The Effects of Tax-Law Changes on Property-Casualty Insurance Prices

During the 1980s, the federal income tax treatment of property-casualty insurers and their policyholders underwent several important changes, the most significant of which came in 1986. This paper develops theoretical predictions for how these changes should have affected the equilibrium prices of property-casualty insurance policies, and explores the extent to which the theoretical predictions are reflected in data on industry experience. The paper is devoted mainly to a careful specification of the income tax rules, and to deriving the connection between predictions about simple forms of insurance policy and industry data on premiums earned. Although the predicted impact of the changes in the tax rules enacted in 1986 translates into a tax on premiums (net of the cost of acquisition) of up to 13 percent (on medical malpractice, the longest-tail line of insurance, in 1987), it is small relative to the variability of the actual loss experience.

Effects of Management and Environmental Variables on Ant Richness, Diversity, and Nest Abundance in Pitch Pine-Scrub Oak Barrens, Heathlands, and Dry Rocky-ridge Communities in Inland Massachusetts, USA

Heathlands and pitch pine-scrub oak (PPSO) barrens are globally-imperiled natural communities threatened by human development and disruption of natural disturbance regimes. To restore these habitats in the northeastern United States, many sites are managed by mechanical tree harvesting, mowing, selective herbicide, and prescribed fire. Restored PPSO barrens and heathlands are important habitat for rare and threatened biota; barrens habitat has been shown to support high ant diversity including rare and threatened species. Ants are important providers of ecosystem services and functions, yet their ecology and response to management in inland Massachusetts barrens are not well known. I used hand-sampling to collect ants and count nests in 82 plots from 18 barrens and heathlands, on rocky and sandy-soil sites mostly in inland Massachusetts. In total, I identified 64 species in 22 genera from 3,908 individuals. I used linear mixed models to analyze how ant nest abundance, richness, and Shannon’s Diversity Index responded to restoration treatments and environmental variables such as vegetation structure and amount of deadwood (coarse woody debris [CWD] and stumps). Treatment group (1-2 years since first treatment [YSFT], 3-6 YSFT, \u3e9 YSFT, power line corridor, sandy soil no treatment, rocky soil no treatment), was an important predictor for all three response variables. Treatment group influenced ant abundance, richness, and diversity differently, but across all three variables, newly treated sites (1-2 years since initial tree harvesting) had the lowest numbers of ant nests, richness, and diversity. Increased understory vegetation structure had significant positive relationships with nest abundance and richness. Amount of deadwood had significantly negative relationships with richness, diversity, and nest abundance (although deadwood was highly correlated with YSFT), and more decayed CWD had positive effects on nest abundance. I also used Non-metric Multidimensional Scaling (NMDS) to assess differences in ant communities among treatment groups. Ant communities differed among the treatment/habitats, and power line corridors had the most unique ant community. I collected six regionally rare and/or barrens specialist species, with four of these found on power line corridors and two on rocky-ridge barrens. My results provide evidence that heterogeneous habitat in barrens, including closed-canopy forest and a variety of early successional habitat, supports high ant diversity (e.g., 54 species currently known from Montague Plains WMA, which is 48% of the total known Massachusetts ant fauna). My results suggest that shrublands (higher understory vegetation structure and density) at barrens sites supports the highest ant richness. However, power line corridors were most important for rare and/or barrens-specialist species. More frequent management on power line corridors (e.g., every 4-5 years) and the use of herbicide may create unique habitat (more forbs/ferns, patchy, low vegetation) compared to silvicultural tree harvests and mowing. Time since initial tree harvesting (generally much longer in power line corridors) is likely a contributing factor to rare, and specialist species occupancy. Landscape context, including connectedness to high-quality habitat to facilitate dispersal, and management type are also likely contributing factors. Overall, my work can help managers understand how to best sustain high ant richness and rare species in these managed habitats and contributes continued evidence that these habitats are important for ant conservation in the region

A Geometric Consideration of the Erd\H{o}s-Straus Conjecture

In this paper we will explore the solutions to the diophantine equation in the Erd\H{o}s-Straus conjecture. For a prime $p$ we are discussing the relationship between the values $x,y,z \in \mathbb{N}$ so that $$\frac{4}{p} = \frac{1}{x} + \frac{1}{y} + \frac{1}{z}.$$ We will separate the types of solutions into two cases. In particular we will argue that the most common relationship found is $$x = \lfloor \frac{py}{4y-p} \rfloor + 1.$$ Finally, we will make a few conjectures to motivate further research in this area

The Effects of Tax Law Changes on Property-Casualty Insurance Prices

One of the most important components of the balance sheet of a property-casualty insurance company is the loss reserve. In spite of what the term may suggest, a loss reserve is not a pot of funds set aside for the uncertain future. It is an accounting entry, a liability on the balance sheet. More precisely termed the unpaid-losses account, the loss reserve expresses the amount the company expects to pay out in the future to cover indemnity payments that will come due on policies already written for losses that have already been incurred and to cover the costs of dealing with the associated claims. The latter category of costs, which includes, for example, the litigation costs associated with settling claims, is called loss-adjustment expenses. If loss reserves were determined solely on the basis of pure insurance accounting theory, they would reflect only those factors that affect the size, frequency, and pattern of future claim payments and loss-adjustment expenses. Such factors would include changes in patterns of actual claim payments; changes in inflation rates, weather patterns, and technology; and, particularly significant in the context of liability insurance, trends in tort doctrines and jury awards. In practice, however, loss reserves are influenced by other considerations as well, considerations such as how the reported reserves will affect the likelihood of regulatory scrutiny, the perceptions of investors, and the firm\u27s income tax liability. In this paper, we begin to examine the effects of income tax rules on property-casualty reserving practices