Government debt in the euro area—Evidence from dynamic factor analysis

Economics Letters 115 (2012) 272–275

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Government debt in the euro area—Evidence from dynamic factor analysis Huiran Pan a,∗ , Chun Wang b a

Economics Department, California State University-Fullerton, Fullerton, CA 92834, United States

b

Brooklyn College, City University of New York, United States

article

info

Article history: Received 16 February 2011 Received in revised form 17 December 2011 Accepted 19 December 2011 Available online 28 December 2011

abstract This paper shows that an unobserved common factor drives the co-movement of government debt in the euro area. The old-age dependency ratio explains the factor after controlling for the Maastricht Treaty, the adoption of the euro, and the ongoing crisis. © 2011 Elsevier B.V. All rights reserved.

JEL classification: H63 C33 Keywords: Government debt Dynamic factor model Old-age dependency ratio

1. Introduction This paper examines the common factors that have driven the co-movement of government debt in the euro area from 1970 to 2010. Government debt in the euro area has been soaring and has become problematic in recent years. The dynamics of government debt have followed a common pattern over the last four decades. Fig. 1 shows the government debt as a share of GDP for the major 12 euro-area countries (Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Portugal, and Spain; hereinafter, the EU-12). In general, these government debt ratios increased in the 1970s–80s, declined or stabilized in the 1990s–early 2000s, and started to rise in 2007 in the wake of the recent global financial crisis. What drives this common pattern? The co-movement of government debt may reflect a common business cycle, aging populations, the 1992 Maastricht Treaty, the adoption of a common currency, and the ongoing crisis in Europe. We apply a dynamic factor model (hereinafter, DFM) to estimate an unobserved common component in the government debt ratios in the EU-12. By introducing a measure of the EU12 business cycle (hereinafter, EBC) as a control variable in the model, we can partial out the effect of the common business cycle following the method used by Albanese and Modica (2010). The unobserved factor mainly captures the effects of structural changes on the debt ratios, while EBC represents the impact

∗

Corresponding author. Tel.: +1 657 278 8694. E-mail addresses: [email protected], [email protected] (H. Pan).

0165-1765/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2011.12.084

of the common economic cycle. We find that this unobserved factor has a significant effect on the debt ratios in all countries except for France, Germany, and Luxemburg. Meanwhile, there exists a systematically negative relationship between EBC and the debt ratios for all 12 economies. This evidence is consistent with the findings in Albanese and Modica (2010) regarding the comovement of public spending in the G7. Furthermore, we attempt to provide explanations for the unobserved factor. In Europe, government obligations to aging populations and rising social insurance costs may contribute to the accumulation of public debt. Checherita and Rother (2010) find that the aging burden proxied by the old-age dependency ratio (the ratio of population over 65 to the working-age population) is an important channel through which government debt can slow down economic growth. We find that the unobserved factor can be explained by the average old-age dependency ratio. It also reflects the influence of the Maastricht Treaty, the common currency, and the ongoing crisis. Therefore, our analysis of the common factors steering government debt can provide valuable evidence for policy makers aiming to reduce the debt. 2. The model DFMs developed by Geweke (1977), Watson and Engle (1983), and Stock and Watson (1991) allow eliminating idiosyncratic shocks and estimating common factors in many variables without running into scarce degrees of freedom problems. Such models also mitigate the need for strong assumptions necessary for structural models.

H. Pan, C. Wang / Economics Letters 115 (2012) 272–275

273

Fig. 1. Government debt (percentage of GDP).

Fig. 2. The unobserved factor and other variables. Note: EBC is EU-12 business cycle; AIP is EU-12 industrial production growth.

We estimate the DFM as follows: Yit = αi Ft + βi Xt + uit Ft = ρ Ft −1 + vt uit = wi uit −1 + εit .

(1)

Yit is the debt-to-GDP ratio for country i at time t. The unobserved common factor Ft is the same across countries and can drive

the movement of debt ratios. It follows an AR(1) process. The coefficients (αi ), called factor loadings, are country-specific and capture the impact of the unobserved common factor on each country. Xt represents a common component in the business cycle of the EU-12. Following the conventional approach, we write the DFM as the state-space model and estimate the model using Kalman filtering.

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H. Pan, C. Wang / Economics Letters 115 (2012) 272–275 Table 1 Estimation results.

