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 fnd 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.

Young people' s willingness to pay for environmental protection

Abstract The cost of the ongoing degradation of natural capital will inevitably be borne by the younger generations. And, as the wave of school strikes for action against climate change have proved, they do not want their voice to be ignored. Discrete Choice Experiments are increasingly used for the valuation of environmental goods, but they have never been conducted with minors. We designed and administered such an experiment to elicit the willingness of children and teenagers, aged 8–19, to pay for environmental projects. The results suggest that their marginal willingness to pay is higher for projects in their own country (Italy) and that the utility of environmental protection is greate…

The Simpson paradox of school grading in Italy

Abstract Data from the 2003 OECD-PISA Survey for Italy reveal a striking difference in the relationship between students’ competence (as measured by PISA score in Mathematics) and school grades across regions: a competence level granting bare sufficiency in the North yields excellence grades in the South. This has spurred a lively debate on education policy in the country, based on the inference drawn from this evidence that grading practices are excessively different in the two areas. We show in this note that this inference overlooks a Simpson paradox hidden in the data. After a more careful analysis, the above inference is seen to be wrong. The crucial omitted variable is the school-leve…

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 un…

Regression with imputed covariates: A generalized missing-indicator approach

A common problem in applied regression analysis is that covariate values may be missing for some observations but imputed values may be available. This situation generates a trade-off between bias and precision: the complete cases are often disarmingly few, but replacing the missing observations with the imputed values to gain precision may lead to bias. In this paper, we formalize this trade-off by showing that one can augment the regression model with a set of auxiliary variables so as to obtain, under weak assumptions about the imputations, the same unbiased estimator of the parameters of interest as complete-case analysis. Given this augmented model, the bias-precision trade-off may the…

Testing for Asymmetric Information in Insurance Markets: A Multivariate Ordered Regression Approach

The positive correlation (PC) test is the standard procedure used in the empirical literature to detect the existence of asymmetric information in insurance markets. This article describes a new tool to implement an extension of the PC test based on a new family of regression models, the multivariate ordered logit, designed to study how the joint distribution of two or more ordered response variables depends on exogenous covariates. We present an application of our proposed extension of the PC test to the Medigap health insurance market in the United States. Results reveal that the risk–coverage association is not homogeneous across coverage and risk categories, and depends on individual so…

Nonlinearities in the Becker-Tomes-Solon model

The aim of this paper is to explore nonlinearities in the relationship between parents and children earnings. We rst discuss a simple extension of the Becker-Tomes-Solon model accounting for nonlinearity. We then test the linearity of intergenerational transmission employing a set of 141 intergenerational mobility tables in 35 di erent countries at di erent time periods, and nd that linearity is rejected in 89 tables. We nally explore the correlation between the \strength of concavity" and income inequality. Our ndings suggest that more unequal societies tend to have a more concave intergenerational transmission process.

Regression with Imputed Covariates: A Generalized Missing Indicator Approach

A common problem in applied regression analysis is that covariate values may be missing for some observations but imputed values may be available. This situation generates a trade-off between bias and precision: the complete cases are often disarmingly few, but replacing the missing observations with the imputed values to gain precision may lead to bias. In this paper we formalize this trade-off by showing that one can augment the regression model with a set of auxiliary variables so as to obtain, under weak assumptions about the imputations, the same unbiased estimator of the parameters of interest as complete-case analysis. Given this augmented model, the bias-precision trade-off may then…

The welfare cost of unpriced heterogeneity in insurance markets

We consider the welfare loss of unpriced heterogeneity in insurance markets, which results when private information or regulatory constraints prevent insurance companies to set premiums reflecting expected costs. We propose a methodology which uses survey data to measure this welfare loss. After identifying some “types” which determine expected risk and insurance demand, we derive the key factors defining the demand and cost functions in each market induced by these unobservable types. These are used to quantify the efficiency costs of unpriced heterogeneity. We apply our methods to the US Long-Term Care and Medigap insurance markets, where we find that unpriced heterogeneity causes substan…

