Initial distribution spread: A density forecasting approach

Ensemble forecasting of nonlinear systems involves the use of a model to run forward a discrete ensemble (or set) of initial states. Data assimilation techniques tend to focus on estimating the true state of the system, even though model error limits the value of such efforts. This paper argues for choosing the initial ensemble in order to optimise forecasting performance rather than estimate the true state of the system. Density forecasting and choosing the initial ensemble are treated as one problem. Forecasting performance can be quantified by some scoring rule. In the case of the logarithmic scoring rule, theoretical arguments and empirical results are presented. It turns out that, if the underlying noise dominates model error, we can diagnose the noise spread

Firms’ Price Markups and Returns to Scale in Imperfect Markets: Bulgaria and Hungary

Under perfect competition and constant returns to scale, firms producing homogeneous products set their prices at their marginal costs which also equal their average costs. However, the departure from these standard assumptions has important implications with respects to the derived theoretical results and the validity of the related empirical analysis. In particular, monopolistic firms will charge a markup over their marginal costs. We show that firms’ markups tend to be directly associated with the employed production technology, more specifically with their returns to scale. Accordingly, we analyze the implications for the markup ratios from the incidence of non-constant returns to scale. We present quantitative results illustrating the effect of the returns to scale index on the firms’ price markups, as well as the relationship between the two indicators, on the basis of firm-level data for Bulgarian and Hungarian manufacturing firms.http://deepblue.lib.umich.edu/bitstream/2027.42/40096/3/wp710.pd

Cultural imagery and statistical models of the force of mortality: Addison, Gompertz and Pearson

We describe selected artistic and statistical depictions of the force of mortality (hazard or mortality rate), which is a concept that has long preoccupied actuaries, demographers and statisticians. We provide a more graphic form for the force-of-mortality function that makes the relationship between its constituents more explicit. The 'Bridge of human life' in Addison's allegorical essay of 1711 provides a particularly vivid image, with the forces depicted as external. The model that was used by Gompertz in 1825 appears to treat the forces as internal. In his 1897 essay Pearson mathematically modernized 'the medieval conception of the relation between Death and Chance' by decomposing the full mortality curve into five distributions along the age axis, the results of five 'marksmen' aiming at the human mass crossing this bridge. We describe Addison's imagery, comment briefly on Gompertz's law and the origin of the term 'force of mortality', describe the background for Pearson's essay, as well as his imagery and statistical model, and give the bridge of life a modern form, illustrating it via statistical animation