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Summary We consider the estimation of the relative median poverty gap (RMPG) at the level of Italian provinces by using data from the European Union Survey on Income and Living Conditions. The overall sample size does not allow reliable estimation of income-distribution-related parameters at the provincial level; therefore, small area estimation techniques must be used. The specific challenge in estimating the RMPG is that, as it summarizes the income distribution of the poor, samples for estimating it for small subpopulations are even smaller than those available in other parameters. We propose a Bayesian strategy where various parameters summarizing the distribution of income at the provincial level are modelled by means of a multivariate small area model. To estimate the RMPG, we relate these parameters to a distribution describing income, namely the generalized beta distribution of the second kind. Posterior draws from the multivariate model are then used to generate draws for the distribution's area-specific parameters and then of the RMPG defined as their functional.

Long-term exposure to ambient air pollutant concentrations is known to cause chronic lung inflammation, a condition that may promote increased severity of COVID-19 syndrome caused by the novel coronavirus (SARS-CoV-2). In this paper, we empirically investigate the ecologic association between long-term concentrations of area-level fine particulate matter (PM2.5) and excess deaths in the first quarter of 2020 in municipalities of Northern Italy. The study accounts for potentially spatial confounding factors related to urbanization that may have influenced the spreading of SARS-CoV-2 and related COVID-19 mortality. Our epidemiological analysis uses geographical information (e.g., municipalities) and negative binomial regression to assess whether both ambient PM2.5 concentration and excess mortality have a similar spatial distribution. Our analysis suggests a positive association of ambient PM2.5 concentration on excess mortality in Northern Italy related to the COVID-19 epidemic. Our estimates suggest that a one-unit increase in PM2.5 concentration (µg/m3) is associated with a 9% (95% confidence interval: 6–12%) increase in COVID-19 related mortality.

The trend in crop yields and yield variability affects food security and impact agricultural and food policies. Recent studies in this area have either focused only on one country or performed global analysis on a handful of crops. We provide the first worldwide analysis of trend and variability for 8088 country-crop yield series taken from the FAO database, employing a robust estimator to cope with the adverse statistical effects of outliers. More than half of the series display a slowdown in yield growth due to a closing of the gap between realised and attainable yields as well as to agricultural policies promoting more sustainable agricultural practices. Around one fourth of the series show also an increase in yield variability as a consequence of climate change and changes in farm management practices. Yield variability is highest in Eastern Europe, Central Asia and Middle East and North Africa, where food security may be threatened.

Summary In business surveys, estimates of means and totals for subnational regions, industries and business classes can be too imprecise because of the small sample sizes that are available for subpopulations. We propose a small area technique for the estimation of totals for skewed target variables, which are typical of business data. We adopt a Bayesian approach to inference. We specify a prior distribution for the random effects based on the idea of local shrinkage, which is suitable when auxiliary variables with strong predictive power are available: another feature that is often displayed by business survey data. This flexible modelling of random effects leads to predictions in agreement with those based on global shrinkage for most of the areas, but enables us to obtain less shrunken and thereby less biased estimates for areas characterized by large model residuals. We discuss an application based on data from the Italian survey on small and medium enterprises. By means of a simulation exercise, we explore the frequentist properties of the estimators proposed. They are good, and differently from methods based on global shrinkage remain so also for areas characterized by large model residuals.

Although the European Union's (EU) Common Agricultural Policy was intended as sectoral, its recent reforms lead to a stronger territorial vocation, allowing for possible overlaps with the objectives of the Cohesion Policy, the main regional policy of the EU. Through a threshold regression approach, we explore if the possible interactions between these policies influence the agricultural productive performance in more and less developed regions. Results show that in regions with agricultural Gross Value Added per worker lower than 25.53 thousand Euros, both policies exhibit a negative effect, mitigated if they are implemented together. In more productive regions, the effects are the opposite. Aunque la Politica Agricola Comun de la Union Europea (UE) fue concebida como sectorial, sus reformas recientes la dirigen a una vocacion territorial mas fuerte, lo que permite posibles solapamientos con los objetivos de la Politica de Cohesion, que es la principal politica regional de la UE. Mediante un enfoque de regresion de umbral, el articulo explora si las posibles interacciones entre estas politicas influyen en el rendimiento productivo agricola en regiones con un mayor y menor desarrollo. Los resultados muestran que en las regiones con un Valor Anadido Bruto agricola por trabajador inferior a 25.530 euros, ambas politicas muestran un efecto negativo, que se ve mitigado si se aplican conjuntamente. En las regiones mas productivas, los efectos son los opuestos. 欧州連合 (EU)の共通農業政策 (Common Agricultural Policy)はセクター別のものとして意図されていたが、最近なされた改定によりより多くの地域的雇用がもたらされ、EUの主要な地域政策である結束政策の目的と重複する可能性が生じた。本稿では、閾値回帰アプローチにより、これらの政策間の相互作用が、より開発の進んだ地域と進んでいない地域の農業生産性に影響を与えるかどうかを探索する。結果から、労働者一人当たりの農業の粗付加価値が2,553万ユーロ以下の地域では、いずれの政策もマイナスの効果をもたらし、政策が一緒に実施されればマイナスの効果が緩和されることが示された。生産性の高い地域では、その効果は逆である。

The analysis of variance, and mixed models in general, are popular tools for analyzing experimental data in psychology. Bayesian inference for these models is gaining popularity as it allows to easily handle complex experimental designs and data dependence structures. When working on the log of the response variable, the use of standard priors for the variance parameters can create inferential problems and namely the non-existence of posterior moments of parameters and predictive distributions in the original scale of the data. The use of the generalized inverse Gaussian distributions with a careful choice of the hyper-parameters is proposed as a general purpose option for priors on variance parameters. Theoretical and simulations results motivate the proposal. A software package that implements the analysis is also discussed. As the log-transformation of the response variable is often applied when modelling response times, an empirical data analysis in this field is reported. Supplementary Information The online version contains supplementary material available at 10.1007/s11336-021-09769-y.