Austria Belgium Finland France Germany Greece Ireland Italy Luxemburg Netherlands Portugal Spain

Factor

Coeff. on factor

Coeff. on EBC

0.294∗∗∗ (0.089) 0.409∗∗∗ (0.083) 0.186∗∗ (0.091) 0.112 (0.078) 0.0542 (0.070) 0.190∗∗ (0.086) 0.229∗∗∗ (0.066) 0.344∗∗∗ (0.101) −0.0172 (0.067) 0.327∗∗∗ (0.087) 0.180∗∗ (0.083) 0.302∗∗∗ (0.082)

−0.425∗∗∗

AR coefficient

% of variance of debt ratio explained by common factors 37.4

(0.132)

−0.399∗∗∗

51.4

(0.117) −0.498∗∗∗ (0.136) −0.674∗∗∗ (0.116) −0.665∗∗∗ (0.123) −0.409∗∗∗ (0.132) −0.441∗∗∗ (0.103) −0.401∗∗∗ (0.127) −0.552∗∗∗ (0.125) −0.335∗∗ (0.133) −0.396∗∗∗ (0.140) −0.558∗∗∗ (0.099)

31.8 47.7 43.3 25.9 39 44 34.2 28.9 21.3 61

0.842∗∗∗ (0.091)

Note: Standard errors are in parentheses. ***, **,* indicate significance at 1%, 5% and 10% level. EBC: EU-12 business cycle.

3. Empirical findings We estimate the DFM using the government debt-to-GDP ratios for the EU-12. The data is from the European Commission AMECO database. Fig. 1 reveals a common pattern. Since the series exhibits unit roots, we take first differences and then standardize the series. Previous research shows that there exists a common component in the business cycle (Norrbin and Schlagenhauf, 1996; Crucini et al., 2011, among others). In order to partial out this common cyclical effect, we construct the measure of EBC following Crucini (1997) and Albanese and Modica (2010): a weighted average of annual output growth rates of the EU-12, where the weights are proportional to GDP (in PPP terms, source: OECD). We also construct the average annual growth rate of the industrial production index of the EU-12 (hereinafter, AIP, source: AMECO) as an alternative measure. Fig. 2 displays the two measures. We include EBC as a control variable in the DFM and report the parameter estimates in Table 1.1 The coefficients of the unobserved factor are statistically significant at the 1% or 5% level, except for France, Germany, and Luxemburg. This exception may be due to the larger GDP weights for Germany (28.4%) and France (20.5%), and higher GDP growth (3.97%) in Luxemburg when measuring EBC. Moreover, this finding can be attributed to the fact that these three countries were not influenced by the debt constraint under the Maastricht Treaty. The unobserved factor is quite persistent with a first-order autocorrelation of 0.842. We also note that EBC has a significantly negative impact on the debt ratios for all 12 economies, reflecting a counter-cyclical reaction to the economic cycle. Using variance decomposition, we measure the relative

contribution of the unobserved factor and EBC to the variation of debt ratios as cov(αi Ft + βi Xt , Yit )/var(Yit ).2 The last column in Table 1 reports the results. Government debt depends on the ratio of public expenditure to GDP, and the ratio could effectively be included in the residuals of the model; therefore, endogeneity problems may arise if EBC is correlated with the residuals. To address this concern, we first confirm that the correlations between EBC and the residuals for each country are nearly zero, suggesting no endogeneity. We further conduct an analysis analogous to the two-stage least squares method. We use AIP as an instrumental variable for EBC. In stage 1, we regress EBC on AIP and the unobserved factor from the initial DFM estimation, and then obtain the fitted value for EBC. The coefficient on AIP is statistically significant, implying that EBC is still correlated with AIP after partialling out the common factor. In stage 2, we estimate a DFM using the fitted EBC as a regressor. The coefficient estimates are close to those in Table 1, with insignificant differences.3 Both results are consistent, but the results in Table 1 are more efficient than the ones using the instrumental variable when no endogeneity exists. Overall, our results indicate the presence of an unobserved factor driving the co-movement of debt ratios. A common question for the DFM is how to interpret the unobserved factor. Fig. 2 illustrates the factor. It reaches peaks after the two oil crises. A sharp decline after 1992 suggests common willingness to control the debt-to-GDP ratios under the Maastricht Treaty, which is consistent with the explanation in Albanese and Modica (2010). A surge has occurred since the recent financial crisis. In an attempt to explain the unobserved factor, we regress the unobserved factor on potential explanatory variables,

1 Our results are robust to the alternative measure AIP. We also run separate DFM estimations using other control variables (the average old-age dependency ratio, inflation rate, etc.) as robustness checks, but they are statistically insignificant.

