gamma discounting and expected net future value recent research suggests that the long term future should be discounted with a declining discount rate one such line of research exemplified by weitzman gamma discounting amer econ rev 91 2001 261 271 shows that the certainty equivalent discount rate is declining when future capital productivity is uncertain however in a recent paper gollier maximising the expected net future value as an alternative strategy to gamma discounting finan res lett 1 2004 85 89 puts forward a puzzle that casts doubt on the validity of this conclusion he asserts that using expected net future value rather than conventional expected net present value implies that the certainty equivalent discount rate increases over time this paper resolves the apparent puzzle by encompassing the models of gollier maximising the expected net future value as an alternative strategy to gamma discounting finan res lett 1 2004 85 89 and weitzman gamma discounting amer econ rev 91 2001 261 271 in fact gollier proves that as the evaluation date moves further into the future the discount rate at a given point in time will increase however given a particular evaluation date the schedule of discount rates is declining

beyond the stern review lessons from a risky venture at the limits of the cost benefit analysis this paper argues that debates amongst economists triggered by the stern review are partly relevant focusing on key parameters translating real ethical issues and partly misplaced in that they do not consider enough other determinants of climate change damages i the specifications of the utility function used for the assessments preference for the environment preference for smooth growth paths ii the interplay between uncertainty and the sequentiality of the decision and iii whether the growth engines behind the integrated assessment models can account for transient disequilibrium and sub optimality we derive some suggestions for any future research agenda in integrated assessment modelling whatever the position of the analysts about the relevance of the intertemporal optimisation framework and the bayesian approach to uncertainty in the climate affair

from malthusian stagnation to modern growth this paper investigates the historical evolution of the relationship among population growth technological change and standard of living the analysis focuses on two most important differences among the malthusian regime post malthusian regime and modern growth regime these were the behavior of income per capita and the relationship between the level of income per capita and the population growth rate the modern growth regime is characterized by steady growth in both income per capita and the level of technology in the malthusian regime technological progress and population growth was glacial by modern standards and income per capita was fairly constant in contrast to the modern growth regime the relationship between per capita income and population growth in the malthusian regime was positive post malthusian regime shared one characteristic with each of the two regimes in addition this paper developed and described an endogenous growth model consistent with the above mentioned transition process

anomalies in intertemporal choice evidence and an interpretation research on decision making under uncertainly has been strongly influenced by the documentation of numerous expected utility eu anomalies behaviors that violate the expected utility axioms the relative lack of progress on the closely related topic of intertemporal choice is partly due to the absence of an analogous set of discounted utility du anomalies we enumerate a set of du anomalies analogous to the eu anomalies and propose a model that accounts for the anomalies as well as other intertemporal choice phenomena incompatible with du we discuss implications for savings behavior estimation of discount rates and choice framing effects

risk adjusted gamma discounting abstract it is widely recognized that the economics of distant future events like climate change is critically dependent upon the choice of a discount rate unfortunately it is unclear how to discount distant future events when the future discount rate itself is unknown in previous work an analytically tractable approach called gamma discounting was proposed which gave a declining discount rate schedule as a simple closed form function of time this paper extends the previous gamma approach by using a ramsey optimal growth model combined with uncertainty about future productivity in order to risk adjust all probabilities by marginal utility weights some basic numerical examples are given which suggest that the overall effect of risk adjusted gamma discounting on lowering distant future discount rates may be significant the driving force is a fear factor from risk aversion to permanent productivity shocks representing catastrophic future states of the world

declining discount rates economic justifications and implications for long run policy should economic policy target immediate problems like malaria and aids or should it target climate change which may have even more dramatic life threatening effects in the very long term we discuss how the pattern of discount rates over the planning horizon bears on this important issue a declining pattern of discount rates is theoretically justified by uncertainty about future economic conditions and its shape and relevance can be estimated from historical data we analyse empirically long term interest rate data from nine countries construct a weighted average representing a possible global discount rate pattern for a very long range of future dates and assess its implications for the valuation of carbon mitigation policies christian gollier phoebe koundouri and theologos pantelidis

infrastructure investment a review essay economists try not to be faddists but they often cannot help themselves while work on a topic should mirror the prospective importance of the topic that situation seems to occur with disappointing frequency instead the usual pattern is that some reasonably important topic will be totally ignored for the longest time then recognized and then the subject of a flurry of work all out of proportion to its likely long run importance nowhere has this speculative bubble of economic research been more clearly illustrated than with infrastructure investment macroeconomists havelong felt that the stock of public capital is an important factor input in the production of total output macroeconomists have known that u s productivity growth slowed dramatically in about 1973 and macroeconomists should have known that united states investment in public capital has been down since the late 1960s yet analysis of the u s productivity slowdown completely ignored infrastructure investment for the first fifteen years of this slowdown concentrating instead on energy prices social regulation the composition of the work force research and development different rates of obsolescence of the private capital stock and any number of other matters the public capital stock was hardly ever even mentioned as a potential factor in the productivity slowdown aschauer changed all that he wrote a series of papers 1989a 1989b 1989c that put these two movements together econometrically infrastructure investment turned down and aggregate productivity turned down slightly later both in the united states and in some other developed countries his work hit the magic button those who had worried about the productivity puzzle for fifteen years welcomed a new suspect those who were worried about low rates of u s national saving welcomed a new way to make their argument even more forcefully than with official figures on saving and investment which do not count infrastructure investment as investment political liberals and liberal politicians saw a way to rescue government spending and projects from the assaults of reaganism and even a way to avoid oth

