Testing for stochastic dominance using the weighted McFadden-type statistic

We demonstrate that when testing for stochastic dominance of order three and above, using a weighted version of the Kolmogorov–Smirnov-type statistic proposed by McFadden [1989. In: Fomby, T.B., Seo, T.K. (Eds.), Studies in the Economics of Uncertainty. Springer, New York, pp. 113–134] is necessary for obtaining a non-degenerate asymptotic distribution. Since the asymptotic distribution is complex, we discuss a bootstrap approximation for it in the context of a real application.     

On properties of division rules lifted by bilateral consistency

We consider the problem of adjudicating conflicting claims in the context of a variable population. A property of rules is “lifted” if whenever a rule satisfies it in the two-claimant case, and the rule is bilaterally consistent, it satisfies it for any number of claimants. We identify a number of properties that are lifted, such as equal treatment of equals, resource monotonicity, composition down and composition up, and show that continuity, anonymity and self-duality are not lifted. However, each of these three properties is lifted if the rule is resource monotonic.     

Fairness and implementability in allocation of indivisible objects with monetary compensations

This paper introduces a general framework for the fair allocation of indivisible objects when each agent can consume at most one (e.g., houses, jobs, queuing positions) and monetary compensations are possible. This framework enables us to deal with identical objects and monotonicity of preferences in ranking objects. We show that the no-envy solution is the only solution satisfying equal treatment of equals, Maskin monotonicity, and a mild continuity property. The same axiomatization holds if the continuity property is replaced by a neutrality property.     

Nonparametric estimation and inference about the overlap of two distributions

This paper develops methodology for nonparametric estimation of a measure of the overlap of two distributions based on kernel estimation techniques. This quantity has been proposed as a measure of economic polarization between two groups, Anderson (2004) and Anderson et al. (2010). In ecology it has been used to measure the overlap of species. We give the asymptotic distribution theory of our estimator, which in some cases of practical relevance is nonstandard due to a boundary value problem. We also propose a method for conducting inference based on estimation of unknown quantities in the limiting distribution and show that our method yields consistent inference in all cases we consider. We investigate the finite sample properties of our methods by simulation methods. We give an application to the study of polarization within China in recent years using household survey data from two provinces taken in 1987 and 2001. We find a big increase in polarization between 1987 and 2001 according to monetary outcomes but less change in terms of living space.     

Edgeworth expansions and normalizing transforms for inequality measures

Finite sample distributions of studentized inequality measures differ substantially from their asymptotic normal distribution in terms of location and skewness. We study these aspects formally by deriving the second-order expansion of the first and third cumulant of the studentized inequality measure. We state distribution-free expressions for the bias and skewness coefficients. In the second part we improve over first-order theory by deriving Edgeworth expansions and normalizing transforms. These normalizing transforms are designed to eliminate the second-order term in the distributional expansion of the studentized transform and converge to the Gaussian limit at rate O(n⁻¹)$O\left(n^{-1}\right)$. This leads to improved confidence intervals and applying a subsequent bootstrap leads to a further improvement to order O(n^−3/2)$O\left(n^{-3/2}\right)$. We illustrate our procedure with an application to regional inequality measurement in Côte d’Ivoire.     

An econometric method of correcting for unit nonresponse bias in surveys

Past approaches to correcting for unit nonresponse in sample surveys by re-weighting the data assume that the problem is ignorable within arbitrary subgroups of the population. Theory and evidence suggest that this assumption is unlikely to hold, and that household characteristics such as income systematically affect survey compliance. We show that this leaves a bias in the re-weighted data and we propose a method of correcting for this bias. The geographic structure of nonresponse rates allows us to identify a micro compliance function, which is then used to re-weight the unit-record data. An example is given for the US Current Population Surveys, 1998–2004. We find, and correct for, a strong household income effect on response probabilities.     

