Declining Discount Rates: Evidence from the UK

1 Introduction

The discussion of discounting in Cost Benefit Analysis (CBA) has come to the fore once more as
policy makers are increasingly required to appraise investments whose costs and benefits accrue
in the far distant future. Climate change and nuclear build exemplify this long-term policy
arena. Largely in response to the dramatic effects of conventional exponential discounting on
welfare changes in the distant future, the discussion has turned to discount rates that decline
with the time horizon, Declining Discount Rates or DDRs, and there is now an evolving body of
theory.¹ For example, Weitzman (1998) shows that uncertainty and persistence of the discount
rate itself provides a rationale for DDRs and of all the theoretical approaches this approach has
proven more amenable to implementation, mainly because the informational requirements stop
at the characterisation of the uncertainty surrounding the discount rate.² In this respect, Newell
and Pizer (2003) (N&P, henceforth) characterise interest rate uncertainty by the parameter
uncertainty typically encountered in any econometric model. Their model of US interest rates,
though simple, yields a working definition and estimation of the Certainty Equivalent forward
Rate (CER) for use in CBA. The authors confirm the declining pattern of discount rates and
its relation to uncertainty and persistence.

Our view in this paper is that such a simple model is not sufficiently versatile to reproduce
the empirical regularities typically found in interest rate series. Our aim therefore is to develop
relatively simple econometric models that characterize the past as accurately as possible and
offer a flexible framework for the future due to their time-heterogeneity properties. We discuss
the in-sample properties of alternative econometric models for the UK interest rates, comment
on the properties of the simulated distribution and finally select among them based on their
out-of-sample forecasting performance. We exemplify the policy relevance of DDRs and model
selection with two UK case studies with long-term impacts: the value of carbon sequestration
and the appraisal of nuclear build.

2 Discounting and interest rate models

Discounting future consequences in period t back to the present is typically calculated using
t

the discount factor Pt, where Pt = exp(-   ri). When r is stochastic, the expected discounted

i=1

value of a dollar delivered after t years is:

Following Weitzman (1998) we define (1) as the certainty equivalent discount factor, and the
corresponding certainty-equivalent forward rate for discounting between adjacent periods at
time t as equal to the rate of change of the expected discount factor:

where ret is the forward rate from period t to period t +1 at time t in the future.

Our focus is on the determination of the stochastic nature of re_t through the observed dy-
namics of the process. Our starting point is the relatively simple AR(p) model employed by
N&P, specified as follows:

^p

rt = η + et,     et =    aiet-i + ξ_t

i=1

¹ See e.g. Pearce et al. (2003) and the references therein for a detailed discussion of the DDR literature.

² For example, the informational requirements do not extend to specific attributes of future generations’ risk
preferences as would be unavoidable in the case of Gollier (2002a, 2002b).

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