A generalized approach to multigeneration project evaluation.

• Author: Liu, Liqun

1. Introduction

   It is well-known that the choice of discount rate plays a significant role in the ranking of projects with varying time paths of costs and benefits. For public projects, the choice of the appropriate social discount rate (SDR) is not clear-cut even in the context of short-lived projects in which costs and benefits occur within a single generation. In particular, when capital taxes produce a wedge between gross and net rates of return, should one discount at the economy's rate of return (the before tax rate) or the individual's rate of return (the after tax rate)? In the single-generation context, the literature falls in two camps. (1) One camp argues that the appropriate SDR is a weighted average of the gross and net rates of return with weights typically determined by the fractions of resources drawn from consumption and private investment, respectively. (2) A second camp argues that future benefits should be discounted at the net rate of return, but that the initial investment should be multiplied by a scale factor so that the direct costs of the project can be expressed in terms of consumption units. (3)

   Both approaches suffer from severe implementation problems. For the first approach, there is no general formula for the weights needed to calculate the SDR as a weighted average of two market rates of return (Dreze 1974). Indeed, the appropriate SDR to use is project-specific (Stiglitz 1982). Without a systematic methodology to derive project specific SDRs, the weighted average approach is hard to implement. For the second approach, which equalizes the SDR to the net rate of return, the scale factor--the opportunity cost of public investment--must be quantified. The opportunity cost of public investment depends on whether resources come from private investment or consumption and on the calculation of the present value of the future consumption yielded by a unit of capital discounted at the net rate of return; that is, the shadow price of capital. As Lind (1997) points out, however, there is no general agreement on a specific procedure for calculating the shadow price of capital. Indeed, the concept of the opportunity cost of public investment suffers the same project dependence problem as the first view of the SDR (Diamond 1968).

   Multigeneration projects such as nuclear waste disposal, natural resource conservation, or even Social Security reform further complicate discount rate choice. Specifically, intergenerational equity, in addition to intertemporal efficiency, plays a role in determining the appropriate social discount rate for multigeneration public project evaluation. (4) As in the single-generation context, there are two competing views on the appropriate discount rate when evaluating multigeneration projects: the descriptive and the prescriptive approaches. (5)

   The descriptive approach to discounting is a market-based approach. It does not rely on an explicit social welfare function (SWF) or the pure time preference rate embedded in the SWF. However, the descriptive approach works under the assumption that intergenerational compensation through changes in the tax/debt policy is available. (6) It is argued that, under appropriate intergenerational compensation, the market rates of return are still relevant for calculating the SDR for multigeneration project evaluation, and, in general, the SDR should be a weighted average of the gross and net rates of return. This descriptive view of setting the SDR equal to the market return appears to underlie the Office of Management and Budget's (OMB) adoption of 7% as the appropriate discount rate for federal programs. (7)

   The intent of the prescriptive approach is to use the social discount rate as an expression of ethical judgment on how consumption of future generations should be compared to consumption of current generations. The starting point of the prescriptive approach is a social welfare function or the pure time preference rate embedded in the SWF. (8) The prescriptive approach is based on the widely accepted principle that if the full impacts of a project's costs and benefits are expressed as net additions to each generation's consumption, then the appropriate discount rate should be the social rate of time preference (SRTP), expressed as the sum of the pure rate of time preference and the product of the elasticity of marginal utility with respect to consumption and the growth rate of per capita consumption. If one believes that future generations' utility should weigh as much as the current generations', the pure rate of time preference is zero. The remaining growth component yields an SRTP in the range of 1.5% to 3.0% if one assumes the growth rate of per capita consumption to be 1% to 2% and the elasticity of marginal utility with respect to consumption to be 1.5. The prescriptive approach is adopted by the Congressional Budget Office (CBO), which requires converting all costs and benefits to consumption units and then applying an SRTP of 2%. (9)

   Emphasizing the difference between the respective discount rates suggested by the two approaches misses the point, as what is discounted is different in the two approaches. (10) The descriptive approach discounts the direct costs and benefits of a project. In contrast, the prescriptive approach discounts the project's net incremental consumption to each and every generation. The two approaches are not necessarily inconsistent, but to date, there are problems with both approaches. First, for the descriptive approach, when taxes falling on capital income drive a wedge between these two returns, it is not clear whether the gross or the net rate of return is the appropriate discount rate. Though it may be argued that the appropriate discount rote should be a weighted average of gross and net rates of return, it is still a point of debate how these weights can be practically determined. Second, although the prescriptive approach using the SRTP to discount converted consumption flows of a project is theoretically sound, it is difficult to apply because there is no general procedure to translate the direct cost--benefit stream of a project into net additions to each generation's consumption. Moreover, there is always the question of what exactly the pure time preference rate is.

   In this article, we generalize the existing descriptive approach to multigeneration public project evaluation, taking into account distortionary taxes on capital income. We show that such a generalization does not lead to a project-specific SDR, which is the weighted average of gross and net rates of return. What emerges is the concept of the marginal cost of public funds (MCF), which has the convenient property of project independence. In a sense, the approach to multigeneration project evaluation presented here can also be regarded as a generalization of the MCF approach to public project evaluation developed in the static setting. Thus, this article connects the two separate literatures on public project evaluation: MCF and SDR. (11) In addition to the key parameter (the MCF) being project-independent, another desirable feature of the MCF-based approach is that it identifies projects that, along with appropriate intergenerational transfers through time-varying head taxes, are Pareto improving, and is, therefore, independent of any utilitarian social welfare function being used. Thus, our approach allows a clean separation between two related, but distinct, issues that arise in literature concerned with the SDR in a multigeneration context. On one hand, it is argued that the SDR should reflect the value placed on the welfare of future generations. On the other hand, it is argued that the SDR should reflect tax distortions, notably distortions of intertemporal decision-making arising from capital income taxes. Availability of time-varying head taxes essentially eliminates the first of these considerations and focuses attention on the second.

   Our analysis yields two primary conclusions that qualify how the social discount rate is used in evaluating multigeneration projects. First, the central role played by the SDR in long-term project evaluation should be replaced with parameters of the marginal cost of funds. Second. for the typical cases where the MCF is larger than one and projects incur costs before they generate benefits, the value of the traditional social discount rate will be larger than the gross return. This higher discount rate exceeds the value currently in use, implying fewer long-term projects would be accepted using our criterion.

   We begin with a simple two-period overlapping generations model with multigeneration public projects financed by an intertemporal tax policy including a distortionary tax on capital income and time-varying head taxes. In section 3, we derive a criterion for evaluating new, small multigeneration projects that is based on the marginal cost of funds. The MCF role, which also holds for a life cycle with an arbitrary number of periods, is a generalization of the descriptive approach in the second-best environment. Two features of the generalized descriptive approach--project-independence and SWF-independence--are highlighted. Then, in section 4, we discuss the implications of the MCF-based criterion for the (traditional) concept of social discount rate. Finally, in section 5 we offer an estimate of the values of involved parameters and discuss extensions to alternative tax structures, followed by a concluding summary.

2. A Formal Framework for Multigeneration Project Evaluation

   Consider a simple overlapping generations (OLG) model in which individuals live two periods, earning wage income in period 1 by supplying a fixed amount of labor and retiring on savings in period 2. Neither the two-period life nor the fixed labor supply is crucial for obtaining our results, but working with an OLG model with few complications significantly simplifies exposition. Assume that...