Determining the amount of shadow economy on the basis of nonlinear dynamics models

Abstract

Shadow economy phenomenon is observed in many countries regardless of their social structure. The shadow economy (SE) parasites on the body or official legal economy (LE), which negatively affects the state budget. Therefore, the study of interaction between LE and SE is an urgent problem nowadays, especially for our country.

Having used the planar dynamic model which is described as  a system of two nonlinear ordinary differential equations, which is a characteristics for the economic state of society where coexist official and illegal economy, it has been received the formula of the shadow economy. The conditions for the coefficients of the dynamic model are formulated. On their basis a growth of the legal economy or a recession of economy occurs and there is a reduction of the shadow economy.

The result is convenient for operational (due to manual simulation) prognosis in arbitrary time t. The quality of prediction depends on the coefficients of the mathematical model, initial conditions and scope of the legal economy. Qualitative and quantitative analysis (integral curves, phase portraits) of behavior of dynamic models provide scenarios of possible developments.

The analytical results of economic and mathematical model allow to calculate the size of the shadow economy quicklier; predict the level of shadow economy, which is determined by the coefficients of nonlinear dynamic models, initial conditions, taking into account the legal sector of the economy.