bgvars: Bayesian Inference for Global Vector Autoregressive (GVAR) and Global Vector Error Correction (GVEC) Models

Overview

The bgvars package provides functions for the specification, estimation and evaluation of Bayesian global autoregressive (GVAR) models. Global vector autoregressive (GVAR) models are convenient tools to model the world economy. They were originally proposed by Pesaran et al. (2004) and further developed by Dees et al. (2007) to study the international transmission of shocks. Since then they have been applied to a range of macroeconomic topics. Chudik and Pesaran (2016) provide an extensive survey of the latest developments in GVAR modelling.

Installation

Development version

# install.packages("devtools")
devtools::install_github("franzmohr/bgvars")

Usage

The bgvars package allows Bayesian inference of GVAR models. It separates a typical GVAR analysis into four steps:

Preparation, which includes the initial transformation of raw data and the generation of regional aggregates as well as the weight matrices $W_{i, t}$;
Specification for setting up country-specific models that should be estimated;
Estimation using Bayesian algorithms to produce draws from the posterior distribution of each country model, which are subsequently combined to a global model;
Evaluation for the generation of forecasts, impulse responses and forecast error variance decompositions.

Data

The bgvars packages comes with the updated GVAR database of Mohaddes and Raissi (2020), which contains economic time series for 33 countries and 3 commodities from 1979Q2 to 2019Q4.[^1]

library(bgvars)
#> Loading required package: bvartools
#> Loading required package: coda
data("gvar2019")

country_data <- gvar2019$country_data # Country series
global_data <- gvar2019$global_data # Global commodities data
region_weights <- gvar2019$region_weights # Data for regional weights
weight_data <- gvar2019$weight_data # Data for trade weights

# Take first differences of non-stationary series  
country_data <- diff_variables(country_data, variables = c("y", "Dp", "r"), multi = 100)
global_data <- diff_variables(global_data, multi = 100)

Preparation

Regional series can be calculated from individual country series with the function create_regions.

# Generate EA area region with 3 year rolling window weights
ea <- c("AT", "BE", "DE", "ES", "FI", "FR", "IT", "NL")
temp <- create_regions(country_data = country_data,
                       regions = list("EA" = ea),
                       period = 3,
                       region_weights = region_weights,
                       weight_data = weight_data)

country_data <- temp$country_data
weight_data <- temp$weight_data

Weight matrices for each country/region can be calculated with the function create_weights.

# Generate weight matrices as 3 year, rolling window averages
gvar_weights <- create_weights(weight_data = weight_data, period = 3,
                               country_data = country_data)

Model specification

bgvars assists in the set-up country models by producing a list, where each element contains all the information required to estimate a model. First, the function create_specifications produces an object, which contains the specifications for each country.

# Create an object with country model specifications
model_specs <- create_specifications(country_data = country_data,
                                     global_data = global_data,
                                     domestic = list(variables = c("y", "Dp", "r"), lags = 2),
                                     foreign = list(variables = c("y", "Dp", "r"), lags = 1),
                                     global = list(variables = c("poil"), lags = 1),
                                     deterministic = list(const = TRUE),
                                     countries = c("EA", "US", "JP", "CA", "GB", "CN"),
                                     iterations = 3000, burnin = 1000,
                                     type = "VAR")

Country specifications can be changed by accessing the elements of the list directly:

model_specs$US$domestic$variables <- c("y", "Dp", "r")
model_specs$US$foreign$variables <- c("y", "Dp")

create_models produces all country models, which should be estimated. This allows for easy parallelisation. The number of elements of the resulting list depends on the specification of domestic lags, foreign lags, global lags, and the rank of the cointegration matrix r, if sepecified. For example, if the lags of domestic variables were set to lags = 1:2, the function produces two country submodels for each specification.

# Create estimable objects
object <- create_models(country_data = country_data,
                        weight_data = gvar_weights,
                        global_data = global_data,
                        model_specs = model_specs)

Finally, priors must be specified with add_priors.

object <- add_priors(object)

Estimate and solve the model

estimate_gvar can be used to estimate the country models. Parallel computating can be activated by specifying the argument mc.cores.

object <- draw_posterior(object)

The estimated country models can be combined and solved with the function combine_submodels.

gvar <- combine_submodels(object)

Impulse response analysis

Impulse response analysis can be done with the girf function.

gvar_irf <- girf(gvar, impulse = c("US", "r"),
                 response = c("EA", "y"),
                 n.ahead = 20, ci = .68)

plot(gvar_irf)

References

Chudik, A. & Pesaran, M. H. (2016). Theory and practice of GVAR modelling. Journal of Economic Surveys 30(1), 165-197. https://doi.org/10.1111/joes.12095

Dees, S., Mauro, F., Pesaran, M. H., & Smith, V. L. (2007). Exploring the international linkages of the euro area: A global VAR analysis. Journal of Applied Econometrics 22(1), 1-38. https://doi.org/10.1002/jae.932

George, E. I., Sun, D., & Ni, S. (2008). Bayesian stochastic search for VAR model restrictions. Journal of Econometrics, 142(1), 553-580. https://doi.org/10.1016/j.jeconom.2007.08.017

Koop, G., Pesaran, M. H., & Potter, S.M. (1996). Impulse response analysis in nonlinear multivariate models. Journal of Econometrics 74(1), 119-147. https://doi.org/10.1016/0304-4076(95)01753-4

Lütkepohl, H. (2007). New introduction to multiple time series analysis (2nd ed.). Berlin: Springer.

Mohaddes, K., & Raissi, M. (2020). Compilation, revision and updating of the global VAR (GVAR) database, 1979Q2–2019Q4 (mimeo). https://www.mohaddes.org/gvar.

Pesaran, H. H., & Shin, Y. (1998). Generalized impulse response analys is in linear multivariate models. Economics Letters, 58(1), 17-29. https://doi.org/10.1016/S0165-1765(97)00214-0

Pesaran, M., Schuermann, T., & Weiner, S. M. (2004). Modeling regional interdependencies using a global error-correcting macroeconometric model. Journal of Business & Economic Statistics 22(2), 129-162. https://doi.org/10.1198/073500104000000019

[^1]: The paper and data set can be downloaded from https://www.mohaddes.org/gvar.

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