DIFFERENTIAL TAX EFFECTS IN EQUILIBRIUM MODELS OF THE TERM STRUCTURE OF INTEREST RATES

This dissertation provides a theoretical investigation of the implications of current tax laws upon the term structure of interest rates for both original issue discount bonds and coupon bonds. Rather than couching the analysis within a single equilibrium framework, the dissertation considers several alternative equilibrium models of the term structure and the impact of differential taxation therein.

Initially, tax effects within a static equilibrium characterization of coupon bond markets are analyzed. A flat and non-stochastic expectation of future spot rates is posited and equilibrium pricing requires the instantaneous equalization of after-tax holding period returns on all available securities. It is established that the tax-adjusted corporate term structure is monotonically increasing while the tax-adjusted municipal term structure is monotonically decreasing. With regard to the coupon effect, discounted corporate issues exhibit a positive coupon effect whereas discounted municipal issues exhibit a negative coupon effect. In addition, the yield to maturity on both corporates and municipals is shown to be a decreasing function of the ordinary income tax rate and an increasing function of the capital gains tax rate.

Discarding this certainty framework, the dissertation subsequently considers differential tax effects within a stochastic equilibrium characterization of original issue discount bonds. In this partial equilibrium framework the value of original issue discount bonds is expressed in terms of a single state variable, the spot interest rate. Tax-adjusted relative equilibrium original issue discount bond prices are shown to exist under U.S. tax laws which prevailed prior to 1954 but not under current U.S. tax laws. The unbiased expectations hypothesis is shown to be unsustainable in equilibrium both in the absence and presence of differential taxation. As would be expected, the corresponding liquidity premia vary with the level of taxation. Fisher's hypothesis and the impact of taxation are also considered.

Since the price of a default-free coupon bond can be expressed as a coupon-weighted integral of the prices of default free unit discount bonds, the preceding analysis allows us to consider differential tax effects within a stochastic equilibrium characterization of coupon bond markets. Explicit tax-adjusted equilibrium coupon bond prices are derived under the assumption that the spot rate evolves according to a trend adjusted Ornstein-Uhlenbeck process and a Cox-Ross square root process. The underlying parameters of these alternative specifications are estimated and numerical simulations of various tax-adjusted equilibrium term structures are presented. However, once the existence of tax-exempt investors is admitted an income tax irrelevance proposition follows: rational taxable investors need not pay ordinary income tax on coupon income. This ordinary income taxable receipt may be risklessly converted into a capital gains taxable receipt provided homemade leverage is made use of.

The dissertation concludes by considering differential tax effects within a general equilibrium stochastic framework. In a general equilibrium framework, as opposed to a partial equilibrium framework, the disposition of tax revenues must be explicitly considered. Rather than positing that they are simply discarded, tax revenues are assumed stochastically redistributed to the individuals of the economy. This rather general specification allows us to give cognizance to the fact that tax revenues in reality are redistributed within the economy. It is established that the underlying real equilibrium of the economy is unaltered by the imposition of differential taxation with the stochastic redistribution of tax revenues provided investors possess logarithmic preferences. However, the equilibrium instantaneous risk-free rate and the equilibrium pricing of contingent claims are shown to be systematically altered.