Definitions

# Social discount rate

Social Discount Rate is a measure used to help guide choices about the value of diverting funds to social projects. It is defined as “the appropriate value of r to use in computing present discount value for social investments” . A social discount rate is sometimes denoted as SDR. Determining this rate is not always easy and can be the subject of discrepancies in the true net benefit to certain projects, plans and policies.

## Use In Cost Benefit Anaylsis

For example, it may be used in estimating the value of creating a highway system, schools, or forcing environmental protection. All of these things require a cost-benefit analysis where policy makers measure the social marginal cost and the social marginal benefit for each project. Almost all new policies will not even be considered until after a cost-benefit analysis has been completed. The social discount rate can appear in both calculations either as future costs such as maintenance or as future benefits such as reduced pollution emissions.

Calculating the true social marginal cost can be a lot easier than measuring the social marginal benefit. Because of the uncertainty involved with calculating benefits, problems may arise. Should you put a dollar amount on time based on average wages, contingent valuations or revealed preferences? One of the big problems today is putting a value on a life. While some might say that a life is priceless, economists usually state the value to be somewhere between three to ten million dollars . Another problem is the fact that a lot of the time the current generation will be paying for most of the costs while future generations will be reaping most of the benefit. Should we weight current and future benefits differently?

The proper discount rate should represent the opportunity cost of what else the firm could accomplish with those same funds . If that means that the money could be instead used to invest in the private sector that would yield 5% and that is the next best alternative for using that money then 5% would be the social discount rate. The government uses a variety of discount rates but something around seven percent is what the Office of Management and Budget (OMB) recommends for a pretax rate of return on private investments.

## How To Calculate

The SDR is directly analogous to concepts found in corporate finance such as the hurdle rate or the project appropriate discount rate; so the mathematics are identical. The benefit or cost per dollar can be calculated by

$\left(1/\left(1+r\right)^t\right)$

where r equals the SDR and t equals time. For benefits or costs that have no end it is just

$\left(1/r\right)$

A higher SDR makes it less likely a social project will be funded. A higher SDR implies greater risk that the benefits of the project will be reaped. A small increase in the social discount rate can matter enormously for benefits far into the future so it is very important to be as accurate as possible when choosing which rate to use.

## Differences Between Private And Social

But there are a number of qualitative differences between social and corporate discount rate and evaluation of projects associated with them. Of course, the governance of social project funding is different, because estimating the benefits of social projects requires making ethically subtle choices about the benefits to others.

For example if we presume that a meteor will wipe all life in a few years the SDR is very high, or alternately if we presume that the population will have many new and wonderful choices capturing benefits (i.e. they will be more wealthy) in the future that too raises the SDR of creating any given benefit. For example, choices about the SDR of environmental protection projects, such as funding the reduction of global warming, place a greater valuation on future generations.

## Importance In Global Climate Changes

This topic has recently been very controversial and highly debated. Since there is such a strong probability that the world will suffer significantly in the future due to global change in temperature, finding the correct social discount rate for the benefits of reducing CO2 emissions and other harmful greenhouse gases, is very important.
"The choice of an appropriate social time discount rate has long been debated. Some very intelligent people have argued that giving future generations less weight than the current generation is “ethically indefensible.” Other equally intelligent people have argued that weighting generations equally leads to paradoxical and even nonsensical results."

The range in the social discount rate for a cost-benefit analysis in this issue range from zero to over 3 percent. Some argue that the only reason for discounting future generations is that these generations might cease to exist in the future. Thus the rate should equal zero since the probability for such a catastrophic event is so low (assumed to be .01 percent per year) . This infers that there is equal weight given to all generations. The Stern Review on the Economics of Climate Change is one such report that argues for zero discounting of future generations. While William D. Nordhaus of Yale

"examines a model of climate change that is similar to the one used in the Stern Review but with a 3 percent social discount rate that slowly declines to 1 percent in 300 years rather than the 0.1 percent discount rate used in the Stern Review. In his model, the welfare of future generations is given less weight than the current generation’s welfare. He finds that preventive measures like a tax on carbon emissions are certainly required. But they are of a much smaller magnitude than those recommended in the [Stern] report.

The problem with these discrepancies in the social discount rate is that they greatly effect the outcome of a cost-benefit analysis. There is an agreed consensus that if we do not do something to stop the overall warming of the globe, there will be drastic effects on GDP but we do not know what is the optimal amount that we should invest to try to stop this trend in climate change.