OIRA Should Stop Calling a Tail a Leg

A social discount rate is not the shadow price of capital

I recently came across this amusing tweet from a Thomas Sowell fan account. I will quote it here in full:

"Abraham Lincoln once asked an audience how many legs a dog has if you count the tail as a leg. When they answered 'five,' Lincoln told them that the answer was four. The fact that you called the tail a leg did not make it a leg."

It sounds funny, but this pithy aphorism perfectly captures a common problem associated with regulatory analysis: namely, that it overlooks the opportunity cost of capital.

How can this obscure policy issue possibly be related to Lincoln’s insight?

If you ask federal regulators, they will probably tell you that their economic analysis does account for the opportunity cost of capital—or how invested resources would evolve through time with or without a government project. They will say it does so using a social discount rate. Usually that rate is seven percent.

But they are calling a tail a leg. In reality, their analyses ignore the opportunity cost of capital, because the social discount rate is used for an altogether different purpose.

The social discount rate serves as a social rate of time preference. It represents how much less weight a social planner places on future consumption, due to factors like impatience and diminishing marginal utility of consumption. It is not how one accounts for the opportunity costs of capital.

Technically, the proper way to account for the opportunity cost of capital in cost-benefit analysis (CBA) is through an altogether different method, using what’s called the “shadow price of capital,” which is an adjustment factor applied to the value of capital. Many economists agree that the shadow price method is the right one. This is not controversial among experts on discounting, although its implementation can appear tricky.

Lay observers and even some economists get confused because in finance, a discount rate is used to account for how capital would be employed in absence of a particular investment. But that’s only because financial analysis is a special case. CBA accounts for benefits and costs of many varieties, from environmental amenities to saved lives, not just cash flows like in finance. Some benefits in CBA are like capital, with monetary returns that can be reinvested. Others are more like consumption that is fleeting and temporary.

The opportunity cost of capital, as its name implies, applies only to capital. A social discount rate, meanwhile, is bluntly applied to all benefits and costs. Only in the special case where all benefits and costs are like cash would it be appropriate for the shadow price adjustment factor to be a discount rate. In all other cases, the shadow price of capital must be applied to capital only.  

Because the shadow price of capital is rarely used in CBA to adjust the value of investment created or displaced by government projects—only a social discount rate is—an implicit assumption in regulatory CBA is that only consumption, but not investment, is displaced by government efforts.

This is an absurd assumption. Regulations impact businesses most directly. Even when compliance costs primarily impact businesses’ operating expenses (as opposed to their capital expenditures), any increase in firm spending affects the firm’s savings deficit or surplus on the margin, which has a spillover effect on capital markets, and hence, on investment.

The assumption that regulation has absolutely no effect on investment is also not borne out in the empirical data. Only in the extreme scenario that government regulation would have no impact on investment whatsoever would it be appropriate to forgo the use of a capital shadow price, as the government does as a routine practice.

Some economists want to use a higher discount rate than the social rate of time preference as a means to account for the opportunity cost of capital. This is the approach, for example, taken in foundational government guidelines issued by the Office of Information and Regulatory Affairs (OIRA) in 2003. If pressed, these economists acknowledge their discount rate approach is theoretically unsound, but they think it’s unrealistic that agencies will adopt any kind of shadow pricing method, either because it’s counterintuitive or because it’s too hard to implement.

People are used to thinking of costs as what is spent. The shadow price method is counterintuitive because it means that the true cost to society of spending one dollar is usually greater than one dollar, so costs have to be adjusted upwards accordingly.

Even if it is counterintuitive, the shadow price method is still the right one. A higher social discount rate does nothing to correct an analysis that ignores the opportunity cost of capital. The social discount rate serves an altogether different purpose, remember. A higher social discount rate simply wipes out the relevance of some benefits and costs in the future. The opportunity cost of capital is still ignored with a higher social discount rate if no capital shadow price is applied to investment.

Nor might the shadow price method be as hard to apply as many seem to think. Keep in mind that financial analysis is in fact a form of the shadow price method, and in that special case, the shadow price of capital can be expressed using a discount rate. Thus, the discount rate in cash flow analysis provides insights into how we should think about the shadow price for capital more generally. It is an annual rate of return forgone when embarking on a project. 

OIRA’s 2003 guidelines have added to the confusion between the social discount rate and this shadow price of capital rate. While those guidelines are strong in some areas, the specific recommendations on discounting have encouraged deeply flawed analytical practices to spread and become ingrained at federal regulatory agencies.

It’s time that OIRA updated its guidelines and acknowledged its mistake. OIRA should stop calling a tail a leg, in other words, because it is not a leg. The social discount rate is not the shadow price of capital.

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