The Shadow Price of Capital: Accounting for Capital Displacement in Benefit–Cost Analysis

Circular A-4 (OMB 2003) is a guidance document that provides recommendations for federal agencies on how to conduct benefit–cost analysis (BCA), such as Regulatory Impact Analysis (RIA), including discounting future impacts depending on when they occur. Circular A-4 recommends two discount rates to adjust estimated future costs and benefits to present-day equivalents: 3 and 7 percent. The 3 percent consumption discount rate is meant to reflect the discount rate applicable to impacts on individual households (as measured by their consumption), with individuals being the ultimate concern of economic welfare analysis. In contrast, the 7 percent investment rate of return—which is sometimes called the “opportunity cost of capital”—is meant to reflect that costs may displace capital investment, which has a higher rate of return than the consumption rate due to taxes, risk, and other factors.However, Circular A-4 notes that the economic literature has shown that the “analytically preferred” method to account for the higher investment rate of return is instead to use the “shadow price of capital” (SPC) approach, in which costs displacing capital investments are converted to consumption-equivalent values. Once all impacts are measured consistently in terms of consumption, all costs and benefits are appropriately discounted at the consumption discount rate. “Analytically preferred” is another way of saying “welfare based,” meaning consistent with maximizing the well-being of households, as measured by their consumption over time.Nonetheless, the analytically preferred SPC approach is rarely used in practice. Instead, federal BCAs typically include a sensitivity case that discounts all costs and benefits at the investment rate of return, currently set at 7 percent by Circular A-4, with the intention that the use of the investment rate serves as a simplified way to account for capital displacement. This issue brief explains why the discounting sensitivity case using a 7 percent investment rate of return is generally incorrect and can yield extremely misleading estimates of the costs and benefits of policies with long-lived impacts, such as climate change.Using an investment rate of return as one of the discount rate sensitivity cases is common practice in RIAs, but economists have demonstrated that it is only conceptually consistent with the analytically preferred SPC method under very restrictive and unrealistic conditions that are almost never satisfied (Li and Pizer 2021). Simply discounting benefits at an investment rate of return ignores the differences between the time pattern of the benefits and that of capital returns being displaced. That is, discounting future benefits at the investment rate of return to account for immediate cost impacts on capital investment mismeasures the value to households if those time patterns differ. This reflects well-known flaws in using investment rates of return to compare policy options, rather than an appropriate consumption discount rate. An appendix elaborates on why the traditional investment rate of return sensitivity case is incorrect.Recent work not only confirms that the longstanding approach of using a 7 percent discount rate is inconsistent with the welfare-based SPC approach but also shows that the degree of embedded inaccuracy tends to compound the longer the time frame of the policy being evaluated (Li and Pizer 2021). It is therefore particularly inaccurate for actions with long-term consequences, such as actions that reduce greenhouse gas emissions.Moreover, this issue brief explains how to move beyond the inconsistent but common practice of applying a 7 percent discount rate to address concerns about capital displacement. Instead, we show how the welfare-based SPC approach is simple to implement in practice, would not involve major changes in analytical procedures, and would simplify federal BCA by dispensing with multiple internally inconsistent discount rates within a given BCA. We demonstrate how one would implement this by re-evaluating the final RIA for the 2015 Clean Power Plan using the SPC framework and Circular A-4’s recommended 3 percent consumption discount rate. This demonstrates that the SPC approach would be simple to implement, account for concerns about capital displacement without resorting to the inconsistent 7 percent discount rate approach, and yield results not dramatically different from those reached by recently conducted RIAs where the time horizon is not particularly long.