Calculating Poverty Measures from the Generalised Beta Income Distribution

Data for measuring poverty are frequently available in a summary form that describes the proportion of income or expenditure for each of a number of population proportions. While various discrete poverty measures can be applied directly to data in this limited form, they typically require an arbitrary approach to within‐group interpolation. This problem can be overcome by fitting either a parametric income distribution or a Lorenz curve to the grouped data and computing the required quantities from estimated parameters. The Lorenz curve approach is widely used by the World Bank, but can encounter problems. As an alternative, in this article we show how to calculate several poverty measures from parameters of the generalized beta income distribution, and its popular special cases. An analysis of poverty changes in countries from South and Southeast Asia is used to illustrate the methodology.     

A NON‐PARAMETRIC MEASURE OF POVERTY ELASTICITY

We estimate the growth elasticity of poverty (GEP) using recently developed non‐parametric panel methods and the most up‐to‐date and extensive poverty data from the World Bank, which exceeds 500 observations in size and represents more than 96 percent of the developing world's population. Unlike previous studies which rely on parametric models, we employ a non‐parametric approach which captures the non‐linearity in the relationship between growth, inequality, and poverty. We find that the growth elasticity of poverty is higher for countries with fairly equal income distributions, and declines in nations with greater income disparities. Moreover, when controlling for differences in estimation technique, we find that the reported values of the GEP in the literature (based on the World Bank's now‐defunct 1993‐PPP based poverty data) are systematically larger in magnitude than estimates based on the latest 2005‐PPP based data.     

Fitting parametric lorenz curves to grouped income distributions — A critical note

Empirical Economics - The paper surveys various parametric Lorenz curves to be fitted to grouped income data in order to obtain an estimate for the Gini measure of inequality. The curves are fitted...     

ESTIMATING SPATIAL CONSUMER PRICE INDICES THROUGH ENGEL CURVE ANALYSIS

In this paper we propose a method of estimating spatial multilateral price index numbers from cross‐section consumer expenditure data on different items using Engel curve analysis. The novelty of the procedure is that it overcomes the problem of data inadequacy, a problem that is shared by most of the developing countries. The procedure does not require item‐specific price/unit value data and price index numbers can be calculated from consumer expenditure data grouped by per capita income/total consumer expenditure class in a situation where unit level data are not available. To illustrate the method, we use published state‐specific data of the 50th round (1993–94) and 55th round (1999–2000) consumer expenditure surveys of India's National Sample Survey Organization (NSSO) and calculate the spatial consumer price index numbers for 15 major states of India, with All‐India taken as base, separately for the rural and the urban sector for each round.     

Testing exact aggregation in income and household characteristics: the effects of aggregation across goods

Exact aggregation in income and household characteristics are tested using Canadian cross-sectional microdata. Over 100 data sets of homogeneous households are used, making it possible to conduct a large number of independent hypothesis tests. Tests are also conducted to determine whether the homogeneous household groups can be grouped into more heterogeneous data sets. Six different kinds of demand systems are estimated to ensure the robustness of the results to separability/aggregation structure.Exact aggregation in income, family size, region of residence and housing tenure status are strongly rejected, but exact aggregation in age of head of household is not. Restrictions which would allow pooling of households of different sizes, regions and tenure status are also strongly rejected. The test results exhibit a little sensitivity to the expenditure aggregates used, but not to the extent that the results would be different.The results imply that aggregate demand functions which use time series data should include many statistics from the joint distribution of income and household characteristics. In addition, when using data at the micro-level, the amount of heterogeneity in households' behaviour is much greater than usually assumed. This calls for the use of much more homogeneous household groups in the estimation of demand models than are typically employed.     

