One of the most important quantitative indicators of the development of the country’s economy and the circulation of capital is the money supply, i.e. the total volume of purchases and means of payment for economic turnover owned by individuals, enterprises and the state [4]. Changes for money circulating in the economic system have a huge impact on output, employment, price levels and other economic variables. This fact determines the relevance of the subject under consideration.

The existence of a relationship between the long-term movement of the money supply and the price level was found in ancient times. This relationship forms the basis of the quantitative theory of money, which was significantly modified in the XX century. The research of monetarists contributed to this. It is based on the mechanism of influence of the money supply on prices, its structure and aggregates. One of the most important fundamental factors of economic stability is the control over the amount of money. However, economists, analysts and politicians need to have the right skills to change the money supply.

There are the following instruments of state regulation of monetary circulation:

– implementation of monetary policy and control over the money supply during it;

– public debt management;

– implementation of tax policy;

– formation of financial markets, etc. [5]

In turn, forecasting the required amount of money supply is carried out in four stages:

1. Calculation of cash receipts in a designated period.
2. Determination of the probable outflow of funds.
3. Assessment of the situation: there is a surplus or shortage of funds.
4. Calculation of the need for short-term financing [1].

Obstacles may appear already at the first stage. As a rule, they arise when revenue is distributed to receipts from buyers and the sale of goods with deferred payment. When the first is only partially covered by credit sales, then all revenue is set as the amount of money received and accounts receivable.

Next, we will consider the basic mathematical methods applicable in the framework of forecasting the money supply.

1. The weighted average method. Let us make a reservation that it is not basic and cannot be used to make significant decisions. The final calculation may differ significantly from the actual one. All values of the indicator periods are summed up, which are further divided by the sum of the weights. This method is simple and fast, and besides — understandable. However, it is worth remembering that the percentage of deviation of the predicted values from the real ones is quite large. It is necessary to note one of the obvious disadvantages of the method: the inability to assess other factors, because it is based only on time and season.
2. The moving average method is used in cases when cash flow forecasting is urgently needed. Assumes the determination of the average cost of the indicator for the specified time. At the same time, the period usually shifts forward, and, taking into account the seasonality factor, smooth smoothing happens.
3. The coefficient method is designed for forecasts over a short distance — for a maximum of a quarter. When using this method, the last financial value from the statements and the prepared coefficient are multiplied. It can be the ratio of certain indicators, or changes (in percentages) either the ratio of certain indicators, or changes in percentages) either over a certain period, or a share of the basic indicators.
4. The extrapolation method is used to model economic trends and find cash flows based on past trends. The essence of the method consists in the change of the indicator observed in the recent past, and the impact on its development with the immutability of the circumstances that determined it before. Functions with one factor are used here (usually it is a time factor).
5. The exponential smoothing method is a combination of weighted average and moving average methods. The only difference between this method and the first is the weighting coefficient. In the current situation, the past actual and projected indicator multiplies a factor. This method fits perfectly into the situation of long-term forecasting of the money supply. In fact, there is a combination of two approaches to the preparation of forecasts, thereby reducing the deviation from the actual value.
6. The method of constructing a multiple regression model is a complex method, for the application of which it is necessary to create a static regression model, where the leading variable will be influenced by a whole set of factors [10].

Today, in the conditions of incessant economic crises, targeting is one of the key ways to regulate and predict the volume of money supply. Let us look at this tool in more detail.

Targeting («target» – goal) – the establishment of targets in the regulation of the increase in the money supply in circulation and credit, established by the Central Bank. Targeting methods vary depending on whether the growth rates of one or several monetary aggregates are limited, in which variant targets are set – in the form of a «corridor» or a certain control figure.

Monetary targeting in practice means that the Central Bank retains the established characteristics of changes in the money supply. This policy is based on two assumptions:

– if there is a stable relationship between the volume of money and the price level, then their stabilization can be achieved by limiting the money supply;

– the amount of money should be regulated by monetary policy over a limited time horizon [2].

With direct targeting, the Central Bank’s policy focuses specifically on the dynamics of inflation. The policy of the Central Bank in this case is reduced to a more or less mechanical reaction to the differences in the forecast values of inflation from the set values on a predetermined time horizon.

It should be noted that targeting seems to be a relatively new instrument of monetary regulation. Until the 1970s, under the influence of Keynesian economic theory, Central banks used, as a rule, indicators characterizing the level and dynamics of interest rates as benchmarks in determining their monetary policy.

Significant changes took place in the 1970s and 1980s. Due to the influence of the ideas of neoclassical theory, interest in controlling the volume and dynamics of the money supply increased. Monetarists considered the correct method of overcoming inflation to be the regulation of the amount of money, because according to their theory, the reason for cyclical fluctuations in market conditions and inflationary processes was a chaotic change in the money supply. Taking these provisions as a guideline, in 1974-1976 in the USA, Germany, Switzerland and Canada, in 1977 in France and Great Britain, in 1978 in Japan, central banks have started using the method of targeting the money supply [11]. Its essence was to fix such quantitative indicators of changes in monetary aggregates (lower and higher limits) for a planned period of time (quarter or year) that would meet the nature and objectives of the monetary policy.