In recent years, M-quantile regression has been applied to small area estimation to obtain reliable and outlier robust estimators without recourse to strong parametric assumptions. In this paper, after a review of M-quantile regression and its application to small area estimation, we cover several topics related to model specification and selection for M-quantile regression that received little attention so far. Specifically, a pseudo-R2 goodness-of-fit measure is proposed, along with likelihood ratio and Wald type tests for model specification. A test to assess the presence of actual area heterogeneity in the data is also proposed. Finally, we introduce a new estimator of the scale of the regression residuals, motivated by a representation of the M-quantile regression estimation as a regression model with Generalised Asymmetric Least Informative distributed error terms. The Generalised Asymmetric Least Informative distribution, introduced in this paper, generalises the asymmetric Laplace distribution often associated to quantile regression. As the testing procedures discussed in the paper are motivated asymptotically, their finite sample properties are empirically assessed in Monte Carlo simulations. Although the proposed methods apply generally to Mquantile regression, in this paper, their use ar illustrated by means of an application to Small Area Estimation using a well known real dataset.

The analysis of poverty persistence received considerable attention in recent years. In this paper we explore the role of the adopted poverty measure in the analysis of its persistence. Specifically, we consider three measures: the risk of poverty, the severe material deprivation and subjective poverty, motivated by the understanding of poverty as a complex phenomenon and for which no single measure can effectively capture its several dimensions. The empirical analysis is based on the 2013-2016 longitudinal sample of the EU-SILC survey. We focus on Italian households with dependent children. We apply a correlated random effects probit models with endogenous initial conditions to assess genuine state dependence after controlling for structural household characteristics and variables related to participation in the labour market. A strong state dependence emerges, regardless of the considered poverty measure thus providing evidence of poverty and social exclusion persistence. We also find evidence of relevance of initial conditions for all measures in focus. Nonetheless, structural household characteristics and household level economic variables play roles that are often different in the three parallel models; these differences are consistent with the aims and nature of the alternative measures.

Quantile and M-quantile regression have been applied successfully to small area estimation within the frequentist approach. Quantile regression is applied in the same context but from a Bayesian perspective. Joint modelling of the quantile function is considered, adopting a non parametric assumption on the data generating process that nonetheless explicitly includes the normal distribution as a special case. A specification of the random part of the model that is simple and consistent with the predictive aim of small area estimation is proposed. Although the main output of the method is the estimation of the whole quantile function, estimators of the small area means based on the integration of the quantile function are proposed and discussed. A simulation exercise is used to assess the frequentist properties of these proposed predictors, that result at least as efficient as frequentist small area estimators based on quantile regression in scenarios characterized by the presence of outliers. The proposed method is illustrated using data from the European survey on Income and Living Conditions (EU-SILC).

This issue is devoted to survey sampling methods. It carries on a tradition of Mathematical Population Studies, after the issues guest-edited by Malay Ghosh and Tomasz Żadlo (2014) and Vera Toepoe...

This paper employs data from the Bangladesh Demographic and Health Survey (2004) to explore how women’s empowerment is related to partner’s attitudes, participation in microcredit programmes and a set of other socio-economic factors. We use a structural equation model with categorical observed variables. We get that participation in microcredit programmes has a positive impact on both the empowerment’s dimensions considered, while partner’s attitudes effect is weaker, proving that gender community norms are likely to be rooted in women’s minds regardless of the partners’ perceptions of women’s status.

The Gini coefficient is a popular concentration measure often used in the analysis of economic inequality. Estimates of this index for small regions may be useful to properly represent inequalities within local communities. However, the small area estimation for the Gini coefficient has not been thoroughly investigated. A method based on area level models, thereby avoiding the assumption of the availability of Census data at the micro level, is proposed. A modified design based estimator for the coefficient with reduced small sample bias is suggested as input for the small area model, while a hierarchical Beta mixed regression model is introduced to combine survey data and auxiliary information. The methodology is illustrated by means of an example based on Italian data from the European Union Survey on Income and Living Conditions.

Summary We consider the estimation of the number of severely disabled people by using data from the Italian survey on ‘Health conditions and appeal to Medicare’. In this survey, disability is indirectly measured by using a set of categorical items, which consider a set of functions concerning the ability of a person to accomplish everyday tasks. Latent class models can be employed to classify the population according to different levels of a latent variable connected with disability. The survey is designed to provide reliable estimates at the level of administrative regions (‘Nomenclature des unités territoriales statistiques’, level 2), whereas local authorities are interested in quantifying the number of people who belong to each latent class at a subregional level. Therefore, small area estimation techniques should be used. The challenge is that the variable of interest is not observed. Adopting a full Bayesian approach, we base small area estimation on a latent class model in which the probability of belonging to each latent class changes with covariates and the influence of age is learnt from the data by using penalized splines. Demmler–Reinsch bases are shown to improve speed and mixing of Markov chain Monte Carlo chains used to simulate posteriors.