Stochastic Productivity of Investment as Basis for Discounting

Investment is often productive in the sense of giving back over time a total product larger or more valuable than the invested resources. In brief, investment often has a positive net marginal product.

There are three fundamental and inter-related characteristics of the net marginal product of investment (MPI) that may be summarized in three “Ps”: it is protracted, probabilistic and positive. It is protracted in the sense that it can be realised only through time. Every real investment starts by using up valuable resources, and gives back a stream of benefits spread over several future periods.

MPI is also probabilistic or risky or uncertain. It may be positive, negative or zero in the sense that the value of MPI over time may be less, more, or just equal to the resources used up in investment.

But even though the net MP of any single investment is uncertain and may turn out to be negative, its expected value is usually positive. Investment, though always risky, has on the average a positive net marginal product.

These characteristics of MPI mean that resources received earlier have the opportunity to be invested longer, and hence are potentially more productive on the average. This justifies discounting future benefits and costs as long as they are exchangeable into investible resources and the opportunity to invest them does really exist. The benefits and costs of most investments are such that the logic of discounting applies to them, but this need not be always true as we shall show below.

Discounting, thus viewed, is an application of the concept of opportunity cost of investing resources over time. It stands to reason that the extent of discounting (or the magnitude of the discount factor) should be related to the marginal product of other possible investments having a similar degree of uncertainty.

a. When Not to Discount

It is possible to find exceptional cases where the justification for discounting is lacking. One such case is the lack of suitable investment opportunities because of international or local institutional factors. In some oil countries, for instance, an extra barrel of oil produced now (whose proceeds had to be hoarded or put into dubious investments) is not more productive than a barrel produced later, when institutional changes favourable to effective investment would have been achieved. For such countries it would be reasonable not to discount future proceeds of oil production, or even to apply negative discounting whereby future proceeds are inflated instead of discounted.

Another case emerges when the output of a proposed investment is not conceptually exchangeable into investible resources. For instance:

1. A mosque where the number of people attending or praying is one measure of output,
2. A hospital or a health unit whose output is the number of people relieved from a certain pain,
3. A road improvement to reduce fatal accidents (i.e. save so many lives per year).

The costs of investment in all three cases should be subject to discounting because they can be used elsewhere in the economy. But it is not clear why the benefits of such projects should be discounted. Are ten persons relieved from pain (or provided prayer space) twenty years from now less “valuable” than the same number provided the same benefits next year?

Source: Fiscal Policy and Resource Allocation in Islam, Ziauddin Ahmed, Munawar Iqbal and M. Fahim Khan. Republished with permission.