The distribution of personal income: Revisited

In a recent paper, Majumder and Chakravarty (1990) propose a four-parameter model which they find provides a better fit to some income data than the lognormal, gamma, Singh-Maddala, Dagum, and generalized beta of the second kind (GB2) distributions. This note (1) demonstrates that the model proposed by Majumder and Chakravarty is a reparameterization of the GB2 and (2) reconciles the corresponding contradictory empirical findings reported by Majumder and Chakravarty.     

Community income distributions in a metropolitan area

We extend de Bartolome and Ross [C.A.M. de Bartolome, S.L. Ross, Equilibrium with local governments and commuting: Income sorting vs. income mixing, Journal of Urban Economics 54 (2003) 1–20] to the case when the income distribution in the metropolitan area is a continuous distribution. In particular, we consider a circular central city surrounded by a suburban community. All households must commute to the metropolitan center and public service levels differ in the two jurisdictions. There is intra-jurisdictional and inter-jurisdictional capitalization. Our model has an equilibrium in which the income distributions of the central city and of the suburban community do overlap. Our finding contrasts with the traditional finding of Alonso–Mills–Muth-type models of spatial sorting and of Tiebout-type models of fiscal sorting, both of which have been shown to predict that the income distributions of the two communities do not overlap. In addition, the model explains the fixedness in jurisdictional boundaries.     

Empirical evidence of income dynamics across EU regions

This paper analyses the distribution of purchasing power standardized per capita income across EU‐12 regions between 1977 and 1996. Dispersion of incomes between regions is measured taking into account their population sizes. The cross‐sectional distributions are initially described by weighted kernel density estimates, revealing a multimodal structure of the distributions, less evident over the period. This evidence is supported by a bootstrap test. To detect homogeneous groups of regions, the empirical distributions are approximated by a finite mixture of normal densities. The components of the mixture represent clusters of poor/rich regions, while the mixing proportions the allocation over the poor and the rich components. The number of components is assessed by a bootstrap LR test, and the goodness of fit by a kernel density‐based test. Income mobility is modelled by the stochastic kernel, the continuous counterpart of the transition probability matrix. The main implication is a very slow process of catching up of the poorest regions with the richer ones and a process of shifting away of a small group of very rich regions. This evidence is reflected in the shape of the ergodic distribution, which is well fitted by a two‐component mixture model. Copyright © 2006 John Wiley & Sons, Ltd.     

Income distribution and income dynamics in the United Kingdom

In this paper, we propose a model of income dynamics which takes account of mobility both within and between jobs. The model is a hybrid of the mover‐stayer model of income dynamics and a geometric random walk. In any period, individuals face a discrete probability of ‘moving’, in which case their income is a random drawn from a stationary recurrent distribution. Otherwise, they ‘stay’ and incomes follow a geometric random walk. The model is estimated on income transition data for the United Kingdom from the British Household Panel Survey (BHPS) and provides a good explanation of observed non‐linearities in income dynamics. The steady‐state distribution of the model provides a good fit for the observed, cross‐sectional distribution of earnings. We also evaluate the impact of tertiary education on income transitions and on the long‐run distribution of incomes. Copyright © 2001 John Wiley & Sons, Ltd.     

Efficient estimation of income distribution parameters

The parameters of several families of distributions are estimated by means of minimum χ²; use is made of random samples taken from Dutch income-earning groups in 1973. The numerical search routine used, is the Complex method due to Box. The χ² function is evaluated by standard numerical integration procedures. The lognormal and the Gamma families are rejected because of a poor fit. The log t and the log Pearson IV families are introduced. This results in a considerable improvement of χ² critical levels. The generalized Gamma and the Champernowne function describe the income distribution reasonably well in some cases.     

Linkages between income inequality,international remittances and economic growth in Pakistan

This paper explores the dynamic linkages between income inequality, international remittances and economic growth using time series data over the period of 1976–2006 in case of Pakistan. The cointegration analysis based on the bounds test confirms the existence of a long-run relationship between income inequality, international remittances and economic growth. Our results reveal that income inequality and international remittances enhance economic growth. The causality analysis based on innovative accounting approach shows bidirectional causal relationship between income inequality and economic growth and same is true for international remittances and income inequality. International remittances are cause of economic growth but not vice versa. Although we find support for Kuznets hypothesis but Pakistan is yet to benefit, in terms of reducing the gaps of income inequality, from the international flow of remittances and economic growth. The paper argues that, from a policy perspective, there is an urgent need for policy makers in Pakistan to reduce the widening gap of income inequality by focusing on income redistribution policies and to go beyond the traditional factors in balancing income inequality.     

