Unlikely Estimates of the Ex Ante Real Interest Rate: Another Dismal Performance from the Dismal Science1

The ex ante real rate of interest is one of the most important concepts in economics and finance. Because the universally-used Fisher theory of interest requires positive ex ante real interest rates, empirical estimates of the ex ante real interest rate derived from the Fisher theory of interest should also be positive. Unfortunately, virtually all estimates of the ex ante real interest rate published in economic journals and textbooks or used in macroeconomic models and policy discussions for the past 35 years contain negative values for extended time periods and, thus, are theoretically flawed. Moreover, the procedures generally used to estimate ex ante real interest rates were shown to produce biased estimates of the ex ante real rate over 30 years ago. In this article, we document this puzzling chasm between the Fisherian theory that mandates positive ex ante real interest rates and the practice of macroeconomists who generate and use ex ante real interest rate estimates that violate this theory. We explore the reasons that this problem exists and assess some alternative approaches for estimating the ex ante real interest rate to determine whether they might resolve this problem.ex ante real interest rate, Fisher theory of interest, biased real interest rate estimates

Group Size Effect on the Success of Wolves Hunting

Social foraging shows unexpected features such as the existence of a group size threshold to accomplish a successful hunt. Above this threshold, additional individuals do not increase the probability of capturing the prey. Recent direct observations of wolves in Yellowstone Park show that the group size threshold when hunting its most formidable prey, bison, is nearly three times greater than when hunting elk, a prey that is considerably less challenging to capture than bison. These observations provide empirical support to a computational particle model of group hunting which was previously shown to be effective in explaining why hunting success peaks at apparently small pack sizes when hunting elk. The model is based on considering two critical distances between wolves and prey: the minimal safe distance at which wolves stand from the prey, and the avoidance distance at which wolves move away from each other when they approach the prey. The minimal safe distance is longer when the prey is more dangerous to hunt. We show that the model explains effectively that the group size threshold is greater when the minimal safe distance is longer. Although both distances are longer when the prey is more dangerous, they contribute oppositely to the value of the group size threshold: the group size threshold is smaller when the avoidance distance is longer. This unexpected mechanism gives rise to a global increase of the group size threshold when considering bison with respect to elk, but other prey more dangerous than elk can lead to specific critical distances that can give rise to the same group size threshold. Our results show that the computational model can guide further research on group size effects, suggesting that more experimental observations should be obtained for other kind of prey as e.g. moose.Comment: 20 pages, 4 figures, 8 references. Other author's papers can be downloaded at http://www.denys-dutykh.com

N=4 Supersymmetric Quantum Mechanics with Magnetic Monopole

We propose an N=4 supersymmetric quantum mechanics of a charged particle on a sphere in the background of Dirac magnetic monopole and study the system using the CP(1) model approach. We explicitly calculate the symmetry algebra taking the operator ordering ambiguity into consideration. We find that it is given by the superalgebra SU(1|2)x SU(2). We show that the Hamiltonian can be written in terms of the Casimir invariant of SU(2). Using this relation and the lower bound for angular momentm we obtain the energy spectrum. We then examine the ground energy sector to find that the N=4 supersymmetry is spontaneously broken to N=2 for certain values of the monopole charge.Comment: 7 page