Features of the Development of the Banking Services Market of Ukraine: The Effect of Bank Size and Gibrat's Law

Quantitative description of the development of the banking services market is important for making optimal decisions in the regulation of the banking sector. The importance of the question lies in the fact that such a description makes it possible to take into account the transformation of banks, sources of risks, to identify the main trends or regularities in the process of evolution. The aim of this article is to test Gibrat's law as a hypothesis for the development of the banking services market of Ukraine, by an empirical experiment where all existing banks are tracked over time on an annual basis and the distribution of banks by the size of assets or income is constructed annually. The work assumes the possibility of establishing a statistical size (assets or income) distribution of banks with certain average values and variances according to the lognormal distribution of banks. The research methodology is based on statistical analysis and verification of the correspondence of the empirical size distribution of banks to the logarithmically normal one provided by Gibrat's law. The study period covers the banking sector from 2014 to 2023 and includes all operating banks. The information base for the analysis was the annual official reporting data (report on the financial state) of banks, published by the National Bank of Ukraine and on the banks' official websites. The data set defines the assets and income of all banks and each bank separately, annually. It has been proven that Gibrat's law is not fulfilled for banks of Ukraine, the size distributions do not obey the Gaussian distribution law. The rate of growth of banks is not random (as it is assumed by Gibrat's hypothesis). The trend of gradual approximation of income distributions to the lognormal type and the potential possibility of implementation of Gibrat's law for the period of 2022–2023 has been revealed.