On the time-varying nature of the debt-growth nexus: evidence from the euro area

ABSTRACT This article uses the DCC-generalized autoregressive conditional heteroskedasticity model to investigate the existence of time-varying correlations between public debt and economic growth. To that end, we use annual data from both central and peripheral countries of the euro area for the period 1961–2015. The results suggest that the relationships between these variables are time-varying and that in some countries and for some periods, there is a positive association between them.


I. Introduction
Over the last two decades, considerable attention has been devoted to the role of public debt in economic growth, and although there is a large body of theoretical and empirical literature devoted to this issue, the results are far from conclusive (see Panizza and Presbitero (2013) for a survey).
The empirical studies have concentrated predominantly on the effect of the level of public debt on economic growth and largely ignored the possible relationship in the volatility of these variables. 1 Economic agents react negatively on the uncertainties about future taxes and the future behaviour of fiscal parameters implied by higher public debt. As Pindyck (1988) suggested, predictable policies and clear rules of the game are important for private investors. 2 More recently, Fatás and Mihov (2013) show that the volatility of fiscal policy has a firstorder effect on long-term economic performance.
In this article, we use the DCC model developed by Engle (2002) to estimate and examine the timevarying nature of the debt-growth relationship between public debt and economic growth. The article is organized as follow. Section II outlines econometric strategy. Section III presents the data and the empirical results. Section IV provides some concluding remarks.

II. Econometric strategy
We use Engle's (2002) DCC model. This model is able to capture the volatility correlation between two series, either directly through its conditional variance or indirectly through its conditional covariances. The model is also able to examine the volatility spillover from one series to another, providing insight on both series' synchronization. The DCC has two stages. In the first step, the generalized autoregressive conditional heteroskedasticity (GARCH) parameters are estimated. In the second step, the conditional correlations are estimated using the DCC method as follows: where H t is a kxk conditional covariance matrix, R t is the conditional correlation matrix and D t is diagonal matrix of time-varying SDs. The likelihood of the DCC estimator is: The volatility (D t ) and the correlation (R t ) components may vary; thus, the estimation process is achieved in two steps. First, the volatility (L v ) is maximized: CONTACT Simón Sosvilla-Rivero sosvilla@ccee.ucm.es 1 Cecchetti, Mohanty, and Zampolli (2011) report negative correlations of per capita GDP volatility with government debt. 2 The role of policy volatility can also be detected in Barro (1990).
then the correlation (L c ) is maximized: Engle (2002) proposed a two-step estimation. The DCC model is estimated by a two-step procedure: (a) in the first step, univariate GARCH models are fitted for each the log-difference of each series, and estimates of their variances are thus obtained; (b) the log-differences are filtered out of the GARCH effect by dividing by their estimated SDs and then are used to estimate the dynamics of correlation, In the second step, the standardized residuals are used to estimate the time-varying correlation matrix. The model developed by Engle (2002) has the following non-linear GARCH specification for the conditional correlation: where Q t ¼ ðq ij;t Þ is a nxn symmetric positive definite matrix, a and b are non-negative scalars such as a + b < 1, a is the news coefficient and b is the decay coefficient.
t Þ is the unconditional variance matrix of the standardized residuals (the unconditional correlation). The conditional correlations q ij;t are time-varying and follow a structure similar to a GARCH (1, 1) model.
For ensuring a conditional correlation between −1 and +1, by normalization the correlation can be expressed. ρ ij;t ¼ q ij;t = ffiffiffiffiffiffiffiffiffiffiffiffiffi q ii:t q jj:t p The correlations are obtained by transforming this to: where ðdiagðQ t Þ 0:5 is a diagonal matrix of the square root of the diagonal elements of Q t :

III. Data and empirical results
We use annual data for 11 euro area countries, both central (Austria, Belgium, Finland, France, Germany and the Netherlands) and peripheral countries (Greece, Ireland, Italy, Portugal and Spain), covering the period 1961-2015. The ratio of public debt to GDP comes from European Commission's AMECO database, and the growth rate of real per capita GDP comes from the World Bank. Figure 1 shows the evolution of sovereign debt-to-GDP and real GDP per capita growth in the 11 countries of our sample. Figure 2 reports the estimated DCCs. 3 As can be seen, the time-varying conditional correlation is negative throughout all the period in Austria, Germany and Italy and through all the period but very few exceptions in Finland (1.82%). However, it moves from positive to negative values in France, Greece, Ireland, the Netherlands, Portugal and Spain. Especially striking is the behaviour of the DCC between debt and growth in the Netherlands and Spain, where it presents positive values in 41.82% and 38.18% of sample period, respectively. As for the temporal distribution of positive DCC, 27.17% are detected in the 1980s, 25% in the 1990s, 19.57% in the 1970s and 17.39% in the 2000s. Interestingly, a comparison of Figures 1 and 2 suggests that most of the estimated positive values coincide with significant reductions in debt-to-GDP ratios associated with serious fiscal adjustment processes. This finding is in line with the experience of middle-income developing countries in the late 1980s (Chari and Henry 2014), providing further support to the possibility of reducing the debt burden as important part of a pragmatic growth strategy when it is implemented in concert with reforms that raise productivity and provide a business environment in which firms have an incentive to generate output, invest in capital and employment.

IV. Concluding remarks
This article can be thought of as a re-examination of the standard paradigm relating public debt to economic growth, by using the DCC-GARCH model to investigate the existence of time-varying correlations between those variables.
If correct, the results of our empirical analyses have strong policy implications, since countries are often advised to make strong and rapid fiscal adjustments during recessions. We find that, in some countries and for some periods, there is a positive association between public debt and economic growth coinciding with significant consolidation efforts. This result seems to provide some support the popular policy recipe,  1961 1964 1967 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012 2015 prominently advocated by Perotti (1995, 1997) and Giavazzi and Pagano (1990), that large spending-based fiscal consolidations are likely to have expansionary effects on the economy. Nevertheless, the speed of progress toward a specified fiscal target is an open question, since gradualism can be a powerful tool in helping achieve the objectives of a broader growth strategy (Dewatripont and Roland 1995). A natural extension to the analysis presented in this article would be to explore the main determinants of the detected differences in the relationships between public debt and economic growth across countries, with special emphasis in the institutional factors as suggested by Hall and Jones (1999), Acemoglu (2009) and Acemoglu and Robinson (2012), as well as their economic structure, the nature of the shocks they face and the government's policy regime. This is an item in our future research agenda.