Mathematical Assessment of the Impact of Corruption Growth on Changes in the Work of State Authorities

Corruption is one of the key factors that undermine the effectiveness of public administration, reduce citizens' trust in institutions, and inhibit socio-economic development.  Despite the presence of legislative and political countermeasures, the level of perception of corruption in Ukraine remains consistently high: during 2018–2024, the Corruption Perceptions Index (CPI) fluctuated between 31 and 36 points out of 100 possible, which indicates the limited results of anti-corruption reforms.  This makes it urgent to develop scientifically based mathematical methods that can not only record the level of corruption, but also quantitatively assess its impact on the effectiveness of the functioning of state authorities.  The purpose of the study is to apply a mathematical scientific approach to analyzing the impact of corruption dynamics on changes in the work of the state administrative apparatus of Ukraine.  To achieve the goal, a step-by-step methodology was used, which includes the normalization of macroeconomic factors using the min-max method taking into account the economic sign of the impact, building a multiple linear regression model, regularization of Ridge-type parameters to eliminate multicollinearity, checking statistical significance using the $t$, $F$, $R^{2}$ and $p$ criteria, as well as visualization of the relationships between key macrofactors and the CPI.  This approach provides an opportunity to quantitatively describe the cause-and-effect relationships between the level of corruption and the management effectiveness of state authorities.  The results of the study confirmed the hypothesis of the interdependence between the level of corruption and the quality of the functioning of state authorities.  The obtained quantitative relationships allow a reasonable assessment of the impact of corruption risks on the effectiveness of management decisions, which opens up prospects for creating a system for forecasting and early warning of institutional degradation.