Package 'SVARtca'

Transmission Channel Analysis in Structural VAR Models

Description

The SVARtca package implements Transmission Channel Analysis (TCA) for decomposing impulse response functions in structural vector autoregressive (SVAR) models. The package follows the methodology presented in Wegner, Lieb, Smeekes (2025).

TCA enables researchers to decompose the total impulse response to a shock into contributions from different transmission channels. Supported channels include effects passing through specific intermediate variables, allowing analysts to distinguish direct effects from indirect effects that operate through identified transmission mechanisms.

Key features:

• Multiple decomposition modes: overlapping, exhaustive 3-way, and exhaustive 4-way.

• Support for VAR and SVAR models via integration with the vars package.

• Visualization of channel contributions using ggplot2.

• Diagnostic tools for validating decomposition accuracy.

Main Functions

tca_systems_form

Build the systems form representation (B and Omega matrices) from VAR coefficients and structural impact matrix.

tca_analyze

Run the main TCA analysis with specified decomposition mode.

tca_decompose_binary

Decompose IRF into "through" and "not_through" components for a single variable.

tca_validate_additivity

Validate that the binary decomposition satisfies exact additivity.

tca_from_var

Convenience wrapper to run TCA directly from a fitted VAR model object.

plot_tca

Create publication-quality visualizations of channel contributions.

Identification

The package supports two identification schemes:

• Cholesky: Lower-triangular Cholesky decomposition of the residual covariance matrix. Set Phi0 = t(chol(Sigma)).

• Manual: User-supplied structural impact matrix for alternative identifications (e.g., sign restrictions, zero restrictions).

Citation

If you use the SVARtca package in your research, please cite the original methodology paper:

Wegner, E., Lieb, L., Smeekes, S. (2025). Transmission Channel Analysis in Dynamic Models. arXiv:2405.18987. https://github.com/enweg/tca-matlab-toolbox

Author(s)

Muhammad Alkhalaf

References

Wegner, E., Lieb, L., Smeekes, S. (2025). Transmission Channel Analysis in Dynamic Models. arXiv:2405.18987.

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Plot TCA Channel Decomposition

Description

Creates a stacked bar chart (for exhaustive modes) or a line chart (for overlapping mode) showing channel contributions over horizons.

Usage

plot_tca(x, target = NULL, type = NULL, title = NULL,
  colors = NULL)

Arguments

x	A tca_result object from tca_analyze.
target	Integer index of the response variable to plot (default: first variable after shock).
type	Plot type: "bar" for stacked bar chart (default for exhaustive modes), "line" for overlaid lines (default for overlapping mode). If NULL, chosen automatically.
title	Custom plot title (optional).
colors	Named character vector of colours for channels (optional).

Value

A ggplot object.

Examples

K <- 4
A1 <- matrix(c(0.7,-0.1,0.05,-0.05, -0.3,0.6,0.10,-0.10,
                -0.2,0.1,0.70,0.05, -0.1,0.2,0.05,0.65), K, K, byrow=TRUE)
Sigma <- matrix(c(1,0.3,0.2,0.1, 0.3,1.5,0.25,0.15,
                   0.2,0.25,0.8,0.1, 0.1,0.15,0.1,0.6), K, K, byrow=TRUE)
Phi0 <- t(chol(Sigma))
sf <- tca_systems_form(Phi0, list(A1), h = 20)
res <- tca_analyze(from = 1, B = sf$B, Omega = sf$Omega,
                    intermediates = c(2, 4), K = K, h = 20,
                    order = 1:K, mode = "exhaustive_4way",
                    var_names = c("IntRate","GDP","Inflation","Wages"))
plot_tca(res, target = 3)

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Print TCA Result

Description

S3 print method for tca_result objects. Displays a formatted table of transmission channel contributions across horizons.

Usage

## S3 method for class 'tca_result'
print(x, target = NULL, ...)

Arguments

x	A tca_result object.
target	Target variable to display (default: first intermediate).
...	Additional arguments (ignored).

Value

Invisibly returns x.

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Transmission Channel Analysis

Description

Decomposes impulse response functions into transmission channel contributions using the methodology of Wegner, Lieb, Smeekes (2025).

Three decomposition modes are supported:

"overlapping"

Each channel is through(j) = total - not_through(j). Channels may overlap, so their sum may differ from the total.

"exhaustive_3way"

(2 intermediates only) Non-overlapping: (1) through var1 inclusive, (2) through var2 only, (3) direct. Sum equals total.

"exhaustive_4way"

(2 intermediates only) Full inclusion-exclusion: (1) var1 only, (2) var2 only, (3) both, (4) direct. Sum equals total.

Usage

tca_analyze(from, B, Omega, intermediates, K, h, order,
  mode = "overlapping", var_names = NULL)

Arguments

from	Shock variable number (1-based).
B	Systems form B matrix (from tca_systems_form).
Omega	Systems form Omega matrix.
intermediates	Integer vector of intermediate variable numbers (1-based, original ordering).
K	Number of variables.
h	Maximum horizon.
order	Transmission ordering vector.
mode	Decomposition mode: "overlapping", "exhaustive_3way", or "exhaustive_4way".
var_names	Character vector of variable names (optional).

