Dilemmas relating to mode estimation of wages and salaries

The mode of wages and salaries is an important indicator describing their distribution; however, due to the strong asymmetry of the distribution of this feature in Poland, mode estimation is not a standard procedure in the analysis of the structure of wages and salaries. The aim of the article is to discuss selected methods of estimating the mode and to compare the mode estimation results obtained by means of various methods. The research is based on data on individual gross wages and salaries registered in October 2018 in Poland. The data came from a survey of the structure of wages and salaries conducted by Statistics Poland.
In the case of the standard method based on the interpolation formula and histogram, the mode estimate is sensitive to the assumed span of intervals in the frequency table and the beginning of the first interval. Reducing the span of the intervals causes the mode to reach the value of the minimum wage. The application of advanced methods, including those using a kernel estimator, leads to significantly different estimates of the mode depending on the method used (the dispersion reaches the value of approximately PLN 800).
Additionally, the analysis of the obtained results gives grounds to considering a thesis that wage and salary distribution is a mixture of the following distributions: discrete (for the minimum wage) and continuous (for wages and salaries above the minimum wage), and is characterised by cyclicality (in Poland, more contracts offer remunerations which are a multiple of PLN 50 or PLN 100 than remunerations for other amounts).

