Exploring the effects of aggregation error in the estimation of consumer demand elasticities

Errors introduced by using aggregate data in estimating a consumer demand model have long been a concern. We study the effects of such errors on elasticity estimates derived from AIDS and QUAIDS models. Based on a survey of published articles, a generic parameterization of the income distribution, and the range of Gini coefficients reported for 28 OECD countries, we generate and analyze a large number of “observations” on the differences between elasticities calculated at the aggregate level and those calculated at the micro level. We suggest a procedure for evaluating the likely range of aggregation error when a model is estimated with aggregate data.     

Dynamic factor models of consumption,hours and income

This paper addresses two questions in the economics of intertemporal choice. First, what are the key factors that drive fluctuations in income and what are the time paths of their effects? Second, how do consumers respond to these factors? We answer these questions by estimating dynamic factor models of consumption, hours, wages, unemployment, and income that account for measurement error and the fact that variables used in the study are measured at different time intervals and/or are aggregates for the calendar year. We pay special attention to a dynamic factor representation of a joint life cycle model of consumption and labour supply, which permits us to quantify the effect of wages, unemployment, and other factors on the marginal utility of income as well as to estimate the substitution effects of wage changes on labour supply and consumption.     

Equivalence Scales in an Intertemporal Setting with an Application to the Former West Germany

Equivalence scales provide answers to questions like how much a household with two children needs to spend compared to a couple to attain the same welfare level. These are important questions for child allowances, social benefits and to assess the cost of children over the life-cycle for example. We discuss equivalence scales in an intertemporal setting with uncertainty. To estimate equivalence scales we use a panel from German households (GSOEP) containing subjective data on satisfaction with life and satisfaction with income to represent the welfare level. Because satisfaction is measured on a discrete scale we use limited dependent variable models for panel data in estimation. Using satisfaction with life data we find that larger households do not need any additional income to be as satisfied as a couple. Using satisfaction with income, however, yields equivalence scales that increase with household size.     

Implications of seeing economic variables through an aggregation window

A variety of cross-sectional and temporal aggregation cases are considered. It is shown that if cointegration is found at an aggregate level then, strictly, many surprising constraints are implied at the micro level. However, a suitable approximation is suggested using common factors. It is shown that series may not be cointegrated at the time period of generation, but that after temporal aggregation cointegration could occur. This possibility arises because temporal aggregation can move a nuit root at a seasonal frequency to the zero frequency. Finally, the possibility of aggregating income distributions is considered and it is shown that, strictly, the Pareto distribution does not have the required property.     

Income inequality analysis in the period of economic transformation in poland

This paper presents some statistical methods of income inequality analysis based on the theoretical income distribution models that are well-fitted to the empirical models. As theoretical curves, the lognormal, gamma, Burr Type XII, and the Dagum models were used. They were applied to the earnings distributions in Poland in the period of economic transformation from a centrally-planned to a market economy. On the basis of the Dagum model, showing the perfect consistency with the considered earnings distributions, the maximun likelihood estimators of inequality parameters and economic distance ratios between men and women were calculated.     

Measurement of redistributive effect of tax rates from a longitudinal perspective: an application of the fixed taxable income approach

The primary objective of this article is to explore how the redistributive effects of tax rate change when using the fixed taxable income approach – where tax rates for each year in a period are applied to taxable income for a base year to calculate rate effects – instead of using an existing procedure to compute the rate effects. Standard rate effects are found to differ considerably from those calculated using the fixed taxable income approach in terms of both level and longitudinal trend.     

Income taxation of U.S. households: Facts and parametric estimates

We use micro data from the U.S. Internal Revenue Service to document how Federal Income tax liabilities vary with income, marital status and the number of dependents. We report facts on the distributions of average taxes, properties of the joint distributions of taxes paid and income, and discuss how taxes are affected by marital status and the number of children. We also provide multiple parametric estimates of tax functions for use in applied work in macroeconomics and public finance.     

农村生态经济建设的社会效应分析——李嘉诚基金项目实施前后农户家庭收入水平及生活质量比对

本文以兰州大学干旱农业生态研究所2001～2005年在甘肃省榆中县中连川乡实施李嘉诚基金项目前后的经济状况为例,从农民收入结构、收入水平、消费水平和生活满意度方面,探讨我国西部贫困山区实施农村生态经济建设的社会经济效应,提出项目实施效应中突显的问题及相应的政策思考。     

Household inequality, social welfare, and trade

Working with Sen social welfare functions (meaning explicit separability between mean income and income dispersion), we develop a generalized dual approach to tracking household inequality aspects of social welfare in general equilibrium. We highlight how household equity can be examined analytically alongside production efficiency in duality-based models, using our dual framework to explore potential trade-offs between efficiency and equity effects of trade policy. Our results complement the set of standard inequality results in trade theory focused on functional rather than household inequality. We also find that the relative distributional impact of tariffs on welfare is conditional on the initial level of inequality.     

