Individual Income Distribution Research Articles

Effects of the German Minimum Wage on Wages and Household Income

Abstract This article examines the effects of the introduction of the statutory minimum wage on the distribution of individual income from wages, as well as gross and net means-weighted income of workers in Germany. For the first time, data from the Survey of Income and Consumption was used, in which incomes are recorded in great detail. Both descriptive findings and the results of Unconditional Quantile Regressions indicate that the incomes of workers in regions with a high level of minimum wage intervention experienced significant increases after the introduction of the minimum wage, ranging into the middle band of the income distribution. Accordingly, the minimum wage has positively influenced the incomes of a large number of employee households.

The effect of administrative divisions on the distribution of individual income in the new territories of Chile

Developing countries often subdivide territory as a means to address excessive centralization; however, there is no existing empirical evidence to support this tool as an effective policy in increasing the living standards of residents. We focus on Chile and analyze the impact of a change in the Administrative Division on income distribution via two regions created in 2007 (Los Ríos, Arica and Parinacota). This is done via a multilevel structured additive regression (STAR) model between 2003 and 2011. Our results indicate an increase in the mean, median, and mode of individual income in the post-treatment period in the region of Los Ríos versus individuals in unaltered regions. However, we do not observe beneficial effects in the income distribution for Arica and Parinacota. The effect from subdividing territory is therefore not transversal but can depend on the quality of (and the relationship between) the regional and municipal governments as well as the initial socioeconomic and demographic conditions of each territory.

Regional Evaluation of Individual Income Distribution in Turkey with Stochastic Dominance Criteria

Ülkemizde gelir dağılımı analizi için kullanılan en yaygın yaklaşımlar yüzde paylar ve Lorenz Eğrisi üzerinden hesaplanan Gini katsayısıdır. Parametrik olmayan bir yaklaşım olarak stokastik baskınlık, klasik yaklaşımlardan farklı bir yorumla gelir dağılımları arasında mikro düzeyde karşılaştırma sağlamaktadır. Lorenz eğrisinin hesaplama süreci stokastik baskınlık kriteri ile direkt ilişkilidir. İkinci Dereceden Stokastik Baskınlık (SSD) kriteri günümüzde daha çok finans alanında yapılan analizlerde kullanılırken Lorenz Eğrisi gelir dağılımı eşitsizliği üzerine yapılan analizlerde kullanılmaktadır. Bu çalışmada, Türkiye’de bölgeler arası gelir dağılımının keşfedilmesi amacıyla, TÜİK’in Gelir ve Yaşam Koşulları Araştırması 2007-2016 yılları arası anketleri İstatistiki Bölge Birimleri Sınıflamasına göre Düzey-1’e göre incelenmiştir. Bölgeler arası gelir dağılımı farklılıkları SSD kriteri ile karşılaştırılmakta ve bireysel gelirlerin birbirlerine baskınlığı incelenmektedir. Bireysel gelir dağılımlarının karşılaştırmalarından elde edilen sonuçlara göre; İstanbul ve Doğu Karadeniz diğer bölgelere en fazla sayıda baskınlık sağlayan bölgelerdir. Güney Doğu Anadolu bölgesinin hiçbir bölgeye karşı bireysel gelir dağılımları açısından baskın olmayan bir bölge olduğu söylenebilmektedir. Dolayısıyla SSD kriteri açısından değerlendirildiğinde gelir eşitsizliğinin, özellikle diğer bölgelere göre fazla sayıda baskınlık alabilen bölgeler ile baskınlık alamayan bölgeler arasında büyük boyutta olduğu söylenebilir. Çalışmada elde edilen bulguların bölgelere göre politika geliştirme sürecinde karar alıcılar açısından değerlendirilebilir nitelikte olduğu düşünülmektedir.

