Discounting the Benefits of Climate Change Policies Using Uncertain Rates

Evaluating environmental policies, such as the mitigation of greenhouse gases, frequently requires balancing near-term mitigation costs against long-term environmental benefits. Conventional approaches to valuing such investments hold interest rates constant, but the authors contend that there is a real degree of uncertainty in future interest rates. This leads to a higher valuation of future benefits relative to conventional methods that ignore interest rate uncertainty.

Discounting the distant future: How much do uncertain rates increase valuations?

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. © 2003 Elsevier Science (USA). All rights reserved.

An approach to the study of G-protein-coupled receptor kinases: an in vitro-purified membrane assay reveals differential receptor specificity and regulation by G beta gamma subunits.

Phosphorylation of GTP-binding-regulatory (G)-protein-coupled receptors by specific G-protein-coupled receptor kinases (GRKs) is a major mechanism responsible for agonist-mediated desensitization of signal transduction processes. However, to date, studies of the specificity of these enzymes have been hampered by the difficulty of preparing the purified and reconstituted receptor preparations required as substrates. Here we describe an approach that obviates this problem by utilizing highly purified membrane preparations from Sf9 and 293 cells overexpressing G-protein-coupled receptors. We use this technique to demonstrate specificity of several GRKs with respect to both receptor substrates and the enhancing effects of G-protein beta gamma subunits on phosphorylation. Enriched membrane preparations of the beta 2- and alpha 2-C2-adrenergic receptors (ARs, where alpha 2-C2-AR refers to the AR whose gene is located on human chromosome 2) prepared by sucrose density gradient centrifugation from Sf9 or 293 cells contain the receptor at 100-300 pmol/mg of protein and serve as efficient substrates for agonist-dependent phosphorylation by beta-AR kinase 1 (GRK2), beta-AR kinase 2 (GRK3), or GRK5. Stoichiometries of agonist-mediated phosphorylation of the receptors by GRK2 (beta-AR kinase 1), in the absence and presence of G beta gamma, are 1 and 3 mol/mol, respectively. The rate of phosphorylation of the membrane receptors is 3 times faster than that of purified and reconstituted receptors. While phosphorylation of the beta 2-AR by GRK2, -3, and -5 is similar, the activity of GRK2 and -3 is enhanced by G beta gamma whereas that of GRK5 is not. In contrast, whereas GRK2 and -3 efficiently phosphorylate alpha 2-C2-AR, GRK5 is quite weak. The availability of a simple direct phosphorylation assay applicable to any cloned G-protein-coupled receptor should greatly facilitate elucidation of the mechanisms of regulation of these receptors by the expanding family of GRKs.

Differential developmental trajectories of magnetic susceptibility in human brain gray and white matter over the lifespan

As indicated by several recent studies, magnetic susceptibility of the brain is influenced mainly by myelin in the white matter and by iron deposits in the deep nuclei. Myelination and iron deposition in the brain evolve both spatially and temporally. This evolution reflects an important characteristic of normal brain development and ageing. In this study, we assessed the changes of regional susceptibility in the human brain in vivo by examining the developmental and ageing process from 1 to 83 years of age. The evolution of magnetic susceptibility over this lifespan was found to display differential trajectories between the gray and the white matter. In both cortical and subcortical white matter, an initial decrease followed by a subsequent increase in magnetic susceptibility was observed, which could be fitted by a Poisson curve. In the gray matter, including the cortical gray matter and the iron-rich deep nuclei, magnetic susceptibility displayed a monotonic increase that can be described by an exponential growth. The rate of change varied according to functional and anatomical regions of the brain. For the brain nuclei, the age-related changes of susceptibility were in good agreement with the findings from R2* measurement. Our results suggest that magnetic susceptibility may provide valuable information regarding the spatial and temporal patterns of brain myelination and iron deposition during brain maturation and ageing. © 2013 Wiley Periodicals, Inc.