Discounting and Confidence

Abstract: The paper analyzes the discount rate under uncertainty. The analysis complements the probabilistic characterization of uncertainty by a measure of confidence. Special cases of the model comprise discounting under smooth ambiguity aversion as well as discounting under a disentanglement of risk aversion from aversion to intertemporal substitution. The paper characterizes the general class of preferences for which uncertainty implies a reduction of the discount rate. It also characterizes how the more comprehensive description of uncertainty changes the discount rate with respect to the standard model. The paper relates different results in the literature by switching between different risk measures. It presents a parametric extension of the Ramsey discounting formula that takes into account confidence into future growth estimates and a measure of aversion to the lack of confidence. If confidence decreases in the futurity of the growth forecast, the discount rates have a falling term structure even in the case of an iid growth process. JEL Codes: D61, Q54, D81, D9

Upper limits on the strength of periodic gravitational waves from PSR J1939+2134

The first science run of the LIGO and GEO gravitational wave detectors presented the opportunity to test methods of searching for gravitational waves from known pulsars. Here we present new direct upper limits on the strength of waves from the pulsar PSR J1939+2134 using two independent analysis methods, one in the frequency domain using frequentist statistics and one in the time domain using Bayesian inference. Both methods show that the strain amplitude at Earth from this pulsar is less than a few times $10^{-22}$.Comment: 7 pages, 1 figure, to appear in the Proceedings of the 5th Edoardo Amaldi Conference on Gravitational Waves, Tirrenia, Pisa, Italy, 6-11 July 200

Improving the sensitivity to gravitational-wave sources by modifying the input-output optics of advanced interferometers

We study frequency dependent (FD) input-output schemes for signal-recycling interferometers, the baseline design of Advanced LIGO and the current configuration of GEO 600. Complementary to a recent proposal by Harms et al. to use FD input squeezing and ordinary homodyne detection, we explore a scheme which uses ordinary squeezed vacuum, but FD readout. Both schemes, which are sub-optimal among all possible input-output schemes, provide a global noise suppression by the power squeeze factor, while being realizable by using detuned Fabry-Perot cavities as input/output filters. At high frequencies, the two schemes are shown to be equivalent, while at low frequencies our scheme gives better performance than that of Harms et al., and is nearly fully optimal. We then study the sensitivity improvement achievable by these schemes in Advanced LIGO era (with 30-m filter cavities and current estimates of filter-mirror losses and thermal noise), for neutron star binary inspirals, and for narrowband GW sources such as low-mass X-ray binaries and known radio pulsars. Optical losses are shown to be a major obstacle for the actual implementation of these techniques in Advanced LIGO. On time scales of third-generation interferometers, like EURO/LIGO-III (~2012), with kilometer-scale filter cavities, a signal-recycling interferometer with the FD readout scheme explored in this paper can have performances comparable to existing proposals. [abridged]Comment: Figs. 9 and 12 corrected; Appendix added for narrowband data analysi

Subjective Risk, Confidence, and Ambiguity

The paper incorporates qualitative differences of probabilistic beliefs into a rational (or normatively motivated) decision framework. Probabilistic beliefs can range from objective probabilities to pure guesstimates. The decision maker in the present model takes into account his confidence in beliefs when evaluating general uncertain situations. From an axiomatic point of view, the approach stays as close as possible to the widespread von Neumann-Morgenstern framework. The resulting representation uses only basic tools from risk analysis, but employs them recursively. The paper extends the concept of smooth ambiguity aversion to a more general notion of aversion to the subjectivity of belief. As a special case, the framework permits a threefold disentanglement of intertemporal substitutability, Arrow-Pratt risk aversion, and smooth ambiguity aversion. A decision maker’s preferences can nest a variety of widespread decision criteria, which are selected according to his confidence in the uncertainty assessment of a particular setting

What's the rate? Disentangling the Weitzman and the Gollier effect

The uncertainty of future economic development affects the term structure of discount rates and, thus, the intertemporal weights that are tobe used in cost benefit analysis. The U.K. and France have recently adopteda falling term structure to incorporate uncertainty and the U.S. is consideringa similar step. A series of publications discusses the following concern: Aseemingly analogous argument used to justify falling discount rates can alsobe used to justify increasing discount rates. We show that increasing anddecreasing discount rates mean different things, can coexist, are created bydifferent channels through which risk affects evaluation, and have the samequalitative effect of making long-term payoffs more attractive

Intertemporal Risk Aversion, Stationarity and Discounting

Abstract: The paper develops an axiomatic framework that derives a new relation between discounting and uncertainty evaluation. The von Neumann and Morgenstern axioms give rise to a richer form of risk attitude than captured in the discounted expected utility standard model. I derive three models that permit a more comprehensive uncertainty evaluation. These preference representations differ in the consistency requirements imposed on the evaluation of uncertain scenarios. A central result is that for an intertemporal risk averse decision maker a stationary risk evaluation can restrict the rate of pure time preference to zero (no impatience). Such a decision maker still gives reduced weight to expected future utility when uncertainty is increasing over time. If uncertainty is endogenous to the decision process, this new rationale for discounting can yield very different policy implications

Discounting and confidence

The paper analyzes the discount rate under uncertainty. The analysis complements the probabilistic characterization of uncertainty by a measure of confidence. Special cases of the model comprise discounting under smooth ambiguity aversion as well as discounting under a disentanglement of risk aversion from aversion to intertemporal substitution. The paper characterizes the general class of preferences for which uncertainty implies a reduction of the discount rate. It also characterizes how the more comprehensive description of uncertainty changes the discount rate with respect to the standard model. The paper relates different results in the literature by switching between different risk measures. It presents a parametric extension of the Ramsey discounting formula that takes into account confidence into future growth estimates and a measure of aversion to the lack of confidence. If confidence decreases in the futurity of the growth forecast, the discount rates have a falling term structure even in the case of an iid growth process

Interemporal Risk Aversion - or - Wouldn't it be Nice to Tell Whether Robinson Crusoe is Risk

The paper introduces a new notion of risk aversion that is independent of the good under observation and its measure scale. The representational framework builds on a time consistent combination of additive separability on certain consumption paths and the von Neumann & Morgenstern (1944) assumptions. In the one-commodity special case, the new notion of risk aversion closely relates to a disentanglement of standard risk aversion and intertemporal substitutability

What's the rate? Disentangling the Weitzman and the Gollier effect

The uncertainty of future economic development affects the term structure of discount rates and, thus, the intertemporal weights that are tobe used in cost benefit analysis. The U.K. and France have recently adopteda falling term structure to incorporate uncertainty and the U.S. is consideringa similar step. A series of publications discusses the following concern: Aseemingly analogous argument used to justify falling discount rates can alsobe used to justify increasing discount rates. We show that increasing anddecreasing discount rates mean different things, can coexist, are created bydifferent channels through which risk affects evaluation, and have the samequalitative effect of making long-term payoffs more attractive