Discounting Benefits and Costs Over Time
2. SELECTING THE INTEREST OR DISCOUNT RATE
2. SELECTING THE INTEREST OR DISCOUNT
be zero. In this case the real discount rate for public investments would be 6%, just the real rate of return. We now turn to the economic theory underlying what real rate of return should be used.
2.2 Theories for Determining the Discount Rate
There are several competing theories on the determination of what the discount rate should be given the many real world distortions. One of the most prominent theories dates back to a macroeconomic view of a national economy as a closed economy (i.e., an economy where imports and exports of both goods and capital are nonexistent or minimal). A simple macroeconomic model of such an economy requires that the sum of consumers' savings and taxes equal government spending and private investment. In this economy, if the government wishes to spend more money to invest in a public project, one of the other three elements must change accordingly. If the government borrows the money for the project, this simple model argues that private investment must fall by the amount of money the government must borrow (i.e., complete crowding out of private investment). If the government raises taxes to finance the project, then consumption and savings will fall by the amount of the tax increase.
Given these relationships between government financing of a public project and displacement of economic activity elsewhere in the economy, one group of economists argue that the discount rate should emphasize the opportunity costs in the private sector (foregone investment, consumption and savings) that results from diverting the funds to the public sector (Baumol, 1978). The opportunity costs in the private sector are made up of two components: the rate of return on displaced private investments, and the value of foregone consumption. The rate of return on investments can be obtained from financial reports of companies. The value of foregone consumption (for small changes in consumption) can be inferred from the interest rate people would earn on savings. That is, as consumers decide whether to consume their last dollar or save their last dollar, they compare the value of consumption to the interest rate they would earn on savings.
The overall social discount rate is the weighted sum of the private investment rate of return and the interest rate on savings. The weight is determined by how much of the monies to be transferred to the public sector come from displaced private investment and how much comes from displaced savings/consumption. This ultimately depends on how the government raises the money for the investment project. If special financing legislation, dedicated trust fund dollars, or specific excise taxes are used, then, in principle, a project- or policy-specific discount rate could be calculated. In practice this is unusual; the weights would come from the
proportion of the government's budget that comes from individual income taxes, corporate income taxes, other business taxes, and other consumer taxes received by the government.
Today, however, most national economies are part of an open world economy, where substantial exports and imports (including foreign capital) make the closed economy view somewhat misleading (Feldstein, 1985). No longer must private investment be reduced dollar per dollar with the increase in a deficit-financed public project. Directly or indirectly, foreign owners of capital can meet the new increased demand for funds arising from the government's project. In an open world economy there is very little crowding out of domestic private investment (Lind, 1990: 15). As such, Lind's recent reassessment of determination of the discount rate recommends the appropriate government discount rate (in open world economies) be the interest rate the government must pay when it borrows (1990: 25).
Of course an interesting wrinkle to this occurs when the government policy does not require the government to make investments, but instead requires the private sector to make investments. For example, workplace- based regulation that requires firms to invest in reducing worker exposure to carcinogens may require the firm to spend millions of dollars on new filtration systems. In this case, it is industry's opportunity cost of capital or their cost of borrowing, not the government's, that may be relevant for determining the present value of the costs. In this case, risk would be a real cost, but taxes are still a transfer.
Another set of arguments (e.g., Arrow, 1965) stresses the "social time preference"in determining the discount rate. In particular, these arguments start by viewing the discount rate as a measure of people's preferences for present versus future consumption. They then introduce a public goods or beneficial externality argument. This argument is that individuals care more about future generations than their private savings decisions might indicate. Acting individually, their individual savings decisions have little effect on the welfare of future generations. However, collectively society does care, and if all people would save more (and consume less) for future generations, we would all be better off. This theory is an argument for discount rates lower than the individual savings rate to encourage investing for future generations.
Recently, Weitzman (1998) has addressed the issue of selecting discount rates for environmental projects and policies whose effects may last for centuries. Examples of such policies include global climate change, disposal of radioactive waste, groundwater pollution, and species extinction. Normal exponential discounting as given in equation (8-1) with discount rates typically used by Federal agencies would render even large
benefits received or costs incurred 200 years from now as trivial. For example, at 7%, a dollar 200 years from now would be one-millionth of a dollar today. Thus, foregoing $2 in benefits today to prevent a $1 million dollar cost 200 years from now would not pass a benefit-cost test. As Weitzman points out, this makes even most economists feel uneasy, let alone those who feel a strong moral obligation not to impose costs on unrepresented future generations. But what's a policy analyst to do?
Weitzman suggests a potential solution for policies with such far distant effects. Using the view that discount rates should reflect the long-run productivity of capital, he suggest there is little reason to treat the discount rate as a fixed constant over several centuries. There is a great deal of uncertainty over technological progress and a host of factors influencing the productivity of capital over the next 2-3 centuries. What we really have is a distribution of long-run productivities of capital and associated distribution of discount rates. As Weiztman then demonstrates, it is only the realization of the lowest discount rates that really have any impact on current decision- making (1998:205). The high discount rates result in such high discount factors that those future benefits and costs do not matter today. This can be made more intuitive by looking back at Figure 8-1 and comparing the far more rapid rate of decline of the present value of $1 with the 7% as compared to 4% discount rate. Weitzman (1998:207) concludes, "Thus, the paper is suggesting at least the possibility that it may be essential to incorporate declining discount rates into any benefit-cost methodology for evaluating long-term environmental projects." While this does not provide a simple solution, it does suggest that a sensitivity analysis of the net present value of environmental policies with long term effects be performed. For example, the analyst could have discount rates declining each decade from their current level toward something approaching zero by the end of the next century.
Weitzman (2001) has recently gone further to indicate that, rather than relying on a single discount rate, a discount function should be used, with a discount rate of 4% for projects in the immediate future, 3% for near term (6-25 years), 2% for projects of 26 to 75 years, and finally 1% for effects of up to 300 years in duration.