This article develops a new family of Gaussian macro-dynamic term structure models (MTSMs) in which bond yields follow a low-dimensional factor structure and the historical distribution of bond yields and macroeconomic variables is characterized by a vector-autoregression with order p > 1. Most formulations of MTSMs with p > 1 are shown to imply a much higher dimensional factor structure for yields than what is called for by historical data. In contrast, our "asymmetric" arbitrage-free MTSM gives modelers the flexibility to match historical lag distributions with p > 1 while maintaining a parsimonious factor representation of yields. Using our canonical family of MTSMs we revisit: (i) the impact of no-arbitrage restrictions on the joint distribution of bond yields and macro risks, comparing models with and without the restriction that macro risks are spanned by yield-curve information; and (ii) the identification of the policy parameters in Taylor-style monetary policy rules within MTSMs with macro risk factors and lags.
