MultiATSM (version 1.5.0)

GVAR: Estimates a GVAR(1) and VARX(1,1,1) models

Description

Estimates a GVAR(1) and VARX(1,1,1) models

Usage

GVAR(GVARinputs, N, CheckInputs = FALSE)

Value

list. Contains:

1. parameters of the country-specific VARX(1,1,1):

   • intercept (M + N x 1)

   • phi_1 (M + N x M + N)

   • phi_1* (M + N x M + N)

   • phi_g (M + N x M + N)

   • Sigma (M + N x G)

2. parameters of the GVAR:

   • F0 (K x K)

   • F1 (K x K)

   • Sigma_y (K x K)

Arguments

GVARinputs

list. Inputs for GVAR model estimation:

1. Economies: character vector. Contains the C names of the economies included in the system.

2. GVARFactors: list. All variables used in the estimation of the VARX model
   (see e.g. GVARFactors file for details);

3. VARXtype: Permissible:

   • 'unconstrained': model is estimated without constraints (each equation is estimated individually by ordinary least square);

   • 'constrained: Spanned Factors': The model is estimated with the restriction that foreign pricing factors do NOT affect (i) domestic economic variables and (ii) domestic pricing factors (estimation via restricted least squares).

   • 'constrained : [factor_name]': The model is estimated with the restriction that the specified risk factor is influenced only by its own lagged values and the lagged values of its corresponding star variables. (estimation via restricted least squares.)

4. Wgvar: The GVAR transition matrix (C x C) used in the model solution.
   (See the output from the Transition_Matrix function.).

N

positive integer. Number of country-specific spanned factors.

CheckInputs

logical. Whether to perform a prior consistency check on the inputs provided in GVARinputs. Default is FALSE.

General Notation

• C: number of countries in the system

• G: number of global unspanned factors

• M: number of country-specific unspanned factors

• N: number of country-specific spanned factors

• K: total number of risk factors (K = C x (N + M) + G)

References

Chudik, A. and Pesaran, M. H. (2016). "Theory and Practice of GVAR modelling" (Journal of Economic Surveys)

Examples

data(GVARFactors)

GVARinputs <- list(
  Economies = c("China", "Brazil", "Mexico", "Uruguay"),
  GVARFactors = GVARFactors, VARXtype = "unconstrained"
)

GVARinputs$Wgvar <- matrix(c(
  0, 0.83, 0.86, 0.38,
  0.65, 0, 0.13, 0.55,
  0.32, 0.12, 0, 0.07,
  0.03, 0.05, 0.01, 0
), nrow = 4, ncol = 4)
N <- 3

GVARPara <- GVAR(GVARinputs, N)