### Discussion Paper

## Abstract

In this paper, we elaborate on an idea initially developed by Weitzman (1998) that justifies taking the lowest possible discount rate for far-distant future cash flows. His argument relies on the arbitrary assumption that when the future rate of return of capital (RRC) is uncertain, one should invest in any project with a positive expected net present value. We examine an economy with a risk-averse representative agent facing an uncertain evolution of the RRC. In this context, we characterize the socially efficient stochastic consumption path, which allows us in turn to use the Ramsey rule to characterize the term structure of socially efficient discount rates. We show that Weitzman’s claim is qualitatively correct if shocks on the RRC are persistent. On the contrary, in the absence of any serial correlation in the RRC, the term structure of discount rates should be flat.

Paper submitted to the special issue “Discounting the Long-Run Future and Sustainable Development”

## Comments and Questions

The paper's purpose is to link that ENPV rule and the ENFV rule in the determination of the term structure of the discount rates. The two approaches are linked with the help of an optimal growth model with an AK production function, where the productivity of capital is stochastic. ...[more]

... It is shown that in the context of the model both the NPV and the FV approaches lead to the same results. (On page 9 it should read . and the future value formula (12) are right, .).

I found the paper interesting and I recommend publication.

My major comment relates to the modeling of the productivity parameter. In section 3.2 it is assumed that the productivity parameter θ, is i.i.d. How would the results be affected if the productivity term follows a well specified stochastic process? What would be the impact of a concave production function?

The paper reconsiders the well-known Weitzman (1998) result that long-run discounting should take place at the lowest possible rate by developing a simple model of intertemporal utility maximizing behavior with uncertain returns on capital. Weitzman’s result is derived in a situation in which all uncertainty about the return on capital ...[more]

... is resolved immediately after the investment has taken place if utility is logarithmic. This suggests strongly that Weitzman’s result is not a general one but is better interpreted as an (interesting) special case. Next, the author discusses a model in which the rate of return on capital follows a random walk. In that setting the term structure of the social rate of discount is flat. This show’s that – in the setting of this paper - Weitzman’s result depends on the serial correlation of the shocks in the rate of return on capital. Permanent shocks and a random walk can be considered as extremes.

The paper is well written and concentrates on the precise statement and derivation of formal results. It succeeds admirably in this respect.

Many readers would appreciate a bit more discussion about the implications of the results. Is there relevant empirical evidence on the value of the index of relative risk aversion? And about the serial correlation in the rate of return on capital?

Minor

- Last line of page 4: transfers that are explicit?

- Halfway page 9 starts a new paragraph: It must be stressed …formula (10)and the future value formula (10) ….?

- Page 12, 9 lines before the start of section 4: sets of assumptions ?

A very clear treatment of the "Weitzman-Gollier puzzle". Pedagogically describes issues concerning the term structure of discount rates in the long run. See further attached note.

see attached file