Stochastic dominance and decomposable measures of inequality and poverty

In this paper, we characterize some new links between stochastic dominance and the measurement of inequality and poverty. We show that: for second-degree normalized stochastic dominance (NSD), the weighted area between the NSD curve of a distribution and that of the equalized distribution is a decomposable inequality measure; for first-degree and second-degree censored stochastic dominance (CSD), the weighted area between the CSD curve of a distribution and that of the zero-poverty distribution is a decomposable poverty measure. These characterizations provide graphical representations for decomposable inequality and poverty measures in the same manner as Lorenz curve does for the Gini index. The extensions of the links to higher degrees of stochastic dominance are also investigated.     

Stochastic convexity in dynamic programming

Summary. This paper explores sufficient conditions for a continuous stationary Markov optimal policy and a concave value function in stochastic dynamic programming problems. Also, the paper addresses conditions needed for the differentiability of the value function. The paper uses conditions such as first order stochastic dominance, second order stochastic dominance and concave stochastic dominance that are widely applied in economics. Received: February 23, 2001; revised version: May 19, 2002 RID="*" ID="*" I am deeply indebted to Prajit Dutta for patient assistance and advice. This paper has benefited from discussions with Tsz Cheong Lai, Tackseung Jun, Werner Stanzl and Satyajit Bose as well as feedback from an anonymous referee.     

Second‐Order Discrimination and Generalized Lorenz Dominance

We propose a definition of second‐order discrimination that does not require the reference distribution to first‐order dominate the comparison one, and allows rankings of discrimination patterns when both the reference and the comparison distributions differ. It involves comparing the probabilities that randomly selected individuals in the reference and comparison distributions belong to subgroups having the same cumulative mean income, yields orderings of distributions equivalent to those from generalized Lorenz dominance, and allows orderings of discrimination patterns, partial or complete, across pairs of distributions. We compare discrimination against U.S. seniors (inter‐distributional inequality between seniors and non‐seniors) by ethnicity.     

Asymmetric first price auctions

A new approach to asymmetric first price auctions is proposed which circumvents the need to examine bidding strategies directly. Specifically, the ratio of bidders' (endogenous) payoffs is analyzed and compared to the ratio of the (exogenous) distribution functions that describe beliefs. Most of the results are inferred from this comparison. In the existing theoretical literature, assumptions of first order stochastic dominance or stronger imply that the latter ratio has very specific properties, but no such assumptions are imposed here. It is proven that first order stochastic dominance is necessary for bidding strategies not to cross. When this assumption is relaxed in the numerical literature it is done in a manner that leads to exactly one crossing. However, it is straightforward to construct examples with several crossings. Finally, bid distributions will cross in auctions with two bidders whenever second order (but not first order) stochastic dominance applies.     

The effect of feedback consistency on success in markets with positive feedbacks

In this paper, we show how the finite time expected outcomes in a stochastic ball and urn model depend on the variation in feedbacks by applying the concept of second order stochastic dominance to the feedback distribution. We find that less variation leads to greater expected outcomes.     

Elementary multivariate rearrangements and stochastic dominance on a Fréchet class

A Fréchet class collects all multivariate joint distribution functions that have the same marginals. Members of a Fréchet class only differ with respect to the interdependence between their marginals. In this paper, I study orders of interdependence on a Fréchet class using two multivariate generalizations of the bivariate rearrangement proposed by Epstein and Tanny (1980) [4] and Tchen (1980) [16]. I show how these multivariate rearrangements are underlying multivariate first order stochastic dominance in terms of the joint distribution function and the survival function. A combination of both rearrangements is shown to be equivalent to the concordance order proposed by Joe (1990) [9].     

Restricted and Unrestricted Dominance for Welfare, Inequality, and Poverty Orderings

This paper extends the previous literature on the ethical links between the measurement of poverty, social welfare and inequality. We show inter alia, how, when the range of possible poverty lines is unbounded above, a robust ranking of absolute poverty may be interpreted as a robust ranking of social welfare, and a robust ranking of relative poverty may be interpreted as a robust ranking of inequality, and this, for any order of stochastic dominance.     

