A specification analysis of discrete-time no-arbitrage term structure models with observable and unobservable factors

We derive a canonical representation for the no-arbitrage discrete-time term structure models with both observable and unobservable state variables, popularized by Ang and Piazzesi (2003). We conduct a specification analysis based on this canonical representation. We show that some of the restrictions commonly imposed in the literature, most notably that of independence between observable and unobservable variables, are not necessary for identification and are rejected by formal statistical tests. Furthermore, we show that there are important differences between the estimated risk premia, impulse response functions and variance decomposition of unrestricted models, parametrized according to our canonical representation, and those of models with overidentifying restrictions.