The Long-Term Discount Rate

Abstract

We study the term structure of interest rates in a two-tree exchange economy. Even when one of the trees is very small, interest rates are determined differently than in a single tree economy. Rather than always being flat, the yield curve is usually upward sloping but may be downward sloping. In the latter case, the slope predicts a future increase in consumption growth rates and lower future short-term interest rates. In addition, the short and the long interest rates are driven by different variables. As in the one-tree model, the short rate depends on risk aversion; however the long rate depends on consumption growth and volatility, but \emph{not} on the representative investor's risk aversion. Therefore, our results provide a resolution of the risk-free rate puzzle, and demonstrate the fragility of the one-tree model.

Keywords: Term structure, yield curve, risk-free rate puzzle, two trees, Lucas model, asset pricing

JEL Classification: E43, G12