pvarx: Estimation of VAR models for heterogeneous panels

In pvars: VAR Modeling for Heterogeneous Panels

Estimation of VAR models for heterogeneous panels

Description

Performs the (pooled) mean-group estimation of a panel VAR model. First, VAR models are estimated for all N individual entities. Then, their (pooled) mean-group estimate is calculated for each coefficient.

Usage

pvarx.VAR(
  L.data,
  lags,
  type = c("const", "trend", "both", "none"),
  t_D = NULL,
  D = NULL,
  n.factors = FALSE,
  n.iterations = FALSE
)

pvarx.VEC(
  L.data,
  lags,
  dim_r,
  type = c("Case1", "Case2", "Case3", "Case4", "Case5"),
  t_D1 = NULL,
  t_D2 = NULL,
  D1 = NULL,
  D2 = NULL,
  idx_pool = NULL,
  n.factors = FALSE,
  n.iterations = FALSE
)

Arguments

L.data	List of 'data.frame' objects for each individual. The variables must have the same succession k = 1,\ldots,K in each individual 'data.frame'.
lags	Integer or vector of integers. Lag-order of the VAR models in levels, which is either a common p for all individuals or individual-specific p_i for each individual. In the vector, p_i must have the same succession i = 1,\ldots,N as argument 'L.data'.
type	Character. The conventional case of the deterministic term.
t_D	List of vectors. The activating break periods \tau for the period-specific deterministic regressors in d_{it} of the VAR model in levels.
D	List. A single 'data.frame' of common deterministic regressors or a list of N 'data.frame' objects of the individual deterministic regressors added to d_{it}. These customized regressors correspond to 'exogen' in vars' VAR, which is fixed over bootstrap iterations.
n.factors	Integer. Number of common factors to be used for SUR. Deactivated if FALSE (the default).
n.iterations	Integer. The (maximum) number of iterations for the estimation of SUR resp. the pooled cointegrating vectors.
dim_r	Integer. Common cointegration-rank r of the VECM.
t_D1	List of vectors. The activating break periods \tau for the period-specific deterministic regressors in d_{1,it}, which are restricted to the cointegration relations. Just as in pcoint, the accompanying lagged regressors are automatically included in d_{2,it}.
t_D2	List of vectors. The activating break periods \tau for the period-specific deterministic regressors in d_{2,it}, which are unrestricted.
D1	List. A single 'data.frame' of common deterministic regressors regressors or a list of N 'data.frame' objects of individual deterministic regressors added to d_{1,it}, which are restricted to the cointegration relations. Unlike 't_D1', these customized regressors require potential accompanying lagged regressors to be manually included in d_{2,it}
D2	List. A single 'data.frame' of common deterministic regressors or a list of N 'data.frame' objects of individual deterministic regressors added to d_{2,it}, which are unrestricted. These customized regressors correspond to 'dumvar' in urca's ca.jo, which is fixed over bootstrap iterations.
idx_pool	Vector. Position k = 1,...,K+n_1 of each variable to be pooled using the two-step estimator by Breitung (2005). The integer vector specifies throughout heterogeneous coefficients up to the uniform upper block I_{r} estimated with the individual estimator by Ahn and Reinsel (1990) if exclusively in the interval [0,...,r]. Deactivated if NULL (the default).

Value

A list of class 'pvarx' with the elements:

A	Matrix. The lined-up coefficient matrices A_j, j=1,\ldots,p for the lagged variables in the panel VAR estimated by mean-group.
B	Matrix. Placeholder for the structural impact matrix.
beta	Matrix. The ((K+n_{d1}) \times r) cointegrating matrix of the VAR model if transformed from a rank-restricted VECM.
L.varx	List of 'varx' objects for the individual estimation results.
L.data	List of 'data.frame' objects for each individual.
CSD	List of measures for cross-sectional dependency. NULL if the individual VAR models have been estimated under independence.
args_pvarx	List of characters and integers indicating the estimator and specifications that have been used.

Functions

• pvarx.VAR(): Mean Group (MG) of VAR models in levels.

• pvarx.VEC(): (Pooled) Mean Group (PMG) of VECM.

References

Canova, F., and Ciccarelli, M. (2013): "Panel Vector Autoregressive Models: A Survey", Advances in Econometrics, 32, pp. 205-246.

Hsiao, C. (2014): Analysis of Panel Data, Econometric Society Monographs, Cambridge University Press, 3rd ed.

Luetkepohl, H. (2005): New Introduction to Multiple Time Series Analysis, Springer, 2nd ed.

Pesaran, M. H., and Smith R. J. (1995): "Estimating Long-Run Relationships from Dynamic Heterogeneous Panels", Journal of Econometrics, 68, pp. 79-113.

Rebucci, A. (2010): "Estimating VARs with Long Stationary Heterogeneous Panels: A Comparison of the Fixed Effect and the Mean Group Estimators", Economic Modelling, 27, pp. 1183-1198.

Ahn, S. K., and Reinsel (1990): "Estimation for Partially Nonstationary Multivariate Autoregressive Models", Journal of the American Statistical Association, 85, pp. 813-823.

Breitung, J. (2005): "A Parametric Approach to the Estimation of Cointegration Vectors in Panel Data", Econometric Reviews, 24, pp. 151-173.

Johansen, S. (1996): Likelihood-based Inference in Cointegrated Vector Autoregressive Models, Advanced Texts in Econometrics, Oxford University Press, USA.

Pesaran, M. H., Shin, Y, and Smith R. J. (1999): "Pooled Mean Group Estimation of Dynamic Heterogeneous Panels", Journal of the American Statistical Association, 94, pp. 621-634.

Examples

data("PCAP")
names_k = c("g", "k", "l", "y")  # variable names
names_i = levels(PCAP$id_i)      # country names 
L.data  = sapply(names_i, FUN=function(i) 
  ts(PCAP[PCAP$id_i==i, names_k], start=1960, end=2019, frequency=1), 
  simplify=FALSE)
R.lags = c(2, 4, 2, 3, 2, 4, 4, 2, 2, 3, 3, 3, 2, 4, 4, 2, 2, 2, 4, 2, 2, 2, 4)
names(R.lags) = names_i

### MG of VAR by OLS ###
R.t_D  = list(t_shift=10)  # common level shift for all countries 
R.pvar = pvarx.VAR(L.data, lags=R.lags, type="both", t_D=R.t_D)
R.pirf = irf(R.pvar, n.ahead=50)  # MG of individual forecast-error IRF
plot(R.pirf)

### Pooled MG of rank-restricted VAR ###
R.pvec = pvarx.VEC(L.data, lags=R.lags, dim_r=2, idx_pool=1:4, type="Case4")
R.pirf = irf(R.pvec, n.ahead=50)  # MG of individual forecast-error IRF
plot(R.pirf)

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