# Factor Augmented Vector Autoregressions, Panel VARs, and Global VARs

## Abstract

This chapter provides a thorough introduction to panel, global, and factor augmented vector autoregressive models. These models are typically used to capture interactions across units (i.e., countries) and variable types. Since including a large number of countries and/or variables increases the dimension of the models, all three approaches aim to decrease the dimensionality of the parameter space. After introducing each model, we briefly discuss key specification issues. A running toy example serves to highlight this point and outlines key differences across the different models. To illustrate the merits of the competing approaches, we perform a forecasting exercise and show that it pays off to introduce cross-sectional information in terms of forecasting key macroeconomic quantities.

## Notes

### Acknowledgement

The authors gratefully acknowledge financial support by the Austrian Science Fund (FWF): ZK 35-G.

## References

- Aguilar, O., & West, M. (2000). Bayesian dynamic factor models and portfolio allocation.
*Journal of Business & Economic Statistics, 18*(3), 338–357.Google Scholar - Allenby, G. M., Arora, N., & Ginter, J. L. (1998). On the heterogeneity of demand.
*Journal of Marketing Research, 35*(3), 384–389.CrossRefGoogle Scholar - Arellano, M., & Bond, S. (1991). Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations.
*Review of Economic Studies, 58*(2), 277–297.CrossRefGoogle Scholar - Banerjee, A., Marcellino, M., & Masten, I. (2014). Forecasting with factor augmented error correction models.
*International Journal of Forecasting, 30*(3), 589–612.CrossRefGoogle Scholar - Bernanke, B. S., Boivin, J., & Eliasz, P. (2005). Measuring the effects of monetary policy: A factor-augmented vector autoregressive (FAVAR) approach.
*Quarterly Journal of Economics, 120*(1), 387–422.Google Scholar - Canova, F. (2007).
*Methods for applied macroeconomic research*. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar - Canova, F., & Ciccarelli, M. (2004). Forecasting and turning point predictions in a Bayesian panel VAR model.
*Journal of Econometrics, 120*(2), 327–359.CrossRefGoogle Scholar - Canova, F., & Ciccarelli, M. (2009). Estimating multicountry VAR models.
*International Economic Review, 50*(3), 929–959.CrossRefGoogle Scholar - Canova, F.,& Ciccarelli, M. (2013). Panel vector autoregressive models: A survey. In
*Var models in macroeconomics–new developments and applications: Essays in honor of Christopher A. Sims*(pp. 205–246). Bingley, UK: Emerald Group Publishing Limited.Google Scholar - Carriero, A., Clark, T. E., & Marcellino, M. (2016). Common drifting volatility in large Bayesian VARs.
*Journal of Business & Economic Statistics, 34*(3), 375–390.CrossRefGoogle Scholar - Carter, C. K., & Kohn, R. (1994). On Gibbs sampling for state space models.
*Biometrika, 81*(3), 541–553.CrossRefGoogle Scholar - Chudik, A., Grossman, V., & Pesaran, M. H. (2016). A multi-country approach to forecasting output growth using PMIs.
*Journal of Econometrics, 192*(2), 349–365.CrossRefGoogle Scholar - Crespo Cuaresma, J., Doppelhofer, G., Feldkircher, M., & Huber, F. (2019). Spillovers from US monetary policy: Evidence from a time varying parameter global vector autoregressive model.
*Journal of the Royal Statistical Society: Series A, 182*, 831–861.CrossRefGoogle Scholar - Crespo Cuaresma, J., Feldkircher, M., & Huber, F. (2016). Forecasting with global vector autoregressive models: A Bayesian approach.
*Journal of Applied Econometrics, 31*(7), 1371–1391.CrossRefGoogle Scholar - Dées, S., di Mauro, F., Pesaran, H., & Smith, L. (2007). Exploring the international linkages of the euro area: A global VAR analysis.
*Journal of Applied Econometrics, 22*(1), 1–38.CrossRefGoogle Scholar - Dées, S., & Güntner, J. (2017). Forecasting inflation across Euro area countries and sectors: A panel VAR approach.
*Journal of Forecasting, 36*, 431–453.Google Scholar - Dovern, J., Feldkircher, M., & Huber, F. (2016). Does joint modelling of the world economy pay off? Evaluating global forecasts from a Bayesian GVAR.
*Journal of Economic Dynamics and Control, 70*, 86–100.CrossRefGoogle Scholar - Eickmeier, S., Lemke, W., & Marcellino, M. (2015). A classical time varying FAVAR model: Estimation, forecasting, and structural analysis.
*European Economic Review, 74*, 128–145.CrossRefGoogle Scholar - Eickmeier, S., & Ng, T. (2015). How do US credit supply shocks propagate internationally? A GVAR approach.
*European Economic Review, 74*, 128–145.CrossRefGoogle Scholar - Eickmeier, S., & Ng, T. (2011). Forecasting national activity using lots of international predictors: An application to New Zealand.
