In the paper, the interaction between public debt and inflation including mutual impulse response will be analysed. The European sovereign debt crisis brought once again the focus on the consequences of public debt in combination with an expansive monetary policy for the development of consumer prices. Public deficits can lead to inflation if the money supply is expansive. The high level of national debt, not only in the Euro-crisis countries, and the strong increase in total assets of the European Central Bank, as a result of the unconventional monetary policy, caused fears on inflating national debt. The transmission from public debt to inflation through money supply and long-term interest rate will be shown in the paper. Based on these theoretical thoughts, the variables public debt, consumer price index, money supply m3 and long-term interest rate will be analysed within a vector error correction model estimated by Johansen approach. In the empirical part of the article, quarterly data for Germany from 1991 by 2010 are to be examined.

In this work we deal with the Beveridge-Nelson decomposition of a linear process into a trend and a cyclical component. First, we generalize the decom- position for multidimensional linear process and then we use it to prove some of the limit theorems for the process and its special cases, processes VAR and VARMA. Further, we define the concept of cointegration and introduce the po- pular VEC model for cointegrated time series. Finally, we show a method how to deal with infinite sums appearing in calculation of the Beveridge-Nelson decom- position and apply it to real data. Then we compare the results of this method with approximations using partial sums.

Vektorfehlerkorrekturmodelle (VECM) erlauben es, Abhängigkeiten zwischen den Veränderungen mehrerer potenziell endogener Variablen simultan zu modellieren. Die Idee, ein langfristiges Gleichgewicht gleichzeitig mit kurzfristigen Veränderungen zu modellieren, lässt sich vom Eingleichungsansatz des Fehlerkorrekturmodells (ECM) zu einem Mehrgleichungsansatz für Variablenvektoren (VECM) verallgemeinern. Die Anzahl der kointegrierenden Beziehungen und die Koeffizientenmatrizen werden mit dem Johansen-Verfahren geschätzt. An einer einfachen Verallgemeinerung einer Konsumfunktion wird die Schätzung und Wirkungsweise eines VECM für Verbrauch, Einkommen und Aktienkurse in Deutschland gezeigt. Die Anwendung der Beveridge- Nelson-(BN)-Dekomposition auf vektorautoregressive Prozesse ermöglicht zudem, Abhängigkeiten zwischen den aus den kointegrierten Zeitreihen extrahierten zyklischen Komponenten zu schätzen. / Vector error correction models (VECM) allow to simultaneously model dependencies between the changes of several potentially endogenous variables. The idea is the modelling of a long-run equilibrium together with the short-run dynamics. Therefore a single equation approach (ECM) can be generalised to a multi equation approach (VECM) for variable vectors. The number of cointegration relations and the coefficient matrices are estimated with the Johansen procedure. The estimation of a VECM for income, consumption and stock prices for Germany is demonstrated by using a generalised consumption function. The Beveridge-Nelson-(BN)-Decomposition procedure for vectorautoregressive processes allows extracting cyclical components of cointegrated time series and estimating the degree of co-movement between these transitory components.