2 This is not a unique variance decomposition since we do not impose orthogonality assumptions. 3 Results are available upon request.

H. Pan, C. Wang / Economics Letters 115 (2012) 272–275

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Table 2 Regression output. Dependent variable: Factort

1

2

3

4

5

Old-age dependencyt−1

−1.977∗∗∗

−1.680∗∗∗

−1.436∗∗∗

−1.110∗∗∗

−1.204∗∗∗

Youth dependencyt−1

−0.799∗∗∗

(0.261) (0.256)

(0.268)

(0.359)

−0.610∗∗ (0.231)

−0.479∗ (0.270)

(0.336)

−0.293 (0.258)

(0.418)

−0.116

Average inflationt−1 0.404∗∗∗ (0.138) −0.428 (0.283)

US long-term interest ratet−1 Dummy9210

(0.356)

−0.155

−0.510∗ (0.287)

0.430∗∗∗ (0.143)

(0.363) 0.401∗∗ (0.176)

Dummy9910

−0.947∗∗∗

−0.896∗∗∗

−0.776∗∗∗

Dummy0710

1.807∗∗ (0.864)

(0.293) 1.953∗∗ (0.852)

1.604∗ (0.907)

(0.257) 1.756∗ (0.898)

(0.255) 1.835∗ (0.914)

Adjusted R-squared

0.660

0.682

0.680

0.707

0.713

Note: Robust standard errors in parentheses. ***, **, * indicate significance at 1%, 5% and 10% level.

such as the average old-age and youth dependency ratios, the average inflation rate of the EU-12, and interest rates in Germany and the US. We also include three time dummy variables for 1992–2010, 1999–2010, and 2007–2010 to capture the influence of the Maastricht Treaty, the adoption of the euro, and the recent global financial crisis, respectively. Given the relatively short time dimension of our annual data, we lag the explanatory variables by one period and conduct Granger causality tests. Table 2 reports the selected results.4 The main finding is that the unobserved factor is Granger-caused by the old-age dependency ratio and the US longterm interest rate, after controlling for the Maastricht Treaty, the adoption of the euro, and the ongoing crisis. It is noteworthy that the impact of the Maastricht Treaty is less prominent before 1999. 4. Conclusions This paper studies the common pattern of government debt in the EU-12 using a dynamic factor model. The empirical results show that the co-movement of government debt ratios reflects a counter-cyclical reaction to the common business cycle, but there also exists an unobserved factor driving such co-movement. We find that the old-age dependency ratio and the US long-term interest rate can explain the unobserved factor after controlling for the Maastricht Treaty, the adoption of a common currency, and the ongoing crisis.

4 All residuals have a zero mean and are uncorrelated with the regressors.

Acknowledgment We would like to thank the anonymous referee for useful comments. All remaining errors are our own. References Albanese, G., Modica, S., 2010. Co-movement of public spending in the G7. Economics Letters 109, 121–123. Checherita, C., Rother, P., 2010. The impact of high and growing government debt on economic growth-an empirical investigation for the euro area. European Central Bank Working Paper Series No. 1237. Crucini, M.J., 1997. Country size and economic fluctuations. Review of International Economics 5, 204–220. Crucini, M.J., Kose, M.A., Otrok, C., 2011. What are the driving forces of international business cycles? Review of Economic Dynamics 14 (1), 156–175. Geweke, J., 1977. The dynamic factor analysis of economic time series models. In: Aigner, J., Goldberger, A.S. (Eds.), Latent Variables in Socioeconomic Models. North-Holland, Amsterdam, pp. 365–383. Norrbin, S.C., Schlagenhauf, D.E., 1996. The role of international factors in the business cycle: a multi-country study. Journal of International Economics 40, 85–104. Stock, J.H., Watson, M.W., 1991. A probability model of the coincident economic indicators. In: Lahiri, K., Moore, G.H. (Eds.), Leading Economic Indicators: New Approaches and Forecasting Records. Cambridge University Press, Cambridge, pp. 63–89. Watson, M.W., Engle, R.F., 1983. Alternative algorithms for the estimation of dynamic factor, MIMIC and varying coefficient regression models. Journal of Econometrics 23, 385–400.