A note on the relationship between additive separability and decomposability in measuring income inequality

This note introduces original technical results in the theoretical measurement of inequality by specifying the relationships between additive separability and homotheticity (of measures of welfare closely related to measures of inequality), and decomposability and homogeneity in measures of inequality. More specifically, an interrogation is made of the resonances and dissonances between the classic contributions of Atkinson and Shorrocks, which are key representatives, respectively, of the 'social welfare function' and the 'axiomatic' approaches to measuring inequality. In brief, in the presence of otherwise common assumptions, it is shown that additive separability and homotheticity of welfare are stronger combined conditions than decomposability and homogeneity (of degree zero) of income inequality. The gap between the two, however, can be closed by adding an extra term around total income to the measure of welfare, allowing for wider considerations of the relationship between social welfare, total income, and the distribution of individual incomes.

The principle of least effort and Zipf distribution

”Each individual will adopt a course of action that will involve the expenditure of the probably least average of his work.” This statement was named ”the principle of least effort”. The principle of least effort is often known as a ”deterministic description of human behavior”. In this paper, we present a brief introduction of this principle. Applications of the principle in different fields are also summarized. As the principle of least effort is proposed by Zipf, it is also called Zipf’s law. We then discuss the correlation between three widely considered distributions: Zipf distribution, Pareto distribution and probability distribution. With empirical investigations, it is often stated that, most social behaviors are controlled by the pure Zipf’s law that corresponds to the Zipf distribution of exponent -1. We summarily present the discovery of Zipf’s law in different social behaviors. Some empirical studies are also given as examples, verifying that, in most countries, the distribution of city size by population follows Zipf’s law, and the exponent of Zipf distribution of individual income is about -0.5, the same as Zipf predicted in theory.

Semi-parametric estimation of income mobility with D‑vines using bivariate penalised splines

The article evaluates the distribution of income mobility in Germany. We employ official data from the German Federal Employment Agency and compare relative changes in income and their serial dependency over time during the 1980s, 1990s and 2000s to obtain both a cross-sectional and a longitudinal perspective with an intra-generational focus. The data set is separated with respect to the education of the individuals and job changes. Nonparametric smoothing techniques are applied for the modelling of the multivariate distribution of individual income. We detect very low income mobility for the low-educated workforce but significantly higher income mobility for highly educated individuals.

Evolution of consumption distribution and model of wealth distribution in China between 1995 and 2012

We study the evolution of the distribution of consumption of individuals in the majority population in China during the period 1995–2012 and find that its probability density functions (PDFs) obey the rule Pc(x)=K(x−μ)e−(x−μ)22σ2. We also find (i) that the PDFs and the individual income distribution appear to be identical, (ii) that the peaks of the PDFs of the individual consumption distribution are consistently on the low side of the PDFs of the income distribution, and (iii) that the average of the marginal propensity to consume (MPC) is large, MPC¯=0.77, indicating that in the majority population individual consumption is low and strongly dependent on income. The long right tail of the PDFs of consumption indicates that few people in China are participating in the high consumption economy, and that consumption inequality is high. After comparing the PDFs of consumption with the PDFs of income we obtain the PDFs of residual wealth during the period 1995–2012, which exhibit a Gaussian distribution. We use an agent-based kinetic wealth-exchange model (KWEM) to simulate this evolutional process and find that this Gaussian distribution indicates a strong propensity to save rather than spend. This may be due to an anticipation of such large potential outlays as housing, education, and health care in the context of an inadequate welfare support system.

Testing the Goodwin growth-cycle macroeconomic dynamics in Brazil

This paper discusses the empirical validity of Goodwin’s (1967) macroeconomic model of growth with cycles by assuming that the individual income distribution of the Brazilian society is described by the Gompertz–Pareto distribution (GPD). This is formed by the combination of the Gompertz curve, representing the overwhelming majority of the population (∼99%), with the Pareto power law, representing the tiny richest part (∼1%). In line with Goodwin’s original model, we identify the Gompertzian part with the workers and the Paretian component with the class of capitalists. Since the GPD parameters are obtained for each year and the Goodwin macroeconomics is a time evolving model, we use previously determined, and further extended here, Brazilian GPD parameters, as well as unemployment data, to study the time evolution of these quantities in Brazil from 1981 to 2009 by means of the Goodwin dynamics. This is done in the original Goodwin model and an extension advanced by Desai et al. (2006). As far as Brazilian data is concerned, our results show partial qualitative and quantitative agreement with both models in the studied time period, although the original one provides better data fit. Nevertheless, both models fall short of a good empirical agreement as they predict single center cycles which were not found in the data. We discuss the specific points where the Goodwin dynamics must be improved in order to provide a more realistic representation of the dynamics of economic systems.

