Fuzzy measures of the incidence of relative poverty and deprivation: a multi-dimensional perspective

In this paper we present a methodology for the study of multi-dimensional aspects of poverty and deprivation. The conventional poor/non-poor dichotomy is replaced by defining poverty as a matter of degree, determined by the place of the individual in the income distribution. The fuzzy poverty measure proposed is in fact also expressible in terms of the generalised Gini measure. The same methodology facilitates the inclusion of other dimensions of deprivation into the analysis: by appropriately weighting indicators of deprivation to reflect their dispersion and correlation, we can construct measures of non-monetary deprivation in its various dimensions. These indicators illuminate the extent to which purely monetary indicators are insufficient in themselves in capturing the prevalence of deprivation. An important contribution of the paper is to identify rules for the aggregation of fuzzy sets appropriate for the study of poverty and deprivation. In particular, we define a ‘composite’ fuzzy set operator which takes into account whether the sets being aggregated are of a ‘similar’ or a ‘dissimilar’ type. These rules allow us to meaningfully combine income and the diverse non-income deprivation indices at the micro-level and construct what we have termed ‘intensive’ and ‘extensive’ indicators of deprivation. We note that mathematically the same approach can be carried over to the study of persistence of poverty and deprivation over time.     

Empirical Likelihood-Based Inference for Poverty Measures with Relative Poverty Lines

In this article, we propose an empirical likelihood-based method of inference for decomposable poverty measures utilizing poverty lines which are some fraction of the median of the underlying income distribution. Specifically, we focus on making poverty comparisons between two subgroups of the population which share the same poverty line. Our proposed method is assessed using a Monte Carlo simulation and is applied to some Canadian household income data.     

Poverty as a System: Human Contestability Approach to Poverty Measurement

Since Sen's (1976) paper on poverty measurement, a substantial literature, both theoretical and empirical, has emerged. There have been several recent efforts to drive poverty measures based on different approaches and axioms. These poverty indices are based on head count ratio, poverty gaps and distribution of income. These are very narrow in approach and suffer from several drawbacks. However, the purpose of the present paper is to introduce a new poverty measure based on a holistic and system modelling approach. Based on Chopra's human contestability (Chopra, 2003, 2007) approach to poverty, this new approach to measuring poverty has been developed using a structure equation model based on Kanji's business excellence model (Kanji, 2002) to create the proposed poverty model. We construct a latent variable structural equation model to measure the contestability excellence within certain boundaries of the societal system. It will provide us with a measurement of poverty in a society or community in terms of human contestability. A higher human contestability index will indicate the lower poverty within the society. Strengths and weakness as of various components will also indicate that a characteristic of the individual requires extra society or government support to remove poverty. However, there remains considerable disagreement on the best way to achieve this.     

贫困缺口总指数的构造、分解与应用

本文构造了一个新贫困指数 ,通过对 指数的因素分解及衍生指数的构造,提出了一些重要贫困指标的预测和推算办法。基于CHNS1991-2011年跨度20年的8轮调查数据进行实证分析,结果表明,我国农村近20年来总贫困缺口率呈现年均6.39%的缩减率,其贡献全部来自贫困人口总规模递减这一因素的影响,而另外两个因素,即平均贫困缺口水平和贫困差异度则呈现年均小幅上升趋势,表明减贫质量不容乐观;以现有减贫模式对我国农村2020年的平均贫困缺口水平、贫困不平等程度、贫困规模等指标进行预测显示,减贫目标依然任重道远;提出了采用精准减贫,重心在于提升贫困人口获取收入的能力和缩小贫困不平等程度的相关建议。     

Contingency tables with fuzzy information

ABSTRACT

This paper extends the classical methods of analysis of a two-way contingency table to the fuzzy environment for two cases: (1) when the available sample of observations is reported as imprecise data, and (2) the case in which we prefer to categorize the variables based on linguistic terms rather than as crisp quantities. For this purpose, the α-cuts approach is used to extend the usual concepts of the test statistic and p-value to the fuzzy test statistic and fuzzy p-value. In addition, some measures of association are extended to the fuzzy version in order to evaluate the dependence in such contingency tables. Some practical examples are provided to explain the applicability of the proposed methods in real-world problems.     

贫困测度指标及其评价

一、引言一般来说,研究贫困问题主要涉及三个方面:一是贫困的识别;二是贫困程度测定;三是反贫困效果判定以及相应的战略选择。贫困识别问题主要指贫困的基本范畴及贫困线的合理确定,关系到贫困集合的准确界定;贫困程度的测定主要指贫困指数的定义和计算,关系到贫困程度大小的判     

A general class of poverty measures

Measurement of poverty in the spirit of Sen essentially consists of two steps, namely (1) the identification of the poor and (2) the aggregation of the income distribution of the poor into an indicator called poverty measure. We contribute to the second step from a mathematical and statistical point of view by defining a class of poverty measures and investigating its properties including sensitivity with respect to changes in the income distribution. Various poverty orderings are defined and their relation to stochastic dominance is investigated. Finally estimation of the class of poverty measures from individual and grouped data is considered.     

