Structural Models of the Demand for Bonds and the Term Structure of Interest Rates

Abstract

The effect of quantities outstanding on the term structure of interest rates has provoked much discussion in the literature. De Leeuw (1965) tests whether the levels and the change in levels of various debt categories affect the spread between the long-term US government bond rate and the Treasury bill rate: only the changes in debt outstanding prove significant, so that in his model there are no permanent rate effects of the quantity of debt outstanding. Modigliani and Sutch (1966) also find no significant quantity effects in a reduced-form regression of the spread between the long-term US government bond rate and the bill rate on a distributed lag of short-term interest rates; and Modigliani and Shiller (1973) do not mention the possible effects of quantities: they identify the difference between long and short rates that is not explained by expectations with a risk premium and relate it to the variability of interest rates. Feldstein and Eckstein (1970) find a significant positive effect for real per capita government debt in an equation for the US long-term corporate bond rate, but the magnitude is small. Furthermore, in a more recent study emphasizing price expectations in several markets by Feldstein and Chamberlain (1973), this variable is no longer significant in explaining the rate on newly issued corporate bonds. For the United Kingdom, both Rowan and O'Brien (1970) and Buse (1975) test supply variables in equations explaining the spread between long and short rates; but in some specifications Rowan and O'Brien get the wrong sign for them, and Buse, after correction for autocorrelation, gets a t-value of only 1-67 on the proportion of long-term bonds in total British government debt. In the Canadian context, Dobson (1973) and Christofides (1975) find significant quantity effects for some maturities of Canadian government bonds, but the impact of even such a massive change in outstanding quantities as the Conversion Loan of 1958 appears to be small. All of the studies cited above have relied on reduced-form regressions rather than estimating structural models of the demand and supply for the various maturities of bonds, though some of the reduced forms are derived from explicit structural models. (A more recent exception is Friedman (1977), who estimates a structural model.) The advantages of structural models are well known, however. An over-identified structural model implies certain restrictions on the reduced form, and ordinary least squares estimation of the unrestricted reduced form will be (asymptotically) inefficient relative to three-stage least squares or full information maximum likelihood estimation of the structural model (see Dhrymes, 1973). Consequently, even though quantity variables may not be significant when an unrestricted reduced-form term structure equation is estimated, because of lower standard errors they may be significant when a structural model is estimated and its reduced form is calculated.