Value

A list of class "tca_result" with components:

irf_total

Matrix (h+1) x K of total IRFs.

irf_channels

Named list of channel IRF matrices, each (h+1) x K.

channel_names

Character vector of channel names.

mode

Decomposition mode used.

from

Shock variable number.

K

Number of variables.

h

Maximum horizon.

order

Transmission ordering.

var_names

Variable names.

References

Wegner, E., Lieb, L., Smeekes, S. (2025). Transmission Channel Analysis in Dynamic Models. arXiv:2405.18987.

Examples

# Monetary policy model
K <- 4
A1 <- matrix(c(0.7,-0.1,0.05,-0.05, -0.3,0.6,0.10,-0.10,
                -0.2,0.1,0.70,0.05, -0.1,0.2,0.05,0.65), K, K, byrow=TRUE)
Sigma <- matrix(c(1,0.3,0.2,0.1, 0.3,1.5,0.25,0.15,
                   0.2,0.25,0.8,0.1, 0.1,0.15,0.1,0.6), K, K, byrow=TRUE)
Phi0 <- t(chol(Sigma))
sf <- tca_systems_form(Phi0, list(A1), h = 20)
result <- tca_analyze(from = 1, B = sf$B, Omega = sf$Omega,
                       intermediates = c(2, 4), K = K, h = 20,
                       order = 1:K, mode = "exhaustive_4way",
                       var_names = c("IntRate","GDP","Inflation","Wages"))
print(result)

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Binary Decomposition: Total = Through + Not-Through

Description

Decomposes the total IRF into the effect passing through a variable and the effect not passing through it. This is an exact decomposition (residual is zero at machine precision).

Usage

tca_decompose_binary(from, B, Omega, var_idx, K, h, order)

Arguments

from	Shock variable (1-based).
B	Systems form B matrix.
Omega	Systems form Omega matrix.
var_idx	Variable to decompose through (1-based).
K	Number of variables.
h	Maximum horizon.
order	Transmission ordering.

Value

A list with matrices total, through, not_through (each (h+1) x K).

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Run TCA from a VAR Estimation Object

Description

Extracts coefficient matrices and residual covariance from a fitted VAR model (from the vars package) and runs TCA.

Usage

tca_from_var(var_model, from, intermediates, h = 20,
  order = NULL, mode = "overlapping",
  identification = "cholesky", Phi0 = NULL)

Arguments

var_model	A fitted VAR model object from VAR.
from	Shock variable (integer or name).
intermediates	Integer vector or character vector of intermediate variable names.
h	Maximum horizon (default: 20).
order	Transmission ordering (default: variable ordering in the VAR).
mode	Decomposition mode: "overlapping", "exhaustive_3way", or "exhaustive_4way".
identification	Identification scheme: "cholesky" (default) or "manual".
Phi0	Manual impact matrix. Required if identification = "manual".

Value

A tca_result object (see tca_analyze).

Examples

library(vars)
data(Canada)
var_est <- VAR(Canada, p = 2, type = "const")
result <- tca_from_var(var_est, from = "e",
                        intermediates = c("prod", "rw"),
                        h = 20, mode = "exhaustive_4way")
plot_tca(result, target = "U")

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Build Complete Systems Form

Description

Constructs both B and Omega matrices for the systems form representation x = Bx + Omega*epsilon, following the methodology of Wegner, Lieb, Smeekes (2025).

Usage

tca_systems_form(Phi0, As, h, order = NULL, Psis = NULL)

Arguments

Phi0	Structural impact matrix (K x K). For Cholesky identification, use t(chol(Sigma)).
As	List of VAR coefficient matrices (A_1, A_2, ..., A_p).
h	Maximum IRF horizon.
order	Transmission ordering vector (default: 1:K).
Psis	List of reduced-form MA coefficients (optional, for DSGE/VARMA models).

Value

A list with components:

B

Systems form B matrix (K*(h+1) x K*(h+1)).

Omega

Systems form Omega matrix (K*(h+1) x K*(h+1)).

References

Wegner, E., Lieb, L., Smeekes, S. (2025). Transmission Channel Analysis in Dynamic Models. arXiv:2405.18987. https://github.com/enweg/tca-matlab-toolbox

Examples

# 2-variable VAR(1)
Phi0 <- matrix(c(1, 0.3, 0, 0.95), 2, 2)
As <- list(matrix(c(0.5, -0.1, 0.2, 0.4), 2, 2))
sf <- tca_systems_form(Phi0, As, h = 10)
dim(sf$B)  # 22 x 22

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Validate Binary Additivity

Description

Tests that total = through(j) + not_through(j) holds for all variables at machine precision. This is a diagnostic to verify correct implementation.

Usage

tca_validate_additivity(from, B, Omega, K, h, order,
  var_names = NULL, verbose = TRUE)

Arguments

from	Shock variable (1-based).
B	Systems form B matrix.
Omega	Systems form Omega matrix.
K	Number of variables.
h	Maximum horizon.
order	Transmission ordering.
var_names	Character vector of variable names (optional).
verbose	Logical; print results? Default TRUE.

Value

Invisibly returns TRUE if all tests pass.

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