城镇贫困的特征演变

本文利用中国家庭收入调查数据研究了1988-2013年间我国城镇居民的贫困问题。以利用“马丁法”计算的各省历年贫困线作为贫困识别标准,发现25年间城镇地区的贫困率下降明显,尤其暂时性贫困和持久性贫困的贫困率已经很低,贫困人口以选择性贫困为主,即消费不足成为我国城镇人口贫困的主要特征。家庭人口多、有未成年子女会有更大概率陷入贫困,而教育和稳定的就业则可以有效缓解贫困。当前我国城镇地区的贫困人口认定和救助主要以收入为标准,本文认为应充分重视贫困人口消费不足的问题,拓展专项救助的范围,同时增大对教育、卫生、住房等基本民生保障的投入,减少低收入群体的过度储蓄,并特别关注贫困青少年的精神和物质消费需求。     

教育改善贫困效应的地区异质性研究

教育对于增加收入、改善贫困无疑是一个重要的途径。在目前多维贫困越来越受到重视的情况下,本文在收入贫困和多维贫困两种贫困识别标准下,分析了教育改善贫困的效应在地区之间的异质性,考察了该效应是否受地区经济发展的影响。根据分层LOGIT模型的估计,本文认为地区经济发展水平是发挥教育改善收入贫困效应的重要舞台,对于多维贫困的改善效应则不明显。本文得到的一个重要扶贫政策建议是要发挥教育改善贫困的效应,必须注重精准扶贫与发展地区经济相结合;但仅仅发展经济,不一定能保证教育对多维贫困的改善效应,减轻多维贫困需要更加重视公共产品供给和民生保证。     

A fuzzy robust regression approach applied to bedload transport data

Fuzzy least-square regression can be very sensitive to unusual data (e.g., outliers). In this article, we describe how to fit an alternative robust-regression estimator in fuzzy environment, which attempts to identify and ignore unusual data. The proposed approach concerns classical robust regression and estimation methods that are insensitive to outliers. In this regard, based on the least trimmed square estimation method, an estimation procedure is proposed for determining the coefficients of the fuzzy regression model for crisp input-fuzzy output data. The investigated fuzzy regression model is applied to bedload transport data forecasting suspended load by discharge based on a real world data. The accuracy of the proposed method is compared with the well-known fuzzy least-square regression model. The comparison results reveal that the fuzzy robust regression model performs better than the other models in suspended load estimation for the particular dataset. This comparison is done based on a similarity measure between fuzzy sets. The proposed model is general and can be used for modeling natural phenomena whose available observations are reported as imprecise rather than crisp.     

Inference for Income Distributions Using Grouped Data

We develop a general approach to estimation and inference for income distributions using grouped or aggregate data that are typically available in the form of population shares and class mean incomes, with unknown group bounds. We derive generic moment conditions and an optimal weight matrix that can be used for generalized method-of-moments (GMM) estimation of any parametric income distribution. Our derivation of the weight matrix and its inverse allows us to express the seemingly complex GMM objective function in a relatively simple form that facilitates estimation. We show that our proposed approach, which incorporates information on class means as well as population proportions, is more efficient than maximum likelihood estimation of the multinomial distribution, which uses only population proportions. In contrast to the earlier work of Chotikapanich, Griffiths, and Rao, and Chotikapanich, Griffiths, Rao, and Valencia, which did not specify a formal GMM framework, did not provide methodology for obtaining standard errors, and restricted the analysis to the beta-2 distribution, we provide standard errors for estimated parameters and relevant functions of them, such as inequality and poverty measures, and we provide methodology for all distributions. A test statistic for testing the adequacy of a distribution is proposed. Using eight countries/regions for the year 2005, we show how the methodology can be applied to estimate the parameters of the generalized beta distribution of the second kind (GB2), and its special-case distributions, the beta-2, Singh–Maddala, Dagum, generalized gamma, and lognormal distributions. We test the adequacy of each distribution and compare predicted and actual income shares, where the number of groups used for prediction can differ from the number used in estimation. Estimates and standard errors for inequality and poverty measures are provided. Supplementary materials for this article are available online.     

Panel regression models for measuring multidimensional poverty dynamics

This work concerns the study of poverty dynamics and the analysis of the influencing socio-demographic factors. A fuzzy and multidimensional approach has been chosen in order to define two different poverty measures. A panel regression model has been estimated and particular attention has been paid to the treatment of the unobservable heterogeneity among longitudinal units. The specified model combines autoregression with variance components. The empirical analysis has been conducted using the data set of the British Household Panel Survey (BHPS) from 1991 to 1997. This work was co-financed by Murst funds for the projects “Occupazione e disoccupazione in Italia: misura e analisi dei comportamenti”. The paper is the result of the common work of all the authors; in particular G. Betti has written Sects. 2,5.1 and 5.3.1; A. D’Agostino has written sections 4, 5.2 and 5.4; L. Neri has written Sects. 1, 3, 5.3.2 and 6.     

