Toward the modeling of Russia's monetary system

the paper gives an explanation of the dynamics of the money masses in Russia through cross-border flows of rubles and (foreign) currency and the creation of deposits by commercial banks. Volumes of flows and deposits in turn depend on changes in the currency/ruble exchange rate. It was found that the growth/fall of the USD rate by 1 RUB for the month, for the same month decreases/increases: currency outflow abroad by $0.111 billion and creation of ruble deposits and the inflow of rubles from outside by $0.133 billion.


INTRODUCTION
The economics and finances of modern Russia are deeply integrated into the global system, when rubles and currency, on equal terms, fulfill the function of money. However, for proper monetary regulation it is necessary to clearly realize their volumes and mutual transitions. From the statistics of the Central Bank's balance of payments [1], it is difficult to understand how much of which money is involved in cross-border transfer when acquiring assets or making commitments.
The objective of this work: to build a framework model of the Russian monetary system, covering the most important money flows and suitable for further clarification. The basic principles of the model: rubles and currency in the accounts of residents change under the influence of foreign trade, other arrivals from the outside /creation of rubles and currency outflows, purchase and sale of currency for rubles from abroad. It is generally recognized that forecasting of exchange rates is very difficult, as information shocks and political decisions have a decisive influence on them. But the changes in exchange rate have a significant impact on the Russian monetary system and should be used as explaining variables in the model, as well as replenishment of international reserve assets of the Russian Federation, for example, at favorable oil prices.

MODEL AND DATA
1 22 1 33 1 04 The first coefficient on the right-hand side (1) provides a conversion to the currency of the passing part of the ruble deposits. The coefficients for export and import are taken from [3]: "if Russia receives only 14.4% in rubles for export, then it pays 31% of import in its own currency". For clarification, you can take the actual data on rubles and currency for each month. We assume (3), that the change in magnitude RES -international reserve assets of the Russian Federation at time t in billion USD. The meaning of the term 1 0 t RES   is that when the accumulation of reserves took place, then these were favorable months for the build-up t D . An attempt to directly include the known increase / decrease of reserves in the accounts (1) and (2) worsened the description, which means that reserves are not replenished from them.
We introduce the directly unobservable state vector of the system ( ) Then the model of the system in the state space, in accordance with (1)

KALMAN FILTER AND INTERPRETATION OF CALCULATION RESULTS
Kalman filter is widely used in economic studies (see, for example, [5 -7]). It makes it possible to evaluate the parameters of the system, evaluate and predict the unobservable characteristics of the state of the system and its output.
where  -is the vector of standard deviations of errors in (1) - (5). We choose the initial state estimate 0|0 x (a rough assessment) ( )  For the random walk model (when the previous value is the prediction) RMSE = 1150 billion RUB.

Models in the enhancement order:
If we assume that deposits are unchanged (only the ruble is recalculated in accordance with exchange rate, only the first and last terms are in the right-hand sides of (1) and (2) ), then RMSE = 1028 billion RUB, small observation errors (estimate 0 v  = 28 billion RUB) will ensure coincidence with a slight increase in ruble deposits. Thus, observing only M2 and M4, it might be assumed that nothing is happening in the country at all (though with a poor forecast error RMSE).
If we connect the trade in goods, which causes a slight departure of rubles and a significant influx of currency (see  • increases/decreases by $0.002 billion purchase of currency for rubles abroad (direction is associated with the habit of panic, purchase volumes are small, in the last 2 years negative, i.e. there is a purchase of rubles at $0.13 billion per month), • decreases/increases by $0.111 billion currency outflow (why export if it is more valuable to use here),