds to the transmission effect on variable x_i. If x_k is the variable in the transmission condition with the highest index, all entries in the returned vector with index less than k are NaN, since interpretation of those results is nonsensical.

Example:

k = 6;
h = 3;
s = "(x1 | x2) & !x3";
cond = makeCondition(s);

B = randn(k*(h+1), k*(h+1));
Omega = randn(k*(h+1), k*(h+1));

effect = transmission(1, B, Omega, cond, "BOmega");

irfs = randn(k, k, h+1);
irfsOrtho = randn(k, k, h+1);

irfs = toTransmissionIrfs(irfs);
irfsOrtho = toTransmissionIrfs(irfsOrtho);

effect = transmission(1, irfs, irfsOrtho, cond, "irf");

Notes:

  • If method = "BOmega", the function applies transmissionBOmega.
  • If method = "irf", the function applies transmissionIrfs.
  • If order is provided, the returned effects will be a 3D array of dimension (nVariables, 1, horizons) where the variables are in the original ordering (before applying the transmission matrix).
  • If order is not provided, the returned effects will be a (nVariable*horizons, 1) dimensional vector following the ordering after applying the transmission matrix. This is similar to the matrix obtained via (I−B)−1Ω using the matrices from the systems form.

See also transmissionBOmega, transmissionIrfs, makeCondition, through, notThrough