The Measurement of Rank Mobility

In this paper we investigate the problem of measuring social mobility when the social status of individuals is given by their rank. In order to sensibly represent the rank mobility of subgroups within a given society, we address the problem in terms of partial permutation matrices which include standard (“global”) matrices as a special case. We first provide a characterization of a partial ordering on partial matrices which, in the standard case of global matrices, coincides with the well-known “concordance” ordering. We then provide a characterization of an index of rank mobility based on partial matrices and show that, in the standard case of comparing two global matrices, it is equivalent to Spearman’s index.Mobility measurement, Concordance, Partial matrices, Sperman's index.

How Demanding Should Equality of Opportunity Be, and How Much Have We Achieved?

[Excerpt] This chapter proposes tests of various notions of equality of opportunity and applies them to intergenerational income data for the United States and Britain. Agreement is widespread that equality of opportunity holds in a society if the chances that individuals have to succeed depend only on their own efforts and not on extraneous circumstances that may inhibit or expand those chances. What is contentious, however, is what constitutes effort and circumstances. Most people, we think, would say that the social connections of an individual\u27s parents would be included among circumstances: equality of opportunity is incomplete if some individuals get ahead because they have well-connected parents. This and other channels through which circumstances affect income opportunities in an intergenerational context are discussed in Section 2. Section 3 then formulates four, increasingly stringent criteria for equality of opportunity. In Section 4, we turn to an empirical implementation of these criteria to test for equality of opportunity in the United States and Britain. The results, presented in Section 5, provide only the weakest of support for equality of opportunity in the United States and no support at all in Britain. Concluding remarks are presented in Section 6

Inference for Lorenz curve orderings

Summary In this paper we consider the issue of performing statistical inference for Lorenz curve orderings. This involves testing for an ordered relationship in a multivariate context and making comparisons among more than two population distributions. Our approach is to frame the hypotheses of interest as sets of linear inequality constraints on the vector of Lorenz curve ordinates, and apply order-restricted statistical inference to derive test statistics and their sampling distributions. We go on to relate our results to others which have appeared in recent literature, and use Monte Carlo analysis to highlight their respective properties and comparative performances. Finally, we discuss in general terms the issue and problems of framing hypotheses, and testing them, in the context of the study of income inequality, and suggest ways in which the distributional analyst could best proceed, illustrating with empirical examples

Uncertainty and the demand for medical care

This paper analyses the effects of uncertainty on the demand for medical care. It employs a simplified version of Grossman’s human capital model of the demand for health to examine the consequences for the demand for medical care of increased uncertainty surrounding the effectiveness of medical treatment and the incidence of ill-health. We show that under plausible assumptions the demand for medical care will increase following increased uncertainty over the incidence of ill-health. We also show that though the effects of increased uncertainty over the effectiveness of medical care are indeterminate a prion, it is possible to identify situations in which one can make unambiguous predictions about how the demand for medical care responds to increased uncertainty over the effectiveness of medical care. In addition to presenting the comparative static results, we also discuss their policy implications.

Do we value mobility?

Is there a trade-off between people’s preference for income equality and income mobility? Testing for the existence of such a trade-off is difficult because mobility is a multifaceted concept. We analyse results from a questionnaire experiment based on simple precise concepts of income inequality and income mobility. We find no direct trade-off in preference between mobility and equality, but an indirect trade-off, applying when more income mobility can only be obtained at the expense of some income inequality. Mobility preference—but not equality preference—appears to be driven by personal experience of mobility

Inferring cognitive heterogeneity from aggregate choices

Theories of bounded rationality often assume a rich dataset of choices from many overlapping menus, limiting their practical applicability. In contrast, we study the problem of identifying the distribution of cognitive characteristics in a population of agents from a minimal dataset that consists of aggregate choice shares from a single menu, and includes no observable covariates of any kind. With homogeneous preferences, we find that “consideration capacity” and “consideration probability” distributions can both be recovered effectively if the menu is sufficiently large. This remains true generically when tastes are heterogeneous with a known distribution. When the taste distribution is unknown, we show that joint choice share data from three “occasions” are generically sufficient for full identification of the cognitive distribution, and also provide substantial information about tastes

Inferring cognitive heterogeneity from aggregate choices

One potentially important drawback of existing theories of limited attention is that they typically assume a rich dataset of choices from many menus. We study the problem of identifying the distribution of cognitive characteristics in a population of agents when only aggregate choice behavior from a single menu is observable. We show how both “consideration probability” and “consideration capacity” distributions can be substantially identified by aggregate choice shares. We also suggest how to embed the attention models in an econometric specification of the inference problem. Finally, we sucessfully use our results to recover the true parameters in Monte Carlo simulations of both models

A Pedagogical Proof of Arrow's Impossibility Theorem

In this note I consider a simple proof of Arrow's Impossibility Theorem (Arrow 1963). I start with the case of three individuals who have preferences on three alternatives. In this special case there are 133=2197 possible combinations of the three individuals' rational preferences. However, by considering the subset of linear preferences, and employing the full strength of the IIA axiom, I reduce the number of cases necessary to completely describe the SWF to a small number, allowing an elementary proof suitable for most undergraduate students