The paper proposes a mechanism for the impact of changes in the key rate on the volume of newly issued loans. The volume depends on the price (interest rates on loans), and the price depends on the key rate and the actual consumption of loans in the previous period (generalized cobweb cycle). The model was estimated by a Kalman filter, adequacy was confirmed by simulation. It is possible to forecast the average rate on loans for a month in advance according to the information published by the Central Bank of the Russian Federation (CB). By playing various scenarios for changing the key rate, it was found that in quiet periods of economic development, the usual laws of supply and demand operate in the loan market and by raising the key rate, you can reduce inflation. In the turbulent (overheated) state of the economy, an increase in the key rate can, on the contrary, provoke an increase in the issuance of loans and unconventional manipulations with the key rate are required.

The work proposes a model of funds formation in current and fixed-term (ruble and currency) accounts and transfers of funds between them. The sources of money are loans issued by commercial banks, placement of government domestic debt, the positive balance of foreign trade. The financial parameters and characteristics of the system are estimated using the Kalman filter. The adequacy of the model is confirmed by simulation modeling. It was found that the rate of creation of rubles in current accounts increased from ≈ 8% per annum in 2015-16 ≈ to 12% in 2017-18 and to 29% in 2019-20. The leakage of foreign currency from accounts (in addition to the official outflow of capital) was ≈ 12, 50, 35 billion dollars per annum during the same periods.

The influence of both the absolute values of the dollar/ruble exchange rate (rate) and its changes per day on the balance of the Bank of Russia operations for ruble liquidity provision and absorption (saldo) was investigated. Daily data were used from January 2015 to April 2018. It was found that the change in the rate 6 days ago is the cause (according to Granger) of the saldo value. For the saldo dynamics, an oscillatory model with an external force - a change in the rate - is proposed. Using the Kalman filter, the model parameters were estimated and saldo forecasted. Found period of self-oscillation is 4.218 days and attenuation of the amplitude for a day in 2.179 times. The rate growth of 1 RUB, after 6 days, causes saldo increase of approximately 20 billion rubles. In fact, the changes in rate cause the variability of the saldo not more than for found coefficient of determination (26.7%), but the "change in the rate-liquidity saldo" system during the crisis-free period has a high "Q-factor," and changes in the rate, repeated with a period close to self-one, can cause large-amplitude fluctuations in saldo.

This paper based on systems - theoretic approach to the definition of a country's GDP as not directly observable characteristic of system state. Leontief dynamic model is generalized to take into account the stimulating effect of consumption on GDP growth. In consumption, apart from final consumption, terms are considered: balance of foreign trade, fictitious investments and hidden costs. The Kalman filter uses Rosstat's gross output (for system output) and final consumption (for system control) data from 1995 to 2015. It is concluded that if in the years 2014, 2015 it was possible to increase consumption by 5% by, say, price cuts or some increase in money supply, then GDP would be greater by about 2.5%. GDP real values in recent years are most likely greater than official values. Fictitious investments and hidden costs are found in the amount of up to third the value of final consumption. The accuracy of one-year forecasts of true GDP by the methodology of this article is approximately 1.5%.