Probabilistic dominance and status quo bias

Decision makers have a strong tendency to retain the current state of affairs. This well-documented phenomenon is termed status quo bias. We present the probabilistic dominance approach to status quo bias: an alternative is considered acceptable to replace the status quo only if the chances of a (subjectively) severe loss, relative to the status quo, are not too high. Probabilistic dominance is applied and behaviorally characterized in a choice model that allows for a range of status quo biases, general enough to accommodate unanimity, but also standard expected utility maximization. We present a comparative notion of “revealing more bias towards the status quo” and study its implications to the probabilistic dominance model of choice. Lastly, the model is applied to the endowment effect phenomenon and to a problem of international portfolio choice when investors are home biased.     

Bivariate almost stochastic dominance

Univariate almost stochastic dominance has been widely studied and applied since its introduction by Leshno and Levy (Manag Sci 48:1074–1085, 2002). This paper extends this construction to the bivariate case by means of suitable two-attribute utility functions. After having confined correlation aversion and correlation loving to some acceptable levels, bivariate almost stochastic dominance rules are introduced for the preferences exhibiting confined correlation aversion and confined correlation loving. The impact of a change in risk in terms of bivariate almost stochastic dominance on optimal saving is analyzed as an application, as well as the effect of envy and altruism on income distributions. Finally, alternative definitions of bivariate almost stochastic dominance are discussed, as well as testing procedures for such dominance rules in financial problems.     

Third-degree stochastic dominance and random variables

This paper addresses the question of whether there is a random-variables characterization of third-degree stochastic dominance under equal means and variances that is similar to a well-known characterization of second-degree stochastic dominance under equal means. The answer given is mixed.     

Bayesian assessment of Lorenz and stochastic dominance

We introduce a Bayesian approach for assessing Lorenz and stochastic dominance. For two income distributions, say X and Y, estimated via Markov chain Monte Carlo, we describe how to compute posterior probabilities for: (i) X dominates Y, (ii) Y dominates X and (iii) neither Y nor X dominates. The proposed approach is applied to Indonesian income distributions using mixtures of gamma densities that ensure flexible modelling. Probability curves depicting the probability of dominance at each population proportion are used to explain changes in dominance probabilities over restricted ranges relevant for poverty orderings. They also explain some seemingly contradictory outcomes from the p-values of some sampling theory tests.     

Apportioning of risks via stochastic dominance

Consider a simple two-state risk with equal probabilities for the two states. In particular, assume that the random wealth variable dominates via ith-order stochastic dominance for i=M,N. We show that the 50-50 lottery dominates the lottery via (N+M)th-order stochastic dominance. The basic idea is that a decision maker exhibiting (N+M)th-order stochastic dominance preference will allocate the state-contingent lotteries in such a way as not to group the two “bad” lotteries in the same state, where “bad” is defined via ith-order stochastic dominance. In this way, we can extend and generalize existing results about risk attitudes. This lottery preference includes behavior exhibiting higher-order risk effects, such as precautionary effects and tempering effects.     

Quantile forecast combination using stochastic dominance

This paper derives optimal forecast combinations based on stochastic dominance efficiency (SDE) analysis with differential forecast weights for different quantiles of forecast error distribution. For the optimal forecast combination, SDE will minimize the cumulative density functions of the levels of loss at different quantiles of the forecast error distribution by combining different time-series model-based forecasts. Using two exchange rate series on weekly data for the Japanese yen/US dollar and US dollar/Great Britain pound, we find that the optimal forecast combinations with SDE weights perform better than different forecast selection and combination methods for the majority of the cases at different quantiles of the error distribution. However, there are also some very few cases where some other forecast selection and combination model performs equally well at some quantiles of the forecast error distribution. Different forecasting period and quadratic loss function are used to obtain optimal forecast combinations, and results are robust to these choices. The out-of-sample performance of the SDE forecast combinations is also better than that of the other forecast selection and combination models we considered.     

