Averaging Income Distributions

Various inequality and social welfare measures often depend heavily on the choice of a distribution of income. Picking a distribution that best fits the data involves throwing away information and does not allow for the fact that a wrong choice can be made. Instead, Bayesian model averaging utilizes a weighted average of the results from a number of income distributions, with each weight given by the probability that a distribution is ‘correct’. In this study, prior densities are placed on mean income, the mode of income and the Gini coefficient for Australian income units with one parent (1997–8). Then, using grouped sample data on incomes, posterior densities for the mean and mode of income and the Gini coefficient are derived for a variety of income distributions. The model‐averaged results from these income distributions are obtained.     

Entropy-based China income distributions and inequality measures

ABSTRACT

We use information theoretic information recovery methods, on a 2005 sample of household income data from the Chinese InterCensus, to estimate the income distribution for China and each of its 31 provinces and to obtain corresponding measures of income inequality. Using entropy divergence methods, we seek a probability density function solution that is as close to a uniform probability distribution of income (with the least inequality), as the data will permit. These entropy measures of income inequality reflect how the allocation and distribution systems are performing, and we show the advantages of investigating province variation in income inequality using entropy measures rather than Gini coefficients. Finally, we use a sample of data from the China Family Panel Study to recover an estimate of the 2010 and the 2016 to investigate possible directions of inequality changes using these different additional data sources, given that the 2015 Inter-Census is not yet available.     

Bayesian estimation of social welfare and tax progressivity measures

This paper examines Bayesian methods of examining posterior distributions of inequality, concentration, tax progressivity and social welfare measures. Use is made of an explicit income distribution assumption and two alternative assumptions regarding the distribution of pre-tax mean incomes within each income group. The methods are applied to a simulated distribution of individual incomes and tax payments. It is possible to identify a minimum acceptable number of income classes to be used. The results suggest support for the use of group means in practical applications, particularly where large sample sizes are available. First version received: August 2000/Final version received: July 2001 RID="*" ID="*"  This research was supported by a Melbourne University Faculty of Economics and Commerce Research Grant. We should like to thank Bill Griffiths and two referees for comments on an earlier draft.     

Pricing farm-level agricultural insurance: a Bayesian approach

This paper applies Hierarchical Bayesian Models to price farm-level yield insurance contracts. This methodology considers the temporal effect, the spatial dependence and spatio-temporal models. One of the major advantages of this framework is that an estimate of the premium rate is obtained directly from the posterior distribution. These methods were applied to a farm-level data set of soybean in the State of the Paraná (Brazil), for the period between 1994 and 2003. The model selection was based on a posterior predictive criterion. This study improves considerably the estimation of the fair premium rates considering the small number of observations.      

Posterior Analysis of Environmental Damage Evaluation in Europe

In this paper we consider environmental damage evaluation using two types of econometric models to analyse tree damage due to acid deposits, using cross-country data for several European countries. First, we use a set of univariate Poisson models and second, a multinomial probit model with the difference that we do not observe class specific data. The damage function is parameterized in terms of a number of economic and environmental variables. Statistical inference is conducted using Bayesian methods relying on Markov Chain Monte Carlo simulation. Natural by-products of our method include an implied ranking of countries according to environmental damage, and (exact, finite sample) posterior distributions of average country-specific environmental damage.     

Climate Response Uncertainty and the Benefits of Greenhouse Gas Emissions Reductions

Some recent research suggests that uncertainty about the response of the climate system to atmospheric greenhouse gas concentrations can have a disproportionately large influence on benefits estimates for climate change policies, potentially even dominating the effect of the discount rate. In this paper we conduct a series of numerical simulation experiments to investigate the quantitative significance of climate response uncertainty for economic assessments of climate change. First we characterize climate uncertainty by constructing two probability density functions—a Bayesian model-averaged and a Bayesian updated version—based on a combination of uncertainty ranges for climate sensitivity reported in the scientific literature. Next we estimate the willingness to pay of a representative agent for a range of emissions reduction policies using two simplified economic models. Our results illustrate the potential for large risk premiums in benefits estimates as suggested by the recent theoretical work on climate response uncertainty, and they show that the size and even the sign of the risk premium may depend crucially on how the posterior distribution describing the overall climate sensitivity uncertainty is constructed and on the specific shape of the damage function.     

Individual labour income,stock prices and whom it may concern

In this paper, a panel model which describes the relationship between individual labour income and stock prices in Germany is estimated. The specification allows the individuals to cluster concerning the model parameters that describe first the individual labour income dynamics and second the relationship between the individual labour income and financial markets. Methodically, a Bayesian model-based non-Gaussian panel data approach, proposed by Juarez and Steel (2010a), is used. A group of individuals with a high cluster assignment probability is found. The characteristics of this group, whose individuals share the same autoregressive dynamics and a common, relatively high dependence on financial markets, are investigated further. It can be shown that this group has a statistically significantly different partition of the major occupational groups. This leads to implications for various branches of the literature, such as the pricing of human capital contracts, the hedging of individual income risk, portfolio optimization or asset pricing.     