School grading and institutional contexts

We study how the relationship between students' cognitive ability and their school grades depends on institutional contexts. In a simple abstract model, we show that unless competence standards are set at above-school level or the variation of competence across schools is low, students' competence valuation will be heterogeneous, with weaker schools inflating grades or flattening their dependence on competence, therefore reducing the information content and comparability of school grades. Using data from the OECD-PISA 2003 Survey, the model is applied to a sample of four countries, namely Australia, Germany, Italy, and the Netherlands. We find that in Australia, schools' heterogeneity does …

A Generalized Missing-Indicator Approach to Regression with Imputed Covariates

We consider estimation of a linear regression model using data where some covariate values are missing but imputations are available to fill in the missing values. This situation generates a tradeoff between bias and precision when estimating the regression parameters of interest. Using only the subsample of complete observations does not cause bias but may imply a substantial loss of precision because the complete cases may be too few. On the other hand, filling in the missing values with imputations may cause bias. We provide the new Stata command gmi, which handles such tradeoff by using either model reduction or Bayesian model averaging techniques in the context of the generalized miss…

REPORTING HETEROGENEITY IN SUBJECTIVE HEALTH MEASURES: AN EXTENDED LATENT CLASS APPROACH

CONSUMPTION DECISIONS WITH INCOME UNCERTAINTY AND A KINKED BUDGET CONSTRAINT

Nonlinearity in intergenerational income transmission: A cross-country analysis

Abstract The aim of this paper is to explore nonlinearity in intergenerational income transmission. We use a set of occupational tables in different countries to test nonlinearity. We also empirically address how policy variables can affect nonlinearity. Our findings suggest that concavity is supported in those societies with less credit constraints, but with more poverty and income inequality; education has an increasing effect on convexity.

Reporting heterogeneity in health: an extended latent class approach

This article explores how individual socio-economic characteristics affect unobserved heterogeneity in self-reporting behaviour and health production using a multivariate finite mixture model. Results show a positive relationship between objective and subjective observable health indicators and true health and support the existence of self-reporting bias related to socio-economic characteristics and individual life styles.

Measuring and Evaluating Intergenerational Mobility: Evidence from Students’ Questionnaires

Three fundamental ideas in the study of intergenerational mobility are those of structural mobility, origin independence and rank reversal. We review the theoretical literature focused on the three ideas and present evidence from a questionnaire designed to test students’ views regarding the different notions. The questionnaire is conducted under both a “measurement” and an “evaluation” frame; it uses questions involving both verbal statements of the principles tested and pairwise comparisons of simple hypothetical mobility situations; for the latter exercise, the questionnaire introduces a new intuitive display based on mobility trees. The evidence provides various results: most notably, o…

Horizontal inequity comparisons

In this paper, we expound the idea that horizontal inequity (HI) in different tax systems be compared by transplanting the HI from one tax system into the other, as a mapping between its pre- and post-tax living standard distributions, and then applying known results to compare the extent of association present in the two joint distributions. We make this idea operational by means of axioms which, we show, lead to an implementable procedure based on the `copula'. Statistical inference procedures are discussed, and illustrative empirical exercises are undertaken for the UK, Canadian and Israeli tax and benefit systems.

The Effect Of Supplemental Insurance On Health Care Demand With Multiple Information: A Latent Class Analysis

The Medicare program, which provides insurance coverage to the elderly in the United States, does not protect them fully against high out-of-pocket costs. For this reason private supplementary insurance, named Medigap, has been available to cover Medicare gaps. This paper studies how Medigap affects the utilization of health care services. The decision to take out supplemental insurance is likely to be infuenced by unobservable attributes such as actual risk type and insurance preferences. Empirical appraisals to this problem typically rely on the recursive bivariate probit. We exploit the Health and Retirement Study data and some recent advances on latent class analysis to jointly model th…

