Modeling the Budget Dynamics of Kazan in the Post-Reform Period: From Structural Indices to ARIMAX Forecast for 1871–1885

The subject of the study is the dynamics and structure of revenues and expenditures of the budget of the Kazan City Duma in 1871-1885. The object of the study is the budget of the Kazan City Duma in the post-reform period. The authors analyze income items (19 items) and expenses (22 items) of the budget of the Kazan City Duma in 1871-1880 to calculate descriptive statistics and identify the nature of the distribution and variation of the initial data. Special attention is paid to counterfactual forecasts of the revenue and expenditure dynamics of the Kazan City Duma budget for 1881-1885, which are modeled and compared with the actual values of budget indicators during this period. The purpose of the work is to identify structural changes and dynamic patterns in the formation of the municipal budget in the context of institutional transformations in the 1870s and 1880s. The empirical basis of the study is the reports of the Kazan City Public Administration for 1871-1885. The research methodology is based on a combination of structural shift analysis (A. Salai, V. Ryabtsev indexes, K. Gatev coefficient) and counterfactual modeling of time series using ARIMA and ARIMAX models. The counterfactual approach is implemented in relation to the conditions for comparing the actual budget dynamics in 1881-1885 with the inertial trajectory formed on the basis of trends in 1871-1880. The scientific novelty of the research lies in the integration of methods for analyzing structural shifts and counterfactual modeling to study the budgetary practice of urban thought in post-reform Russia. It has been established that the revenue side of the budget in 1871-1880 was characterized by relative structural stability and inertia in the formation of revenue sources. The expenditure side demonstrated a higher degree of structural mobility and redistribution of funds between urban areas. Counterfactual analysis showed no signs of a radical transformation of the budget model in the early 1880s; the revealed deviations are in the nature of parameter adjustments within the established system of municipal finance. The findings make it possible to clarify the understanding of the mechanisms of adaptation of municipal finances to institutional changes and expand the possibilities of inter-regional comparisons. The scope of the results is related to the research of economic history, the history of urban self-government and municipal finance of the Russian Empire.