pid.cvm: Independence-based identification of panel SVAR models via...

In pvars: VAR Modeling for Heterogeneous Panels

Independence-based identification of panel SVAR models via Cramer-von Mises (CVM) distance

Description

Given an estimated panel of VAR models, this function applies independence-based identification for the structural impact matrix B_i of the corresponding SVAR model

y_{it} = c_{it} + A_{i1} y_{i,t-1} + ... + A_{i,p_i} y_{i,t-p_i} + u_{it}

= c_{it} + A_{i1} y_{i,t-1} + ... + A_{i,p_i} y_{i,t-p_i} + B_i \epsilon_{it}.

Matrix B_i corresponds to the unique decomposition of the least squares covariance matrix \Sigma_{u,i} = B_i B_i' if the vector of structural shocks \epsilon_{it} contains at most one Gaussian shock (Comon, 1994). A nonparametric dependence measure, the Cramer-von Mises distance (Genest and Remillard, 2004), determines least dependent structural shocks. The minimum is obtained by a two step optimization algorithm similar to the technique described in Herwartz and Ploedt (2016).

Usage

pid.cvm(
  x,
  combine = c("group", "pool", "indiv"),
  n.factors = NULL,
  dd = NULL,
  itermax = 500,
  steptol = 100,
  iter2 = 75
)

Arguments

x	An object of class 'pvarx' or a list of VAR objects that will be coerced to 'varx'. Estimated panel of VAR objects.
combine	Character. The combination of the individual reduced-form residuals via 'group' for the group ICA by Calhoun et al. (2001) using common structural shocks, via 'pool' for the pooled shocks by Herwartz and Wang (2024) using a common rotation matrix, or via 'indiv' for individual-specific B_i \forall i using strictly separated identification runs.
n.factors	Integer. Number of common structural shocks across all individuals if the group ICA is selected.
dd	Object of class 'indepTestDist' generated by 'indepTest' from package 'copula'. Simulated independent sample(s) of the same size as the data. If the sample sizes T_i - p_i differ across 'i', the strictly separated identification requires a list of N individual 'indepTestDist'-objects with respective sample sizes. If NULL (the default), a suitable object will be calculated during the call of pid.cvm.
itermax	Integer. Maximum number of iterations for DEoptim.
steptol	Numeric. Tolerance for steps without improvement for DEoptim.
iter2	Integer. Number of iterations for the second optimization.

Value

List of class 'pid' with elements:

A	Matrix. The lined-up coefficient matrices A_j, j=1,\ldots,p for the lagged variables in the panel VAR.
B	Matrix. Mean group of the estimated structural impact matrices B_i, i.e. the unique decomposition of the covariance matrices of reduced-form errors.
L.varx	List of 'varx' objects for the individual estimation results to which the structural impact matrices B_i have been added.
eps0	Matrix. The combined whitened residuals \epsilon_{0} to which the ICA procedure has been applied subsequently. These are still the unrotated baseline shocks! NULL if 'indiv' identifications have been used.
ICA	List of objects resulting from the underlying ICA procedure. NULL if 'indiv' identifications have been used.
rotation_angles	Numeric vector. The rotation angles suggested by the combined identification procedure. NULL if 'indiv' identifications have been used.
args_pid	List of characters and integers indicating the identification methods and specifications that have been used.
args_pvarx	List of characters and integers indicating the estimator and specifications that have been used.

References

Comon, P. (1994): "Independent Component Analysis: A new Concept?", Signal Processing, 36, pp. 287-314.

Genest, C., and Remillard, B. (2004): "Tests of Independence and Randomness based on the Empirical Copula Process", Test, 13, pp. 335-370.

Herwartz, H., and Wang, S. (2024): "Statistical Identification in Panel Structural Vector Autoregressive Models based on Independence Criteria", Journal of Applied Econometrics, 39 (4), pp. 620-639.

Herwartz, H. (2018): "Hodges Lehmann detection of structural shocks - An Analysis of macroeconomic Dynamics in the Euro Area", Oxford Bulletin of Economics and Statistics, 80, pp. 736-754.

Herwartz, H., and Ploedt, M. (2016): "The Macroeconomic Effects of Oil Price Shocks: Evidence from a Statistical Identification Approach", Journal of International Money and Finance, 61, pp. 30-44.

See Also

... the individual id.cvm by Lange et al. (2021) in svars. Note that pid.cvm relies on a modification of their procedure and thus performs ICA on the pre-whitened shocks 'eps0' directly.

Other panel identification functions: pid.chol(), pid.dc(), pid.grt(), pid.iv()

Examples

# select minimal or full example #
is_min = TRUE
idx_i  = ifelse(is_min, 1, 1:14)

# load and prepare data #
data("EURO")
data("EU_w")
names_i = names(EURO[idx_i+1])  # country names (#1 is EA-wide aggregated data)
idx_k   = 1:4   # endogenous variables in individual data matrices
idx_t   = 1:76  # periods from 2001Q1 to 2019Q4
trend2  = idx_t^2

# individual VARX models with common lag-order p=2 #
L.data = lapply(EURO[idx_i+1], FUN=function(x) x[idx_t, idx_k])
L.exog = lapply(EURO[idx_i+1], FUN=function(x) cbind(trend2, x[idx_t, 5:10]))
L.vars = sapply(names_i, FUN=function(i) 
  vars::VAR(L.data[[i]], p=2, type="both", exogen=L.exog[[i]]), 
  simplify=FALSE)

# identify under common orthogonal matrix (with pooled sample size (T-p)*N) #
S.pind = copula::indepTestSim(n=(76-2)*length(names_i), p=length(idx_k), N=100)
R.pcvm = pid.cvm(L.vars, dd=S.pind, combine="pool")
R.irf  = irf(R.pcvm, n.ahead=50, w=EU_w)
plot(R.irf, selection=list(1:2, 3:4))

# identify individually (with same sample size T-p for all 'i') #
S.pind = copula::indepTestSim(n=(76-2), p=length(idx_k), N=100)
R.pcvm = pid.cvm(L.vars, dd=S.pind, combine="indiv")
R.irf  = irf(R.pcvm, n.ahead=50, w=EU_w)
plot(R.irf, selection=list(1:2, 3:4))

pvars documentation built on Nov. 5, 2025, 6:57 p.m.