11], economists have developed a substantial literature relating the forward interest rates implied by currently prevailing rates on debts of differing maturity to market participants' expectations of interest rates in the future.Hicks suggested that implied forward rates might differ from the corresponding expected future rates by a liquidity premium, or term premium, and more recently Stiglitz [19] and others have formalized how market partici- pants' risk aversion would give rise to such a premium.While in principle the premium could be either positive or negative, the usual upward slope of the yield curve suggests a positive premium that itself varies positively with the debt's term to maturity.Kessel [10] subsequently suggested that the premium for a given maturity might vary with real economic activity, and Culbertson [2] argued that relative outside debt supply quantities should als' affect the premium.More recently Nelson [16] offered an explanation for the premium even in the absence of risk aversion, and Friedman [5] related changes in the premium to shifts in wealth ownership among heterogenous investors.An accompanying empirical literature has repeatedly tested each of these various hypotheses about forward rates and expected future rates, but usually with somewhat inconclusive results.A key reason for the weakness of much of this empirical literature has been the absence of independent information about market participants' expectations.Not surprisingly, the very early attempts based on the assumption of perfect foresight were most unsuccessful and this approach quickly went out of fashion.The traditional procedure since then has been either to apply the Hicks-Lutz theory to derive expectations proxies from the same term-structure data that generate the forward rates, or to use some other device like autoregressive or 'rational' expectations proxies.In either case, any hypoth- esis submitted to statistical testing is necessarily a joint hypothesis embodying both the relation of forward rates to expectations and the formation of expecta- tions themselves.Failure of the hypothesis to conform to the data may then indicate rejection of the proposition relating forward rates to expectations, or rejection of the identifying restrictions imposed to derive the expectations proxy (or both).The object of this paper is to test several familiar hypotheses about the relationship between the forward rates implied by the term structure and interest

Benjamin M. Friedman, The Effects of Tax Policy on Capital Formation, Corporate Liquidity and the Availability of Investible Funds: A Simulation Study: Discussion, The Journal of Finance, Vol. 31, No. 2, Papers and Proceedings of the Thirty-Fourth Annual Meeting of the American Finance Association Dallas, Texas December 28-30, 1975 (May, 1976), pp. 309-312

The fact that most eldealy individuals in the United States choose to maintain a flat age-wealth profile, rather than buy individual life annuities, stands in contrast to central implications of the standard life-cycle model of consumption-saving behavior. The analysis in this paper lends support to an explanation for this phenomenon based either on the cost of annuities, importantly including the element of that cost due to adverse selection, or on the interaction of that cost and an intentional bequest motive. Expected yields offered on individual life annuities in the United States are lower by some 4-6%, or 2 1/2-4 1/2% after allowing for adverse selection, than yields on alternative long-term fixed-income investments. Simulations of an extended model of life-cycle saving and portfolio behavior, allowing explicitly for uncertain lifetimes and Social Security, show that yield differentials in this range can account for the observed behavior, even in the absence of a bequest motive, during the early years of retirement. By contrast, at older ages the combination of yield differentials in this range and a positive bequest motive is necessary to do so.

Benjamin M. Friedman, V. Vance Roley, Investors' Portfolio Behavior under Alternative Models of Long-Term Interest Rate Expectations: Unitary, Rational, or Autoregressive, Econometrica, Vol. 47, No. 6 (Nov., 1979), pp. 1475-1497

This paper uses a model of the valuation of bonds bearing call options, together with observed market yields on callable bonds, to infer information about the uncertainty associated with interest rate expectations. A dynamic programming solution of the model simultaneously determines both the bond price and the issuer's optimal refunding strategy, given the relevant data describing the bond and the market's expectations of future interest rates. Application of the valuation model in reverse, for quarterly average data for 1969-76, generates a time series representing the uncertainty which the market associated with its expectations of future interest rates during this interval, given the then-prevailing yields on new issues of utility bonds and industrial bonds callable after 5 years and 10 years, respectively. This uncertainty, parameterized as the standard deviation of a truncated normal distribution, fluctuated between 1/2 percent and 3/4 percent between 1969 and early 1974, then rose to sharply higher levels from mid-1974 through mid-1975, and has fluctuated between 3/4 percent and 1 percent since late 1975.