Distribution of individual incomes in China between 1992 and 2009

This paper presents comprehensive analysis of the evolution of the distribution of individual annual incomes across the majority of the population in China from 1992–2009. The cumulative distribution functions (CDFs) and probability density functions (PDFs) are presented. Overall, the CDFs follow the Gaussian function C(x)=Ae−(x−μ)22σ2 for the majority of individuals in the population, while the PDFs obey the function P(x)=B(x−μ)e−(x−μ)22σ2. The width of the PDF has widened from 1992 to 2009, suggesting the factor (x−μ) has been progressively skewing the curve to the right. This long tail representing the high income range is reminiscent of an exponential distribution curve. This indicates that a few individuals obtain extremely high incomes, leading to increasing levels of financial inequality in China.

Effective factor endowments, trade openness and income distribution in China

This paper studies the empirical relationship among factor endowment, trade openness and individual income distribution. Using panel data, we show that factor endowment characters, to some extent, explains income gap in China. First, land and Capital intensive provinces have a more equal income distribution while human capital and labor-intensive provinces have a less equal income distribution. Second, Trade openness has a significant effect on China’s income distribution; the interaction between a special endowment and openness has different effect on income distribution; we also show that FDI, economy development, unemployment and reform have considerable negative effect on income distribution. Our results are robust to various kinds of test.

Understanding Italian Inequality Trends*

This article develops a unifying framework for analysing the effects of: (i) the changing distribution of individual incomes by main factor sources, (ii) the increasing participation of wives in the labour force, and (iii) the changing distribution of family types on the distinctive trends towards inequality in equivalent household income in Italy between 1977 and 2004. Changes in the distribution of work and pension incomes explain most of the trend. The higher average likelihood of wage-earning wives had an unequalizing effect on households on the left tail of the income distribution. Little is explained by the changing distribution of family types.

Job match and income distributions

This paper studies the income distributions from the view of job match. By numerical simulation, we present different income distributions cases with different degrees of job match. In particular, we analyze the probability distribution of individual income, and we also discuss the economic efficiency and economic equality in different job match cases. Our basic results are that different job matchs can change income distributions, and good job matchs can not only improve economic efficiency but also aggravate economic inequality.

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.

Der Einfluß von Imputed Rent auf die personelle Einkommensverteilung. The Impact of Imputed Rent on the Personal Distribution of Income

Zusammenfassung Die vorliegende Untersuchung befaßt sich mit alternativen Verfahren zur Berücksichtigung von Einkommensvorteilen aus selbstgenutztem Wohneigentum („Imputed Rent“) und deren Einfluß auf individuelle Einkommen sowie die personelle Einkommensverteilung in Deutschland. Nach einer theoretischen Darstellung der Verfahren und ihrer jeweiligen Vor- und Nachteile werden diese mit Hilfe der Mikrodaten des Sozio-oekonomischen Panels (SOEP) empirisch vergleichend umgesetzt. Abschließend erfolgen aufgrund theoretischer Vorüberlegungen und der empirischen Ergebnisse Empfehlungen zum Umgang mit „Imputed Rent“ bei Analysen zur personellen Einkommensverteilung und Einkommensmobilität. Neben der quantitativen Bedeutung dieser nicht-monetären Einkommenskomponente ist aus sozialpolitischer Sicht insbesondere eine tendenziell die Einkommensungleichheit reduzierende Wirkung zu konstatieren, wobei auch die zunehmende Rolle von Wohneigentum zur Altersvorsorge bestätigt wird.

Evidence for the exponential distribution of income in the USA

Using tax and census data, we demonstrate that the distribution of individual income in the USA is exponential. Our calculated Lorenz curve without fitting parameters and Gini coefficient 1/2 agree well with the data. From the individual income distribution, we derive the distribution function of income for families with two earners and show that it also agrees well with the data. The family data for the period 1947-1994 fit the Lorenz curve and Gini coefficient 3/8=0.375 calculated for two-earners families.