Stronger measures of higher-order risk attitudes

This paper aims to extend the results by Ross (1981) [15] and by Modica and Scarsini (2005) [13] to stochastic dominance of degree 4 and over. Specifically, it is shown that Ross' approach can be extended to any order of risk attitude beyond the generalization proposed by Modica and Scarsini by means of sth degree increase in risk defined by Ekern (1980) [8].     

Stochastic Dominance Analysis of Soil and Water Conservation in Subsistence Crop Production in the Eastern Ethiopian Highlands: The Case of the Hunde-Lafto Area

The aim of this paper is to analyze whether investment in soil and water conservation results in a higher yield and income and/or mitigate variability in yield and income to subsistence farm households in the Hunde-Lafto area. Net returns from crop production with and without soil and water conservation (SWC) are compared based on stochastic dominance (SD) criteria. A non-parametric first order SD and normalized second order are used for data analysis. Analysis is based on the Soil Conservation Research Program (SCRP) database for the Hunde-Lafto research unit. The results of the analysis suggest that adopting a conservation strategy results in higher grain yield and net return than in not adopting. The normalized second order SD analysis results do not support the hypothesis that conservation strategy is unambiguously better than a noconservation strategy in reducing variability in yield and net return to farmers. However, conservation strategy has shown second order dominance at lower levels of yield and income that often correspond to unfavorable rainfall conditions. This makes it a preferred strategy to cope with the most prevalent risk factor of moisture shortage. Therefore, appropriate policies to help and encourage farmers to adopt SWC structures will contribute to improving the welfare of subsistence farm households in the study area and in other similar settings in the country. Designing and implementing SWC techniques that may result in unambiguous second order SD dominance will further improve the desirability and adoption of conservation measures.     

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.     

SEQUENTIAL STOCHASTIC DOMINANCE AND THE ROBUSTNESS OF POVERTY ORDERINGS

When comparing poverty across distributions, an analyst must select a poverty line to identify the poor, an equivalence scale to compare individuals from households of different compositions and sizes, and a poverty index to aggregate individual deprivation into an index of total poverty. A different choice of poverty line, poverty index or equivalence scale can of course reverse an initial poverty ordering. This paper develops easily-checked sequential stochastic dominance conditions that throw light on the robustness of poverty comparisons to these important measurement issues. These general conditions extend well-known results to any order of dominance, to the choice of individual versus family based aggregation, and to the estimation of "critical sets" of measurement assumptions. Our theoretical results are briefly illustrated using data for four countries drawn from the Luxembourg Income Study databases.     

A Spatial Stochastic Frontier Model with Spillovers: Evidence for Italian Regions

Efficiency measurement using stochastic frontier models is well established in applied econometrics. However, no published work seems to be available on efficiency analysis using spatial data dealing with possible spatial dependence between regions. This article considers a stochastic frontier model with decomposition of inefficiency into an idiosyncratic and a spatial, spillover component. Exact posterior distributions of parameters are derived, and computational schemes based on Gibbs sampling with data augmentation are proposed to conduct simulation‐based inference and efficiency measurement. The new method is illustrated using production data for Italian regions (1970–1993). Clearly, further theoretical and empirical research on the subject would be of great interest.     

Poverty Reducing Reforms and Subgroup Consumption Dominance Curves

One vexed question of anti-poverty strategies is that of setting a reasonable poverty line. To escape its specification, recent developments by Yitzhaki and Slemrod (1991 ) have introduced the correspondence between non-intersecting concentration curves and poverty reducing directions of reforms. Makdissi and Wodon (2002 ) have derived consumption dominance curves for any order of restricted stochastic dominance. In this paper, consumption dominance curves are extended to subgroups of population. Empirical evidence of the approach will be shown using the 1997 data from Belarus, considering public subsidies on rents and utilities, health care and public transport in six groups of population.     