A GENERAL METHOD FOR CREATING LORENZ CURVES

A general method to construct parametric Lorenz models of the weighted‐product form is offered in this paper. Initially, a general result to describe the conditions for the weighted‐product model to be a Lorenz curve, created by using several component parametric Lorenz models, is given. We show that the key property for an ideal component model is that the ratio between its second derivative and its first derivative is increasing. Then, a set of Lorenz models, consisting of a basic group of models, along with their convex combinations, is proposed, and it is shown that any model in the set possesses this key property. We introduce the concept of balanced fit, which provides a means of assigning weights, according to the preferences of the practitioner, to two alternative objectives for developing Lorenz curves in practice. These objectives are generating an acceptable Lorenz curve and improving the accuracy of the density estimation. We apply the balanced fit approach to income survey data from China to illustrate the performance of our models. We first show that our models outperform other popular traditional Lorenz models in the literature. Second, we compare the results generated by the balanced fit approach applied to one of the Lorenz models that we develop with those generated by the kernel method to show that the approach proposed in the paper generates plausible density estimates.     

Estimation of Household Expenditure Functions:An Application of a Class of Heteroscedastic Regression Models*

A class of heteroscedastic regression models is applied to the estimation of household expenditure functions using data from the 1966-68 Macquarie University survey. Under the assumption that expenditure observations are normally distributed, the hypothesis that their variances are proportional to the squares of their expectations is investigated. In addition, the hypotheses tests derived by Amemiya (1973a) for discriminating between heteroscedastic regression models with gamma or lognormal distributions are applied to the same expenditure data.     

The Distribution of Household Health Expenditures in Australia*

Out‐of‐pocket health expenditures in Australia are high in international comparisons and have been growing at a faster rate than most other health costs in recent years. This raises concerns about the extent to which out‐of‐pocket costs have constrained access to health services for low income households. Using data from the ABS Household Expenditure Survey 2003–2004, we model the relationships between health expenditure shares and equivalised total expenditure for categories of out‐of‐pocket health expenditures and analyse the extent of protection given by concession cards. To allow for flexibility in the relationship we adopt Yatchew's semi‐parametric estimation technique. This is the first detailed distributional analysis of household health expenditures in Australia. We find mixed evidence for the protection health concession cards give against high out‐of‐pocket health expenditures. Despite higher levels of subsidy, households with concession cards do not have lower out‐of‐pocket expenditures than non‐cardholder households except for the highest expenditure quintile. Cards provide most protection for GP out‐of‐pocket expenditures.     

Modeling of Income and Indicators of Poverty and Social Exclusion Using the Generalized Beta Distribution of the Second Kind

There are three reasons why estimation of parametric income distributions may be useful when empirical data and estimators are available: to stabilize estimation; to gain insight into the relationships between the characteristics of the theoretical distribution and a set of indicators, e.g. by sensitivity plots; and to deduce the whole distribution from known empirical indicators, when the raw data are not available. The European Union Statistics on Income and Living Conditions (EU‐SILC) survey is used to address these issues. In order to model the income distribution, we consider the generalized beta distribution of the second kind (GB2). A pseudo‐likelihood approach for fitting the distribution is considered, which takes into account the design features of the EU‐SILC survey. An ad‐hoc procedure for robustification of the sampling weights, which improves estimation, is presented. This method is compared to a non‐linear fit from the indicators. Variance estimation within a complex survey setting of the maximum pseudo‐likelihood estimates is done by linearization (a sandwich variance estimator), and a simplified formula for the sandwich variance, which accounts for clustering, is given. Performance of the fit and estimated indicators is evaluated graphically and numerically.     

Pareto–lognormal distributions: Inequality,poverty, and estimation from grouped income data

The (double) Pareto–lognormal is an emerging parametric distribution for income that has a sound underlying generating process, good theoretical properties, and some limited favorable evidence of its fit to data. We extend existing results for this distribution in 3 directions. (1) We derive closed form formula for its moment distribution functions, and for various inequality and poverty measures. (2) We show how it can be estimated from grouped data using GMM. (3) Using grouped data from ten countries, we compare its performance with that of another leading 4-parameter income distribution, the generalized beta-2 distribution. The results confirm that, when using grouped data, both distributions provide a good fit, with the double Pareto–lognormal distribution outperforming the beta distribution in 4 out of 10 cases.     