*International Journal of Forecasting, 27*(2), 496–511.CrossRefGoogle Scholar - Feldkircher, M., & Huber, F. (2016). The international transmission of US shocks—evidence from Bayesian global vector autoregressions.
*European Economic Review, 81*(100), 167–188.CrossRefGoogle Scholar - Fischer, M., Huber, F., & Pfarrhofer, M. (2019). The regional transmission of uncertainty shocks on income inequality in the United States.
*Journal of Economic Behavior & Organization*, forthcoming.Google Scholar - Frühwirth-Schnatter, S. (1994). Data augmentation and dynamic linear models.
*Journal of Time Series Analysis, 15*(2), 183–202.CrossRefGoogle Scholar - Frühwirth-Schnatter, S., Tüchler, R., & Otter, T. (2004). Bayesian analysis of the heterogeneity model.
*Journal of Business & Economic Statistics, 22*(1), 2–15.CrossRefGoogle Scholar - George, E., & McCulloch, R. (1993). Variable selection via Gibbs sampling.
*Journal of the American Statistical Association, 88*, 881–889.CrossRefGoogle Scholar - George, E., Sun, D., & Ni, S. (2008). Bayesian stochastic search for VAR model restrictions.
*Journal of Econometrics, 142*(1), 553–580.CrossRefGoogle Scholar - Geweke, J., & Amisano, G. (2010). Comparing and evaluating Bayesian predictive distributions of asset returns.
*International Journal of Forecasting, 26*(2), 216–230.CrossRefGoogle Scholar - Greenwood-Nimmo, M., Nguyen, V. H., & Shin, Y. (2012). Probabilistic forecasting of output growth, inflation and the balance of trade in a GVAR framework.
*Journal of Applied Econometrics, 27*, 554–573.CrossRefGoogle Scholar - Griffin, J. E., & Brown, P. J. (2010). Inference with normal-gamma prior distributions in regression problems.
*Bayesian Analysis, 5*(1), 171–188.CrossRefGoogle Scholar - Hamilton, J. (1994).
*Time series analysis*. Princeton, NJ: Princeton University Press.Google Scholar - Han, F., & Ng, T. H. (2011). ASEAN-5 macroeconomic forecasting using a GVAR model.
*Asian Development Bank, Working Series on Regional Economic Integration, 76*.Google Scholar - Huber, F. (2016). Density forecasting using Bayesian global vector autoregressions with stochastic volatility.
*International Journal of Forecasting, 32*(3), 818–837.CrossRefGoogle Scholar - Huber, F., & Feldkircher, M. (2019). Adaptive Shrinkage in Bayesian Vector Autoregressive Models.
*Journal of Business & Economic Statistics, 37*(1), 27–39.CrossRefGoogle Scholar - Jacquier, E., Polson, N. G., & Rossi, P. E. (2002). Bayesian analysis of stochastic volatility models.
*Journal of Business & Economic Statistics, 20*(1), 69–87.CrossRefGoogle Scholar - Jarociński, M. (2010). Responses to monetary policy shocks in the east and the west of Europe: A comparison.
*Journal of Applied Econometrics, 25*(5), 833–868.CrossRefGoogle Scholar - Kastner, G. (2016). Dealing with stochastic volatility in time series using the R package stochvol.
*Journal of Statistical Software, 69*(1), 1–30.Google Scholar - Koop, G. (2003).
*Bayesian econometrics*. London: Wiley.Google Scholar - Koop, G., & Korobilis, D. (2016). Model uncertainty in panel vector autoregressive models.
*European Economic Review, 81*, 115–131.CrossRefGoogle Scholar - Koop, G., & Korobilis, D. (2019). Forecasting with high-dimensional panel VARs.
*Oxford Bulletin of Economics and Statistics, 81*(5), 937–959.CrossRefGoogle Scholar - Litterman, R. B. (1986). Forecasting with Bayesian vector autoregressions: Five years of experience.
*Journal of Business & Economic Statistics, 4*(1), 25–38.Google Scholar - McCracken, M. W., & Ng, S. (2016). FRED-MD: A monthly database for macroeconomic research.
*Journal of Business & Economic Statistics, 34*(4), 574–589.CrossRefGoogle Scholar - Moench, E. (2008). Forecasting the yield curve in a data-rich environment: A no-arbitrage factor-augmented VAR approach.
*Journal of Econometrics, 146*(1), 26–43.CrossRefGoogle Scholar - Pesaran, M., Schuermann, T., & Smith, L. (2009). Forecasting economic and financial variables with global VARs.
*International Journal of Forecasting, 25*(4), 642–675.CrossRefGoogle Scholar - Pesaran, M., Schuermann, T., & Weiner, S. (2004). Modeling regional interdependencies using a global error-correcting macroeconometric model.
*Journal of Business & Economic Statistics, 22*(2), 129–162.CrossRefGoogle Scholar - Stock, J. H., & Watson, M. W. (2016). Dynamic factor models, factor-augmented vector autoregressions, and structural vector autoregressions in macroeconomics. In J. B. Taylor & H. Uhlig (Eds.),
*Handbook of Macroeconomics*. Amsterdam: Elsevier.Google Scholar - Wang, P., & Wen, Y. (2007). Inflation dynamics: A cross-country investigation.
*Journal of Monetary Economics, 54*(7), 2004–2031.CrossRefGoogle Scholar