Self-selection and risk selection on the Swiss health insurance market

Abstract This thesis presents three empirical studies in the field of health insurance in Switzerland. First we investigate the link between health insurance coverage and health care expenditures. We use claims data for over 60 000 adult individuals covered by a major Swiss Health Insurance Fund, followed for four years; the data show a strong positive correlation between coverage and expenditures. Two methods are developed and estimated in order to separate selection effects (due to individual choice of coverage) and incentive effects ("ex post moral hazard"). The first method uses the comparison between inpatient and outpatient expenditures to identify both effects and we conclude that both selection and incentive effects are significantly present in our data. The second method is based on a structural model of joint demand of health care and health insurance and makes the most of the change in the marginal cost of health care to identify selection and incentive effects. We conclude that the correlation between insurance coverage and health care expenditures may be decomposed into the two effects: 75% may be attributed to selection, and 25 % to incentive effects. Moreover, we estimate that a decrease in the coinsurance rate from 100% to 10% increases the marginal demand for health care by about 90% and from 100% to 0% by about 150%. Secondly, having shown that selection and incentive effects exist in the Swiss health insurance market, we present the consequence of this result in the context of risk adjustment. We show that if individuals choose their insurance coverage in function of their health status (selection effect), the optimal compensations should be function of the se- lection and incentive effects. Therefore, a risk adjustment mechanism which ignores these effects, as it is the case presently in Switzerland, will miss his main goal to eliminate incentives for sickness funds to select risks. Using a simplified model, we show that the optimal compensations have to take into account the distribution of risks through the insurance plans in case of self-selection in order to avoid incentives to select risks.Then, we apply our propositions to Swiss data and propose a simple econometric procedure to control for self-selection in the estimation of the risk adjustment formula in order to compute the optimal compensations.

Self-organized criticality induced by diversity

We have studied the collective behavior of a population of integrate-and-fire oscillators. We show that diversity, introduced in terms of a random distribution of natural periods, is the mechanism that permits one to observe self-organized criticality (SOC) in the long time regime. As diversity increases the system undergoes several transitions from a supercritical regime to a subcritical one, crossing the SOC region. Although there are resemblances with percolation, we give proofs that criticality takes place for a wide range of values of the control parameter instead of a single value.

Self-similarity properties of natural images resemble those of turbulent flows

We show that the statistics of an edge type variable in natural images exhibits self-similarity properties which resemble those of local energy dissipation in turbulent flows. Our results show that self-similarity and extended self-similarity hold remarkably for the statistics of the local edge variance, and that the very same models can be used to predict all of the associated exponents. These results suggest using natural images as a laboratory for testing more elaborate scaling models of interest for the statistical description of turbulent flows. The properties we have exhibited are relevant for the modeling of the early visual system: They should be included in models designed for the prediction of receptive fields.

Long-tailed trapping times and Lévy flights in a self-organized critical granular system

We present a continuous time random walk model for the scale-invariant transport found in a self-organized critical rice pile [K. Christensen et al., Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that the dynamics of the experiment can be explained in terms of Lvy flights for the grains and a long-tailed distribution of trapping times. Scaling relations for the exponents of these distributions are obtained. The predicted microscopic behavior is confirmed by means of a cellular automaton model.

Viral self-assembly as a thermodynamic process

The protein shells, or capsids, of nearly all spherelike viruses adopt icosahedral symmetry. In the present Letter, we propose a statistical thermodynamic model for viral self-assembly. We find that icosahedral symmetry is not expected for viral capsids constructed from structurally identical protein subunits and that this symmetry requires (at least) two internal switching configurations of the protein. Our results indicate that icosahedral symmetry is not a generic consequence of free energy minimization but requires optimization of internal structural parameters of the capsid proteins

Self-similarity of complex networks and hidden metric spaces

We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization.

Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality

A stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The dynamic renormalization group (DRG) enables one to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.

Self-similar community structure in a network of human interactions

We propose a procedure for analyzing and characterizing complex networks. We apply this to the social network as constructed from email communications within a medium sized university with about 1700 employees. Email networks provide an accurate and nonintrusive description of the flow of information within human organizations. Our results reveal the self-organization of the network into a state where the distribution of community sizes is self-similar. This suggests that a universal mechanism, responsible for emergence of scaling in other self-organized complex systems, as, for instance, river networks, could also be the underlying driving force in the formation and evolution of social networks.

Noise and dynamics of self-organized critical phenomena

Different microscopic models exhibiting self-organized criticality are studied numerically and analytically. Numerical simulations are performed to compute critical exponents, mainly the dynamical exponent, and to check universality classes. We find that various models lead to the same exponent, but this universality class is sensitive to disorder. From the dynamic microscopic rules we obtain continuum equations with different sources of noise, which we call internal and external. Different correlations of the noise give rise to different critical behavior. A model for external noise is proposed that makes the upper critical dimensionality equal to 4 and leads to the possible existence of a phase transition above d=4. Limitations of the approach of these models by a simple nonlinear equation are discussed.

