through

through Construct a transmission condition enforcing paths through specific variables.

q = through(idx, horizons, order) creates a transmission condition Q where paths must pass through the variables specified in idx. The variable indices refer to their positions in the original dynamic system (e.g., in the SVARMA model), before applying the transmission matrix.

Arguments

For a single variable:

idx (integer): Index of the variable that paths must go through, using its original index in the dynamic system (before transmission ordering).
horizons (vector of integers): Time horizons at which the paths must pass through the variable.
order (vector of integers): Variable ordering determined by the transmission matrix.

For multiple variables:

idx (vector of integers): Indices of the variables that paths must go through, using their original indices in the dynamic system.
horizons (cell array of vectors or vector of integer): If a single vector of integers is provided, then it will be applied to each idx. Alternatively, a cell array of integer vectors can be provided in which case each element in the cell array applies to the respective element in idx.
order (vector of integers): Variable ordering determined by the transmission matrix.

Returns

q (Q): A transmission condition.

Notes

The resulting transmission condition can be used in transmission to compute the transmission effect.

Example

% Contemporaneous channel (Section 5.1 in Wegner)
contemporaneous_channel = through(1, [0], 1:4);

% Effect through the federal funds rate in the first two periods
q = through(1, [0, 1], 1:4);

% Effect through both the federal funds rate and output gap
q = through([1, 2], {[0, 1], [0, 1]}, 1:4);

% Adjusting for a re-ordered system where the output gap comes first
q = through([1, 2], {[0, 1], [0, 1]}, [2, 1, 3, 4]);