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Graf, Eric
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Graf, Eric
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- PublicationMétadonnées seulementFormula for revenue equalization with progressive redistribution rates(2015-3-1)
; ; Revenue equalization consists of reducing disparity in taxing power between cantons or municipalities (hereafter administrative divisions) within cantons, transferring fiscal revenue from strong taxing power administrative divisions to weak taxing power administrative divisions. A method for revenue equalization leads a constant redistribution if the transferred amounts are computed independently from the taxing power of administrative divisions. By contrast, a method for revenue equalization leads a progressive redistribution if it takes the taxing power into account in the transferred amounts computation. Hence, the amounts transferred are negligible for administrative divisions with a taxing power close to the mean taxing power and these amounts increase as the taxing power of administrative divisions moves away from the mean taxing power. A formula for revenue equalization is proposed. This formula induces a progressive redistribution and makes it possible for the user to control the strength of the progressiveness. A method based on the Gini index is proposed in order to optimally tune the redistribution rates under some constraints. - PublicationMétadonnées seulementSondage dans des registres de population et de ménages en Suisse : coordination d’échantillons, pondération et imputation(2014-11-24)
; L’Office Fédéral de la Statistique harmonise ses enquêtes par échantillonnage auprès des personnes et des ménages en Suisse. Dans cet article, nous présentons un aperçu des méthodes actuellement utilisées. Les échantillons sont sélectionnés de manière coordonnée afin de répartir au mieux la charge d’enquête sur les ménages et les personnes. Le calcul des pondérations, dont on présente les principales étapes, est adapté aux différents besoins et aux différentes situations rencontrées. L’Office se base sur les recommandations internationales, dont il participe à l’élaboration, pour le traitement des données d’enquête et les imputations. La précision des estimateurs est systématiquement évaluée en tenant compte des traitements réalisés. - PublicationMétadonnées seulementVariance Estimation for Regression Imputed Quantiles, A first Step towards Variance Estimation for Inequality Indicators(2014-8-20)In a sample survey only a sub-part of the selected sample has answered (total non-response, treated by re-weighting). Moreover, some respondents did not answer all questions (partial non-response, treated through imputation). One is interested in income type variables. One further supposes here that the imputation is carried out by a regression. The idea presented by Deville and Särndal in 1994 is resumed, which consists in constructing an unbiased estimator of the variance of a total based solely on the known information (on the selected sample and the subset of respondents). While these authors dealt with a conventional total of an interest variable y, a similar development is reproduced in the case where the considered total is one of the linearized variable of quantiles or of inequality indicators, and that, furthermore, it is computed from the imputed variable y. By means of simulations on real survey data, one shows that regression imputation can have an important impact on the bias and variance estimations of inequality indicators. This leads to a method capable of taking into account the variance due to imputation in addition to the one due to the sampling design in the cases of quantiles.
- PublicationMétadonnées seulementVariance Estimation Using Linearization for Poverty and Social Exclusion Indicators(2014-6-27)
; We have used the generalized linearization technique based on the concept of influence function, as Osier has done (Osier 2009), to estimate the variance of complex statistics such as Laeken indicators. Simulations conducted using the R language show that the use of Gaussian kernel estimation to estimate an income density function results in a strongly biased variance estimate. We are proposing two other density estimation methods that significantly reduce the observed bias. One of the methods has already been outlined by Deville (2000). The results published in this article will help to significantly improve the quality of information on the precision of certain Laeken indicators that are disseminated and compared internationally. - PublicationMétadonnées seulementEstimation de variance par linéarisation pour des indices de pauvreté et d’exclusion sociale(2014-6-19)
; Nous avons implémenté la technique de linéarisation généralisée reposant sur le concept de fonction d’influence tout comme l’a fait Osier pour estimer la variance de statistiques complexes telles que les indices de Laeken. Des simulations réalisées avec le langage R montrent que, pour les cas où l’on a recours à une estimation par noyau gaussien de la fonction de densité des revenus considérés, on obtient un fort biais pour la valeur estimée de la variance. On propose deux autres méthodes pour estimer la densité qui diminuent fortement le biais constaté. L’une de ces méthodes a déjà été esquissée par Deville. Les résultats publiés ici permettront une amélioration substantielle de la qualité des informations sur la précision de certains indices de Laeken diffusées et comparées internationalement. - PublicationMétadonnées seulementImputation of Income Data with Generalized Calibration Procedure and GB2 distribution: Illustration with SILC dataIn sample surveys of households and persons, questions about income are important variables and often sensitive and thus subject to a higher nonresponse rate. The distribution of such collected incomes is neither normal, nor log-normal. Hypotheses of classical regression models to explain the income (or their log) are not satisfied. Imputations using such models modify the original and true distribution of the data which is not. Empirical studies have shown that the generalized beta distribution of the second kind (GB2) it fits income data very well. We present a parametric method of imputation relying on weights obtained by generalized calibration. A GB2 distribution is fitted on the income distribution in order to assess that these weights can compensate for nonignorable nonresponse that affects the variable of interest. The success of the operation greatly depends on the choice of auxiliary and instrumental variables used for calibration, which we discuss. We validate our imputation system on data from the Swiss Survey on Income and Living Conditions (SILC) and compare it to imputations performed through the use of IVEware software running on SAS. We have made great efforts to estimate variances through linearization, taking all the steps of our procedure into account.