the social cost of carbon and its policy implications the shadow price or social cost of carbon is an important indicator of the global incremental damage done by emitting greenhouse gases today cost benefit analysis would set the optimal amount of greenhouse gas emission reduction at the point where this social cost just equals the incremental cost of controlling emissions the higher the value for the social cost of carbon the more control is warranted this comparison assumes that cost benefit analysis is the correct way of determining climate change policy and many believe this is not the case because of the very long term irreversible and potentially catastrophic nature of global warming but in the short run at least a comparison of cost and benefits is required and in any event all decisions imply costs and benefits but what is the right figure for the social cost of carbon this paper reviews the uk government s assessment of the cost and concludes that it has been set far too high because of a misreading of the integrated assessment models used to balance costs and benefits moreover adoption of the uk government s shadow price would have formidable implications for energy policy in the uk and for policies on afforestation copyright 2003 oxford university press

why the far distant future should be discounted at its lowest possible rate abstract a critical feature of the distant future is currently unresolvable uncertainty about what will then be the appropriate rate of return on capital to use for discounting this paper shows that there is a well defined sense in which the lowest possible interest rate should be used for discounting the far distant future part of any investment project some implications are discussed for evaluating long term environmental projects or activities like measures to mitigate the possible effects of global climate change

public investment in infrastructure in a simple growth model abstract in this paper we examine the implications for capital accumulation when infrastructure enters as an external input into private production functions in our model infrastructure is nonexclusive but may exhibit varying degrees of nonrivalry revenues from uniform taxes on capital and labor income are used to finance public investment in infrastructure we show that the optimal tax rate is independent of the degree of nonrivalry when production exhibits constant returns to augmentable factors the equilibrium displays constant growth for most parameters the growth rate depends on the population size under decreasing returns the optimal trajectory exhibits monotonic convergence to a steady state level

the social discount rate what discount rate should be applied to social investments it is standard to use the market interest rate thereby respecting private preferences we show that application of this revealed preference criterion rests on faith not on logic it is justified only if preferences over all choices including past choices are time invariant the conditions for this to be true are stringent under more reasonable conditions policy makers should be more patient than private citizens whose choices define the most short sighted pareto optimum

time horizon and the discount rate abstract we consider an economy a la lucas 1978 econometrica46 1429 1446 with a risk averse representative agent the exogenous growth rate of the economy follows a random walk we characterize the set of utility functions for which it is efficient to discount more distant cash flows at a lower rate the benchmark result is that when the growth rate is almost surely nonnegative the yield curve is decreasing if and only if relative risk aversion is decreasing with wealth relaxing the assumption on the absence of recession requires more restrictions on preferences such as increasing relative prudence journal of economic literature classification numbers d81 d91 q25 q28

numerical analysis of non constant pure rate of time preference a model of climate policy abstract when current decisions affect welfare in the far distant future as with climate change the use of a declining pure rate of time preference prtp provides potentially important modeling flexibility the difficulty of analyzing models with non constant prtp limits their application we describe and provide software available online to implement an algorithm to numerically obtain a markov perfect equilibrium for an optimal control problem with non constant prtp we apply this software to a simplified version of the numerical climate change model used in the stern review for our calibration the policy recommendations are less sensitive to the prtp than widely believed

on the electricity shortage price and electricity theft nexus abstract pakistan is facing severe electricity shortfall of its history since 2006 several measures have been implemented in order to mitigate electricity shortage the focus has been on raising the installed capacity of electricity generation and transmission the present policy results in expensive thermal electricity generation mostly using expensive and environmentally hazardous furnace oil and inability of utilities to recover their cost of supply although there is unprecedented rise in electricity tariffs this study concentrates on the electricity demand and traces the relationship between electricity shortfalls tariff rate and electricity theft in the background of recent electricity crisis using the data for the period 1985 2010 we employed the granger causality test through error correction model and out of sample causality through variance decomposition method empirical evidence shows that electricity theft greatly influences electricity shortfalls through lowering investment and inefficient use of electricity the study concludes that electricity crisis cannot be handled without combating rampant electricity theft in the country

discount rate and the social cost of carbon dioxide a korean forecast this paper is to forecast the korean long term social discount rate of carbon dioxide sdrc and the social cost of carbon dioxide scc it is estimated using the ramsey function savings behavior

ramsey meets laibson in the neoclassical growth model the neoclassical growth model is modified to include a variable rate of time preference with no commitment ability and log utility the equilibrium features a constant effective rate of time preference and is observationally equivalent to the standard model the extended framework yields testable linkages between the extent of commitment ability and the rates of saving and growth the model also has welfare implications including the optimal design of institutions that facilitate household commitments steady state results are obtained for general concave utility functions and some properties of the transitional dynamics are characterized for isoelastic utility

