Long-term bond yields’ convergence between each new EU country and the Eurozone is examined in the present paper, in the framework of the current debt crisis in the Eurozone. As the German dominance was established during the crisis, convergence implies that the long-term bond yield of each new EU country must converge to that of Germany. As shown in this paper, under the conditions of uncovered interest rate parity (UIP) and ex-ante relative purchasing power parity (PPP) long-term bond yield spreads are equal to expected inflation differentials. Thus, evidence of yields’ convergence between a new EU country and Germany can be interpreted as monetary policy convergence of this country to Germany. However, lack of yields’ convergence does not necessarily imply monetary policy divergence with Germany. There is the possibility that a new EU country has achieved monetary policy convergence to Germany, but its yields to diverge with those of Germany. The reason is that the recent debt crisis in the Eurozone might increase the sovereign default risk of this country and thus, led to large and persistent risk premium. Of course, such information has practical implications regarding the evaluation of each new EU country in order to join the Eurozone.1 Hence, a proper evaluation of bond yield linkages or, in other words, monetary policy convergence should take the above arguments into account, especially in the period of the debt crisis. Otherwise, invalid conclusions may be drawn.

The empirical literature on interest rate convergence within the EU is extensive, and convergence has been linked to the concepts of unit roots and cointegration in most studies. Among others, Karfakis and Moschos (1990) investigated interest rate linkages between Germany and each of Belgium, France, Ireland, Italy and the Netherlands. Using short rates from the late 1970s to the late 1980s, they found no evidence of long-run interest rates convergence. Evidence against the German leadership hypothesis within the European Monetary System (EMS) for the same period, was also found by Katsimbris and Miller (1993). By including the USA to their sample, they showed that both the US and the German rates have important causal influences on the interest rates of the EMS members. Hafer and Kutan (1994) examined long-run co-movements of short rates and money supplies in a group of five EMS countries from the late 1970s to the early 1990s, and found evidence that implies partial monetary policy convergence.

Similar evidence was provided by Kirchgässner and Wolters (1995), who used money market rates from mid-1970s to mid-1990s, and showed that Germany has a strong long-run influence within the EMS. Haug et al. (2000) tried to determine which of the twelve original EU countries would form a successful monetary union based on the nominal convergence criteria of the Treaty on European Union (TEU). Using data from 1979 to 1995, they found that the formation of a successful monetary union would require significant adjustments in fiscal and monetary policies by several of these countries.

Camarero et al. (2002) investigated convergence of long-term interest rate differentials for the EU countries in relation to the TEU criterion, using 10-year bond yields from 1980 to mid-1990s. Departing from the literature, they adopted the definitions of long-run convergence of per capital output and catching-up convergence (Bernard and Durlauf, 1995, 1996),2 and accounted for structural breaks in the data using the one-break unit root test of Perron (1997). They showed that six countries satisfied the criterion of long-run convergence, seven countries satisfied the conditions of catching-up convergence, and only Italy did not converge in either sense. Holtemöller (2005) studied the degree of monetary integration to the Eurozone for Greece and the Central and Eastern European EU countries, based on interest rate spreads and ex-post deviations from the UIP. Using interbank rates from mid-1990s to the early 2000s, his evidence implied high degree of monetary integration for Estonia and Lithuania, medium degree of monetary integration for Greece and Slovakia, and low degree of monetary integration for the Czech Republic, Hungary, Latvia, Poland and Slovenia.

Jenkins and Madzharova (2008) investigated real interest rate convergence for the original EU countries, using 10-year bond yields from the late 1990s to mid-2000s. Their evidence implied failure of the real interest rate parity, mainly due to inflation rate differences. Gabrisch and Orlowski (2010) departed from cointegration analysis and applied GARCH methodology in order to investigate interest rate convergence for the Czech Republic, Hungary, Poland, Slovakia and Slovenia in relation to the Eurozone yields. They focused on 10-year bond yields from the early to the late 2000s and found evidence of stronger convergence for the Czech Republic, Slovenia, and Poland, in which the macroeconomic fundamentals are solid and the financial markets are stable, and weaker convergence for Hungary and Slovakia. Frömmel and Kruse (2015) studied interest rate convergence by implementing a changing persistence model for Belgium, France, Italy and The Netherlands in relation to Germany as the reference country. Using 3-month treasury bill rates from the early 1980s to the late 2000s, they found evidence of very different convergence periods for the sample countries, and showed that fiscal and monetary policy coordination were the main factors that led to interest rate convergence.

Several limitations of the existing studies can be pointed out, which may have affected the reported results. Firstly, most of the aforementioned studies, with the exception of Camarero et al. (2002), did not account for structural shifts in the data. Secondly, the existing studies have not distinguished in a systematic way between stochastic and deterministic trends in the structure of interest rates. This is an important issue because evidence of cointegration between, for example, two interest rates implies the presence of a single common stochastic trend that ties them in the long run. On the other hand, deterministic trends depend on the underlying process that generates the stochastic variables under study. Thus, for two interest rates it is not enough to cointegrate with cointegrating vector (1.-1); it is also required that they are cotrended, so that the deterministic trends cancel out in the differential of the two series. Thirdly, in most of the existing studies, interest rate convergence has been examined without an explicit formal definition of convergence or a data generation process (DGP) for the interest rates. The above omissions make the interpretation of the empirical results less transparent and informative.

The present study attempts to deal with these considerations. Firstly, consistent with the Eurozone’s nominal convergence criteria, this study focuses on nominal 10-year bond yields’ convergence between each new EU country and Germany, in the framework of an explicit DGP for bond yields and a new definition of convergence that allows for a constant non-negative deviation in each pair of bond yields. The inclusion of these elements leads to explicit testable cointegration and cotrending restrictions that makes the interpretation of the econometric results more informative and meaningful. Furthermore, under the UIP and PPP conditions, deviations from yields’ parity are equal to expected inflation differentials. Such deviations can be eliminated in the long run, if monetary authorities (or market forces) in each new EU country contribute in establishing common deterministic and stochastic trends with Germany, regarding the long-term yields or expected inflation rates. This case can be interpreted as strong convergence with Germany, which more than satisfies the TEU criterion for yields’ convergence. On the other hand, if the UIP and PPP conditions do not hold due to time-varying stationary risk premia, different tax rates (Mark, 1985) or transactions costs (Goodwin and Grennes, 1994) across countries, yields convergence can be defined broader as weak convergence, in which yields converge to a non-negative constant. If this constant is less than 2%, the TEU criterion is also satisfied. Hence, the empirical results are interpreted in terms of strong or weak monetary policy convergence between each new EU country and Germany.

Secondly, I employ the cointegration test developed by Lütkepohl, Saikkonen and Trenkler in several papers noted below, in order to capture possible structural shifts in the data. The omission of such shifts in the data when they actually exist can distort substantially standard inference procedures for cointegration. In this analysis, such shifts cannot be omitted as the current debt crisis in the Eurozone has probably altered the deterministic components of the new EU countries’ yields. In addition, as the deterministic components of yields are assumed to be independent of the stochastic components, the Gonzalo and Granger (1995) methodology for estimating and testing for the common stochastic trend in each pair of yields has been implemented.