Modelling of Wage and Income Distributions Using the Method of L-Moments

Commonly used statistical procedure to describe the observed statistical sets is to use their conventional moments or cumulants. When choosing an appropriate parametric distribution for the data set is typically that parameters of a parametric distribution are estimated using the moment method of creating a system of equations in which the sample conventional moments lay in the equality of the corresponding moments of the theoretical distribution. However, the moment method of parameter estimation is not always convenient, especially for small samples. An alternative approach is based on the use of other characteristics, which the author calls L-moments. L-moments are analogous to conventional moments, but they are based on linear combinations of order statistics, i.e., L-statistics. Using L-moments is theoretically preferable to the conventional moments and consists in the fact that L-moments characterize a wider range of distribution. When estimating from sample L-moments, L-moments are more robust to the presence of outliers in the data. Experience also shows that, compared to conventional moments, L-moments are less prone to bias of estimation. Parameter estimates obtained using L-moments are mainly in the case of small samples often even more accurate than estimates of parameters made by maximum likelihood method. Using the method of L-moments in the case of small data sets from the meteorology is primarily known in statistical literature. This paper deals with the use of L-moments in the case for large data sets of income distribution （individual data） and wage distribution （data are ordered to form of interval frequency distribution of extreme open intervals）. This paper also presents a comparison of the accuracy of the method of L-moments with an accuracy of other methods of point estimation of parameters of parametric probability distribution in the case of large data sets of individual data and data ordered to form of interval frequency distribution.

Development of Wages and Salaries of Czech Employees During the Last Period by Educational Attainment and Forecasts for 2011 and 2012

This paper deals with the development of sample characteristics of wage distribution in recent years in the Czech Republic by the highest educational attainment. Gross monthly wage is the variable investigated. We distinguish the following scale of the highest educational attainment： primary and incomplete education, secondary education without GCSE, secondary education with GCSE, higher vocational and bachelor education and tertiary education. Forecasts of wage distribution have been developed for the next two years for all of these categories. Three-parametric lognormal curve formed the basis of the theoretical probability distribution. Parameter values of relevant three-parametric lognormal curves were then estimated using the method of L-moments of parameter estimation. Forecasts of sample values of L-moments were calculated using trend analysis of their past development and the parameters of three-parametric Iognormal curves for forecasts of wage distribution were calculated using the predicted values of the first three sample L-moments. We have obtained the forecasts of wage distribution by the highest educational attainment on the basis of these probability density functions.

Application of Pareto Distribution in Wage Models

This paper deals with the use of Pareto distribution in models of wage distribution. Pareto distribution cannot generally be used as a model of the whole wage distribution, but only as a model for the distribution of higher or of the highest wages. It is usually about wages higher than the median. The parameter b is called the Pareto coefficient and it is often used as a characteristic of differentiation of fifty percent of the highest wages. Pareto distribution is so much the more applicable model of a specific wage distribution, the more specific differentiation of fifty percent of the highest wages will resemble to differentiation that is expected by Pareto distribution. Pareto distribution assumes a differentiation of wages, in which the following ratios are the same： ratio of the upper quartile to the median; ratio of the eighth decile to the sixth decile; ratio of the ninth decile to the eighth decile. This finding may serve as one of the empirical criterions for assessing, whether Pareto distribution is a suitable or less suitable model of a particular wage distribution. If we find only small differences between the ratios of these quantiles in a specific wage distribution, Pareto distribution is a good model of a specific wage distribution. Approximation of a specific wage distribution by Pareto distribution will be less suitable or even unsuitable when more expressive differences of mentioned ratios. If we choose Pareto distribution as a model of a specific wage distribution, we must reckon with the fact that the model is always only an approximation. It will describe only approximately the actual wage distribution and the relationships in the model will only partially reflect the relationships in a specific wage distribution.

Wages and Salaries of Czech Men and Women at the Beginning of the Third Millennium and the Impact of the Economical Recession on Their Development

This paper deals with the development of the wage distribution in the Czech Republic since 2003, according to gender. It is a development of descriptive characteristics of location, differentiation and shape of wage distribution, but also the development of concentration characteristic of wage distribution. Gross monthly wage of Czech employees represents the variable under research. Emphasis is placed on changes in the development of wage distribution since 2009 in connection with the onset of economic recession. The economic crisis has greatly influenced the development of the wage distribution in the Czech Republic, wage growth virtually stopped at this time. Differences in the development of wage distribution between men and women in the Czech Republic are also under this research. Development of wage distribution has been studied by modelling the distribution. Three-parametric lognormal curves are served as a theoretical probability distribution whose parameters were estimated using the L-moment method of point estimate of parameters. Dependence of gross monthly wage on gender has been the subject of research as well. This dependence was researched using one-way analysis of variance. Forecast of wage distribution of men and women in the Czech Republic for the years 2012 and 2013 is included in this research.

Financial Level of Czech and Slovak Employees

This paper deals with the development of wage distribution by gender in the Czech and Slovak Republics in the years of 2005-2012. Special attention is given to changes in the behavior of wage distribution in relation to the onset of the global economic recession. The different behavior of the wage distribution of Czech and Slovak employees during the period is the subject of research. The article discusses the differences in the wage level between men and women in the Czech and Slovak Republics. There are the total wage distributions of men and women together, both in the Czech Republic and in the Slovak Republic on one hand, and wage distributions according to the gender separately for men and women on the other hand. Special attention was paid to the development of Gini coefficient of the concentration in both countries according to the gender in the period under review, too.