it s not now or never implications of investment timing and risk aversion on climate adaptation to extreme events abstract public investment into risk reduction infrastructure plays an important role in facilitating adaptation to climate impacted hazards and natural disasters in this paper we provide an economic framework to incorporate investment timing and insurance market risk preferences when evaluating projects related to reducing climate impacted risks the model is applied to a case study of bushfire risk management we find that optimal timing of the investment may increase the net present value npv of an adaptation project for various levels of risk aversion assuming risk neutrality while the market is risk averse is found to result in an unnecessary delay of the investment into risk reduction projects the optimal waiting time is shorter when the insurance market is more risk averse or when a more serious scenario for climatic change is assumed a higher investment cost or a higher discount rate will increase the optimal waiting time we also find that a stochastic discount rate results in higher npvs of the project than a discount rate that is assumed fixed at the long run average level

declining discount rates in this paper we ask whether the us government should replace its current discounting practices with a declining discount rate schedule as the united kingdom and france have done or continue to discount the future at a constant exponential rate to address the question we briefly present the theoretical basis for a declining discount rate ddr schedule and focus on how in practice a ddr could be estimated for use by policy analysts we discuss the empirical approaches in the literature and review how the united kingdom and france estimated their ddr schedules we conclude with advice on how the united states might proceed to consider modifying its current discounting practices i the expected net present value approach to ddrs

productivity convergence in the european regions 1980 2003 a sectoral and spatial approach this article analyses the evolution of the eu productivity between 1980 and 2003 both across regions and sectors by making use of various techniques cross section nonparametric and spatial approaches it concludes that 1 the regional and sectoral dispersion of productivity is quite high 2 the gains experienced in aggregate productivity are due entirely to the sectors productivity growth effect 3 there is a weak beta convergence process at the aggregate and sectoral levels 4 the accounting decomposition of the aggregate productivity convergence process reveals the sectoral productivity growth effect to be the only responsible factor for regional catching up 5 finally there are clear signs of spatial dependence which when properly addressed increase the speed of convergence at the aggregate level

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

the ramsey discounting formula for a hidden state stochastic growth process the long term discount rate is critically dependent upon projections of future growth rates that are fuzzier in proportion to the remoteness of the time horizon this paper models such increasing fuzziness as an evolving hidden state stochastic process the underlying trend growth rate is an unobservable random walk hidden by noisy transitory shocks and recoverable only as a probability distribution via bayesian updating a simple expression is derived for the time declining ramsey discount rate the components of this hidden state ramsey discounting formula are then analyzed followed by a few remarks about possible implications and applications

long forward and zero coupon rates can never fall in frictionless markets having no arbitrage the asymptotic zero coupon rate never falls the same is true of the long forward rate the long par coupon rate can rise and fall due to forward rate movements at short maturities this article relates the three types of interest rates and formalizes and proves the impossibility results for falling asymptotic rates these results can be tested in a parametric term structure specification that is rich enough to identify a time series of long rates the results show that it is not possible to specify arbitrarily the long forward or zero coupon rate process copyright 1996 by university of chicago press

valuing the future recent advances in social discounting the perplexing issue of discounting prescriptive economics requires that unless there are very good reasons to the contrary economic policy should be based on the principle that individuals preferences should count indeed the entire body of welfare economics centres round the formal identity of the statement x prefers a to b and the statement x has higher welfare in a rather than b this combination of a seemingly innocuous and democratic value judgement preferences should count and a formal definition about the meaning of welfare improvement involves many complications the entire history of policy analysis focuses on those complications whose preferences should count over what time period what constitutes a legitimate attenuation of the basic value judgement one of the problem areas concerns timediscounting the process whereby society places a lower value on a future gain or loss than on the same gain or loss occurring now the rationale for time discounting follows logically from the basic value judgement of welfare economics if people s preferences count and if people prefer now to the future those preferences must be integrated into social policy formulation time discounting is thus universal in economic analysis but it remains as it always has controversial the controversy has a parallel in another form of discounting spatial discounting when translated into economic terms the ethical principle

