دینامیک منحنی بازده جهانی و تعاملات: روش پویا نلسون-سیگل

The popular Nelson–Siegel [Nelson, C.R., Siegel, A.F., 1987. Parsimonious modeling of yield curves. Journal of Business 60, 473–489] yield curve is routinely fit to cross sections of intra-country bond yields, and Diebold–Li [Diebold, F.X., Li, C., 2006. Forecasting the term structure of government bond yields. Journal of Econometrics 130, 337–364] have recently proposed a dynamized version. In this paper we extend Diebold–Li to a global context, modeling a potentially large set of country yield curves in a framework that allows for both global and country-specific factors. In an empirical analysis of term structures of government bond yields for the Germany, Japan, the UK and the US, we find that global yield factors do indeed exist and are economically important, generally explaining significant fractions of country yield curve dynamics, with interesting differences across countries.

The yield curve is of great interest both to academics and market practitioners. Hence yield curve modeling has generated a huge literature spanning many decades, particularly as regards the term structure of government bond yields. Much of that literature is unified by the assumption that the yield curve is driven by a number of latent factors (e.g., Litterman and Scheinkman (1991), Balduzzi et al. (1996), Bliss, 1997a and Bliss, 1997b and Dai and Singleton (2000)). Moreover, in many cases the latent yield factors may be interpreted as level, slope and curvature (e.g., Andersen and Lund (1997) and Diebold and Li (2006)). The vast majority of the literature studies a single country’s yield curve in isolation and relates domestic yields to domestic yield factors, and more recently, to domestic macroeconomic factors (e.g., Ang and Piazzesi (2003), Diebold et al. (2006) and Mönch (2006)). Little is known, however, about whether common global yield factors are operative, and more generally, about the nature of dynamic cross-country bond yield interactions. One might naturally conjecture the existence of global bond yield factors, as factor structure is routinely present in financial markets, in which case understanding global yield factors is surely crucial for understanding the global bond market. Numerous questions arise. Do global yield factors indeed exist? If so, what are their dynamic properties? How do country yield factors load on the global factors, and what are the implications for cross-country yield curve interactions? How much of country yield factor variation is explained by global factors, and how much by country-specific factors, and does the split vary across countries in an interpretable way? Has the importance of global yield factors varied over time, perhaps, for example, increasing in recent years as global financial markets have become more integrated? In this paper we begin to address such questions in the context of a powerful yet tractable yield curve modeling framework. Building on the classic work of Nelson and Siegel (1987) as dynamized by Diebold and Li (2006), we construct a hierarchical dynamic factor model for sets of country yield curves, in which country yields may depend on country factors, and country factors may depend on global factors. Using government bond yields for the US, Germany, Japan, and the UK, we estimate the model and extract the global yield curve factors. We then decompose the variation in country yields and yield factors into the parts dues global and idiosyncratic components. Finally, we also explore the evolution (or lack thereof) of global yield curve dynamics in recent decades. Our generalized Nelson–Siegel approach is related to, but distinct from, existing work that tends to focus on spreads between domestic bond yields and a “world rate” (e.g., Al Awad and Goodwin (1998)), implicit one-factor analyses based on the international CAPM (e.g., Solnik, 1974 and Solnik, 2004 and Thomas and Wickens (1993)), multi-factor analyses of long bond spreads (e.g., Dungey et al. (2000)), and affine equilibrium analyses (e.g., Brennan and Xia (2006)). Instead we work in a rich environment where each country yield curve is driven by country factors, which in turn are driven both by global and country-specific factors. Hence we achieve an approximate global bond market parallel to the global real-side work of Lumsdaine and Prasad (2003), Gregory and Head (1999) and Kose et al. (2003). We proceed as follows. In Section 2 we describe our basic global bond yield modeling framework, and in Section 3 we discuss our bond yield data for four countries. In Section 4 we provide full-sample estimates and variance decompositions for the global yield curve model, and in Section 5 we provide sub-sample results. We conclude in Section 6.

We have extended the yield curve model of Nelson and Siegel (1987) and Diebold and Li (2006) to a global setting, proposing a hierarchical model in which country yield level and slope factors may depend on global level and slope factors as well as country-specific factors. Using a monthly dataset of government bond yields for Germany, Japan, the US and the UK from 1985:9 to 2005:8, we extracted global factors and country-specific factors for both the full sample and the 1985:9–1995:8 and 1995:9–2005:8 sub-samples. The results indicate strongly that global yield level and slope factors do indeed exist and are economically important, accounting for a significant fraction of variation in country bond yields. Moreover, the global yield factors appear linked to global macroeconomic fundamentals (inflation and real activity) and appear more important in the second sub-sample. We look forward to future work producing one-step estimates in an environment with many countries, richer country-factor and global-factor dynamics, richer interactions with macroeconomic fundamentals, non-normal shocks, and time-varying yield volatility. Such extensions remain challenging, however, because of the prohibitive dimensionality of the estimation problem. Presently we are estimating 240+17=257 parameters in each of our separate global level and slope models, composed of the 17 parameters discussed earlier, plus the 240 parameters corresponding to the values of the state vector at 240 different times. Incorporating the generalizations mentioned above could easily quadruple the number of parameters, necessitating the use of much longer Markov Chains.