A RESPECIFIED TAX‐ADJUSTED FISHER RELATION

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Abstract
How much will a 1% increase in expected inflation increase nominal interest rates? Irving Fisher's famous equation implies that nominal interest rates will rise in proportion to an increase in expected inflation. Darby and Feldstein, correcting the Fisher equation for taxation, predict a nominal interest rate increase of [1/(1 ‐ T)]% where T is the marginal tax rate: i.e., if T =3, then a 1 % increase in expected inflation should cause a 1.4 % rise in interest rates.Empirical evidence, however, suggests that the rise in interest rates is much smaller than the Darby/Feldstein prediction. Estimates are around 9, varying mostly between 5 and 1.15, which is much closer to Fisher's original prediction. It is important to know the size of the interest rate response to inflation expectations in a world in which inflation and interest rates are volatile and in which tax laws are designed to influence savings and investment through interest rates.In this paper we attempt to close the gap between theorized and estimated effects of inflation by incorporating into the Fisher equation two important aspects of the U.S. tax code: historic cost depreciation and the lower tax rate on capital gains. Our model shows that the effect of expected inflation on interest rates is dampened by the lower benefits from depreciation deductions arid the capital gains tax.Our corrected Fisher equation predicts a 1.12 % nominal interest rate increase, rather than the 1.4 % increase implied by the Darby/Feldstein model. The, our model closes about 56 % of the gap between theory and empirical evidence. The remainder could be closed by additional refinements in the model or better empirical modeling.

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