ESSAYS ON INTEREST RATES, EXPECTATIONS, AND INFLATION

Under certainty, the yield curve is an "average" of short-term rates, permitting inference of future rates from the yield curve's shape. Prior to the advent of uncertainty pricing models for bonds, an ad hoc unbiased "expectations" theory evolved, implying a log-linear relationship between bond prices and expected short-term interest rates. In the absence of hedging premia, resultant yield curves coincide with "average expected rate curves": their shapes accurately reflect the future course of expected short rates. Equivalently, forward rates are unbiased estimators of future expected spot rates. Recently, rigorous bond valuation models have evolved to describe uncertainty characterized by jointly Markov variables. All such "probabilistic asset valuation models" result in yield curves consistently negatively biased relative to corresponding average expected rate curves even if investors require no hedging premia for future uncertainty. Consequently, for any set of equilibrium bond prices, forward rates will always be biased relative to future expected spot rates. Furthermore, the factor traditionally defined as a "term" or "liquidity" premium actually consists of two components: a hedging premium and a negative bias resulting because expectations of future short rates do not enter the pricing relationship in a log-linear fashion. By specifying the dynamics of uncertainty, both components of the "premium" and resulting properties can be precisely identified. Traditionally, a humped yield curve is associated with expectations of both rising and falling future rates. This standard economic interpretation is never valid under autonomous instantaneous rate processes since they display monotonic expectations. However, traditional economic content can be restored by a mean-reverting process with a non-autonomous adjustment speed suggesting a business cycle. Thus the operational effectiveness of the yield curve's shape can be determined only from the parameters describing underlying sources of uncertainty. The essays close by demonstrating that previous tests suggesting that Treasury bill returns efficiently reflect expected inflation result from selection of a sample period of unprecedented U.S. price stability and cannot be substantiated in general. Results with recent data require rejection of a joint hypothesis of efficient markets and a constant "real" rate.