Marginal Tax Rate

270 Marginal effective tax rate Marginal effective tax rate rate δ. The corporate income tax is levied at statutory rate u, and local property tax at rate w is de- Don Fullerton ductible against it. Net returns are discounted at the University of Texas firm’s nominal after-tax discount rate r, and the present value of depreciation allowances per dollar of Designed to measure incentives for investment, investment is z. The particular value for z will re- a calculation that takes into account effects of flect the discount rate, the tax lifetime for the asset, measurement and timing of income in the depreciation schedule, and whether allowances determining the impact of a tax applied to an are based on historical or replacement cost. In equi- additional dollar of capital income. librium, the net outlay must be exactly matched by the present value of new returns: ∞ The marginal effective tax rate on capital income is ()11− kq=−∫ () u• the expected pretax rate of return minus the ex- 0 t pected after-tax rate of return on a new marginal in- ()− ()πδ− −rt + vestment, divided by the pretax rate of return. It c wq e e dt uzq (1) typically accounts for an investment tax credit, a statutory tax rate, accelerated depreciation allow- This condition can be used to solve for the Hall and ances, and historical cost depreciation that falls in Jorgenson (1967) “cost of capital” formula provid- real value with inflation. It may include just corpo- ing ρc, the real social rate of return in the corporate rate income taxes, or it may also include personal sector, gross of tax but net of depreciation: taxes and local property taxes. It may account for nominal interest deductions, inventory accounting, ρδc =−c the alternative minimum tax, and other detailed q provisions of the tax law. Several studies have r −+πδ estimated effective marginal tax rates for different = ()1 −−kuzw+−δ (2) assets under different laws (see Jorgenson and ()1 − u Yun 1991 for a time series in the United States and Jorgenson and Landau 1993 for nine different In calculations below, common values are used for countries). r, π, and u, but each asset has a specific value for δ, The marginal effective tax rate is a forward- k, z, and w. (If u and the corporate discount rate are looking measure that summarizes the incentives to replaced by the noncorporate entrepreneur’s per- invest in a particular asset as provided by compli- sonal marginal tax rate and corresponding discount cated tax laws. It may bear little relation to an in- rate, then equation (2) gives an analogous expres- dustry’s “average effective tax rate,” defined as the sion for ρnc, the social rate of return in the noncorpo- actual tax paid in a particular year divided by the rate sector.) actual capital income in that year, because that The “marginal effective corporate tax rate” t can measure averages over taxes on income from all be found by setting the property tax w to zero and past investment (minus credits on that year’s new then taking the gross-of-tax return (ρc) minus the investment). net-of-tax return (r − π), all divided by the gross-of- Any particular estimate of a marginal effective tax return. Simple algebra can then be used to dem- tax rate will depend on particular assumptions about onstrate several important conceptual results. First, equilibrium in capital markets, the rate of discount, this effective rate t is equal to the statutory rate u if the rate of inflation, expectations of investors, the investment tax credit is zero and depreciation churning, financing, the treatment of risk, and even allowances are based on replacement cost [because the choice between the “old view” (where dividend z is then δ/(δ + r − π)]. Second, this effective rate taxes matter) and the “new view” (where they do still equals the statutory rate if the investor receives not). For the simplest example, consider a perfectly only an immediate deduction equal to the purchase competitive firm contemplating a new investment price times the fraction z = δ/(δ + r − π), the first- with outlay q that has return c in a world with no year recovery proposal of Auerbach and Jorgenson uncertainty. Assume that the firm has sufficient tax (1980). Third, the effective tax rate is equal to zero liability to take associated credits and deductions with expensing of new investment (because z is then and that it does not resell the asset. An investment one). Thus uniform effective taxation of all assets tax credit at rate k reduces the asset’s net cost to can be achieved either with economic depreciation (1 − k)q. The return c grows with inflation at con- (all t = u) or expensing (all t = 0). Fourth, uniform stant rate π, but the