中国居民家庭的收入变动及其对长期平等的影响

本文利用“中国经济、人口、营养和健康调查”1 989— 1 997年期间 4期家庭收入和家长特征的模块数据 (paneldata) ,用时间依赖定义收入变动 ,度量了全体家庭和分4种类型的家庭在上世纪 80年末至 90年后半期的收入变动。发现在总体收入分配中 ,高比例持续贫困的发生比较分散 ,并不固定在哪一类型的家庭上。平均而言 ,农村家庭的持续贫困比例稍高。与此相反 ,持续高收入的家庭集中在城市、郊区和城镇 ,农村的富裕家庭变动大 ,收入不稳定。分组家庭之间 ,农村家庭的收入变动最大。分组家庭内部 ,家长为中年和壮年人的家庭人收入景况较好 ,富裕老人家庭能否保持富裕在农村和在其它分组差别很大。总体而言 ,我国居民家庭收入分配的变动在这一时期减慢 ;收入变动在所有4个时期内都有利于分配的平等 ,2 0世纪 90年代中期后在农村和城镇家庭的作用大幅减弱 ,但对改善城市家庭的平等分配作用增强。     

Investigating the distribution of personal income obtained from the recent U.S. data

This study considered the conservation of money in a closed economic system. In such system, the probability distribution of money is exponential, and similar to the Boltzmann-Gibbs function in a closed energy system. The theoretical concept of econophysics is compared here with empirical data. The current work analyzes the recent data with regard to personal income distribution obtained from United States Census Bureau for the years 2006, 2007 and 2008. The data was best fitted with the exponential function, which supports the theoretical assumption for the income of the majority of the population. This study also investigates this distribution for a population with high personal income.     

Probability models and robust policy rules

We consider Sims's (2008) argument that robust policy making requires that policy models be treated as “probability models”. In a welfare-based setting, we estimate by Bayesian methods a number of variants of a New Keynesian macroeconomic model and use both the model odds and posterior densities to design robust interest rate rules consisting of an inflation-forecast-based rule and a wage-targeting one. Each are shown to have distinct robustness qualities and distinct implications for the probability-models approach. To ensure feasible policy, we further impose that rules are stable, determinate and lower-bound compatible. Our results have important implications for the design, evaluation and analysis of the probability models approach to robust monetary policy making.     

中国城镇居民的劳动供给行为——倒S型劳动供给曲线在中国城镇劳动力市场上的实证检验

依据2002年中国家庭收入项目(CHIP)数据,本文应用微观经济计量方法估计了城镇居民的就业方程和工作时间方程。研究结果表明,随着教育年限的增加,个体就业概率不断增加;随着家庭其他收入的增加,个体就业倾向逐渐降低,工作时间逐渐减少;随着家庭人口数的增加,就业个体的工作时间逐渐增加。低收入群体女性和男性工作时间的工资弹性分别为-0.3237和-0.3167,而女性中高收入群体工作时间的工资弹性为0.1429,说明倒S型劳动供给曲线在2002年中国城镇劳动力市场是存在的。因此,政府部门应结合经济发展水平适时地提高最低工资标准,完善社会保障制度,同时加大对低收入群体教育和培训投入力度,促进低收入群体社会福利水平的改善。     

Modeling Nonlinear Autoregressive Distributed Lag Models: A New Approach

It is a common practice in econometrics that estimation is carried out in terms of the reduced form parameters and the structural form parameters are retrieved using the functional relationship between structural form parameters and the reduced form parameters. The reduced form of many useful economic models is a nonlinear distributed lag model (NLADL) with error structure which may have autocorrelation. In addition, the relationship between the reduced form and the structural parameters is often nonlinear and in a ratio form. In such situations existing sampling theory estimation procedures result in estimators for the structural parameters which do not have finite moments and do not possess optimal sampling properties. As an alternative, we propose a two step Bayesian estimation method. The Bayesian method has great potential and allows us to obtain the posterior probability density functions of all parameters of interest. In particular, its application for the analysis of adaptive expectation partial adjustment models for which the reduced form is a NLADL model, has been found extremely useful. An application to Nerlove’s supply response function supports the proposed methodology.

     

Income mobility and the middle class in Russia, 1995–2007

This article analyzes the determinants of income mobility between 1995 and 2007, using the Russia Longitudinal Monitoring Survey (RLMS-HSE). The analysis uses the mixture model method and is carried out between and within income groups, defined on the basis of household income. The results of the within-group analysis suggest that the probability of remaining in the middle of the income distribution is greater than that of remaining poor or rich. However, if a household moves away from the middle group, the probability of falling into the bottom group is much higher than that of moving upwards.     

