Modeling the Size of Tax Revenues by Probabilistic Laws

Abstract

In order to obtain objective data based on the results of the study, the planned indicators of the budgets of all subjects of the Russian Federation for the upcoming financial year are not taken as a basis, but the actual parameters obtained for the execution of budgets for the past financial year. Practice shows that every year almost all budgets of subjects and the consolidated budget of the state receive significantly more tax funds than was provided for when adopting budgets for the coming year. It would be erroneous to attribute this excess of actual tax revenues over planned ones due to the more efficient operation of the economic sector. The subjective factor plays an important role here. Local tax and financial authorities, the Federal Tax Service and the Ministry of Finance of the Russian Federation, which are responsible for developing draft budgets for the upcoming financial period and ensuring their execution, sometimes underestimate the actual possible amount of tax revenues for pragmatic reasons. Based on the above, the analysis is based on statistical data on the execution of budgets of the constituent entities of the federation for the past year. This research is devoted to modeling the size of tax revenues to the consolidated budget of the Russian Federation. In the article, the reporting data on the size of tax revenues are approximated by the following probabilistic laws: exponential distribution, Pareto distribution, gamma distribution (Erlanger distribution), and lognormal distribution. For each class of distributions, the problem of estimating unknown parameters using maximum likelihood and moments methods is solved. As a result of the study, it was found that the distribution of tax revenues is best described by the Pareto law and the log-normal mode.