A No-Arbitrage Vector Autoregression of Term Structure Dynamics with Macroeconomic and Latent Variables

Abstract

We describe the joint dynamics of bond yields and macroeconomic variables in a Vector Autoregression, where identifying restrictions are based on the absence of arbitrage. Using a term structure model with inflation and economic growth factors, together with latent variables, we investigate how macro variables affect bond prices and the dynamics of the yield curve. We find that the forecasting performance of a VAR improves when no-arbitrage restrictions are imposed and that models with macro factors forecast better than models with only unobservable factors.Variance decompositions show that macro factors explain up to 85% of the variation in bond yields. Macro factors primarily explain movements at the short end and middle of the yield curve while unobservable factors still account for most of the movement at the long end of the yield curve.

Another View on U.S. Treasury Term Premiums

“…where 0  is a scalar, and 1  is an 1 n  vector, and X is an 1 n  vector of state variables, which in applications are wholly observable (Li and Wei, 2012), purely latent (Kim and Wright, 2005), or some combination thereof (Ang and Piazzesi, 2003;Lemke and Werner, 2009;Joyce et al, 2009). An observable approach may have particular theoretical appeal for researchers at the intersection of macroeconomics and finance, especially if the factors are truly exogenous to the term structure, perhaps akin to a policy rule framework for expected short rates.…”

“…Indeed, (2) nests simple econometric expressions of the Taylor rule, and accordingly active views among investors regarding, say, expected inflation or the output gap from t to t +  , might plausibly form the basis for    t EX through any horizon. 19 However, even studies that incorporate macroeconomic variables readily acknowledge that additional factors are required to fit the term structure with satisfactory precision (e.g., Ang and Piazzesi, 2003;Ang et al, 2006). If the data were not as discouraging, exogenous macroeconomic factors might exclusively comprise X, instead of the common addition of the first few principal components of the term structure.…”

Term structure transmission of monetary policy

“…16 In the model of section 3, term premiums of bond rates were assumed to be constant over time and drop out of equilibrium deviations. 17 Recent examples of empirical estimates of the term structure exploring macro variable determinants of term premiums include Ang and Piazzesi (2003), Rudebusch and Wu (2007, forthcoming), Ang, Dong, and Piazzesi (2005), Duffee (2006), Dewachter and Lyrio (2006a), and Dewachter, Lyrio, and Maes (2006). is equal to the expected policy rate in the ith period, r t,i , plus a possibly time-varying forward rate term premium, ψ t,i .…”

“…In the absence of an explicit specification of investor utility functions, no additional theoretical restrictions are imposed on the λ ′ 1 matrix. As the dimensions of the pricing matrix can be large, empirical investigations of essentially affine formulations of asset pricing often impose zero restrictions on elements of the λ ′ 1 matrix, such as Ang and Piazzesi (2003), Ang, Dong, and Piazzesi (2005), and Dewachter and Lyrio (2006 a,b). Kim and Orphanides (2005) suggest fewer zero restrictions are required if measurements include both bond rate data and surveys of interest-rate forecasts over short and long horizons.…”

“…Other research, such as Ang and Piazzesi (2003), and Dewachter, Lyrio, and Maes (2006) relate yields to macro factors. However, in typical DSGE formats, the possibility of a distinct role for bond yields in explaining economic behaviour is generally not admitted.…”