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.

Information relaxations and duality in stochastic dynamic programs

We describe a general technique for determining upper bounds on maximal values (or lower bounds on minimal costs) in stochastic dynamic programs. In this approach, we relax the nonanticipativity constraints that require decisions to depend only on the information available at the time a decision is made and impose a "penalty" that punishes violations of nonanticipativity. In applications, the hope is that this relaxed version of the problem will be simpler to solve than the original dynamic program. The upper bounds provided by this dual approach complement lower bounds on values that may be found by simulating with heuristic policies. We describe the theory underlying this dual approach and establish weak duality, strong duality, and complementary slackness results that are analogous to the duality results of linear programming. We also study properties of good penalties. Finally, we demonstrate the use of this dual approach in an adaptive inventory control problem with an unknown and changing demand distribution and in valuing options with stochastic volatilities and interest rates. These are complex problems of significant practical interest that are quite difficult to solve to optimality. In these examples, our dual approach requires relatively little additional computation and leads to tight bounds on the optimal values. © 2010 INFORMS.

Asset pricing in created markets

We investigate the applicability of the present-value asset pricing model to fishing quota markets by applying instrumental variable panel data estimation techniques to 15 years of market transactions from New Zealand's individual transferable quota (ITQ) market. In addition to the influence of current fishing rents, we explore the effect of market interest rates, risk, and expected changes in future rents on quota asset prices. The results indicate that quota asset prices are positively related to declines in interest rates, lower levels of risk, expected increases in future fish prices, and expected cost reductions from rationalization under the quota system. © 2007 American Agricultural Economics Association.

Fishing quota markets

In 1986, New Zealand responded to the open-access problem by establishing the world's largest individual transferable quota (ITQ) system. Using a 15-year panel dataset from New Zealand that covers 33 species and more than 150 markets for fishing quotas, we assess trends in market activity, price dispersion, and the fundamentals determining quota prices. We find that market activity is sufficiently high in the economically important markets and that price dispersion has decreased. We also find evidence of economically rational behavior through the relationship between quota lease and sale prices and fishing output and input prices, ecological variability, and market interest rates. Controlling for these factors, our results show a greater increase in quota prices for fish stocks that faced significant reductions, consistent with increased profitability due to rationalization. Overall, this suggests that these markets are operating reasonably well, implying that ITQs can be effective instruments for efficient fisheries management. © 2004 Elsevier Inc. All rights reserved.

Can exchange rates forecast commodity prices?

We show that "commodity currency" exchange rates have surprisingly robust power in predicting global commodity prices, both in-sample and out-of-sample, and against a variety of alternative benchmarks. This result is of particular interest to policy makers, given the lack of deep forward markets in many individual commodities, and broad aggregate commodity indices in particular. We also explore the reverse relationship (commodity prices forecasting exchange rates) but find it to be notably less robust. We offer a theoretical resolution, based on the fact that exchange rates are strongly forward-looking, whereas commodity price fluctuations are typically more sensitive to short-term demand imbalances. © 2010 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.

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.

Sensitivity to switching rates in stochastically switched ODEs

We consider a stochastic process driven by a linear ordinary differential equation whose right-hand side switches at exponential times between a collection of different matrices. We construct planar examples that switch between two matrices where the individual matrices and the average of the two matrices are all Hurwitz (all eigenvalues have strictly negative real part), but nonetheless the process goes to infinity at large time for certain values of the switching rate. We further construct examples in higher dimensions where again the two individual matrices and their averages are all Hurwitz, but the process has arbitrarily many transitions between going to zero and going to infinity at large time as the switching rate varies. In order to construct these examples, we first prove in general that if each of the individual matrices is Hurwitz, then the process goes to zero at large time for sufficiently slow switching rate and if the average matrix is Hurwitz, then the process goes to zero at large time for sufficiently fast switching rate. We also give simple conditions that ensure the process goes to zero at large time for all switching rates. © 2014 International Press.

A Pharmacology-Based Enrichment Program for Undergraduates Promotes Interest in Science.

There is a strong need to increase the number of undergraduate students who pursue careers in science to provide the "fuel" that will power a science and technology-driven U.S. economy. Prior research suggests that both evidence-based teaching methods and early undergraduate research experiences may help to increase retention rates in the sciences. In this study, we examined the effect of a program that included 1) a Summer enrichment 2-wk minicourse and 2) an authentic Fall research course, both of which were designed specifically to support students' science motivation. Undergraduates who participated in the pharmacology-based enrichment program significantly improved their knowledge of basic biology and chemistry concepts; reported high levels of science motivation; and were likely to major in a biological, chemical, or biomedical field. Additionally, program participants who decided to major in biology or chemistry were significantly more likely to choose a pharmacology concentration than those majoring in biology or chemistry who did not participate in the enrichment program. Thus, by supporting students' science motivation, we can increase the number of students who are interested in science and science careers.