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

drifting together or falling apart the empirics of regional economic growth in post unification germany the objective of this article is to address the question of convergence across german districts in the first decade after german unification by drawing out and emphasizing some stylized facts of regional per capita income dynamics we achieve this by employing nonparametric techniques which focus on the evolution of the entire cross sectional income distribution in particular we follow a distributional approach to convergence based on kernel density estimation and implement a number of tests to establish the statistical significance of our findings this article finds that the relative income distribution appears to be stratifying into a trimodal bimodal distribution

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

a one factor model of interest rates and its application to treasury bond options 1990 a one factor model of interest rates and its application to treasury bond options financial analysts journal vol 46 no 1 pp 33 39

term structure movements and pricing interest rate contingent claims this paper derives an arbitrage free interest rate movements model ar model this model takes the complete term structure as given and derives the subsequent stochastic movement of the term structure such that the movement is arbitrage free we then show that the ar model can be used to price interest rate contingent claims relative to the observed complete term structure of interest rates this paper also studies the behavior and the economics of the model our approach can be used to price a broad range of interest rate contingent claims including bond options and callable bonds

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

assessing the economic viability of alternative water resources in water scarce regions combining economic valuation cost benefit analysis and discounting abstract this paper demonstrates a comprehensive methodology for assessing the viability of an environmental management plan that has long run economic and ecological impacts the case study under consideration is the implementation of a water resource management plan in a water scarce region of the world namely cyprus specifically this plan proposes to replenish a depleting aquifer with treated wastewater the proposed methodology first identifies the key stakeholder groups farmers and the general public who are hypothesized to derive economic values benefits from implementation of this plan and then uses stated preference methods to capture the total economic value of these benefits benefits are aggregated over the relevant populations of these stakeholder groups and weighed against the total costs of implementing the plan in a long run cost benefit analysis cba an econometrically estimated time declining trajectory of discount rates is used for the cba in order to assess the long run sustainability of the plan the results reveal that the net benefit trajectory estimated with the time declining discount rate takes one and a half to three times as long to come to a plateau compared to the constant discount rates of 3 5 and 6 emphasizing the importance of using declining discount rates and capturing the entirety of the benefits generated by such plans this methodology is particularly recommended for providing much needed information to support the implementation of the eu water framework directive which advocates the use of cba with consideration of the notion of sustainability for achieving the good water status for all european waters

declining discount rates and the fisher effect inflated past discounted future uncertain and persistent real interest rates underpin one argument for using a declining term structure of social discount rates in the expected net present value enpv framework despite being controversial this approach has influenced both the inter agency working group on cost benefit analysis and the uk government s guidelines on discounting we first clarify the theoretical basis of the enpv approach then rather than following previous work which used a single series of u s treasury bond returns we treat nominal interest rates and inflation as co integrated series and estimate the empirical term structure of discount rates via the fisher effect this nests previous empirical models and is more flexible it also addresses an irregularity in previous work which used data on nominal interest rates until 1950 and real interest rates thereafter as we show the real and nominal data have very different time series properties this paper therefore provides a robustness check on previous discounting advice and updated methodological guidance at a time when governments around the world are reviewing their guidelines on social discounting the policy implications are discussed in the context of the social cost of carbon nuclear decommissioning and public health

discounting the distant future how much do uncertain rates increase valuations abstract we demonstrate that when the future path of the discount rate is uncertain and highly correlated the distant future should be discounted at significantly lower rates than suggested by the current rate we then use two centuries of us interest rate data to quantify this effect using both random walk and mean reverting models we compute the certainty equivalent rate that summarizes the effect of uncertainty and measures the appropriate forward rate of discount in the future under the random walk model we find that the certainty equivalent rate falls continuously from 4 to 2 after 100 years 1 after 200 years and 0 5 after 300 years at horizons of 400 years the discounted value increases by a factor of over 40 000 relative to conventional discounting applied to climate change mitigation we find that incorporating discount rate uncertainty almost doubles the expected present value of mitigation benefits