Incorporating Gender Inequality into Income Distribution Research

Income distribution research assumes equal sharing of resources within the household. This assumption has been criticized for leading to an underestimation of the extent of gender inequality in modern societies. In this paper two alternative methods of deriving an income distribution are presented, both of which make other assumptions about the extent of sharing of resources within households. The first is a partial sharing distribution modelled from survey data; the second is a distribution of individual income, i.e. no sharing of resources. The methods are then applied to income distribution data from the 1991 Swedish Level of Living Survey and the respective distributions are compared with the baseline distribution, assuming equal pooling of resources. As expected, the results indicate that differences between men and women increase but the extent of this increase is somewhat less than expected. Nevertheless, the analysis highlights how gender inequality can be brought into the field of income distribution.

Longer Run Changes in the Distribution of Income in Australia*

This paper brings new evidence to bear on the question of changes in income distribution amongst individuals in Australia between 1942–43and 1989–90. The changes observed over this period are analyzed in the context of previous studies of the changing distribution of income in Australia over the past 80 years. The main conclusions of the paper are that the distribution of individual income in J 989–90is very similar to that estimated for 1942–43, and there is evidence that income inequality has been increasing during the 1980s

Economic heterogeneity within large metropolitan areas.

ABSTRACTRecent research has indicated that individual income distribution in the United States has tended toward greater inequality in recent years. Hypotheses are presented on the expected effect of that trend on suburban municipalities within large metropolitan areas. One major expectation is that the distribution of per capita incomes among the municipalities will be found to bifurcate. A methodology that rests on a graphical depiction of income and a revision of the famous Pearson plane is used to identify trends. Results indicate that the long term trend (at least since 1960) toward income homogeneity came to a halt by 1979 and began to reverse itself in the early 1980s, although bimodal distributions of income are not yet (1983) in evidence. Rapidly growing and rich communities are tending toward greater internal income homogeneity.

Income-Share Elasticity and the Size Distribution of Income

The main purpose of this paper is to introduce the notion of Income-Share Elasticity as a convenient description of the size distribution of income. This concept, as an alternative to density functions, offers many advantages from both the theoretical and the applied point of view. On the one hand, it can help to capture some common features in seemingly unrelated density functions. On the other hand, it leads to a rather different approach to the description of the size distribution of income. Empirical research on the size distribution of income has been mainly confined to the descriptive task of fitting density functions to data. Most contributions consist of introducing a new density function and showing that it fits better than the functions previously considered. But there seems to be no clear rationale with regard to the search for new functions. This situation is essentially due to the lack of a theory on the size distribution of income, which is bound to persist unless we change the way of analysing empirical data. We must admit that the knowledge that, for instance, the Gamma function gives a better fit than the Log-Normal is not very inspiring. An alternative approach could be that of the identification of stylized facts about the distribution of individual incomes. Indeed, if the size distribution is to be analyzed, the data must show some sort of stable structure. Therefore, it would seem natural to identify these regularities for applied work. Once these stylized facts have been well established, we shall have a smaller set of density functions from which to choose. As an illustration of this approach, we consider a simple case in which we hypothesize three stylized facts and show that the three-parameter Generalised Gamma is the only density function that behaves accordingly. These three hypotheses are: a) distributions satisfy a modified version of Mandelbrot's [1960] Weak Pareto Law, which we call the Weak-WPL; b) they have a mode; and c) the Income-Share Elasticities have a constant rate of decline. These hypotheses can be subject to direct, independent tests. However, it is not our purpose to claim that they do satisfactorily correspond to observed facts. We cannot expect to have determined the class of functions that fit actual income distributions. The aim of the paper is to introduce an alternative way of approaching the description of the size distribution of incomes. We begin by defining the Income-Share Elasticity and showing that there is a

A multivariate analysis of Argentina's urban income distribution, 1974–1975 and 1978

Between 1974 and 1978 large changes took place in Argentina's individual income distribution. The purpose of this study is to analyze the nature of the relationships between the urban income distribution and a series of explanatory socioeconomic variables.