Short- and long-run behaviour of long-term sovereign bond yields

Abstract

We assess the short- and long-run behaviour of long-term sovereign bond yields in OECD countries using a dynamic panel approach to reflect financial and economic integration. Given the existence of cross-country dependence regarding sovereign yields and its determinants, we resort to simulation and bootstrap methods. Results based on the Common Correlated Effect estimator of Pesaran and on Panel Error Correction Models to sort out short- and long-run fiscal developments show that in addition to common movements in sovereign yields, investors also consider country differences arising from specific factors (inflation, budgetary and current account imbalances, real effective exchange rates, and liquidity).

Keywords:

• long-term yields
• EU
• financial integration
• panel cointegration
• bootstrap

JEL Classification:

• C23
• E43
• E62
• G15
• H62

Acknowledgements

We are grateful to an anonymous referee for very useful suggestions, to Vítor Gaspar, Ad van Riet, Thomas Werner, participants at the ECB Pubic Finance Workshop, at an ISEG-UTL Department of Economics Seminar, at the Portuguese Economic Journal conference, at the 36^th Eastern Economic Association Conference for helpful comments on the previous versions of the paper. Christophe Rault thanks the Fiscal Policies Division of the ECB for its hospitality. The opinions expressed herein are those of the authors and do not necessarily reflect those of the European Central Bank or the Eurosystem.

Notes

¹ Indeed, bootstrap techniques enable to obtain the empirical distributions of the tests statistics considered which is essential to make valid statistical inference (see, for instance, Maddala and Wu, 1999 for further details). Moreover, not taking into account cross-sectional if it exists in the data (using inappropriate critical values) can entail important size distortion in panel unit root and cointegration tests (see Banerjee et al., 2005).

² Two main reasons could explain this feature: (i) First, as pointed out by Breitung and Pesaran (2005) the problem of cross-section dependence is particularly difficult to deal with since it could arise for a variety of reasons, including spatial spillover effects, common unobserved shocks, social interactions or a combination of these factors. Besides, even if there is empirical evidence of such cross-section dependence it is very difficult to have more precise information on them, that is, how they look like, and also to attribute them to a specific reason or event. (ii) Second, cross-sectional dependence, if present in the data, requires generating appropriate critical values using simulations methods (which is time-consuming, and requires specific algorithms).

³ Such results are in line with the Gale and Orszag (2003) assessment of the existence of statistically significant effects from anticipated budget deficits on long-term interest rates.

⁴ Afonso and Rault (2010) report that over the period 1970–2006 some EU countries may have been threading unsustainable public finances’ paths.

⁵ Afonso and Rault (2008) uncover significant effects between budget balances and current account balances for several OECD countries.

⁶ Note that a specific form of cross-sectional dependence that has become popular is the factor structure approach. This has been used extensively in empirical work (see, for instance, Barro and Sala-i-Martin, 1992) and it has been analysed in theoretical treatments at even greater length. Therefore, in our study, we use the notions of error cross-sectional dependence and factor structure dependence interchangeably.

⁷ The results are not very sensitive to the size of the bootstrap blocks.

⁸ The order of the sieve is allowed to increase with the number of time series observations at the rate T^1/3 while the lag length of the individual unit root test regressions are determined using the Campbell and Perron (1991) procedure. Each test regression is fitted with a constant term only.

⁹ The lag order in the individual ADF type regressions is selected for each series using the AIC model selection criterion. Another crucial issue is the selection of the order of the deterministic component. In particular, since the cross-sectional dimension is rather large here, it may seem restrictive not to allow at least some of the units to be trending, suggesting that the model should be fitted with both a constant and trend. However, since the trending turned out not to be very pronounced, we have considered that a constant is enough in our analysis. Actually, the results of the bootstrap tests of Smith et al. (2004) are not very sensitive to the inclusion of a trend in addition to a constant in the estimated equation (see Statistic b in Table 4). We have of course also checked using the tests by Pesaran (2007) and the bootstrap tests of Smith et al. (2004) that the first difference of the series are stationary, hence confirming that the series expressed in level are integrated of order 1.

¹⁰ Note that in order to estimate the long-run coefficients we have also implemented the PMG estimators (see Pesaran and Smith, 1995; Pesaran et al., 1999), which allowed us to identify significant differences in country behaviour. However, we only report the results of the Common Correlated Effects (CCE) estimators developed by Pesaran (2006), since they allow taking unobservable factors into account, which would not be the case of the PMG estimators.

¹¹ Actually, the big issue here in computing appropriate critical values by simulations is how to carry out bootstrap methods such that the original dependence structure of the data, both over time as well as across units, is suitably replicated. In this optic, Westerlund and Edgerton (2007) suggest implementing a bootstrap based on a sieve-sampling scheme, which approximates the time-series dependence of the equilibrium errors using a finite-order autoregressive model. Besides, to keep the cross-sectional dependence of the original data, their bootstrap draws are obtained from the joint empirical distribution of the regression errors. Using a small simulation experiment they show that this way of computing critical values was significantly reducing the distortions of the asymptotic test, hence leading to more robust conclusions (in the case of existence of cross-sectional dependence) than those based on conventional asymptotic critical values. Note also that provided that the bootstrap method is appropriate for the problem and implemented correctly, then the bootstrap critical values will be appropriate also in the absence of cross-sectional correlation: they would just be closer to the asymptotic ones.

¹² Note that before considering Equation 7, we first used a Wald statistic to test for common parameters across countries (i.e. λ_i = λ, and γ_i = γ, for i = 1,…,N) with the CCE techniques of Pesaran (2006), that allow common factors in the cross-equation covariances to be removed. We found that only the null hypothesis γ_i = γ, for i = 1,…,N was not rejected by data, whereas the speeds of adjustment λ_i vary considerably across countries (results are available upon request).

Additional information

Funding

UECE (Research Unit on Complexity and Economics) is supported by the Portuguese Foundation for Science and Technology through the project PEst-OE/EGE/UI0436/2011.