Union wage setting and progressive income taxation with heterogeneous labor: theory and evidence from the German income tax reforms 1986–1990

This paper analyzes the effects of tax shifting in a model with union wage setting and progressive income taxation. The setup allows for different skill levels of the workforce and accounts for the union's distributional objective of income equality. The theoretical predictions of the model are empirically tested with a panel of German micro-data covering the period of the income tax reforms 1986–1990. It is shown that average taxes raise wages, whereas increasing the progressivity of the tax system reduces wages. The effect of progressivity on high-skilled labor tends to be less significant and smaller. Stronger preferences for equality compress the (pre-tax) wage distribution.     

Economic reforms and income distribution in Turkey

The aim of this paper is, first, to find out the income sources of the improvement in income inequality in the reform period between 2002 and 2007. s, we aim to assess the distributional impacts of macroeconomic policies over the 2002–2007 reform period by examining the contributions of different income groups to overall inequality. Income data obtained from the Household Budget Surveys of TurkStat covering the 2002–2013 period are used. The results show that there have been significant improvements in the income distribution after 2002. The extent of this improvement seems to have been higher during the 2002–2007 reform period than for the rest of the period after 2007. Entrepreneurial and financial income groups were the most distinctive for this improvement. The results also indicate that the contribution of transfer payments was very small, but surprisingly positive in both the 2002–2007 and 2007–2009 periods, and expectedly negative in the 2009–2013 period.     

An alternative model for fair share allocation of lower income housing

A linear programming model was developed and presented for fair-share allocation of lower income housing as an alternative to existing heuristic models. The model is applied for the Middlesex County region in pursuit of a regional fair-share of lower income housing needs for the year 1975 for each township in the county. The results are presented and compared with those of the Court's allocation, held by the Superior Court of New Jersey in May 1976 for the Middlesex County region.     

Some Early Multiplier Models of the Relationship between Income Distribution and Production Structure

Early efforts to endogenize consumption and hence to model the inter-relationships between production structures and income distribution via multiplier models are reviewed in this paper. It is suggested that, unlike the multipliers in Pyatt et al. (1973), the so-called Miyazawa multipliers cannot be sustained in the context of a model of the distribution of income among institutions (households, companies, etc) i.e. the institutional distribution of income. They can, however, be sustained within a model of the distribution of income among factors, i.e. the factorial distribution of income. Both distributions are modelled by Pyatt & Round (1979) which therefore provides a more general framework for analysing the relationship between the distribution of income and the structure of production.     

The structure of strategy-proof random social choice functions over product domains and lexicographically separable preferences

We characterize the class of dominant-strategy incentive-compatible (or strategy-proof) random social choice functions in the standard multi-dimensional voting model where voter preferences over the various dimensions (or components) are lexicographically separable. We show that these social choice functions (which we call generalized random dictatorships) are induced by probability distributions on voter sequences of length equal to the number of components. They induce a fixed probability distribution on the product set of voter peaks. The marginal probability distribution over every component is a random dictatorship. Our results generalize the classic random dictatorship result in Gibbard (1977) and the decomposability results for strategy-proof deterministic social choice functions for multi-dimensional models with separable preferences obtained in LeBreton and Sen (1999).     

A flexible parametric GARCH model with an application to exchange rates

Many asset prices, including exchange rates, exhibit periods of stability punctuated by infrequent, substantial, often one‐sided adjustments. Statistically, this generates empirical distributions of exchange rate changes that exhibit high peaks, long tails, and skewness. This paper introduces a GARCH model, with a flexible parametric error distribution based on the exponential generalized beta (EGB) family of distributions. Applied to daily US dollar exchange rate data for six major currencies, evidence based on a comparison of actual and predicted higher‐order moments and goodness‐of‐fit tests favours the GARCH‐EGB2 model over more conventional GARCH‐t and EGARCH‐t model alternatives, particularly for exchange rate data characterized by skewness. Copyright © 2001 John Wiley & Sons, Ltd.     

GMM estimation of a maximum entropy distribution with interval data

We develop a generalized method of moments (GMM) estimator for the distribution of a variable where summary statistics are available only for intervals of the random variable. Without individual data, one cannot calculate the weighting matrix for the GMM estimator. Instead, we propose a simulated weighting matrix based on a first-step consistent estimate. When the functional form of the underlying distribution is unknown, we estimate it using a simple yet flexible maximum entropy density. Our Monte Carlo simulations show that the proposed maximum entropy density is able to approximate various distributions extremely well. The two-step GMM estimator with a simulated weighting matrix improves the efficiency of the one-step GMM considerably. We use this method to estimate the U.S. income distribution and compare these results with those based on the underlying raw income data.     

Some notes on the non-central negative binomial distribution

Summary In this paper we shall record some facts and further examine certain properties of the non-central negative binomial (NNB) distribution (Laguerre series distribution of Gurland, Chen and Hernandez 1983). We consider, among others, a stochastic formulation (birth-and-death process), the series expansion of the probability distribution and the corresponding series expansion of a generalized exponential distribution (Ong/Lee 1986), and the connection of the NNB distribution with the non-central beta, gamma and non-central gamma distributions. A four-parameter version of the NNB distribution is also presented.     