In principle, the establishment of suitable benchmarks for the money supply follows from the premise that it grows from year to year as the gross domestic product increases. In this case, the benchmarks for the growth of the money supply are set in accordance with the projected growth in output, taking into account the planned price increase.

The guidelines for the growth of the money supply as an integral element of the developed trends of the completely state monetary policy are considered and approved by law. Thus, in the United States, in accordance with the amendment of 1978 to the Federal Reserve System Act, the Board of Governors submits information to Congress 2 times a year on the planned limits of changes in monetary indicators, while providing for the dynamics of nominal GDP.

By implementing monetary regulation, Central banks monitor not only the adopted targets, but also the deposit and loan operations of credit institutions. By regulating them, they affect the credit potential of commercial banks, which in turn affects the dynamics of monetary indicators. This is because credit appears to be the main source of money supply creation. Despite the fact that during the control period of targeting, the set benchmarks can be adjusted, the problem of Central Banks and other bodies responsible for conducting a unified state monetary policy is the correct, economically reasoned definition of the money supply benchmarks and the desire to achieve them using all available funds.

There is a direct connection between the establishment of guidelines for the dynamics of the money supply and the effectiveness of other monetary regulation instruments used by the Central Bank. This activity allows you to accurately determine the period during which the intervention of regulatory authorities is necessary, and the urgency of taking measures increases their effectiveness.

At the same time, it is important that the objectives of monetary policy are clear to all market participants and the population. The extent to which economic agents will be able to take into account the entered parameters in their calculations is one of the decisive factors in achieving the set goals.

Based on the above, one of the key tasks of regulating the money supply is to optimize the amount of money in circulation, the displacement of monetary surrogates. In a normal economy and natural market conditions, the volume of output and price changes regulates the excess of means of payment.

Significant prospects for the development of the cash circulation system can be guaranteed by improving the practice of interaction between the Central Bank and market participants. In the Russian Federation, one of the key innovative solutions in this direction is the admission of credit institutions to work with cash belonging to the Bank of Russia.

In 2017, the practice of cash servicing in credit institutions with the use of cash owned by the Bank of Russia was tested and approved. The necessary legal framework formed in 2018-2020 contributed to the wide spread of the new format of relations. The combination of these factors made it possible to conclude new contracts with individual banks in 2020 [3].

The presence in the cash departments of special storerooms or sections in which cash is saved by the Bank of Russia grants the right to credit organizations at the beginning of the day promptly, without significant costs and expenses for transportation, collection, recalculation, registration to receive reinforcements in cash in the required volumes. At the end of the working day, it is just as soon and fruitfully to reduce cash balances by moving excess cash to special storerooms and sections. This practice gives a chance to drastically reduce labor costs and expenses of both credit institutions and the Bank of Russia, as well as the opportunity to optimize the inappropriate cash turnover. Another indirect positive effect is achieved by increasing the length of stay of banknotes in circulation due to an impressive reduction in the number of their recalculations, which would need to be carried out if the regular transportation of cash from the Bank of Russia to credit institutions and back is maintained.

A new approach to relations with credit institutions in terms of transferring cash belonging to the Bank of Russia to them for safekeeping contributed to increasing the stability and efficiency of the supply of cash turnover increased its reliability to fluctuations in demand for cash.

One of the obvious results of the current spread of non-cash forms of payment in trade, transport, and other enterprises and organizations is the blocking of ways to return coins to the payment turnover. The number of trading enterprises that order and receive coins for the delivery of change is increasing, but they themselves prefer not to accept them from the population in order to reduce the cost of recalculation and collection.

Maximizing the turnover of coins contributes to the solution and implementation of three main tasks:

‒ reducing the level of demand for coins;

‒ optimization of coin flows;

‒ stimulating the return of coins into circulation [8].

Reducing the need for coins is carried out as part of measures aimed at a more functional use of non-cash payment methods. There is no doubt that this task will be solved. This is due to the formation of the Coin Platform of the Bank of Russia (MPDB), which performs the function of redirecting coin flows from those organizations that collect them from the population to organizations that need it. The MPDB guarantees the probability of an effective information exchange of the largest number of organizations that have a need to deposit coins on the one hand, and receive it on the other.

In 2020, the sample of the MPDB functioned in 8 regions and covered 132 divisions of credit institutions. The total turnover for 2020 amounted to 724 million rubles (909 tons of coins). The formation of the Coin Platform of the Bank of Russia made it possible to reduce the costs of participants in the payment turnover, increase the transparency of coin circulation, increase the availability of coins and optimize their inappropriate turnover. The transfer of part of the costs of collecting coins from circulation from supplier organizations to consumer organizations served as an additional incentive for the implementation of this activity.

Summing up, it should be noted once again that the amount of money that «circulates» in the economic system has a great influence on the price level, employment of the population and other economic constants. Proceeding from this, the most important attention should be paid to the mechanism of the influence of the money supply on prices, to the structure of itself and related aggregates. In this regard, the monetary policy pursued by the Central Bank should become the basis of one of the key components of economic stability — control over the amount of money. A promising tool in these conditions is targeting, which implies the introduction of benchmarks for the growth of the money supply. It involves fixing the amount of money at a given level by adjusting interest rates and the base.