An analysis of housing expenditure using semiparametric cross-section models

In this paper we model expenditure on housing for owners and renters by means of endogenous switching regression models using cross-section data. We explain the share of housing in total expenditure from family characteristics and total expenditure, where the latter is allowed to be endogenous. We apply various existing parametric and semiparametric techniques for cross-section data. Exogeneity of total expenditure is rejected for the parametric models but not for most semiparametric models. The results are compared on the basis of budget elasticities and graphs of the estimated relationship between the budget share spent on housing and the logarithm of total expenditure. First version received: November 1997 / Final version received: January 2000     

Parametric Lorenz Curves and the Modality of the Income Density Function

Similar looking Lorenz curves can imply very different income density functions and potentially lead to wrong policy implications regarding inequality. This paper derives a relation between a Lorenz curve and the modality of its underlying income density: given a parametric Lorenz curve, it is the sign of its third derivative which indicates whether the density is unimodal or zeromodal (i.e., downward‐sloping). The density modality of several important Lorenz curves such as the Pareto, Weibull, Singh–Maddala parametrizations and hierarchical families of Lorenz curves are discussed. A Lorenz curve performance comparison with Monte Carlo simulations and data from the UNU–WIDER World Income Inequality Database underlines the relevance of the theoretical result: curve‐fitting based on criteria such as mean squared error or the Gini difference might lead to a Lorenz curve implying an incorrectly‐shaped density function. It is therefore important to take into account the modality when selecting a parametric Lorenz curve.     

On the distributional effects of income in an aggregate consumption relation

Abstract .  In this paper we analyse the influence of characteristics of the income distribution in modelling aggregate consumption expenditure. We model the aggregate consumption relation of a heterogeneous population, using a statistical distributional approach of aggregation, and apply it to UK-Family Expenditure Survey data. A bootstrap test based on a non-parametric estimation methodology, which accounts for the presence of continuous and discrete variables, suggests that the mean and the dispersion of the income distribution significantly influence aggregate consumption expenditure. Also, the parameters of the aggregate relation are time varying. These findings have implications for constructing empirically sound models of aggregate consumption expenditure.     

EFFECT OF INCOME DISTRIBUTION ON THE ENVIRONMENTAL KUZNETS CURVE

This paper augments the model of Andreoni and Levinson by analyzing the effect of income distribution on the inverted U‐shaped relationship between some forms of pollution and income, the so‐called ‘environmental Kuznets curve’. In a context in which pollution abatement technology shows increasing returns to scale and an inverse U‐shaped pollution–income path is present, this study demonstrates the existence of a majority voting equilibrium, and concludes that the inverted U‐shaped relationship is between median income and environmental degradation rather than between per capita income and environmental degradation. Our results suggest that an increase in equality in income distribution improves environmental quality and social efficiency. The implication of the model for the empirical estimation of environmental Kuznets curves is examined using a panel data set of 36 countries over a 20‐year period. Estimation results using different models show that income distribution might be an important factor in the empirical estimation of these curves.     

Effects of Changes in Household Size,Consumer Taste & Preferences on Demand Pattern in India

Current research in applied demand analysis has been addressing the twin issues of degree of non-linearity or curvature of the Engel curves and the ability to capture price effects appropriately by the demand system. Further, in addition to income and prices, the role of demographic variables like household size, composition and dynamic aspects like consumer taste & preferences are also being ’ emphasized in recent literature. Continuous efforts are being made to modify the existing models and propose new ones to incorporate the above developments. The purpose of this study is to re-examine the usefulness of the popular linear expenditure system vis-à-vis the two other flexible models viz. Nasse expenditure system, a generalization of the linear expenditure system itself, and the almost ideal demand system in the above context for India.The empirical results indicate wide variation in marginal budget shares and demand elasticities across income groups, rural-urban sectors and alternative models. The household size and consumer taste & preferences are found to be statistically significant. The results confirm the earlier findings that there are significant changes in consumer tastes away from cereals and pulses in favor of other food and nonfood commodities. The results also show that flexible models, which are theoretically superior, gave unacceptable positive price responses for some commodities and violated second order conditions of utility maximization. It is found that some ad-hoc separability restrictions are needed, thereby limiting the flexibility of the model, to get negative own-price responses in these models. But, second order conditions are still violated. The tests of nested hypotheses also confirm the need for inclusion of household size, consumer taste, income group and rural-urban dummies along with their interaction variables in the demand system.

