This paper develops a general affine macro-finance model of the U.S. macroeconomy and the Treasury bond market. As the name suggests the macro-finance approach allows bond yields to reflect macro-economic variables as well as latent variables representing financial market factors. It is based on the central bank model (CBM) developed by Svensson (1999), Rudebusch (2002), Smets (1999), Kozicki and Tinsley (2005), and others, which represents the behavior of the macroeconomy in terms of the output gap (*g*_{t}), inflation (π_{t}) and the short-term interest rate (*r*_{t}). The model developed in this paper allows bond yields to reflect changes in macro-economic volatility related to the underlying rate of inflation.

In turn, the behavior of bond yields helps inform the specification of the macroeconomy, yielding new insights into the operation of monetary policy. In particular, early macro-finance studies showed that although macro-economic variables provide a good description of the behavior of short rates they do not provide an adequate description of long-term yields (Kozicki and Tinsley 2001, Ang and Piazzesi 2003). This finding has spawned an important macro-econometric literature that augments the CBM with latent variables, capturing exogenous changes in inflation and interest rates (Kozicki and Tinsley 2005 provide a useful summary). This literature shows that these rates are characterized by a nonstationary common trend (or unit root) that seems to be explained by the underlying rate of inflation. It follows the standard macro-econometric literature in assuming a homoskedastic (fixed) variance structure. This situation is familiar to macro-economic modelers but poses a potential problem for term structure researchers: it is well known that asymptotic (long-maturity) yields are not properly defined if the interest rate is driven by a random walk (a homoskedastic unit root process).

This theoretical problem was first raised as an empirical issue by Dewachter and Lyrio (2006), but with this notable exception, macro-finance modelers have avoided it by assuming that the underlying inflation variable follows a near-unit-root process (Ang and Piazzesi 2003, Rudebusch and Wu 2003, Dewachter, Lyrio, and Maes 2006). However, because this variable is stationary, it mean-reverts to a constant rather than the variable end-point suggested by unit root macro-economic models. As Kozicki and Tinsley (2005), Dewachter and Lyrio (2006), and others note, this means that it cannot be interpreted as a long-run inflation expectation because it is anchored to a constant that cannot be influenced by monetary policy.

Mainstream finance yield curve research avoids these problems by using heteroskedastic (stochastic volatility) interest rate models based on Cox, Ingersoll, and Ross (1985, hereafter CIR). I modify their continuous time specification for use with discrete-time macro-economic data, getting a sensible forward rate asymptote without placing constraints on the roots of system. The stochastic trend is estimated using the extended Kalman filter, which is also standard in the mainstream finance literature. Model restrictions allow the stochastic trend-volatility term to be interpreted as an inflation trend, consistent with the hypothesis that macro-economic volatility is influenced by the underlying rate of inflation (Okun 1971, Friedman 1977, Engel 1982).^{1} This specification encompasses the standard macro-finance model, which is decisively rejected by the data.

The research described in this paper was initially motivated by my interest in the asymptotic yield problem raised by early drafts of the Dewachter and Lyrio (2006) paper. I expected the new specification to outperform the standard one in explaining long maturity yields and with this in mind I extended the conventional (10-year maximum) maturity data set to include a 15-year yield, the longest available historically. However, the results are surprising in this respect. The new specification does give a dramatic improvement in fit, but the main reason for this is the importance of the Okun–Friedman heteroskedasticity effect found in the macro-data. Once this is allowed for, its more flexible yield curve specification adds very little. This finding suggests that this new macro-finance framework—which uses estimates of macro-economic volatility to inform the stochastic volatility parameters of the term structure model—should be better at discriminating between rival models than the mainstream finance one (Chen and Scott 1993, Dai and Singleton 2002), which does not. It further suggests that CBM-based studies of monetary policy should use the heteroskedastic framework rather than the current homoskedastic one, allowing the effects of the stochastic trend on the second as well as the first moments of the system to be analyzed.

The paper is set out as follows. The next section describes the macro-economic model and its stochastic structure, supported by Appendix A. Section 2 derives the bond pricing model, supported by Appendix B. It discusses the theoretical problems posed by the unit root in the standard specification and shows how these are avoided in the general affine specification. The two respective empirical models are compared in Section 3. Section 4 offers a brief conclusion and suggestions for further research.