Co-movement of Government Debt and Economic Growth in the Euro-area: A Bayesian Dynamic Factor Model Analysis

Abstract

This paper applies a Bayesian dynamic factor model to analyze the co-movement of government debt and economic growth in 12 euro-area countries from 1970–2009. We decompose the variations in output growth and government debt into three distinct factors: (i) a common factor capturing co-movement across the 24 series in all 12 countries; (ii) a country factor common to the two series in each country; and (iii) an idiosyncratic factor specific to each series. We find that the common factor affects output growth positively but government debt negatively. Furthermore, the common factor dominates the country and idiosyncratic factors in accounting for the fluctuations in output growth and government debt, especially in the period 1999–2009 when the common factor became less volatile but more important for macroeconomic fluctuations. Our results suggest some convergence in output growth and government debt in the 12 euro-area countries after the launch of the euro.

Keywords:

• Government debt
• economic growth
• dynamic factor model

JEL CLASSIFICATIONS:

• H63
• C33

Acknowledgements

The authors express their thanks to Editor Sunwoong Kim and anonymous referees for valuable comments. All remaining errors are our own.

Notes

¹They use Bayesian dynamic factor models to investigate the evolution and driving forces of international business cycles.

²As shown by Boivin and Ng (2006), including too many variables with important idiosyncratic components in the dataset may distort factor estimates.

³See Stock and Watson (2011) for a detailed survey of dynamic factor models.

⁴The lag polynomials φ_F (L),φ_f (L) and φ_u (L) can be of different orders. We report our results based on AR(3) processes as those in Kose et al. (2003, 2008, 2010) and Crucini et al. (2011) for comparison purposes. Our results do not change significantly when using other lag lengths or using ARMA(p,q).

⁵For the details and computer codes of the Bayesian estimation procedure, refer to Otrok and Whiteman (1998).

⁶The variance decompositions are calculated at each pass of the Markov chain in the Bayesian estimation of the dynamic factor model. In theory, without imposing orthogonality assumptions, the variance decomposition among the factors would not be unique. In practice, we assume that the factors are uncorrelated, following Kose et al. (2003, 2008, 2010) and Crucini et al. (2011). Even though the factors are uncorrelated, samples taken at each pass of the Markov chain will not be uncorrelated, purely because of sampling error. Taking a further step for these calculations, we orthogonalize the sampled factors and order the common factor first and the country factor second. We confirm that the order of orthogonalization has little impact on the results.

⁷Due to space limits, we only report a few selected countries. Results for other countries in the sample are available upon request.

⁸The actual series shown in Figure 4 are the real GDP growth rate (standardized) and the de-trended government debt ratio (standardized), respectively.

⁹As a robustness check, we look into the correlation of government debt ratios and real GDP growth by estimating a common factor for real GDP growth rates from the EU-12, denoted as F_y, and a common factor for the (de-trended) government debt-to-GDP ratios from the EU-12, denoted as F_d. We then fit F_y and F_din a vector autoregressive framework. The residual tests confirm multivariate normality, no serial correlation, and no heteroskedasticity. We find that the conditional correlation is –0.609. This negative correlation coincides with the opposite sign of the common factor loadings for output growth and government debt ratios.