一个优序融资理论的解析模型

企业资本结构安排决定了资本市场的形成与发展,资本市场的现实状况又制约着企业资本结构的优化决策。本文从逆向选择角度,利用图解及数学模型分析解释了企业优序融资理论。基于假定(两类)企业对于其项目利润控制能力(能否使Rs>Rf)是不同的,通过对"共同均衡"和"个体均衡"的分析,认为企业优序融资行为的原因在于"逆向选择",而非"道德风险"。     

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.     

Dual theory of choice with multivariate risks

We propose a multivariate extension of Yaari?s dual theory of choice under risk. We show that a decision maker with a preference relation on multidimensional prospects that preserves first order stochastic dominance and satisfies comonotonic independence behaves as if evaluating prospects using a weighted sum of quantiles. Both the notions of quantiles and of comonotonicity are extended to the multivariate framework using optimal transportation maps. Finally, risk averse decision makers are characterized within this framework and their local utility functions are derived. Applications to the measurement of multi-attribute inequality are also discussed.     

Variability Measurements and Choice of Exchange Rate System: Asian Versus industrialized Countries

This paper examines whether the exchange rate movements of six Asian countries and six industrialized countries are normally distributed. This study also uses stochastic dominance to determine whether risk averse investors would prefer the fixed exchange rate system to the floating exchange rate system. Our empirical results show that most exchange rate changes are non-normal stable. Results form the stochastic dominance technique indicate that not all risk averse individuals will necessarily prefer one exchange rate system to the other. [F31]     

Decomposition of s‐concentration curves

Abstract. For any given order of inverse stochastic dominance, standard concentration curves are decomposed into three components, called contribution curves. Those components correspond to within‐group inequalities, between‐group inequalities, and transvariational inequalities. We prove, for all orders, that contribution curve dominance implies systematically welfare‐improving tax reforms and conversely. Accordingly, as welfare expansions may be costly in terms of particular inequalities, we propose targeted fiscal reforms.     

On the theory of risk aversion and the theory of risk

Relationships between the theory of risk aversion and the theory of risk have been noted by Diamond and Stiglitz [12], Kihlstrom and Mirman [24], and Leland [29]. The main result of this paper is a characterization of the Pratt and Kihlstrom-Mirman [24, 46] relation “more risk averse” between utility functions in terms of a stochastic dominance or “riskier” relation between certain probability measures derived from these utility functions. This result is used in the comparison of risk-adjusted portfolio yields to extend to the several risky asset case the intuition provided by the Arrow-Pratt [1, 46] portfolio theorem that “more risk averse” means “will take less risk.”     

Asymptotic and small sample analysis of the stochastic properties and certainty equivalents of winning bids in independent private values auctions$\!$

Summary. This paper investigates the stochastic properties of the first price and second price winning bids in auctions with risk neutral bidders with independent and identically distributed valuations. In such an environment, the winning first price bids second order stochastically dominate the second price winning bids. A key result of this paper is that the ratio of the variance of the winning first price bid to that of the winning second price bid is strictly less than one even as the number of bidders goes to infinity. This suggests that the stochastic dominance of the winning first price bids does not vanish even in the limit. Both the asymptotic and small sample properties of winning bids are investigated. In particular, the small sample results suggest that the identification power of econometric procedures that rely on winning bids can decline rapidly as the number of bidders increases. This paper also includes a systematic evaluation of the difference in certainty equivalents between the two auction formats for several common distributions and number of bidders for the case of auctioneers with constant coefficient of absolute risk aversion. These results are presented in a form that makes it easy to apply them to a specific auction of interest.Received: 15 July 2002, Revised: 7 April 2003, JEL Classification Numbers: D44.I would like to thank David Pearce for helpful comments and discussion and a referee for suggestions that have greatly improved this paper.