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.     

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.     

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.     

Probabilistic choice and stochastic dominance

This paper presents an axiomatic model of probabilistic choice under risk. In this model, when it comes to choosing one lottery over another, each alternative has a chance of being selected, unless one lottery stochastically dominates the other. An individual behaves as if he or she compares lotteries to a reference lottery—the least upper bound or the greatest lower bound in terms of stochastic dominance. The proposed model is compatible with several well-known violations of expected utility theory such as the common ratio effect and the violations of betweenness. Necessary and sufficient conditions for the proposed model are completeness, weak stochastic transitivity, continuity, common consequence independence, outcome monotonicity, and odds ratio independence.     

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.     

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.     

More on stochastic index numbers

There are three major approaches used to estimate index numbers. The first is Fisher's test approach whereby indexes are judged on their ability to satisfy certain criteria. The economic theory of index numbers is the second approach and this deals with their foundations in utility theory. The third approach is a less well-known methodology, but one which is now attracting considerable attention, the stochastic approach which is a new way of viewing index numbers in which uncertainty and statistical ideas play a central role. While providing a point estimate for the index number like the other two approaches, the stochastic approach additionally provides the SE of the point estimate. This article enhances understanding of stochastic index numbers by showing that they are formally equivalent to the familiar optimal combination of forecasts with the individual prices playing the role of n forecasts of the overall rate of inflation. This leads to new analytical results on the impact of adding additional information within the stochastic approach framework. We provide two concrete examples of the sources of such additional information: (i) the quantity theory of money; and (ii) the use of quantity data in addition to price data. We also illustrate some of these theoretical results using real data.     

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.     

An innovation index based on factor analysis

Factor analysis techniques are applied to develop an innovation index which indicates the relative tendency of various industrial sectors to innovate. The index is derived from various input variables which reflect the extent to which resources are allocated to achieve innovation and output variables which measure the extent to which new product and process innovation is achieved. In constructing the innovation index, each of the variables is weighted in accordance to its involvement in factor patterns which best reproduce correlations in the set of statistics. The innovation index is applied to rank-order various industrial sector and changes in innovation characteristics over time are indicated by index values determined for 1960, 1963 and 1970. Relationships are established between values of the innovation index and interindustry differences in the dynamics of the development of markets created through technological innovation. Application of these relationships for projecting the rate at which markets will develop for new technological innovations is discussed.     

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.     

An environmental performance index for products reflecting damage costs

Several studies have demonstrated how to use DEA (Data Envelopment Analysis) based techniques to estimate environmental performance indices. None of these studies, however, are taking information on the environmental damage costs of the pressure types considered into account. This study is bridging a gap between environmental indices founded in physical pressures and damage costs founded in welfare economics. The aim of the paper is twofold: first, to demonstrate how to implement the information on environmental damage costs within a DEA based environmental performance index, and second, to estimate these indices at product level by using Danish input-output data and environmental data from 1997.     

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.     

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.     

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.     

Measuring environmental performance with stochastic environmental DEA: The case of APEC economies

Data envelopment analysis (DEA) has been widely used for environmental performance measurement at different levels. Most of environmental DEA models take the deterministic form without considering random factors. This paper presents a stochastic environmental DEA model that can measure environmental performance under random conditions. The proposed model has been applied to evaluate the environmental performance of Asia-Pacific Economic Cooperation (APEC) economies in 2010. The results indicate that the stochastic pure environmental performance of APEC economies is indeed affected by random factors. Especially, the fluctuation of Republic of Korea's stochastic pure environmental performance is most obvious among all the APEC economies.