     

城际政府公共投资策略互动行为及其形成机制——基于278个地级及以上城市数据的实证分析

文章基于2007年收支分类改革后新的预算科目和278个地级及以上城市的数据,运用SLM、SEM、Durbin和SAC空间计量模型以及ML估计和工具变量GMM估计方法,通过设定相邻、地表距离和最临近三种空间地理矩阵以及工业化水平、土地出让金收入占比、房地产投资占比、城市化水平和FDI五种经济变量空间矩阵,对当前城市政府间公共投资类财政支出的策略互动情况进行了评估与甄别。结果发现,城市政府在相邻地理位置上的显著互动———以策略互补为主,具有特定的外部性范围和变化轨迹,而工业禀赋型、"土地"财政型和FDI型策略互动的影响则具有同质性,且总体低于以外溢效应和标尺效应为主要源泉的地理空间位置上的策略互动水平。最后,文章对相应理论和政策含义进行了探讨。     

Determinants of food consumption in rural Sierra Leone: Application of the quadratic expenditure system to the consumption-leisure component of a household-firm model

This paper reports the application of a quadratic expenditure system with demographic variables to the household consumption-leisure choice component of a household-firm model. A system of seven commodities is estimated: including five foods, non-food and leisure. Appropriate for such a level of disaggregation a demand system is used, the Quadratic Expenditure System, which allows for a flexible relationship between full income and commodity expenditures without sacrificing parsimony in parameters. Demographic data on households are explicitly incorporated into the model allowing for a richer specification than can be achieved by using per capita variables. The data are from a cross-section survey of households in rural Sierra Leone. Price variation exists by region, permitting estimation of a complete demand system. Engel curves are found to be significantly non-linear, with marginal expenditure on rice, the major staple, declining with higher income. Most foods are found to be reasonably price responsive with sizeable own price substitution effects, declining with higher income. Aggregate labor supply is found to be price inelastic.     

REDISTRIBUTIVE POLITICS AND GOVERNMENT DEBT IN A BORROWING‐CONSTRAINED ECONOMY

We develop a two‐period, three‐class of income model where low‐income agents are borrowing constrained because of capital market imperfections, and where redistributive expenditure is financed by tax and government debt. When the degree of capital market imperfection is high, there is an ends‐against‐the‐middle equilibrium where the constrained low‐income and the unconstrained high‐income agents favour low levels of government debt and redistributive expenditure; these agents form a coalition against the middle. In this equilibrium, the levels of government debt and expenditure might be below the efficient levels, and the spread of income distribution results in a lower debt‐to‐GDP ratio.     

EXPLAINING THE SAVING PUZZLES IN URBAN CHINA

This paper identifies two saving puzzles obtained from the Chinese Urban Household Survey data from 1990 to 2006. The first saving puzzle is identified by the time trend of household saving rates, which were stable before 1998, but surged subsequently. The second saving puzzle is associated with the various age profiles of household saving rates, which are not only inconsistent with the prediction of the Life Cycle Hypothesis, but also different from the patterns observed in other economies. This paper constructs pseudo‐panel data and empirically examines the applicability of the habit‐formation model in solving the second saving puzzle through the existence of saving rates and the effects of income‐related variables. On the other hand, the parametric changes of such variables help explain the first saving puzzle. The parametric changes possibly stem from the adjustment of habit stock, the rising transitory shocks of income, and the higher expenditure needs for housing.     

An empirical comparison of nonparametric and parametric Engel functions

Nonparametric techniques are used to estimate income densities, Engel functions and their derivatives, and income elasticities. Nonparametric kernel methods give less ambiguous estimates of the densities than discrete, maximum penalised likelihood estimation. The nonparametric estimates of the Engel functions, their derivatives, and the income elasticities are compared with some corresponding parametric estimates. The nonparametrically estimated Engel functions provide a better fit to the data. Also, the nonparametric elasticity estimates are qualitatively similar to the parametric estimates. Some statistically significant differences are observed between the parametric versus nonparametric estimates, but not to the extent of having any major policy implications.