Social Mobility

The need for standards in students’ grading

Stochastic monotonicity in intergenerational mobility tables

SUMMARY The aim of this paper is to test for stochastic monotonicity in intergenerational socio-economic mobility tables. In other words, we question whether having a parent from a high socio-economic status is never worse than having one with a lower status. Using existing inferential procedures for testing unconditional stochastic monotonicity, we first test a set of 149 intergenerational mobility tables in 35 different countries and find that monotonicity cannot be rejected in hardly any table. In addition, we propose new testing procedures for testing conditional stochastic monotonicity and investigate whether monotonicity still holds after conditioning on a number of covariates such as…

Measuring andevaluating social mobility: evidence on students’ questionnaire

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

In this paper we provide an application-oriented characterization of a class of distance functions monotonically related to the Euclidean distance in terms of some general properties of distance functions between real-valued vectors. Our analysis hinges upon two fundamental properties of distance functions that we call “value-sensitivity” and “order- sensitivity”. We show how these two general properties, combined with natural monotonicity considerations, lead to characterization results that single out several versions of Euclidean distance from the wide class of separable distance functions. We then discuss and motivate our results in two different and apparently unrelated application are…

Regression models for multivariate ordered responses via the Plackett distribution

AbstractWe investigate the properties of a class of discrete multivariate distributions whose univariate marginals have ordered categories, all the bivariate marginals, like in the Plackett distribution, have log-odds ratios which do not depend on cut points and all higher-order interactions are constrained to 0. We show that this class of distributions may be interpreted as a discretized version of a multivariate continuous distribution having univariate logistic marginals. Convenient features of this class relative to the class of ordered probit models (the discretized version of the multivariate normal) are highlighted. Relevant properties of this distribution like quadratic log-linear e…

Incentive and Selection Effects of Medigap Insurance on Inpatient Care

The Medicare program, which provides insurance coverage to the elderly in the United States, does not protect them fully against high out-of-pocket costs. For this reason private supplementary insurance, named Medigap, has been available to cover Medicare gaps. This paper studies how Medigap affects the utilization of inpatient care, separating the incentive and selection effects of supplementary insurance. For this purpose, we use two alternative estimation methods: a standard recursive bivariate probit and a discrete multivariate finite mixture model. We find that estimated incentive effects are modest and quite similar across models. On the other hand, there seems to be very significant …

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. This special case conveys the nature of Arrow's result. It is well known that the restriction to three options is not really limiting (any larger se…

Organizzazione aziendale del'SSN e cenni di economia sanitaria

What's So Speciall About Euclidean Distance? A Characterization Result with Applications to Mobility and Spatial Voting

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 rep- resent 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 mo- bility based on partial matrices and show that, in the standard case of comparing two global matrices, it is equiv…

Model averaging estimation of generalized linear models with imputed covariates

a b s t r a c t We address the problem of estimating generalized linear models when some covariate values are missing but imputations are available to fill-in the missing values. This situation generates a bias-precision trade- off in the estimation of the model parameters. Extending the generalized missing-indicator method proposed by Dardanoni et al. (2011) for linear regression, we handle this trade-off as a problem of model uncertainty using Bayesian averaging of classical maximum likelihood estimators (BAML). We also propose a block model averaging strategy that incorporates information on the missing-data patterns and is computationally simple. An empirical application illustrates our…

How to standardize (if you must)

In many situations we are interested in appraising the value of a certain characteristic for a given individual relative to the context in which this value is observed. In recent years this problem has become prominent in the evaluation of scientific productivity and impact. A popular approach to such relative valuations consists in using percentile ranks. This is a purely ordinal method that may sometimes lead to counterintuitive appraisals, in that it discards all information about the distance between the raw values within a given context. By contrast, this information is partly preserved by using standardization, i.e., by transforming the absolute values in such a way that, within the s…

7. Mobility comparisons: Does using different measures matter?

In this paper we review alternative measure of intergenerational mobility, emphasizing the distinction between absolute, relative and ordinal mobility. We then compare the performance of various mobility indices using real data. FromTreiman and Ganzeboom (1990) dataset we compare the degree of occupational and educational intergenerational (father-son) mobility in 16 countries in a single year (comprised between 1968 and 1982). From three Bank of Italy surveys (1993, 1995, 1998) we obtain a comparable measure of social prestige and we show that intergenerational mobility in Italy across regions or age cohort exhibits different trends according to different indicators. We suggest that ordina…