- PublicationMétadonnées seulementVariance Estimation for Regression Imputed Quantiles and Inequality IndicatorsThis work is done in the framework of sampling theory. It is based on a scenario in which a sample survey has been carried out and only a sub-part of the selected sample has accepted to answer (total non-response). Moreover, some respondents did not answer all questions (partial non-response). This is common scenario in practice. We are particularly interested in income type variables. Generally, total non-response is treated by re-weighting and partial non-response through imputation. One further supposes here that the imputation is carried out by a regression model adjusted on the respondents. We then resume the idea presented by \citet{dev:sar:94} and tested afterwards by \citet{LeeRancSar:1994} which consists in constructing an unbiased estimator of the variance of a total based solely on the information at our disposal: the information known on the selected sample and the subset of respondents. While the two cited articles dealt with the exercise for a conventional total of an interest variable $y$, we reproduce here a similar development in the case where the considered total is one of the linearized variable of quantiles or of inequality indicators, and that, furthermore, it is computed from the imputed variable $y$. We show by means of simulations that regression imputation can have an important impact on the bias estimation as well as on the variance estimation of inequality indicators. This leads us to a method capable of taking into account the variance due to imputation in addition to the one due to the sampling design in the cases of quantiles. This method could be generalized to some of the inequality indicators.
- PublicationMétadonnées seulementTraitement de la non-réponse dans l’enquête SILC suisse(2013-11-28)On a discuté les traitements actuellement en production à l'Office Fédéral Suisse de la Statistique dans les enquêtes auprès des ménages et des personnes. Le sujet a été illustré à l'aide du pan suisse de l'enquête européenne sur le revenu et les condition de vie où le redressement de la non-réponse est approché par la méthode de segmentation et des calages sur marge. On a mis en évidence un exemple réel de variable où le mécanisme de non-réponse est non-ignorable. On a vu qu'un traitement par calage généralisé est possible et convainquant. On a également illustré l'impact de la non-réponse sur la distribution observée des revenus des personnes et ménages ainsi que sur des statistiques complexes telles que les indices de pauvreté et d'exclusion sociale.
- PublicationMétadonnées seulementImputation of income data with generalized calibration procedure and GB2 law: illustration with SILC data(2013-8-31)
; In sample surveys of households and persons, questions about income are often sensitive and thus subject to a higher non-response rate. Nevertheless, the household or personal incomes are among the important variables in surveys of this type. The distribution of such collected incomes is not normal, neither log-normal. Hypotheses of classical regression models to explain the income (or their log) are not fulfilled. Imputations using such models modify the original and true distribution of the data. This is not suitable and may conduct the user to wrong interpretations of results computed from data imputed in this way. The generalized beta distribution of the second kind (GB2) is a four parameters distribution. Empirical studies have shown that it adapts very well to income data. The advantage of a parametric income distribution is that there exist explicit formulae for the inequality measures like the Laeken indicators as functions of the parameters. We present a parametric method of imputation, based on the fit of a GB2 law on the income distribution by the use of suitably adjusted weights obtained by generalized calibration. These weights can compensate for non ignorable non-response that affects the variable of interest. We validate our imputation system on data from the Swiss Survey on Income and Living Conditions (SILC). - PublicationMétadonnées seulementFormule pour la péréquation des ressources avec facteur de progressivitéL'une des deux composantes de la péréquation financière, la péréquation des ressources, a pour objectif de réduire les disparités de ressources fiscales entres les communes. Les communes financièrement fortes alimentent de leur contribution le fonds de péréquation, alors que les communes faibles bénéficient de transferts du fonds. Le montant total versé au fonds par les communes fortes est identique au montant total des transferts alloués aux communes faibles. Deux modes de redistribution sont possibles: redistribution proportionnelle ou progressive. Dans le premier cas, les communes riches versent au fonds un pourcentage fixe (33% dans le projet) de l'écart total des ressources fiscales. Quant aux communes faibles, elles reçoivent un transfert équivalent à un pourcentage fixe (33%) de l'écart total des ressources fiscales. La présente étude propose une formule qui permet de redistribuer les ressources fiscales d'une manière progressive tout en garantissant l'équilibre des versements et des prélèvements au fonds. La part des ressources fiscales que les communes fortes abandonnent au fonds représente une part croissante de l'écart total des ressources. Cette part est inférieure à 33% pour les communes dont l'indice ne dépasse que modérément la moyenne, supérieure à 33% pour les communes les plus riches. A l'opposé, pour les communes faibles, la réduction relative de l'écart de ressources est plus élevée pour les communes très faibles que pour celles dont l'indice de ressources est proche de la moyenne. Ainsi, le transfert de fonds destiné aux communes les plus faibles excède 33% de l'écart total des ressources, celui destiné aux communes proches de la moyenne est inférieur à 33% de ce même écart. Les versements et les prélèvements au fonds s'équilibrent.
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