Can Economic Growth Make Monetarist Arithmetic Pleasant?

Abstract

The Sargent and Wallace paper has stimulated a debate concerning the relative size of the growth rate vs. the after-tax interest rate, and two different approaches have been followed in this debate. One approach is to simply compare the historical data on the growth rate and the discount rate, and the other approach is to consider optimizing under-pinnings. Darby [8] and McCallum [12] have emphasized that bond-financed deficits are feasible if the growth rate exceeds the discount rate, and, following the first approach, Darby interprets the empirical evidence for the U.S. as showing that this condition is met. Miller and Sargent [14] have replied to Darby, noting that the growth rate exceeding the interest rate condition is only necessary, not sufficient for the feasibility of bond-financing. They also emphasize that a period involving bond-financed deficits may raise interest rates, so that the growth rate should eventually be too low, as it has been in the U.S. since 1980. The alternative reaction to the growth rate vs. the interest rate debate is taken in McCallum [13]. His microeconomic analysis involved infinitely-lived agents with money directly entering the utility function, and his conclusion is that the conditions of optimizing behaviour preclude the growth rate from exceeding the interest rate. Burbidge [6] reaches the same conclusion with an overlapping generations model. However, Buiter and Carmichael [5] and Aiyagari [1] use overlapping generations models which do permit the growth rate to exceed the interest rate. Furthermore, Aiyagari emphasizes that higher deficits need not lead to higher interest rates, as long as the distribution of wealth across young and old agents is not affected by the deficit. What general conclusion can be drawn from these studies? In short, none. Theorists have demonstrated that they do not have a common view regarding the specification of optimizing models, and different historical periods can be cited to support either relative