Inference for Income Distributions Using Grouped Data
Inference for Income Distributions Using Grouped Data
复制标题
使用分组数据推断收入分布
DOI：
10.1080/07350015.2012.707590
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发表时间：
2012
影响因子：
3
通讯作者：
G. Hajargasht
中科院分区：
文献类型：
--
作者：
Gholamreza Hajargsht;W. Griffiths;J. Brice;D. S. P. Rao;D. Chotikapanich;G. Hajargasht
我们开发了一个一般的方法来估计和推断的收入分配使用分组或汇总数据，通常是以人口份额和类平均收入的形式，未知的组界限。我们推导出通用矩条件和最优权重矩阵，可用于广义矩法（GMM）估计的任何参数收入分布。我们推导的权重矩阵和它的逆允许我们表达看似复杂的GMM目标函数在一个相对简单的形式，便于估计。我们表明，我们提出的方法，它结合了类的手段，以及人口比例的信息，是更有效的比最大似然估计的多项分布，它只使用人口比例。与Chotikapanich，Griffiths和Rao以及Chotikapanich，Griffiths，Rao和瓦伦西亚的早期工作相比，没有指定正式的GMM框架，没有提供获得标准误差的方法，并将分析限制在beta-2分布，我们提供了估计参数及其相关函数的标准误差，例如不平等和贫困措施，我们为所有发行版提供方法论。提出了一种检验分布充分性的检验统计量。使用8个国家/地区的2005年，我们展示了如何的方法可以应用于估计参数的广义β分布的第二类（GB 2），其特殊情况下的分布，β-2，Singh-Maddala，Dagum，广义伽玛和对数正态分布。我们测试每个分布的充分性，并比较预测和实际收入份额，其中用于预测的组数可能与估计中使用的组数不同。提供了不平等和贫困措施的估计数和标准误。本文的补充材料可在网上查阅。
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.