A note on first degree stochastic dominance

A link is established between stochastic dominance and a different dominance relationship which we call pointwise dominance. This provides the basis for making several comparisons of expected values of non-decreasing functions of random variables. We discuss economic problems for which the application of stochastic dominance results depends on this link.     

Inverse stochastic dominance,inequality measurement and Gini indices

We investigate the relationship between the third degree inverse stochastic dominance criterion introduced in Muliere and Scarsini (1989) and inequality dominance when Lorenz curves intersect. We propose a new definition of transfer sensitivity aimed at strengthening the Pigou-Dalton Principle of Transfers. Our definition is dual to that suggested by Shorrocks and Foster (1987). It involves a regressive transfer and a progressive transfer both from the same donor, leaving the Gini index unchanged. We prove that finite sequences of these transfers and/or progressive transfers characterize the third degree inverse stochastic dominance criterion. This criterion allows us to make unanimous inequality judgements even when Lorenz curves intersect. The Gini coefficient becomes relevant in these cases in order to conclusively rank the distributions.     

Testing for bivariate stochastic dominance using inequality restrictions

We propose a test of bivariate stochastic dominance within a generalized framework for testing inequality restrictions, utilizing the covariance structure of the estimates of the joint distribution functions. Monte Carlo simulations and an empirical example assess its usefulness.     

Measuring human development: a stochastic dominance approach

We consider a weighting scheme that yields a best-case scenario for measured human development such as the official equally-weighted Human Development Index (HDI) using an approach that relies on consistent tests for stochastic dominance efficiency. We compare the official equally-weighted HDI to all possible indices constructed from a set of individual components to obtain the most optimistic scenario for development. In the best-case scenario index education is weighted considerably more than the other two components, per capita income and life expectancy, relative to the weight that it gets in the official equally-weighted index. It also turns out that the improvement in the official HDI is mainly driven by improvements over time in the education index, the component moving fastest relative to its targets, when compared with per capita income and life expectancy. We find that the best-case scenario hybrid index leads to a marked improvement of measured development over time when compared with the official equally-weighted HDI.     

A stochastic dominance approach to the measurement of discrimination

This note suggests a bridge between stochastic dominance (Rothschild and Stiglitz, 1970 [17], 1973 [18]), inequality measurement (Atkinson, 1970 [1]) and discrimination measurement (Gastwirth, 1975 [10]). Discrimination orderings are defined and illustrated through discrimination curves, in the same spirit as stochastic dominance analysis. The main result, which links the second order discrimination curve and the Gastwirth discrimination index, also generalizes the equivalence between Generalized Lorenz dominance and second order stochastic dominance.     

Arrow's theorem on the optimality of deductibles: A stochastic dominance approach

Summary We provide a new proof for the optimality of deductible insurance that does not depend on the expected-utility hypothesis. Our model uses only first- and second-degree stochastic dominance arguments.This paper was partially written while Schlesinger was visiting at the University of Toulouse. Financial support for this visit from the Fédération Francaise des Société d' Assurance is gratefully acknowledged. The authors also thank Louis Eeckhoudt, Ed Schlee and an anonymous referee for helpful comments.     

On the choice of functional form in stochastic frontier modeling

This paper examines the effect of functional form specification on the estimation of technical efficiency using a panel data set of 125 olive-growing farms in Greece for the period 1987–93. The generalized quadratic Box-Cox transformation is used to test the relative performance of alternative, widely used, functional forms and to examine the effect of prior choice on final efficiency estimates. Other than the functional specifications nested within the Box-Cox transformation, the comparative analysis includes the minflex Laurent translog and generalized Leontief that possess desirable approximation properties. The results indicate that technical efficiency measures are very sensitive to the choice of functional specification. Perhaps most importantly, the choice of functional form affects the identification of the factors affecting individual performance – the sources of technical inefficiency. The analysis also shows that while specification searches do narrow down the set of feasible alternatives, the identification of the most appropriate functional specification might not always be (statistically) feasible. First version received: November 1999/Final version received: July 2001 RID="*" ID="*"  The authors wish to thank Almas Heshmati, Robert Romain, and an anonymous referee for insightful comments and suggestions. Special thanks go to the associate editor who handled the paper, and whose careful reading and suggestions have improved the paper substantially. The second author wishes to acknowledge the financial support from “President SSHRC” from the University of Saskatchewan. The usual caveats with respect to opinions expressed in the paper apply. Senior authorship is shared. This is University of Nebraska-Lincoln Agricultural Research Division Article No. 13270.     

