Help for package SVARtca

Type:

Package

Title:

Transmission Channel Analysis in Structural VAR Models

Version:

1.0.2

Date:

2026-03-15

Description:

Implements Transmission Channel Analysis (TCA) for structural vector autoregressive (SVAR) models following the methodology of Wegner, Lieb, and Smeekes (2025) <doi:10.48550/arXiv.2405.18987>. TCA decomposes impulse response functions (IRFs) into contributions from distinct transmission channels using a systems form representation and directed acyclic graph (DAG) path analysis. Supports overlapping channels, exhaustive 3-way and 4-way decompositions via inclusion-exclusion principle. This is a parallel R implementation of the 'tca-matlab-toolbox' (https://github.com/enweg/tca-matlab-toolbox).

License:

MIT + file LICENSE

URL:

https://github.com/muhammedalkhalaf/SVARtca

BugReports:

https://github.com/muhammedalkhalaf/SVARtca/issues

Encoding:

UTF-8

RoxygenNote:

7.3.2

Depends:

R (≥ 3.5.0)

Imports:

Matrix, ggplot2, rlang

Suggests:

testthat (≥ 3.0.0), knitr, rmarkdown, vars

Config/testthat/edition:

NeedsCompilation:

Packaged:

2026-04-02 15:26:36 UTC; SYSTEM

Author:

Muhammad Alkhalaf

[aut, cre], Emanuel Wegner [ctb] (Original MATLAB toolbox author), Lenard Lieb [ctb] (Original MATLAB toolbox author), Stephan Smeekes [ctb] (Original MATLAB toolbox author)

Maintainer:

Muhammad Alkhalaf <muhammedalkhalaf@gmail.com>

Repository:

CRAN

Date/Publication:

2026-04-08 19:10:27 UTC

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.

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)

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.

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)

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).

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")

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

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.