The Method for Solving Inverse Problems of Economic Analysis Using Statistical Data

Abstract

The inverse problem answers the question "how do I?.." and the purpose of solving such problems is the formation of optimal management decisions. The article presents methods for solving inverse problems of economic analysis using statistical data. In a classic case of use of the mechanism of the inverse computations the calculation of the increments of the arguments is based on the target value of the function, coefficients of relative importance of arguments, the primary arguments values and directions of their change. The proposed method involves the determination of function arguments based on statistical historical data and includes two steps: constructing the regression equation between the argument and the resulting indicator and the definition of the value of the arguments; the solution of the inverse problem using inverse computations. The coefficients of relative importance are calculated based on the magnitude of the gradient, and the sign of the elements of the gradient determines the direction of change of the arguments. The paper describes the solution to the simple problem of forming the revenue of the organization. The article presents an example of application of this method to solve the modeling problem of rating of the Republic of Tuva, which is based on eight groups of indicators: standard of living, financial security, the efficiency of agricultural production, efficiency of construction, availability of labor resources, health, security education, and security of information and communication technologies. Using the method has allowed us to answer the question, how is it possible to increase the integral characteristics of the socio-economic development of the region by 4.68%. The study used the methodology of the theory of inverse calculations, regression analysis, and optimization methods. The developed method can be used in decision support systems for management decisions.