Economic Depreciation and Invariant Valuation: A Constructive Proof of the Samuelson Theorem

Abstract

I elaborate on Samuelson’s (1964) result that a tax on capital income will leave asset values unaffected by the marginal rates of their holders if “economic” depreciation is allowed as a deduction in computing taxable income, extended by Fane (1987) to an economy with state-contingent securities, and by Lyon (1990) to the case of time-varying marginal rates. Those papers leave unexplained why, with economic depreciation, economic agents in a taxable environment should act as if they were (in Lyon’s words) discounting all pre-tax “cash receipts . . . at the pre-tax interest rate.” In discrete time, I formulate a constructive proof of Samuelson’s result, which, drawing on the insight that economic depreciation induces pure accrual taxation, shows that the impact of income taxation on the accrual of value and on discounting exactly offset one another in every period. That is why taxpayers behave as though they were discounting pre-tax cash flows.