Global Vector Autoregression: A demonstration

Abstract

This document describes how to use a GVAR model. The main uses I demonstrate are two. First, to describe the effect of identified structural shocks on economic and financial variables. Both the shocks and the outcomes can be defined at the country, regional, or global levels. Second, to produce out-of-sample forecats as well as conditional forecasts. I employ the Bayesian implementation of the GVAR model, via the R package BGVAR.

Introduction

Individual countries in the global economy are interconnected through trade and financial channels in complex ways. A Global Vector Autoregression (GVAR) is a large system of equations constructed to either analyze those interactions.

In the first stage, \(N\) autoregressive models are estimated, one for each country.

The authors of the BGVAR package have published a vignette, where you can see other examples and functionality. Another recommended piece is the review of the general GVAR method and its applications by Alexander Chudik and M. Hashem Pesaran.

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Data preparation

For this demonstration I use the data set included in GVAR toolbox for Matlab (2016 vintage).

The list of countries is

 [1] "AU" "BR" "CA" "CN" "FR" "DE" "IN" "IT" "JP" "MX" "NO" "ZA"
[13] "SA" "SP" "GB" "US" "OC"

and the time sample is the same for all countries.

c(time(Data$US)[1], time(Data$US)[nrow(Data$US)])

[1] "1979-04-01" "2016-10-01"

The variables included vary across countries. A typical case is Japan:

head(Data$JP)

                  y         Dp        eq       ep          r         lr
1979-04-01 4.094173 0.01618337 0.5090209 1.129781 0.01247056 0.01883871
1979-07-01 4.103451 0.01468711 0.4968770 1.120789 0.01558550 0.01887733
1979-10-01 4.112150 0.01540758 0.4848696 1.191835 0.01797875 0.02063297
1980-01-01 4.125792 0.02429436 0.4883202 1.187949 0.02194678 0.02217054
1980-04-01 4.127529 0.02272514 0.4744530 1.119637 0.02938286 0.02204850
1980-07-01 4.135194 0.01579512 0.4751058 1.048140 0.02847454 0.02168200

where \(y\) is the (log level) of real GDP, \(Dp\) is inflation, \(eq\) are real equity prices, \(ep\) is the real exchange rate, \(r\) is the short-term interest rate, and \(lr\) is the long-term interest rate.

For emerging market countries our demo data set has fewer variables:

head(Data$CN)

                  y          Dp        ep          r
1979-04-01 2.703928 0.001745415 -2.779155 0.01314811
1979-07-01 2.733016 0.001742373 -2.807975 0.01314811
1979-10-01 2.762104 0.001739343 -2.823961 0.01314811
1980-01-01 2.774890 0.004954579 -2.831684 0.01314811
1980-04-01 2.787676 0.004930152 -2.846031 0.01314811
1980-07-01 2.800462 0.004905965 -2.875556 0.01314811

Commodity prices are not endogenous to any country, but world output is weakly exogenous in the commodity price model. That is, world output affects commodity prices, and commodity prices are exogenous to each individual country. You can see the list of variables in the commodity price model here:

head(Data$OC)

where \(poil\) is the price of oil, \(pmetal\) is the metals commodity price index, and \(pmat\) is the price index of agricultural materials.

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