population technology and growth from malthusian stagnation to the demographic transition and beyond this paper develops a unied growth model that captures the historical evolution of population technology and output it encompasses theendogenous transitionbetween three regimes that have characterized economic development the economy evolves from amalthusianregime wheretechnologicalprogressis slow andpopulationgrowthprevents anysustainedriseinincomepercapita intoapost malthusianregime wheretechnological progress rises and population growth absorbs only part of output growth ultimately a demographic transition reverses the positive relationship between income and population growth andtheeconomyentersamoderngrowthregimewithreducedpopulationgrowth

public infrastructure non cooperative investments and endogenous growth two countries strategically invest in productive infrastructure within a general equilibrium model with endogenous growth these public investments generate externalities dynamic analysis reveals that 1 under constant returns the two countries growth rates differ during the transition but are identical on the balanced growth path 2 a country with decreasing returns can experience sustained growth provided that the other country grows at a positive constant rate 3 cooperation does not necessarily lead to higher growth for each country and it can increase or decrease the gap between countries growth rates depending on the countries consumption preferences regarding domestic and foreign goods comportements non cooperatifs en matiere d investissement dans les infrastructures publiques et croissance endogene deux pays investissent strategiquement dans des infrastructures productives au sein d un modele d equilibre general avec croissance endogene ces capitaux publics generent des externalites l analyse dynamique revele que 1 quand les rendements sont constants les taux de croissance des deux pays different au cours de la transition mais sont identiques sur le sentier de croissance equilibree 2 un pays avec des rendements decroissants peut connaitre une croissance soutenue a condition que l autre croisse a un rythme constant positif 3 la cooperation ne conduit pas necessairement a une croissance plus elevee pour chaque pays et elle peut augmenter ou diminuer l ecart des taux de croissance entre les pays en fonction des preferences

the impact of climate change on the balanced growth equivalent an application of fund the stern review added balanced growth equivalents bge to the economic climate change research agenda we first propose rigorous definitions of the bge for multiple regions and under uncertainty we show that the change in the bge is independent of the assumed scenario of per capita income for comparable welfare economic assumptions as the stern review we calculate lower changes in bge between a business as usual scenario and one without climate impacts with the model fund than the stern review found with the model page we find that mitigation policies give even lower changes in bge and argue that those policy choices should be the focus of the research effort rather than total damage estimates according to our results the current carbon tax should be below 55 tc sensitivity analyses show that the stern review chose parameters that imply high impact estimates however for regionally disaggregated welfare functions we find changes in bge that are significantly higher than the results from the stern review both for total damage as for policy analysis with regional disaggregation and high risk aversion we observe fat tails and with that very high welfare losses

ethics of the discount rate in the stern review on the economics of climate change any comparison of the costs and benefits of climate change is dominated by the chosen discount rate but although the stern review emphasises the ethical nature of the parameters entering into its choice of a relatively low discount rate its discussion of the pure time preference parameter is unbalanced in particular no consideration is given to the role of agent relative ethics which i has a wellestablished philosophical pedigree going back to david hume ii is likely to correspond closely to world wide public attitudes towards intergenerational welfare and iii would entail discounting a unit of welfare accruing to future generations compared to an equal unit accruing to people alive today at a positive rate the authors also discuss the other ethical parameter upon which the discount rate depends namely the elasticity of marginal utility with respect to consumption in the conventional model this simultaneously reflects different aspects of inequality aversion as well as risk aversion which complicates its interpretation finally they discuss the divergence between market rates of discount and the low rate chosen in the review and the limitations on the one hand on the normative significance of market rates as well as the danger on the other hand of relying on rates chosen by elites or philosopher kings

valuing the future one of the most controversial areas of economics is the practice of discounting attaching a lower weight to future costs and benefits than present costs and benefits discounting appears to offend notions of sustainable development and the interests of future generations recent advances in the theory of discounting hold out strong hope that the tyranny of discounting can be avoided through the use of time varying discount rates tvdrs this paper reviews the recent rationales for tvdrs and applies the results to issues such as nuclear power and global warming control

declining discount rates the long and the short of it the last few years have witnessed important advances in our understanding of time preference and social discounting in particular several rationales for the use of time varying social discount rates have emerged these rationales range from the ad hoc to the formal with some founded solely in economic theory while others reflect principles of intergenerational equity while these advances are to be applauded the practitioner is left with a confusing array of rationales and the sense that almost any discount rate can be justified this paper draws together these different strands and provides a critical review of past and present contributions to this literature in addition to this we highlight some of the problems with employing ddrs in the decision making process the most pressing of which may be time inconsistency we clarify their practical implications and potential pitfalls of the more credible rationales and argue that some approaches popular in environmental economics literature are ill conceived finally we illustrate the impact of different approaches by examining global warming and nuclear power investment this includes an application and extension of newell and pizer discounting the benefits of climate change mitigation how much do uncertain rates increase valuations journal of environmental economics and management 46 2003 52 to uk interest rate data