The compactification of generalized linear models

The main purpose of this paper is to unify and extend the existing theory of 'estimated zeroes' in log-linear and logit models. To this end it is shown that every generalized linear model (GLM) can be embedded in a larger model with a compact parameter space and a continuous likelihood (a 'CGLM'). Clearly in a CGLM the maximum likelihood estimate (MLE) always exists, easing a major data analysis problem. In the mean-value parametrization, the construction of the CGLM is remarkably simple; except in a rather pathological and rare case, the estimated expected values are always finite., In the β-parametrization however, the compactification is more complex; the MLE need not correspond with a finite β, as is well known for estimated zeros in log-linear models. The boundary distributions of CGLMs are classified in four categories: 'Inadmissible', 'degenerate', 'Chentsov', and 'constrained'. For a large class of GLMs, including all GLMs with canonical link functions and probit models, the MLE in the corresponding CGLM exists and is unique. Even stronger, the likelihood has no other local maxima. We give equivalent algebraic and geometric conditions (in the vein of Haberman (1974, 1977) and Albert and Anderson (1984) respectively), necessary for the existence of the MLE in the GLM corresponding to a finite β. For a large class of GLMs these conditions are also sufficient. Even for log-linear models this seams to be a new result.     

Duality and consumption decisions under income and price risk

This paper uses duality to provide an analysis of compensated and uncompensated decisions under income and/or price risk. We focus on a two-good model, in which the individual maximizes expected utility subject to a stochastic budget constraint. A Slutsky equation is derived that decomposes the derivative of the optimal decision function with respect to any parameter in the model into an income effect and a substitution effect. The total effect of an increase in risk is controlled by the generalized preference intensity, while the compensated effect of an increase in risk is controlled by the generalized risk premium developed in the literature on aversion to one risk in the presence of another.     

The allocation of household income to food consumption

Low-income households - those toward which various income supplement programs are aimed - not only spend a large share of their incomes on food, but exhibit a higher income elasticity of demand for food than does the rest of the population. Further, a greater proportion of the marginal income generated via welfare payments and food subsidy programs (e.g., food stamps) is devoted to food consumption than is true of wage income. These are among the major conclusions emerging from an extensive Engel Curve analysis applied to the data generated by a five-year (1968–1972) panel study of 5000 U.S. households.     

Neighborhood income distributions

This paper studies purely empirically aspects of the distribution of income within small neighborhoods and contrasts it with the income distribution at higher level of aggregation, such as census tracts and metropolitan areas. It relies on a unique feature of the American Housing Survey, whose 1985, 1989 and 1993 waves provide data for small residential neighborhoods. These consist of a dwelling unit and up to ten of its nearest neighbors. The paper employs several parametric and non-parametric econometric tools to measure income sorting in US residential neighborhoods. It documents the patterns of dependence among neighbors' income and imperfect sorting, with moderate but very significant correlation among incomes of neighbors and of considerable income mixing in US neighborhoods. These results persist even if choice-based sampling and heterogeneity across the sample are accounted for. Neighborhoods associated with a randomly selected renter are more sorted than those associated with an owner even though such owners are more likely to define their neighborhoods.     

Who pays for whom? Elements of a macroeconomic approach to income inequality

National income is generated through national production in the form of ‘value added’; it is expended on goods and services in the form of ‘disposable’ or ‘net’ income. In this paper, I investigate what happens in between. The circuit of income flows generated in this way is comparable to the circuit of product flows, in its complexity. It can be analysed, so the tenet of the paper, in a similar way, by means of well-known tools of input–output (IO) analysis; this on the pre-condition, however, that you draw out the institutional framework of an economy in similar detail as is now customarily done for production units in IO analysis. Existing data do not suffice for the purpose, at present; this paper shows, by way of some exemplary calculations, what insight into the mechanism of national income distribution is gained if the necessary data, normally in the form of a large social accounting matrix, are provided.     

Correlated income shocks and excess smoothness of consumption

In the literature, econometricians typically assume that household income is the sum of a random walk permanent component and a transitory component, with uncorrelated permanent and transitory shocks. Using data on realized individual incomes and individual expectations of future incomes from the Survey of Italian Households׳ Income and Wealth, I find that permanent and transitory shocks are negatively correlated. Relaxing the assumption of no correlation between the shocks, I explore the effects of correlated income shocks on the estimated consumption insurance against permanent and transitory shocks, and consumption smoothness using a life-cycle model with self-insurance calibrated to U.S. data. Negatively correlated income shocks result in smoother consumption, and upward-biased estimates of the insurance against transitory (and permanent when borrowing constraints are not tight) income shocks. While the life-cycle model with negatively correlated shocks fits well the sensitivity of consumption to current income shocks observed in U.S. data, it falls short of explaining the sensitivity of consumption to income shocks cumulated over a longer horizon.