how certain are we about the certainty equivalent long term social discount rate theoretical arguments for using a term structure of social discount rates sdr that declines with the time horizon have influenced government guidelines in the us and europe the certainty equivalent discount rate that often underpins this guidance embodies uncertainty in the primitives of the sdr such as growth for distant time horizons the probability distributions of these primitives are ambiguous and the certainty equivalent itself is uncertain yet if a limited set of characteristics of the unknown probability distributions can be agreed upon sharp upper and lower bounds can be defined for the certainty equivalent sdr unfortunately even with considerable agreement on these features these bounds are widely spread for horizons beyond 75 years so while estimates of the present value of intergenerational impacts including the social cost of carbon can be bounded in the presence of this ambiguity they typically remain so imprecise as to provide little practical guidance

rational expectations econometric analysis of changes in regime an investigation of the term structure of interest rates abstract this paper is of interest both for its methodological contribution of new tools for analyzing rational expectations models and for its substantive conclusions concerning the term structure of interest rates during the monetary experiment of october 1979 the paper studies systems subject to changes in regime interpreted here as occasional discrete shifts in the parameters governing the time series behavior of exogenous economic variables the specification is shown to be quite tractable both theoretically and empirically the technique is used to analyze yields on three month treasury bills and ten year treasury bonds during 1962 to 1987 a constant parameter linear model for short term rates is shown to be inconsistent both with the univariate time series properties of short rates and with the observed bivariate relation between long and short rates under the expectations hypothesis of the term structure an alternative nonlinear model that admits the possibility of changes in regime affords a much better description of the univariate process for short rates moreover the cross equation restrictions implied by the expectations hypothesis of the term structure are consistent with the nonlinear specification indeed the residuals of the restricted relation have a standard error of only 0 8 basis points this is a third less than that of a completely unrestricted linear regression of long rates on short rates and compares with an unconditional standard deviation of long rates of 142 basis points i conclude that once the recognition by bond traders of changes in regime is taken into account the expectations hypothesis of the term structure of interest rates holds up fairly well for these data

valuing food store access policy implications for the food stamp program food stamp recipients may lack access to larger stores reducing the availability of nutritious food reliance on smaller stores may have undesirable impacts policy alternatives include limiting food stamp redemption to larger stores and subsidizing store development i estimate that limiting redemption to supermarkets and grocery stores or supermarkets alone results in losses ranging from 499 2 million to 1 05 billion or 1 17 billion to 2 44 billion respectively annual loss in food stamp recipient welfare nationwide the impact of improving access is also significant ranging from 333 6 million to 931 2 million

bond and option pricing when short rates are lognormal this article describes a one factor model for bond and option pricing that is based on the short term interest rate and that allows the target rate mean reversion and local volatility to vary deterministically through time for any horizon the distribution of possible short rates is lognormal so the rate neither falls below zero nor reflects off a barrier at zero a model like this allows one to match the yield curve the volatility curve and the cap curve surprisingly adding to future local volatility lowers the volatility curve a conventional binary tree with probabilities of 0 5 but variable time spacing is used to value bonds and options when the inputs are constant the slope of the yield curve starts out positive and ends up negative while its curvature shifts from negative to positive even when mean reversion is zero the volatility curve has a negative slope the differential cap curve rises steeply through the effects of volatility and then falls steeply through the effects of discounting and a falling forward rate used as the strike price

how should the distant future be discounted when discount rates are uncertain abstract the so called weitzman gollier puzzle is the fact that two seemingly symmetric and equally plausible ways of dealing with uncertain future discount rates appear to give diametrically opposed results the puzzle is resolved when agents optimize their consumption plans the long run discount rate declines over time toward its lowest possible value

determining the generalized discount rate for risky projects it is widely recognized that the evaluation of risky projects critically depends on how the riskiness of future benefits is treated standard discounting theories are based on the assumption that risks that are uncorrelated with aggregate risk are diversified so that projects idiosyncratic risk is not priced however this may not be true for long term risky projects such as those with persistent idiosyncratic shocks in this study we investigate the impact of both aggregate risk and nondiversifiable idiosyncratic risk on the discount rate for risky projects we extend the generalized discount rate to the case of persistent shocks a particular advantage of the generalized discount rate is that it can be applied in the setting of incomplete markets we show that nondiversifiable idiosyncratic risk reduces the discount rate and increases the present value of projects future uncertain benefits we further apply our findings to the evaluation of emissions reduction projects