Qualitative valuation of environmental criteria through a group consensus based on stochastic dominance

This paper introduces a qualitative valuation method to elicit stakeholders' intensities of preferences for a complex environmental issue and multiple social groups. Environmental valuation studies have shown that in any complex environment with a diversity of environmental services, stakeholders have difficulties using a monetary valuation to make trade-offs between different environmental services. Stated preference methods such as the Contingent Valuation Method (CVM) have been criticised for their individualistic format and assumptions of commensurability between environmental criteria. To alleviate both of these criticisms, we propose a qualitative valuation method. The method contains a discursive step to allow stakeholders to discuss and construct a list of environmental criteria and alternative plans. The list of criteria and plans is subsequently used by a group of experts to formulate an Impact Matrix (IM), which is to be used in the succeeding individualistic steps of the methodology. The first individualistic step consists of asking the stakeholders to rank Alternative Impacts (AIs) in the IM for each single criterion. The stakeholders are then asked to express intensities of their preferences through pairwise comparisons between the AIs of the constructed rank order on each single criterion. These intensities are expressed on a qualitative scale. Subsequently, to provide social intensities of preferences, a social preference (social rank order) is first determined for each single criterion. We propose to use the median value among the intensities of preferences as the social intensity of preference by assuming interpersonal comparability and taking into account stochastic monotonocity. This is a pre-processing step, which allows us to reach social intensities of preferences in the Lar rangeland (Iran), where several social groups have conflicting interests on rangeland services, leading to conflicting preferences on environmental criteria.     

‘Regular’ choice and the weak axiom of stochastic revealed preference

We explore the relation between two ‘rationality conditions’ for stochastic choice behavior: regularity and the weak axiom of stochastic revealed preference (WASRP). We show that WASRP implies regularity, but the converse is not true. We identify a restriction on the domain of the stochastic choice function, which suffices for regularity to imply WASRP. When the universal set of alternatives is finite, this restriction is also necessary for regularity to imply WASRP. Furthermore, we identify necessary and sufficient domain restrictions for regularity to imply WASRP, when the universal set of alternatives is finite and stochastic choice functions are all degenerate. Results in the traditional, deterministic, framework regarding the relation between Chernoff’s condition and the weak axiom of revealed preference follow as special cases. Thus, general conditions are established, under which regularity can substitute for WASRP as the axiomatic foundation for a theory of choice behavior.     

Monetary policy and the choice of a monetary instrument in a stochastic setting

Should the FED try to set some monetary aggregate, or should it try to create certain credit conditions by setting interest rates? This question has been examined extensively within models that are essentially non-stochastic or certainty equivalent; however, the question is not meaningful to the monetary authority unless one postulates a stochastic setting. This paper attempts to analyze the question within a stochastic setting. It illustrates the new dimensions added by incorporating risk adverse economic behavior, “rational” expectations, and randomized policy settings.     

The concept of choice: why and how innovative behaviour is not just stochastic

The goal of this paper is to highlight the importance of the concept of choice. To do so, a synopsis of the most important contributions to this topic—featuring an eclectic set of scholars across disciplines—is provided. As central to the argument, John von Neumann’s contributions, game theory and simulation techniques on von Neumann machines, are identified. Innovation (economic and theoretic) as the driving force behind human evolution seems to head for a new scientific paradigm based on von Neumann’s ideas.