The Bond Premium in a DSGE Model with Long-Run Real and Nominal Risks

Abstract

The term premium on long-term nominal bonds compensates investors for inflation and consumption risks over the lifetime of the bond. A large finance literature finds that these risk premiums are substantial and vary significantly over time (e.g., Campbell and Shiller 1991; Cochrane and Piazzesi 2005); however, the economic forces that can justify such large and variable term premiums are less clear. Piazzesi and Schneider (2007) provide some economic insight into the source of a large positive mean term premium in a consumption-based asset pricing model of an endowment economy. Their analysis relies on two crucial features: first, the structural assumption that investors have Epstein-Zin recursive utility preferences; 1 and second, an estimated reduced-form process for consumption and inflation with the feature that positive inflation surprises lead to lower future consumption growth. With these two elements, they show that investors require a premium for holding nominal bonds because a positive inflation surprise 1 Kreps and Porteus (1978) provide the original theoretical framework for these preferences. Epstein and Zin (1989) and Weil (1989) provide extended results and applications for a special case of this framework.

Risk aversion, risk premia, and the labor margin with generalized recursive preferences

“…For generalized recursive preferences (4) with labor, Rudebusch and Swanson (2012) show that the household's stochastic discount factor is given by …”

“…I consider the cases ρ z < 1 and ρ z = 1 in the examples below. Once the period utility function is specified, I solve the model using perturbation methods, as in Rudebusch and Swanson (2012) and Swanson (2012). This involves computing a nonstochastic steady state for the model (or transformed version of the model) and an nth-order Taylor series approximation to the true nonlinear solution for the model's endogenous variables around the steady state.…”

“…Consider first the additively separable period utility function from Rudebusch and Swanson (2009) and Example 3,…”

“…Following Rudebusch and Swanson (2012), I use two equations to compute the value function in the model, as follows: (A.61) which is used in (A.58). We can then solve the system of equations (A.46)-(A.60) numerically using the Perturbation AIM algorithm of Swanson et al (2006) to compute a fifth-order Taylor series approximate solution around the nonstochastic steady state.…”

Risk premiums and macroeconomic dynamics in a heterogeneous agent model

“…Again, there are no immediate measures in the data to compare these to. Relative to estimated models such as Du¤ee (2002) Figure 3 and Table 14 (row 5) we measure the term premium by the di¤erence in yield between the 10 year bond and its risk neutral counterpart (as in Rudebusch and Swanson, 2009). We …nd that in the present model, this measure for the term premium is high on average (1.78), and substantially volatile (0.34).…”