The movement of funds on the residents' accounts in Russia

: 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.


INTRODUCTION
The aim of this work is to reveal the mechanisms for changing funds in current and savings (fixed-term) accounts of residents in the banking system of Russia. Provide an estimation of the key parameters that characterize the financial system of Russia and estimate cash flows between types of accounts. Track trends in this area.

MODEL AND DATA
To identify the relationships and build a model, we will study the correlations of quantities that seem to be related to the processes under study. 0,1,..., t T = -moments of the beginning of successive months over the last 6 years. Data from the website of the Central Bank of Russia [1]. "Review of Credit Institutions": t cu -transferable deposits (current accounts) in rubles, trillion ₽, 1 t sa -other deposits (savings fixed-term accounts) in rubles, trillion ₽, 2 t sa -other deposits (savings fixed-term accounts) in foreign currency, trillion ₽, placed in the banking system by residents of the Russian Federation. "Foreign trade in goods (according to the balance of payments methodology)": $ t st -trade balance in a month from t to t +1, billion $. "Financial operations of the private sector": $ t of -capital outflow for the previous month, billion $. $ t RES -"International Reserve Assets of the Russian Federation" billion $. t S -"Ruble exchange rate"  fig. 1. Estimation of the correlation matrix from data Variables with 0 at the end indicate the true values of the corresponding observables. The first term on the right side of (1) means the exponential growth of current deposits at a rate of 0 β % per annum. 1 t cusa -transfer of money from current accounts to fixed-term ruble ones for a month from the moment t.
1 t stsa , 2 t stsa -similarly, the transfer of money from the balance of trade to fixed-term ruble and currency accounts. The third term on the right side of (1) means approximately 10% government debt yield. The fourth term on the right-hand side of (2) means that the placed public debt is bought (in a share 2 β ) from fixed-term ruble accounts. The first coefficient on the right-hand side (3) where the operator of evolution t F , control t G , and observation t H , t w , t v -is the system and observation noises.

KALMAN FILTER AND INTERPRETATION OF CALCULATION RESULTS
The Kalman filter is widely used in economic research (see, for example, [3,4]). It makes it possible to estimate the parameters of the system, estimate and predict the characteristics of the system's state and output.
Model parameters where σδ -is the vector of standard deviations of errors in (1) -(7). The covariance matrices of vectors t w , t v are considered to be diagonal, the latter being proportional 2 0 v σ . We choose the first components of the initial state estimate  billion a year -this is less than in the previous two years. An increasing part of government debt is bought by residents.

SIMULATION
The issues of the significance of estimates and the adequacy of the model when using the Kalman filter are not as simple as, for example, in regression analysis. In particular, since the filter forecast relies heavily on the known previous output, it will always be good, even with an unsuccessful model. To check the adequacy, it is logical to simulate the functioning of the system with the estimated parameters, in comparison with real behavior. For this, we use the equations of dynamics (9) и (10) without noise elements, where the estimates of parameters β are substituted into the evolution and control operators. We start from the corresponding initial state vector, the last 3 components of which (transfers) are chosen equal to some averages of the values estimated above (and are constant). Controls -real ones (8). We will do this for a quiet time interval (see fig. 3). Initial state vector (8.96 18.79 13.94 0.11 0.083 0.15 0.246) T . The good coincidence (in overall) of the curves in fig. 3 allows us to make a conclusion about the adequacy of the proposed model to the real system. The discrepancy in foreign currency deposits can be explained by an increase in the transition of trade income to foreign currency deposits (see fig. 2), which was not taken into account in the simulation.
Individual peak discrepancies are associated with fluctuations in exchange rates, foreign exchange interventions by the Central Bank and replenishments of international reserve assets of the Russian Federation.

CONCLUSION
In the previous work [4], devoted to cross-border transfers of money, an estimate was obtained for the monthly creation of ruble deposits (current and term together) by Russian Federation commercial banks of about 300 billion ₽. This is consistent with the results of this work: on average 20% per year creation of current deposits (which gives ≈200 billion ₽ per month) plus transfer from current accounts to fixed-term ruble accounts ≈100 billion ₽ per month (see Fig. 2). In general, the work identifies the main reasons, mechanisms and parameters of the movement of funds on various types of accounts of residents in the banking system of the Russian Federation.