The goal is to study GDP (gross domestic product) as an unobservable characteristic of the Russian national economy state on the basis of more reliable observed data on gross output (systems output) and final consumption (systems control). To do this, the dynamic Leontief model is presented in a system-like form and its parameters and GDP dynamics are estimated by the Kalman filter (KF). We consider that all previous year’s investments affect the growth of the gross output by the next year. The weights of these investments in the sum are equal to unity and decrease in geometric progression. The estimation of the model parameters was carried out by the maximum likelihood method. The original data on the gross output and final consumption in the period from 1995 to 2015 years where taken from the Rosstat website, where maximally aggregated economy of Russia is reflected in the system of national accounts. The growth of direct costs and capital expenditures at gross output increase has been discovered, which indicates the extensive character of the development of the economy. Investments are being absorbed 2 - 4 years; any change of them causes a surge of commissioned fixed assets fluctuation with a period of 2 years. Then these parameter values were used in the KF to estimate the states of the system. The emerging tendency of the transition of GDP growth to its fall means that the rate of growth of final consumption is higher than the rate of GDP growth. In general, the behavior of the curve of Rosstat GDP obviously follows the declared investments, whereas in the present calculation it is closer to the behavior of final consumption. Estimated GDP and investments that really increased it were significantly less after the crisis of 2008-2009 years than officially published data.

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