A Negative Equilibrium Interest Rate

The average after-tax real interest rate on U.S. T-bills and the average rate of return on long-term government bonds (LTGB) have been negative over the past 75 years. Is this negative rate an equilibrium phenomenon or simply an empirical fluke? We show that a negative equilibrium interest rate is possible and that the wealthier the nation is, the more negative the equilibrium interest rate can be. This phenomenon results from a positive inflation rate and taxation of nominal profits, and it cannot hold in a period of zero inflation or in a period of deflation. A positive demand for T-bills and for LTGB exists also in a portfolio framework, even when these two assets are characterized by a negative expected rate of return and other risky assets are yielding positive expected returns. Most practitioners and academics would agree that a dollar received today is worth more than a dollar received tomorrow. This idea is reflected in the notion of “the time value of money” and in the positive interest rate that is assumed in most economic models. We find, however, that the empirical after-tax real interest rate is negative. An analysis of the 1926–2000 period reveals that the average after-tax real interest rate on U.S. T-bills was –1.34 percent and the average after-tax real return on long-term government bonds was −0.24 percent. These negative average returns are the result of inflation and the fact that it is nominal profit that is taxed. Is this finding a statistical fluke, or can such a negative interest rate be an equilibrium result?In the absence of inflation, no one would invest in T-bills yielding a negative rate of return when one could, instead, keep the money as cash and obtain a rate of return of zero. In periods of positive inflation, however, holding cash is costly and investment in T-bills may be preferable to holding cash even if T-bills yield a negative after-tax real return. Of course, one could refrain from investing altogether in such conditions and simply spend the dollar today. But could investing in such a situation be optimal? We show that the standard utility functions imply that the optimal saving may be positive even at a negative rate of return. Thus, a negative interest rate can be perfectly compatible with rational equilibrium.We further show that the higher current wealth is, the higher the saving will generally be at a given interest level. Thus, the wealthier the nation is, the more negative the equilibrium interest rate could be. The opposite holds for poor nations with rapid growth.The interest rate can be negative in equilibrium even in a portfolio context when other assets in the market are yielding positive expected rates of return. To produce this result, we used 1926–2000 data on the U.S. market to estimate the means and the variance–covariance matrix for T-bills, long-term government bonds, common stocks, and small-capitalization stocks. We analyzed the mean–variance-efficient frontier to derive the optimal portfolio composition with these four assets. We found that, although equity was characterized in this 75-year period by a positive average after-tax real rate of return (for investors who paid the marginal tax that prevailed in each year) and although T-bills and long-term government bonds had negative average after-tax real rates of return, the portfolio demand for T-bills and long-term government bonds was still positive. The portfolio demand for these two assets stems from their relatively low correlation with equity.The notion of a negative equilibrium interest rate may have far-reaching implications for many of our economic intuitions and models, most of which assume a positive interest rate. Specifically, in light of these findings, we believe that such commonly taught concepts as “the time value of money” should be reconsidered.