A General Equilibrium Model of the Term Structure Under Transaction Costs

Abstract

Simple, qualitative, general equilibrium models of the term structure of interest rates have existed in the literature for some time. In Value and Capital, Hicks [1] considered essentially a two-period model consisting of longand short-term securities. He argued that, on the average, the holding times of borrowers were longer than those of lenders. Borrowers and lenders, being risk-averse, would prefer to issue or hold securities of maturity equal to their holding time. This would give them a certain return or cost. The heavier weighting of borrowers toward longer holding times meant that in an equilibrium shortterm investors would have to be holding some long-term securities. For them to be willing to do this, it was necessary that the long terms in equilibrium pay a premium return above that available on short terms. At about the same time, Lutz [3] extended this same line of reasoning to the effect of transaction costs on the term structure. He argued that transaction costs, as well as uncertainty and risk aversion, would lead to a preference for a maturity equal to holding time. Shorter maturities would require additional transaction costs as securities were turned over to complete the holding time. Longer-term securities would incur additional costs in that they would have to be sold on the market rather than being redeemed at par. Preference for maturity equal to holding time in conjunction with a distribution of holding times weighted toward borrowers at the long end would require a premium on long-term yields in equilibrium. Much of recent work on the term structure has focused on the expectations' mechanism used by investors to forecast future interest rates, and on the measurement of the size of the premium. Of particular note are the studies by Meiselman [5], Malkiel [4], Kessel [2], and Modigliani and Sutch [6]. On a theoretical level, investigators have also dealt explicitly under uncertainty with the portfolio-selection problem faced by investors on the demand side of the model. The work of Tobin [9], and more recently Stiglitz [8], is of particular interest in this regard. The only attempt to formalize and extend the complete general equilibrium approach of Hicks and Lutz, however, appears to be that of Malkiel [4]. He derives the equilibrium term structure in a multi-period case for a given set of values of transaction costs and holding times. Also, under more general conditions, he uses a formal general equilibrium model to show how an increase in the supply of intermediate term securities can produce a hump in the term structure. Some of Malkiel's assumptions will be adopted here. The general equilibrium model developed here completely neglects the effect of uncertainty and risk aversion on the behaviour of borrowers and lenders. It assumes that they know with certainty the future prices at which securities of any maturity can be