OPTIMAL GROWTH, GENUINE SAVINGS AND LONG‐RUN DYNAMICS
| Date | 01 May 2008 |
| Published date | 01 May 2008 |
| DOI | http://doi.org/10.1111/j.1467-9485.2008.00451.x |
| Author | Simone Valente |
OPTIMAL GROWTH, GENUINE SAVINGS
AND LONG-RUN DYNAMICS
Simone Valente
n
Abstract
Green accounting theories have shown that negative genuine savings at some point
in time imply unsustainability. Consequently, recent studies advocate the use of the
genuine savings measure for empirical testing: a negative index implies that
sustainability be rejected. However, this criterion cannot ascertain sustainability,
because positive current genuine savings do not rule out genuine dissaving in the
future. This paper derives a one-to-one relationship between the sign of long-run
genuine savings and the limiting condition for sustained utility in the capital-
resource growth model, assuming technical progress and resource renewability.
This result suggests to extend the genuine saving method to include a test of the
limiting condition: if this condition is empirically rejected, positive current genuine
savings are delivering a false message.
I Intro ductio n
Defining suitable criteria for testing sustainability is a major goal for theoretical
research on economic growth and resource economics. In recent literature,
sustainable development is defined as a path along which utility does not exceed
the maximum level that can be sustained forever by the economy (Pezzey, 1992).
Building on this notion, a number of studies advocate the use of the genuine
saving criterion for testing sustainable development empirically (e.g. Atkinson et
al., 1997; Hamilton and Clemens, 1999; Neumayer, 1999). This criterion consists
of evaluating, at a given point in time, an environmentally adjusted measure of
savings which represents the difference between aggregate investment in
produced assets and the value of net depletion of natural resources (Pearce
and Atkinson, 1993; Pearce et al., 1996): a negative value of genuine savings is
held to imply unsustainability. The rationale for this criterion is provided by the
literature on green accounting: several authors studied the properties of the
genuine saving measure in capital-resource models – i.e. optimal growth models
where aggregate output is produced by means of natural resources, and the
consumption time-path is determined by the Keynes–Ramsey rule (Asheim and
Weitzman, 2001). In this framework, Pezzey (2004) has shown that negative
n
Center of Economic Research, ETH Zurich.
Scottish Journal of Political Economy, Vol. 55, No. 2, May 2008
r2008 The Author
Journal compilation r2008 Scottish Economic Society. Published by Blackwell Publishing Ltd,
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genuine savings at any point in time imply unsustainability, under very general
conditions.
A problem with this method is that the genuine saving criterion cannot
ascertain sustainable development. Positive current genuine savings are not
sufficient for sustainability, as noted by Asheim (1994) and Vellinga and
Withagen (1996). In particular, genuine savings may be positive even for long
intervals in economies where consumption is bound to decrease in the long run.
Consequently, the sign of current genuine savings might deliver a false message
at the empirical level: even if genuine savings are positive in the present, there is
no guarantee that utility can be sustained in the future. The false-message
problem is a critical issue with respect to empirical testing, because a major aim
of applied methods is to check whether present economies satisfy the conditions
for obtaining non-declining welfare in the future. Because the sign of current
genuine savings may be misleading in this regard, additional criteria are needed
in order to test sustainability in a forward-looking manner.
This paper addresses the problem at the theoretical level, and studies
necessary and sufficient conditions for obtaining positive genuine savings in the
long run. The analysis uses an extended version of the capital-resource growth
model (Dasgupta and Heal, 1974; Stiglitz, 1974) including positive rates of
technical progress and natural regeneration. In this setup, long-run utility is
non-declining if a precise limiting condition is satisfied, i.e. if the sum of the rates
of resource regeneration and technical augmentation are at least equal to the
utility discount rate (Valente, 2005).
The main result of this paper is that there exists a one-to-one relationship
between the limiting condition and the sign of long-run genuine savings: if the
sum of the rates of resource regeneration and augmentation exceeds (falls short
of) the utility discount rate, long-run genuine savings are positive (negative).
From the theoretical standpoint, this result extends previous findings of the
recent literature on green accounting (Pezzey, 2004; Hamilton and Hartwick,
2005). From an empirical perspective, testing the limiting condition for genuine
dissaving may detect possible false messages, and more generally, provides a
forward-looking criterion upon which sustainability tests can be built.
The structure of the paper is as follows: Section II lists basic definitions used
in the analysis and briefly summarises the state of the art; Section III presents the
theoretical model and derives the main results; and Section IV concludes.
II Sustainabilit y and Ge nuine Savings
Basic definitions
Sustainable development
Following Pezzey (1992), sustainable development is defined as a path along
which utility never exceeds the maximum level that can be sustained forever. In
the present context, instantaneous social welfare is represented by the ordinal
utility function u(c), where cis consumption. This notion of sustainability is
quite general, and can be related to the alternative definition of ‘forever non-
declining utility’ as follows: because cis scalar and instantaneous welfare at time
GENUINE SAVINGS AND LONG-RUN DYNAMICS 211
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