Strategyproof multiple assignment using quotas

The allocation of heterogeneous and indivisible objects is considered where there is no medium of exchange. We characterize the set of strategyproof, nonbossy, Pareto-optimal, and neutral social choice functions when preferences are monotonic and quantity-monotonic. The characterized sets of social choice functions are sequential; agents are assigned their favorite objects among the objects not given to others before them, subject to a quota. Received: 5 January 1999 / Accepted: 14 June 1999     

A study of proportionality and robustness in economies with a commonly owned technology

Abstract. Studying one-input one-output economies, we say that an allocation is proportional if the input-output ratio is identical among agents and if each agent maximizes her welfare given this ratio. We propose three equity axioms based on this definition, and we use them to compare the main solutions to this simple equity problem. We also combine efficiency, robustness axioms and our proportionality axioms to characterize two solutions. Received: 11 June 1997 / Accepted: 26 May 2000     

Proportionally adjusted marginal pricing method to share joint costs

We consider the cost sharing problem with divisible demands of heterogeneous goods. We propose a cost sharing method called Proportionally Adjusted Marginal Pricing (PAMP) method. PAMP is a nonadditive (in the cost function) extension of average cost pricing. We introduce an axiom called Local Independence (LI) and use LI together with Continuity, Proportionality, and Scale Invariance to characterize PAMP. Received: 23 March 2001 / Accepted: 16 November 2001 I thank Yves Sprumont, Hervé Moulin, and Ahmet Alkan for discussions, comments and suggestions. Thanks also go to the associate editor and the referees, whose comments and suggestions greatly improve the paper.     

Heuristic learning and the discovery of specialization and exchange

I develop and calibrate an agent-based model of boundedly rational, adaptive agents in a two-good production and exchange economy to replicate human-subject outcomes in the same eight-person experimental economy. To test agents’ ability to capture human behavior, I extend the model and use its output to make predictions about a second experimental environment in which the group of eight agents is slowly constructed by merging smaller groups. This environment improves human-subject performance in the specialization and exchange task, and commensurate improvement emerges for some parameterizations of the agent-based model. This iterative process yields incremental improvement of decision-level theories about economic discovery.     

A characterization and an impossibility of finite length anonymity for infinite generations

In the context of ranking infinite utility streams, the impartiality axiom of finite length anonymity requires the equal ranking of any two utility streams that are equal up to a finite length permutation ( Fleurbaey and Michel, 2003). We first characterize any finite length permutation as a composition of a fixed step permutation and an “almost” fixed step permutation. We then show that if a binary relation satisfies finite length anonymity, then it violates all the distributional axioms that are based on a segment-wise comparison. Examples of those axioms include the weak Pareto principle and the weak Pigou-Dalton principle.     

Generalized time-invariant overtaking

We present a new version of the overtaking criterion, which we call generalized time-invariant overtaking. The generalized time-invariant overtaking criterion (on the space of infinite utility streams) is defined by extending proliferating sequences of complete and transitive binary relations defined on finite dimensional spaces. The paper presents a general approach that can be specialized to at least two, extensively researched examples, the utilitarian and the leximin orderings on a finite dimensional Euclidean space.     

Farsighted house allocation

In this note we study von Neumann–Morgenstern farsightedly stable sets for Shapley and Scarf (1974) housing markets. Kawasaki (2010) shows that the set of competitive allocations coincides with the unique von Neumann–Morgenstern stable set based on a farsighted version of antisymmetric weak dominance (cf., Wako, 1999). We demonstrate that the set of competitive allocations also coincides with the unique von Neumann–Morgenstern stable set based on a farsighted version of strong dominance (cf., Roth and Postlewaite, 1977) if no individual is indifferent between his endowment and the endowment of someone else.     

Smooth inequality measurement: Approximation theorems

The main purpose of this paper is to prove that smoothness is not a restrictive assumption in inequality measurement as any inequality measure (preorder) can be approximated in a well defined sense by a smooth inequality measure (preorder).     

A polyhedral approximation approach to concave numerical dynamic programming

This paper introduces a numerical method for solving concave continuous state dynamic programming problems which is based on a pair of polyhedral approximations of concave functions. The method is globally convergent and produces computable upper and lower bounds on the value function which can in theory be made arbitrarily tight. This is true regardless of the pattern of binding constraints, the smoothness of model primitives, and the dimensionality and rectangularity of the state space. We illustrate the method's performance using an optimal firm management problem subject to credit constraints and partial investment irreversibilities.