Jan Heufer

Consistent subsets: Computationally feasible methods to compute the Houtman–Maks-index

We provide two methods to compute the largest subset of a set of observations that is consistent with the Generalised Axiom of Revealed Preference. The algorithm provided by Houtman and Maks (1985) is not comput ationally feasible for larger data sets, while our methods are not limited in that respect. The first method is a variation of Gross and Kaisers (1996) approximate algorithm and is only applicable for two-dimensional data sets, but it is very fast and easy to implement. The second method is a mixed-integer linear programming approach that is slightly more involved but still fast and not limited by the dimension of the data set.

Testing for Utility Maximization with Error and the Loss of Power

Abstract A procedure is suggested to decide whether or not to treat a consumer who violates the Generalized Axiom of Revealed Preference as ‘close enough’ to utility maximization. It is based on the reduction of the power the test has against random behaviour. It can also be used to compare different efficiency indices.

Nonparametric comparative revealed risk aversion

We introduce a nonparametric method to compare risk aversion of different investors based on revealed preference methods. Using Yaaris (1969) [50] definition of “more risk averse than”, we show that it is sufficient to compare the revealed preference relations of two investors. This makes the approach operational; the central rationalisability theorem provides strong support for this approach. We also provide a measure of economic significance to quantify the differences in risk aversion, which can also help to interpret differences in risk aversion in parametric models. The approach is an alternative or complement to parametric approaches and a robustness check. As a necessary first step towards this comparative approach we show how to test data for consistency with stochastic dominance relations, which can also be used to recover larger parts of preferences. We include an application to experimental data by Choi et al. (2007) [10,11] which demonstrates the potential of the comparative approach.

Quasiconcave preferences on the probability simplex: A nonparametric analysis

A nonparametric approach is presented to test whether decisions on a probability simplex could be induced by quasiconcave preferences. Necessary and sufficient conditions are presented which can easily be tested. If the answer is affirmative, the methods developed here allow us to reconstruct bounds on indifference curves. Furthermore we can construct quasiconcave utility functions in analogy to the utility function constructed in the proof of Afriat’s Theorem. The approach is of interest for ex ante fairness considerations when a dictator is asked to choose probabilities to win an indivisible prize. It is also of interest for decisions under risk and stochastic choice. It allows nonparametric interpersonal comparisons.

Homothetic Efficiency. A Non-Parametric Approach

This article provides a robust non-parametric approach to demand analysis based on a concept called homothetic efficiency. Homotheticity is a useful restriction or assumption but data rarely satisfy testable conditions. To overcome this problem, this article provides a way to estimate homothetic efficiency of consumption choices by consumers. The basic efficiency index suggested is similar to Afriats (1972) efficiency index and Varians (1993) violation index. It generalises Heufers (2013b) two-dimensional concept to arbitrary dimensions and is motivated by a form of rationalisation similar to the one proposed by Halevy et al. (2012). The method allows to construct scalar factors which can be used to construct revealed preferred and worse sets. The approach also provides considerably more discriminatory power against irrational behaviour than standard utility maximisation. An application to experimental and household expenditure data illustrates how the method allows to recover preferences and increase test power.