gamma discounters are short termist weitzman 1998 2001 proposed a simple gamma discounting method to characterize the term structure of discount rates today from the sole distribution of future spot interest rates this rule which justifies using a smaller discount rate for longer maturities is now used for long term policy evaluations in the uk france norway and potentially in the us but we show that there is no social preference within the discounted expected utility framework that generically supports this pricing model and its underlying criterion the expected net present value rule considering a standard lucas tree economy we characterize the term structure from a coherent joint distribution of future spot interest rates and future consumption levels when future growth rates are positively serially correlated efficient discount rates today are decreasing with maturity and the gamma discounting rule yields discount rates that are larger than the efficient ones

positively gamma discounting combining the opinions of experts on the social discount rate the aggregated term structure of social discount rates that results from weitzman s 2001 survey of expert opinion is shown to be highly sensitive to the nature of the responses if variation reflects irreducible differences in ethical judgments the term structure can decline rapidly if variation occurred because respondents were forecasting future rates under uncertainty the term structure is much flatter because additional experts provide new information the former approach triples the social cost of carbon when compared to the latter the distinction between heterogeneity and uncertainty illustrates the need for a nuanced treatment of survey data in intergenerational policy making

discounting the distant future how much does model selection affect the certainty equivalent rate evaluating investment with long term consequences using discount rates that decline with the time horizon declining discount rates of ddrs means that future welfare changes are of greater consequence in present value terms recent work in this area has turned towards operationalising the theory and establishing a schedule of ddrs for use in cost benefit analysis using us data we make the following points concerning this transition i model selectionhas important implications for operationalising a theory of ddrs that depends upon uncertainty ii misspecification testing naturally leads to employing models that account for changes in the interest reat generating medanism lastly we provide an analysis of the policy implications of ddrs in the context of climate change for the us and show that the use of a state space model can increase valuations by 150 compared to conventional constant discounting

persistence in variance structural change and the garch model this article examines the persistence of the variance as measured by the generalized autoregressive conditional heteroskedasticity garch model in stock return data in particular we investigate the extent to which persistence in variance may be overstated because of the existence of and failure to take account of deterministic structural shifts in the model both an analysis of daily stock return data and a monte carlo simulation experiment confirm the hypothesis that garch measures of persistence in variance are sensitive to this type of model misspecification

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

income convergence clubs for brazilian municipalities a non parametric analysis this article analyses the evolution of relative per capita income distribution of brazilian municipalities over the period 1970 1996 analyses are based on non parametric methodologies and do not assume probability distributions or functional forms for the data two convergence tests have been carried out a test for sigma convergence based on the bootstrap principle and a beta convergence test using smoothing splines for the growth regressions the results obtained demonstrate the need to model the dynamics of income for brazilian municipalities as a process of convergence clubs using the methodology of transition matrices and stochastic kernels the results show the formation of two convergence clubs a low income club formed by the municipalities of the north and northeast regions and another high income club formed by the municipalities of the center west southeast and south regions the formation of convergence clubs is confirmed by a bootstrap test for multimodality

social discounting under uncertainty a cross country comparison recent research suggests that social cost benefit analysis should be conducted with a declining discount rate for instance newell and pizer discounting the distant future how much do uncertain rates increase valuations j environ econ manage 46 2003 52 71 show that the us certainty equivalent discount rate declines through time using a simple autoregressive model of us interest rates this paper extends that line of research estimating both autoregressive and regime switching models of real interest rates to determine certainty equivalent discount rates in australia canada germany and the uk it is found that the regime switching model is a better model of past interest rate behavior for all four countries this model tends to produce a more rapid decline in certainty equivalent discount rates the paper provides applications to the economics of climate change and nuclear power

pricing interest rate derivative securities this article shows that the one state variableinterest rate models of vasicek 1977 and cox ingersoll and ross 1985b can be extended sothat they are consistent with both the current termstructure of interest rates and either the currentvolatilities of all spot interest rates or the currentvolatilities of all forward interest rates theextended vasicek model is shown to be very tracta ble analytically the article compares option pricesobtained using the extended vasicek model withthose obtained using a number of other models