asset depreciates at exponential effective tax rates can be achieved at any rate Marginal effective tax rate 271 between zero and u, if all assets receive an invest- we get a zero marginal effective tax rate either with ment tax credit that is proportional to (1 − z). That expensing or with debt finance. As a consequence, is, replace k in equation (1) with k(1 − z), where z is we get a negative effective tax rate with expensing based on economic depreciation at replacement cost, and debt finance. Thus, to maintain neutrality, pro- and the resulting effective tax rate is (u − k) on posals for expensing must also disallow interest all assets. deductions. To account for personal taxes and deductibility Under actual laws, the marginal effective tax of interest, assume that the firm can arbitrage be- rate can be large for an asset with no investment tax tween debt and real capital, as in Bradford and credit and slow depreciation allowances based on Fullerton (1981). If i is the nominal interest rate, historical cost with high inflation, especially if the then the corporation can save i(1 − u) by retiring a weight on debt is low and the weights on equity are unit of debt, so any marginal real investment must high. It can be negative for an asset with an invest- earn the same rate of return in equilibrium. All ment tax credit and accelerated depreciation allow- nominal net returns are then discounted at the rate ances, especially if the weight on debt is high. Dif- r = i(1 − u), whatever the source of finance. ferences in effective tax rates among assets can be used to measure the welfare cost of resource mis- A fraction cd of corporate investment is financed by debt, and the personal marginal rate of allocations. τ Actual estimates of effective tax rates depend debt holders is d. The net return to debt holders is − τ on numerical assumptions about parameters. For ex- thus i(1 d). A fraction cre of corporate investment is financed by retained earnings, and the return after ample, Fullerton (1987) calculates marginal effec- corporate taxes i(1 − u) results in share appreciation tive total tax rates for 36 assets in 18 industries, us- that is taxed at the effective accrued personal capital ing 4 percent inflation, 5 percent real net return, τ actual depreciation based on historical cost, one- gains rate re. The net return to the shareholder is − − τ third debt financing, and weighted-average personal then i(1 u)(1 re). The remaining fraction cns of corporate investment is financed by new shares, tax rates on interest, dividends, and capital gains. τ Before the Tax Reform Act of 1986, that paper finds subject to personal taxes at rate ns, so the net return − − τ corporate-sector effective rates equal to −0.18 for is i(1 u)(1 ns). In combination, the real net return in the corporate sector is: equipment, 0.37 for structures, 0.29 for public utility assets, 0.42 for inventories, 0.45 for land, and 0.29 overall. Equipment is subsidized by the combination c =−ττ+−()− scidd[]()111 ciure[]() re of investment tax credit, accelerated depreciation, and interest deductions at the high 46 percent statu- +−()− τπ− tory corporate tax rate. After the Tax Reform Act of cins[]11 u() ns (3) 1986, these rates become 0.37, 0.44, 0.44, 0.41, 0.44, and 0.41, respectively. The overall rate rises The “marginal effective total tax rate” in the from 0.29 to 0.41, suggesting less overall incentive corporate sector, including all corporate, personal, to invest, but the different assets are treated much and property taxes, is t = (ρc − sc)/ρc, the tax wedge more uniformly. The subsidy to equipment is elimi- as a fraction of the pretax return. Similar expres- nated with the repeal of the investment tax credit sions for the noncorporate sector and owner- and with the reduction of the statutory corporate tax occupied housing are detailed in Fullerton (1987). rate to 34 percent. This inclusion of personal taxes, and more sim- We now turn to a discussion of some caveats. ple algebra, can be used to demonstrate additional These calculations assume that the asset is held for- important conceptual results. Consider a tax-exempt ever, but Gordon et al. (1987) show that investors investor such as a university endowment or a pen- could sell a building, pay the capital gains tax, in- sion fund (τd = 0), and suppose that the marginal in- crease the basis for the new owner’s depreciation, vestment is entirely financed by debt (cd = 1). Then and pay less total tax. Churning can reduce the ef- with economic depreciation at replacement cost, the fective tax rate, narrow the difference between marginal effective total tax rate is now zero.

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