Division of Soil Conservation Soil and Water Quality Review, January 2010

Special Points of Interest: • The Division of Soil Conservation celebrated its 70th anniversary July 1, 2009. The Iowa Soil Conservation Laws were enacted in 1939 creating the state soil conservation agency and governing committee and providing for the creation of Iowa’s 100 soil and water conservation districts. • The Mines & Minerals Bureau, through the federal Abandoned Mine Land (AML) Program, worked with various watershed groups to again secure an additional $1 million dollars in funding for the construction on projects in Marion, Mahaska and Monroe Counties. • Iowa hosted the Mississippi River/Gulf of Mexico Hypoxia Task Force tour and meeting in September 2009.

Growth decrease in Alpine whitefish: investigating the relative contribution of fishing induced selection and environmental change and its implication for conservation measures

La pression exercée par les activités humaines menace pratiquement tous les écosystèmes aquatiques du globe. Ainsi, sous l'effet de divers facteurs tels que la pollution, le réchauffement climatique ou encore la pêche industrielle, de nombreuses populations de poissons ont vu leurs effectifs chuter et divers changements morphologiques ont été observés. Dans cette étude, nous nous sommes intéressés à une menace particulière: la sélection induite par la pêche sur la croissance des poissons. En effet, la génétique des populations prédit que la soustraction régulière des individus les plus gros peut entraîner des modifications rapides de certains traits physiques comme la croissance individuelle. Cela a par ailleurs été observé dans de nombreuses populations marines ou lacustres, dont les populations de féras, bondelles et autres corégones des lacs suisses. Toutefois, malgré un nombre croissant d'études décrivant ce phénomène, peu de plans de gestion en tiennent compte, car l'importance des effets génétiques liés à la pêche est le plus souvent négligée par rapport à l'impact des changements environnementaux. Le but premier de cette étude a donc été de quantifier l'importance des facteurs génétiques et environnementaux. Dans le premier chapitre, nous avons étudié la population de palée du lac de Joux (Coregonus palaea). Nous avons déterminé les différentiels de sélection dus à la pêche, c'est-à-dire l'intensité de la sélection sur le taux de croissance, ainsi que les changements nets de croissance au cours du temps. Nous avons observé une baisse marquée de croissance et un différentiel de sélection important indiquant qu'au moins 30% de la diminution de croissance observée était due à la pression de sélection induite par la pêche. Dans le deuxième chapitre, nous avons effectué les mêmes analyses sur deux espèces proches du lac de Brienz (C. albellus et C. fatioi) et avons observé des effets similaires dont l'intensité était spécifique à chaque espèce. Dans le troisième chapitre, nous avons analysé deux autres espèces : C. palaea et C. confusus du lac de Bienne, et avons constaté que le lien entre la pression de sélection et la diminution de croissance était influencé par des facteurs environnementaux. Finalement, dans le dernier chapitre, nous avons étudié les effets potentiels de différentes modifications de la taille des mailles des filets utilisés pour la pêche à l'aide de modèles mathématiques. Nous concluons que la pêche a un effet génétique non négligeable (et donc peu réversible) sur la croissance individuelle dans les populations observée, que cet effet est lié à la compétition pour la nourriture et à la qualité de l'environnement, et que certaines modifications simples de la taille des mailles des filets de pêche pourraient nettement diminuer l'effet de sélection et ainsi ralentir, voir même renverser la diminution de croissance observée.

Self-organized evolution in a socio-economic environment

We propose a general scenario to analyze technological changes in socio-economic environments. We illustrate the ideas with a model that incorporating the main trends is simple enough to extract analytical results and, at the same time, sufficiently complex to display a rich dynamic behavior. Our study shows that there exists a macroscopic observable that is maximized in a regime where the system is critical, in the sense that the distribution of events follow power laws. Computer simulations show that, in addition, the system always self-organizes to achieve the optimal performance in the stationary state.

Self-dynamic structure factor of dense liquids: Theory and simulation

The self-intermediate dynamic structure factor Fs(k,t) of liquid lithium near the melting temperature is calculated by molecular dynamics. The results are compared with the predictions of several theoretical approaches, paying special attention to the Lovesey model and the Wahnstrm and Sjgren mode-coupling theory. To this end the results for the Fs(k,t) second memory function predicted by both models are compared with the ones calculated from the simulations.

Self and cross-velocity correlation functions and diffusion coefficients in liquids: a molecular dynamics study of binary mixtures of soft spheres

Molecular dynamics simulation is applied to the study of the diffusion properties in binary liquid mixtures made up of soft-sphere particles with different sizes and masses. Self- and distinct velocity correlation functions and related diffusion coefficients have been calculated. Special attention has been paid to the dynamic cross correlations which have been computed through recently introduced relative mean molecular velocity correlation functions which are independent on the reference frame. The differences between the distinct velocity correlations and diffusion coefficients in different reference frames (mass-fixed, number-fixed, and solvent-fixed) are discussed.