Measurement of inequality with a finite number of pay states : the majorization set and its applications

I am grateful to Vassily Gorbanov, Tarik Yalcin and Fabrizio Germano for extended discussions and suggestions, and to an associate editor and a reviewer for constructive comments. I also wish to thank Francesco Andreoli, Geoffrey Burton, Joe Swierzbinski, Alain Trannoy, Claudio Zoli and seminar participants at the Aix-Marseille School of Economics for discussions. I am responsible for any errors.Peer reviewedPostprin

Statistical Inference for Multidimensional Inequality Indices

We use the delta method to derive the large sample distribution of mul- tidimensional inequality indices. We also present a simple method for com- puting standard errors and obtain explicit formulas in the context of two families of indiceslarge sample distributions; standard errors; multidimensional inequality indices

Estimating the Intergenerational Correlation of Incomes: An Errors in Variables Framework

The estimation of the intergenerational correlation of incomes is usually carried out by proxying permanent incomes using suitable indicators of economic status, and by treating the resulting measurement error problem using averaging or instrumenting procedures. Here we take the permanent income of the parents' family to be unobserved, but we assume that its determinants are known to the researcher. A two-stage procedure as well as a MIMIC type covariance estimator applied to a US sample of parents and children entail estimates of the order of 0.61 to 0.64 for the coefficient of intergenerational income transmission. OLS estimates this parameter at 0.5. The variance ratio of permanent to total income is also estimated to be in the range of 0.77 to 0.8, implying a correction factor of 1.25 to 1.3 for OLS estimates.Intergenerational mobility, errors in variables

Estimating the Intergenerational Correlation of Incomes : An Errors in Variables Framework

Because the permanent incomes of parents and children are typically unobservable, the estimation of the intergenerational correlation of incomes is usually carried out via averaging methods or instrumentation. In this paper we take the permanent income of the parent family to be unobserved, but we assume that a model for its determinants is known to the researcher. In turn, this leads us to propose two related estimators for the intergenerational correlation: a two-stage least squares procedure and a more efficient MIMIC estimator. The MIMIC framework also provides estimates for the determinants of permanent income and the variance parameters required to evaluate the bias of the OLS estimator. Using a US sample of parents and children we provide estimates for the intergenerational correlation ranging between 0.30 and 0.78. The bias of the OLS estimator is estimated to be in the order of 40%.intergenerational mobility; errors in variables

A Note on the Estimation of Intergenerational Income Correlations by the Method of Averaging

Averaging methods are routinely used in order to limit biases resulting from the mismeasurement of permanent incomes. The Solon/Zimmerman estimator regresses a single-year measurement of the child's resources on a T-period average of the parents' income while the Behrman/Taubman estimator regresses an S-period average of the child's resources on a T-period average of the parents' income. The latter estimator is shown to be the arithmetic mean of the S slope estimates arising from the Solon/Zimmerman methodology. However, because sampling variation produces yearly changes in the variance of children's incomes, it is shown that the Behrman/Taubman estimator is not efficient in the class of estimators which can be expressed as a weighted sum of the S distinct Solon/Zimmerman estimates. The minimum variance estimator in the above class is thus derived and applied to a US sample.Welfare index, inequality, poverty, sample, inference.

A Note on the Estimation of Intergenerational Income Correlations by the Method of Averaging

Averaging methods are routinely used in order to limit biases resulting from the mismeasurement of permanent incomes. The Solon/Zimmerman estimator regresses a single-year measurement of the child's resources on a T-period average of the parents' income while the Behrman/Taubman estimator regresses an S-period average of the child's resources on a T-period average of the parents' income. The latter estimator is shown to be the arithmetic mean of the S slope estimates arising from the Solon/Zimmerman methodology. However, because sampling variation produces yearly changes in the variance of children's incomes, it is shown that the Behrman/Taubman estimator is not efficient in the class of estimators which can be expressed as a weighted sum of the S distinct Solon/Zimmerman estimates. The minimum variance estimator in the above class is thus derived and applied to a US sample.intergenerational mobility ; measurement error; averaging methods; minimum variance estimation.

Prediction and sufficiency in the model factor analysis

We contrast two approaches to the prediction of latent variables in the model of factor analysis. The likelihood statistic is a sufficient statistic for the unobservables when sampling arises from the exponential family of distributions. Linear predictors, on the other hand, can be obtained as distribution-free statistics. We provide conditions under which a class of linear predictors is sufficient for the exponential family of distributions. We also examine various predictors in the light of the following criteria: (I) sufficiency, (ii) mean-square error, and (iii) unbiasedness and illustrate our results with the help of Chinese data on living standards

Inequality Measurement forOrdered Response Health Data

When health status is an ordered response variable, Allison and Foster (2004)postulate that a distribution Q ?exhibits more inequality than a distribution P ?if Q ?isobtained from P ?via a sequence of median preserving spreads. This paper introduces aparametric family of inequality indices which are founded on the Allison and Fosterordering.Self-reported health status, inequality orderings, inequalitymeasures.

Catastrophic Health ExpenditureandHousehold Well-Being

According to the catastrophic health expenditure methodology a household is in catastrophe if its health out-of-pocket budget share exceeds a critical threshold. We develop a conceptual framework for addressing three questions in relation to this methodology, namely: 1. Can a budget share be informative about the sign of a change in welfare? 2. Is there a positive association between a household's poverty shortfall and its health out-of-pocket budget share? 3. Does an increase in population coverage of a health insurance scheme always result in a reduction of the prevalence of catastrophic expenditures?Catastrophic health expenditure, welfare change, poverty, performanceof health insurance schemes.

The minimal Hilbert basis of the Hammond order cone

We characterize the minimal Hilbert basis of the Hammond order cone, and present several novel applications of the resulting basis. From the basis, we extract an invertible matrix, that provides a numerical representation of the Hammond order relation. The basis also enables the construction of a space—that we call the Hammond order lattice—where order-extensions of the Hammond order (i.e. more complete relations) may be derived. Finally, we introduce a class of maximal linearly independent Hilbert bases, in which the specific results derived in relation to the Hammond order cone, are shown to hold more generally.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. Funding for open access charge: Universidad de Málaga / CBUA