Aggregation bias-correcting approach to the health–income relationship: Life expectancy and GDP per capita in 148 countries, 1970–2010

A large amount of data consisting of 148 countries for the years 1970 to 2010 is analysed in the context of the health–income relationship. The literature suggests that the biased income–health effect obtained with macro data can be a result of the aggregation of individual concave income functions on average health. This aggregation problem is analysed in detail, and a bias-correcting method is proposed to overcome it. The results with new model alternatives show that they correct the income effects on average health in the right direction; that is, they produce smaller parameter estimates than biased models. Augmenting the results with the quantile regression approach, which is sensitive to health differences between countries, indicates that the poorest countries’ income gradient is still much larger than that of rich countries. However, the median life expectancy effect of the log of GDP per capita across the countries decreased during the sample decennials. The results for income inequality measured with the Gini coefficient indicate that the effects of inequality on health are still significant in the poorest countries but non-significant among rich countries after the year 2000. We argue that the proposed bias-correcting method retains the interest in macro health modelling and offers new model alternatives in other contexts.     

A Note on Aggregation and the Lucas Critique

The paper investigates the effects of aggregation on different macroeconomic modelling strategies. This is done within the framework of a small example economy, where all households solve the same intertemporal consumption problem, but with different parameters of the utility functions and different exogenous income processes. Three models are fitted to the aggregate data: a representative agent rational expectations model, a simple version of the permanent income hypothesis, and a time series model. If the economic environment is kept stable, the three approaches perform similarly well. However, the representative agent model stands up to the Lucas critique better than its competitors, despite the aggregation error. Unlike the other models, it never gives completely wrong forecasts even after an exogenous change in income processes.     

A panel data model for subjective information on household income growth

Subjective expectations about future income changes are analyzed, using household panel data. The models used are extensions of existing binary choice panel data models to the case of ordered response. We consider static models with random and fixed individual effects. We also look at a dynamic random effects model which includes a measure for permanent and transitory income. We find that income change expectations strongly depend on realized income changes in the past: those whose income fell, are more pessimistic than others, while those whose income rose are more optimistic. Expected income changes are also significantly affected by employment status, family composition, permanent income, and past expectations. Expectations are then compared to the head of household’s ex post perception of the realized income change for the same period. The main finding is that rational expectations are rejected, and that in particular, households whose income has decreased in the past underestimate their future income growth.     

Equity,efficiency, and the structure of indirect taxation

Optimal tax formulae are derived and optimal tax rates calculated for the case where there are many consumers, an income tax is impossible and the government has to trade off efficiency in order to improve the real distribution of income. Consistent aggregation assumptions are used to permit the derivation of simple tax rules depending only on the behaviour of the average consumer and of a socially representative consumer. Calculations for the U.K. in 1972 show how subsidies and taxes vary with the government's revenue requirement and with the degree of egalitarianism in the social welfare function.     

ON THE POSSIBILITY OF MEASURING THE DISTRIBUTION OF PERSONAL INCOME

The income distribution statistics which are based on income for a single year show a far larger inequality of income than actually exists. The distribution of annual incomes differs from the distribution of lifetime income partly because of short run fluctuations because of such things as sickness, unemployment, and unusual gains, and partly because different individuals are at different points in their life cycles. The vertical distribution of income can be considered to be the distribution of lifetime income. The horizontal distribution can be considered to be the differences arising in the current period due to short run fluctuations and differences in the age-income cycle of persons. The observed annual income distribution statistics are a mixture of the vertical and horizontal distributions. The estimation of the lifetime income distribution implies discounting, and also raises questions as to the treatment of transfers, subsidies, public investments and taxes. However, statistics based upon a mixture of the horizontal and vertical distributions of income are of no interest.     

Interpolating the Lorenz Curve: Methods to Preserve Shape and Remain Consistent with the Concentration Curves for Components

C¹‐class interpolation methods that preserve monotonicity and convexity and are thus suitable for the estimation of the Lorenz curve from grouped data are not widely known. Instead, parametric models are usually applied for such estimation. Parametric models, however, have difficulty in accurately approximating every part of income/expenditure distributions. This paper proposes two types of C¹‐class shape‐preserving interpolation methods. One is a piecewise rational polynomial interpolation (proposed independently by Stineman and Delbourgo) that enables consistent interpolation of the concentration curves for income/expenditure components, attaining approximately the same accuracy as that of the existing methods when applied to decile‐grouped data or to more detailed aggregation. Another is a Hybrid interpolation that employs pieces of curves derived from parametric models on end intervals. Empirical comparisons show that the Hybrid interpolation (with the assistance of parametric models for class‐boundary estimation) outperforms the existing methods even when applied to quintile‐grouped data without class boundaries.     

