The Relevance of Irrelevant Alternatives: An experimental investigation of risky choices

Experimental economists have discovered various violations of expected utility theory and offered alternative models that can explain laboratory results. This study discovers a new violation in risky choices that cannot be explained by theories like Prospect Theory, Disappoint- ment or Regret Theory. In an experimental setting using a between- subject design, the influence of a dominated alternative on certainty equivalents is shown. One group of subjects was offered a series of choices between a lottery ticket with a 50-50 chance of winning and a sure payoff. A second group was offered the same choice plus a third alternative, that as it turned out was not chosen by any participant. As a result, the average chosen sure payoff in the second group was higher than in the first group. That means, by adding a dominated alternative to a choice set, the certainty equivalent of a lottery is in- creased.

Optimally Rational Expectations and Macroeconomics

This paper provides an alternative to the theory of rational expectations (RE). Its central idea is that the information set on which agents will choose to condition their expectations will not, in general, include all the available information. Our alternative has many of the attractive features of RE; it emerges from an explicit choice-theoretic framework; it has wide applicability; and it can in principle explain the failure of models incorporating RE to account for the dynamics of many macroeconomic relationships.Rational expectations, incomplete information, macroeconomic dynamics

Model Selection and Testing of Conditional and Stochastic Volatility Models

This paper focuses on the selection and comparison of alternative non-nested volatility models. We review the traditional in-sample methods commonly applied in the volatility framework, namely diagnostic checking procedures, information criteria, and conditions for the existence of moments and asymptotic theory, as well as the out-of-sample model selection approaches, such as mean squared error and Model Confidence Set approaches. The paper develops some innovative loss functions which are based on Value-at-Risk forecasts. Finally, we present an empirical application based on simple univariate volatility models, namely GARCH, GJR, EGARCH, and Stochastic Volatility that are widely used to capture asymmetry and leverage.asymmetry, leverage;model confidence set;non-nested models;volatility model comparison;volatility model selection;Value-at-Risk forecasts

Model Selection and Testing of Conditional and Stochastic Volatility Models

This paper focuses on the selection and comparison of alternative non-nested volatility models. We review the traditional in-sample methods commonly applied in the volatility framework, namely diagnostic checking procedures, information criteria, and conditions for the existence of moments and asymptotic theory, as well as the out-of-sample model selection approaches, such as mean squared error and Model Confidence Set approaches. The paper develops some innovative loss functions which are based on Value-at-Risk forecasts. Finally, we present an empirical application based on simple univariate volatility models, namely GARCH, GJR, EGARCH, and Stochastic Volatility that are widely used to capture asymmetry and leverage.Volatility model selection; volatility model comparison; non-nested models; model confidence set; Value-at-Risk forecasts; asymmetry, leverage

Country effects in ISSP-1993 environmental data: Comparison of SEM approaches

Structural equation models (SEM) are commonly used to analyze the relationship between variables some of which may be latent, such as individual ``attitude'' to and ``behavior'' concerning specific issues. A number of difficulties arise when we want to compare a large number of groups, each with large sample size, and the manifest variables are distinctly non-normally distributed. Using an specific data set, we evaluate the appropriateness of the following alternative SEM approaches: multiple group versus MIMIC models, continuous versus ordinal variables estimation methods, and normal theory versus non-normal estimation methods. The approaches are applied to the ISSP-1993 Environmental data set, with the purpose of exploring variation in the mean level of variables of ``attitude'' to and ``behavior'' concerning environmental issues and their mutual relationship across countries. Issues of both theoretical and practical relevance arise in the course of this application.Structural equation models, factors models, MIMIC models, latent variables, multiple group analysis, non-normality, goodness of fit test, environmental data

Vop\v{e}nka's Alternative Set Theory in the Mathematical Canon of the 20th Century: Author's Translation from Czech

Vop\v{e}nka's Alternative Set Theory can be viewed both as an evolution and as a revolution: it is based on his previous experience with nonstandard universes, inspired by Skolem's construction of a nonstandard model of arithmetic, and its inception has been explicitly mentioned as an attempt to axiomatize Robinson's Nonstandard Analysis. Vop\v{e}nka preferred working in an axiomatic theory to investigating its individual models; he also viewed other areas of nonclassical mathematics through this prism. This article is a contribution to the mapping of the mathematical neighbourhood of the Alternative Set Theory, and at the same time, it submits a challenge to analyze in more detail the genesis and structure of the philosophical links that eventually influenced the Alternative Set Theory.Comment: This is the author's translation into English of her paper published originally in Czech. 14 page

Sheaf Logic, Quantum Set Theory and the Interpretation of Quantum Mechanics

Based on the Sheaf Logic approach to set theoretic forcing, a hierarchy of Quantum Variable Sets is constructed which generalizes and simplifies the analogous construction developed by Takeuti on boolean valued models of set theory. Over this model two alternative proofs of Takeuti's correspondence, between self adjoint operators and the real numbers of the model, are given. This approach results to be more constructive showing a direct relation with the Gelfand representation theorem, revealing also the importance of these results with respect to the interpretation of Quantum Mechanics in close connection with the Deutsch-Everett multiversal interpretation. Finally, it is shown how in this context the notion of genericity and the corresponding generic model theorem can help to explain the emergence of classicality also in connection with the Deutsch- Everett perspective.Comment: 34 pages, 2 figure