DISTRIBUTIONS OF REAL INCOME: WITHIN COUNTRIES AND BY WORLD INCOME CLASSES

Income and expenditure data from 14 countries (representing one-third of the world's population), mostly from the 1970s, are used to construct national income distributions and , after normalizing by purchasing power parities, to construct a "world" distribution of real income. The density of real-income equivalent groups (socio-economic classes) across countries is measured for the "affluent," the "well-off," and the "poor." In comparison with earlier studies, most national distributions of income seem to have been improving, the numbers of those in poverty (based on real income) are lower, and, most important (and disturbing for some) is that the "affluent" class (and those above "middle class" income levels) has (prematurely) swelled in a number of developing countries.     

区域经济收入分布的动态演进分析——以浙江省为例

基于浙江省区域经济人均收入数据,采用核密度函数和马尔科夫分析法,对区域经济收入分布的动态演进过程进行了分析.结果表明,浙江区域人均收入分布特征有别于全国或省区层面上的收入分布特征:浙江区域收入分布整体上呈现单峰、偏态的分布形态,且区域间收入差异呈现扩大的趋势.区域间的状态转移矩阵显示,收入状态的流动性较低,仅在相邻的状态之间转移,难以实现状态问跨越式转移.在经济的长期收入均衡状态中,收入分布分散于四种类型状态空间,其中,不发达地区将占主要比重,不会出现区域经济趋同现象,收入差距会有进一步扩大的趋势.     

Bayesian assessment of Lorenz and stochastic dominance

We introduce a Bayesian approach for assessing Lorenz and stochastic dominance. For two income distributions, say X and Y, estimated via Markov chain Monte Carlo, we describe how to compute posterior probabilities for: (i) X dominates Y, (ii) Y dominates X and (iii) neither Y nor X dominates. The proposed approach is applied to Indonesian income distributions using mixtures of gamma densities that ensure flexible modelling. Probability curves depicting the probability of dominance at each population proportion are used to explain changes in dominance probabilities over restricted ranges relevant for poverty orderings. They also explain some seemingly contradictory outcomes from the p-values of some sampling theory tests.     

Personal Income Distribution and Market Structure

Income distribution affects market demand and its elasticity, and, as a consequence, the optimal behaviour of firms and market equilibrium. This paper focuses on the effects of income polarization, and presents a model where – for any unimodal density function describing income distribution of the consumers – income polarization leads to market concentration, i.e., to a smaller number of firms able to survive in the long run, provided that the firms' fixed costs are sufficiently low.     

Statics and Dynamics of Income Distribution: An Introductory Survey

Abstract
This article discusses some of the issues involved in making comparisons of income distributions using cross-sectional data and in examining the dynamics of income distribution using longitudinal data. Any study of income distribution must consider the unit of analysis, the time period and the measure of income, and these are the focus of the article. Section 2, on annual incomes, begins with problems of intra-household income sharing and the measure of income used, including household production. Comparisons among households of different size are discussed, involving the choice of equivalence scales, the use of decomposition analysis and more general dominance conditions. The role of value judgments in the use of equivalence scales is stressed. Section 3 is concerned with dynamic aspects of income distribution. It discusses methods of constructing synthetic cohorts for use in simulation exercises, the varieties of longitudinal data available, sample attrition and the unit of analysis. An appendix provides further references to the literature and data sources .     

BUSINESS CYCLES IN SMALL OPEN ECONOMIES: EVIDENCE FROM PANEL DATA BETWEEN 1900 AND 2013

Using a novel data set for 17 countries between 1900 and 2013, we characterize business cycles in both small developed and developing countries in a model with financial frictions and a common shock structure. We estimate the model jointly for these 17 countries using Bayesian methods. We find that financial frictions are an important feature for not only developing but also small developed countries. Furthermore, business cycles in both groups of countries are marked with trend productivity shocks. Common disturbances explain one third of the fluctuations in small open economies, especially during important worldwide phenomena.     

Growth,convergence and public investment. A Bayesian model averaging approach

The aim of this study is twofold. First, the determinants of economic growth are studied among a wide set of potential variables for the Spanish provinces (NUTS3). Among others, various types of private, public and human capital in the group of growth factors are included. Also, it is analysed whether Spanish provinces have converged in economic terms in recent decades. The second objective is to obtain cross-section and panel data parameter estimates that are robust to model specification. For this purpose, a Bayesian Model Averaging (BMA) approach is used. Bayesian methodology constructs parameter estimates as a weighted average of linear regression estimates for every possible combination of included variables. The weight of each regression estimate is given by the posterior probability of each model.