A COMPARISON OF DISTRIBUTIONS OF ANNUAL AND LIFETIME INCOME: SWEDEN AROUND 1970.

The concern with income distribution has always mainly existed because of a concern with individuals' economic welfare. In recent years, the question has arisen whether the distribution of annual income—the distribution most often studied—is the best proxy for the distribution of economic welfare. Other measures, such as lifetime income, have been proposed instead.
The paper starts with a discussion of how to define and measure the distribution of lifetime income. By using a simulation model, which partly consists of estimated functions and partly of tax functions taken directly from tax laws, distributions of lifetime income, variously defined, are then constructed. These distributions are compared with each other, and with distributions of annual income. The simulations indicate that the distribution of lifetime income is considerably less unequal than the distribution of annual income. Whether inheritances are included or not seems to be of no importance for the inequality of lifetime income. If, on the other hand, we include the value of leisure time in lifetime income, inequality increases by about 10–15 percent. Distributions of income after tax have Gini coefficients which are approximately 25 percent less than the Ginis for the before-tax distributions. We thus find that the picture of inequality we get is very much dependent on which income concept we use.     

Why do Aggregate Production Functions Work? Fisher’s simulations,Shaikh’s identity and some new results

The literature on aggregation has shown that the conditions for successful aggregation of micro production functions into an aggregate production function are far too stringent to be believable (Fisher 1969, 1971). Despite this, aggregate production functions continue being used. The reason is that they seem to 'work'. This happens, however, because underlying every aggregate production function is the income accounting identity that links input and output, i.e. output equals wages plus profits. A simple algebraic transformation of this identity yields a form that resembles a production function (Shaikh, 1974, 1980). This paper uses Monte Carlo simulations to study two questions. First, how much spuriousness can help explain the relatively good fits of the Cobb-Douglas production function? The simulations show that the contribution of spuriousness to a high R 2 is minor once we properly account for the fact that input and output data used in production function estimations are linked through the income accounting identity. It is mostly the link through this identity that explains the results. Secondly, we study how much factor shares have to vary in an economy so as to render the Cobb-Douglas production function with a time trend a bad choice for modelling and estimation purposes. We conclude that the Cobb-Douglas form is robust to relatively large variations in the factor shares. What makes this form often fail are the variations in the growth rates of the wage and profit rates.     

INCOME POVERTY AND MULTIDIMENSIONAL DEPRIVATION: LESSONS FROM CROSS‐REGIONAL ANALYSIS

The study of multidimensional deprivation has become one of the most relevant lines of research in the analysis of low‐income households. The search for significant relationships between multidimensional deprivation and income poverty has been a central issue and most empirical studies have found a very weak link. This paper aims at examining the possibility of an aggregation bias in national‐level studies, which could conceal disparities between regions. As regional differences and decentralization processes stand out in Spain as compared to other OECD countries, we focus the analysis on this country. Latent class models are used to define deprivation indices using the Spanish EU‐SILC. The results seem to show that the absence of significant relationships between both phenomena still holds at a regional level. The decomposition methods used in the paper show that it might be due to some regional singularities in some determining factors of income and multidimensional poverty.     

HOW MISLEADING ARE INCOME DISTRIBUTIONS?

Starting from the proposition that economic welfare is better measured by the capitalized value of expected future income at age 18 than by income at a point of time, the present paper explores the bias introduced in comparison of earnings and income distributions.
The earning distribution chosen for study is that for males in 1959 in the United States. It is shown that earnings distributions are biased and therfore can be considered highly misleading in most comparisons unless the comparison involves two groups with identical age distributions and identical distributions of earnings over the working life of earners.
Further, a most striking effect can be discerned in comparing the earnings to the present value distributions by educational level. As one moves up the educational ladder, the within-group distribution of lifetime income becomes more and more equal, in sharp contrast to the findings for the distribution of earnings at a point in time.
The result are sufficiently interesting and striking to warrant further studies of distributions of present value of lifetime expected earnings (and income).     

THE INCOME UNIT AND THE ANATOMY OF INCOME DISTRIBUTION*

This paper focuses on a neglected aspect of the treatment of the income unit in the construction of size distributions of income. If the size distribution is to be an indicator of the distribution of economic welfare, and if the economic welfare of each individual in society is to count equally, then conventional distributions are inconsistent with individualistic welfare functions. We estimate size distributions with each person's welfare weighted equally, and contrast these results with those weighting each household unit's welfare equally. The choice of weights is shown to affect both the level and the trend in income inequality.