No-arbitrage Near-Cointegrated VAR(p) Term Structure Models, Term Premia and GDP Growth.

Macroeconomic questions involving interest rates generally require a reliable joint dynamics of a large set of variables. More precisely, such a dynamic modelling must satisfy two important conditions. First, it must be able to propose reliable predictions of some key variables. Second, it must be able to propose a joint dynamics of some macroeconomic variables, of the whole curve of interest rates, of the whole set of term premia and, possibly, of various decompositions of the term premia. The first condition is required if we want to disentangle the respective impacts of, for instance, the expectation part of the term premium of a given long-term interest rate on some macroeconomic variable. The second condition is necessary if we want to analyze the interactions between macro-variables with some global features of the yield curve (short part, long part, level, slope and curvature) or with, for instance, term premia of various maturities. In the present paper we propose to satisfy both requirements by using a Near-Cointegrated modelling of basic observables variables, in order to meet the first condition, and the no-arbitrage theory, in order to meet the second one. Moreover, the dynamic interactions of this large set of variables is based on the statistical notion of New Information Response Function, recently introduced by Jardet, Monfort and Pegoraro (2009). This technical toolkit is then used to propose a new approach to two important issues: the "conundrum" episode and the puzzle of the relationship between the term premia on long-term yields and future economic activity.