Poverty comparisons with common relative poverty lines

Relative poverty lines are increasingly being used in poverty comparison studies. Existing methods assume that the distributions being compared are distinct with independent relative poverty lines. However, this practice may be problematic when comparing two subgroups of a population. We follow up on a recent proposal for the usage of common relative poverty lines in such cases, and develop a test for comparing poverty between subgroups of a single population, using inequality restrictions. Monte Carlo experiments are conducted in order to examine the size and power of our proposed test. We illustrate our procedure using some U.S. household income data.     

中国农村亲贫困增长测度及其分解

摘　　要:亲贫困增长主要是指能够使贫困群体参与经济活动并从中得到更多好处的经济增长。在讨论经济增长、不平等与贫困规模变动相关关系的基础上,本文构建了一种基于收入分布的亲贫困增长测度方法并用Shapley值法对之进行因素分解,并采用CHNS农村住户调查数据进行实证分析,得到中国经济的高速增长并不能够自动缓解贫困,需要进一步采取瞄准式扶贫措施来解决的结论 。     

District-level poverty estimation: a proposed method

This paper develops a method of estimating micro-level poverty in cases where data are scarce. The method is applied to estimate district-level poverty using the household level Indian national sample survey data for two states, viz., West Bengal and Madhya Pradesh. The method involves estimation of state-level poverty indices from the data formed by pooling data of all the districts (each time excluding one district) and multiplying this poverty vector with a known weight matrix to obtain the unknown district-level poverty vector. The proposed method is expected to yield reliable estimates at the district level, because the district-level estimate is now based on a much larger sample size obtained by pooling data of several districts. This method can be an alternative to the “small area estimation technique” for estimating poverty at sub-state levels in developing countries.     

Fuzzy Least-Absolutes Estimates in Linear Models

Fuzzy set theory has been well developed and applied in a wide variety of real problems. Linear models are used frequently in the researches of relations among several variables in a system. In many cases, data are nonprecise (fuzzy). In this article, we proposed a method for least-absolutes estimating of fuzzy parameters in a linear model with fuzzy input and fuzzy output, using “Resolution Identity”.     

A second-order fuzzy time series model for stock price analysis

It is difficult to model stock market because of its uncertainty. Many methods have been introduced to tackle these difficulties, in which fuzzy time series has shown its advantages in dealing with fuzzy and uncertainty data. In recent years, many researchers have applied the fuzzy time series to analyze and forecast the stock price, and how to improve the accuracy of forecasting has attracted many researchers. In this paper, the data are first preprocessed and a new way to divide the universe of discourse is given, after which the data are fuzzified applying the triangular membership function, then three-layer back propagation (BP) neural network is established. Finally, the generalized inverse fuzzy number formula is applied to defuzzify the relation obtained with the prediction results. The proposed method is applied to predict the stock price of State Bank of India (SBI) and Dow-Jones Industrial Average (DJIA). The experimental results show that the proposed method can greatly improve the accuracy of forecasting. Furthermore, the proposed method is not sensitive to its parameters.     

A new generation of process capability indices based on fuzzy measurements

Process capability indices (PCIs) provide numerical measures on whether a process conforms to the defined manufacturing capability prerequisite. These have been successfully applied by companies to compete with and to lead high-profit markets by evaluating the quality and productivity performance. The PCI C_p compares the output of a process to the specification limits (SLs) by forming the ratio of the width between the process SLs with the width of the natural tolerance limits which is measured by six process standard deviation units. As another common PCI, C_pm incorporates two variation components which are variation to the process mean and deviation of the process mean from the target. A meaningful generalized version of above PCIs is introduced in this paper which is able to handle in a fuzzy environment. These generalized PCIs are able to measure the capability of a fuzzy-valued process in producing products on the basis of a fuzzy quality. Fast computing formulas for the generalized PCIs are computed for normal and symmetric triangular fuzzy observations, where the fuzzy quality is defined by linear and exponential fuzzy SLs. A practical example is presented to show the performance of proposed indices.     

U-Statistics and Their Asymptotic Results for Some Inequality and Poverty Measures

U-statistics form a general class of statistics that have certain important features in common. This class arises as a generalization of the sample mean and the sample variance, and typically members of the class are asymptotically normal with good consistency properties. The class encompasses some widely used income inequality and poverty measures, in particular the variance, the Gini index, the poverty rate, the average poverty gap ratios, the Foster-Greer-Thorbecke index, and the Sen index and its modified form. This paper illustrates how these measures come together within the class of U-statistics, and thereby why U-statistics are useful in econometrics.     

U-Statistics and Their Asymptotic Results for Some Inequality and Poverty Measures

U-statistics form a general class of statistics that have certain important features in common. This class arises as a generalization of the sample mean and the sample variance, and typically members of the class are asymptotically normal with good consistency properties. The class encompasses some widely used income inequality and poverty measures, in particular the variance, the Gini index, the poverty rate, the average poverty gap ratios, the Foster-Greer-Thorbecke index, and the Sen index and its modified form. This paper illustrates how these measures come together within the class of U-statistics, and thereby why U-statistics are useful in econometrics.