Ranking Scientific Journals Via Latent Class Models for Polytomous Item Response Data

Summary We propose a model-based strategy for ranking scientific journals starting from a set of observed bibliometric indicators that represent imperfect measures of the unobserved ‘value’ of a journal. After discretizing the available indicators, we estimate an extended latent class model for polytomous item response data and use the estimated model to cluster journals. We illustrate our approach by using the data from the Italian research evaluation exercise that was carried out for the period 2004–2010, focusing on the set of journals that are considered relevant for the subarea statistics and financial mathematics. Using four bibliometric indicators (IF, IF5, AIS and the h-index), some…

A Unified Approach to Likelihood Inference on Stochastic Orderings in a Nonparametric Context

Abstract For data in a two-way contingency table with ordered margins, we consider various hypotheses of stochastic orders among the conditional distributions considered by rows and show that each is equivalent to requiring that an invertible transformation of the vectors of conditional row probabilities satisfies an appropriate set of linear inequalities. This leads to the construction of a general algorithm for maximum likelihood estimation under multinomial sampling and provides a simple framework for deriving the asymptotic distribution of log-likelihood ratio tests. The usual stochastic ordering and the so called uniform and likelihood ratio orderings are considered as special cases. I…

Inference for Lorenz curve orderings

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 gener…

Grading Across Schools

Abstract This paper reports some facts about grading standards across a varied sample of 16 countries participating in the 2003 OCSE-PISA Survey. Our main finding is that in all countries except Ireland and the USA there is conspicuous heterogeneity in standards across schools (Table 3, Figures 1 & 2). In most of the countries where heterogeneity is present a grading-on-a-curve practice emerges, with grading standards increasing with average competence of the school's students (Table 4, Figures 3 & 4). Where this phenomenon is more pronounced, it may be related to existence of a tracking (as opposed to comprehensive) school system (Table 5, Figure 5).

Uno sguardo alle famiglie

Income distribution dynamics: monotone Markov chains make light work

This paper considers some aspects of the dynamics of income distributions by employing a simple Markov chain model of income mobility. The main motivation of the paper is to introduce the techniques of “monotone” Markov chains to this field. The transition matrix of a discrete Markov chain is called monotone if each row stochastically dominates the row above it. It will be shown that by embedding the dynamics of the income distribution in a monotone Markov chain, a number of interesting results may be obtained in a straightforward and intuitive fashion.

La liberta': aspetti teorici ed empirici

Testing for Asymmetric Information in Insurance Markets: A Multivariate Ordered Regression Approach

The positive correlation (PC) test is the standard procedure used in the empirical literature to detect the existence of asymmetric information in insurance markets. This article describes a new tool to implement an extension of the PC test based on a new family of regression models, the multivariate ordered logit, designed to study how the joint distribution of two or more ordered response variables depends on exogenous covariates. We present an application of our proposed extension of the PC test to the Medigap health insurance market in the United States. Results reveal that the risk–coverage association is not homogeneous across coverage and risk categories, and depends on individual so…

Un approccio ordinale alla misurazione delle grandezze sociali: un’analisi empirica

Revealed preference and portfolio choice

Abstract We show that the necessary and sufficient conditions for expected utility rationalizability of a single observed portfolio choice are identical to the necessary and sufficient conditions for non-expected utility rationalizability.

The measurement of rank mobility

Abstract 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 global matrices, it is equi…

Measuring Social Mobility

Abstract The paper considers the ranking of mobility matrices in a simple Markov model of social mobility. The approach is the dynamic counterpart ot the "static" inequality ranking of income distributions by the Lorenz curve. The derived partial ordering is motivated by welfare considerations, is shown to be equivalent to same intuitive mobility concepts, and is used to screen some immobility indices. The equivalence of the ranking with the "permanent income" Lorenz ordering gives support to the claim that this approach is the natural extension of Kolm′s [The optimal production of social justice, in "Public Economics (J. Margolis and H. Guitton, Eds.), MacMillan, London, 1969], Atkinson′s …

Mobilita' sociale