Strategy 2020: A New Growth Model, A New Social Policy states that to achieve its strategic goals, our country needs not just economic growth but rather high rates of it—at least 5% per year, making it possible to reduce the gap with the most developed economies and to increase investment in infrastructure and human capital [1, p. 8]. In the new reality, it becomes relevant to compare the macroeconomic indicators of Russia’s development with the world average estimates. Since 2008, the value of Russia’s GDP per capita (PPP current international $) relative to the world average has been fluctuating without a visible trend in the range of approximately 155–179%. Without considering purchasing power parity (GDP per capita, current $), this figure was 93.4–101.9% from 2017 to 2021 and 99.7% in 2021.Footnote 1

According to the main version of the Forecast of the Long-Term Socioeconomic Development of the Russian Federation until 2030, worked out by the Ministry of Economic Development of Russia, the volume of the world economy by 2030 will increase by two times compared to 2010; the average annual rate will be 3.5% [3]. To at least maintain the achieved level in the world economic space and not worsen the existing correlation with a number of the most important global indicators, the average annual GDP growth rates of the Russian economy in the next 10–15 years should be at least 3.0–3.5%. The urgency of the problem is predetermined by the current geopolitical situation and the need for a new vision in choosing growth factors. The universally recognized sources of long-term development are import substitution and real, not formal, development of the innovation sphere. As for immediate and medium-term factors, their choice is not at all obvious. However, it is precisely this choice that is particularly, perhaps critically, important.

The exceptional importance of developing medium- and long-term forecasts is confirmed by the fact that on October 4, 2022, the Federation Council of the Federal Assembly of the Russian Federation adopted the resolution On the Forecast for the Socioeconomic Development of the Russian Federation for 2023 and for the planned period of 2024 and 2025 [4]. The most authoritative international organizations, such as the World Bank, pay serious attention to this issue [5]. The leading economic agency Bloomberg published a forecast for the development of the Russian economy until 2030 [6]. Domestic organizations, particularly the RAS Institute for Economic Forecasting and VEB.RF, proposed their vision of the future of the Russian economy [7, 8]. The Ministry of Economic Development and the Central Bank of Russia also presented their forecasts, which will be discussed below.

The extreme uncertainty of the future of the world economy and the configuration of global logistics and communications hardly favors building sound economic forecasts using disaggregated information. Apparently, it is not by chance that many scientific organizations focus their tools mainly on the use of compact models with a relatively small number of indicators. Long-term economic forecasts of international organizations are also usually limited to the dynamics of GDP as a whole. At the same time, in conditions of noticeable fluctuations, predictions based on instruments with relatively stable changes in the parameters become more reliable. We mean macroeconomic models. Here, it seems, it is important to use as exogenous characteristics measurable values the nature of which is understandable and relatively stable retrospective trends that are explainable.

The purpose of this article is to predict in operational language the possible dynamics of Russia’s GDP and consumption fund until 2035, relying solely on highly aggregated characteristics of investment activity—the savings rate and the return on a unit of additional capital. One of the important obvious features of such a formulation is that considering any other resources, in particular labor, may not only fail to improve the characteristics of dynamics but rather worsen them. Hypotheses regarding forecast investment parameters are based on their values and trends during the retrospective period 2001–2020. A brief substantiation of the proposed approach is considered below in the section “Forecast Estimates.”

METHODOLOGICAL TOOLS AND THEIR INTERPRETATION

The increase in production in absolute terms (ΔY) in the context of investment parameters can be represented as the interaction of two factors: the volume of investment in fixed assets (I) and the values of the needs in capital for increasing the volume of production per unit of incremental capital−output ratio (k):

$$\Delta Y = \frac{I}{k},\quad {\text{where}}\quad k = \frac{I}{{\Delta Y}}.$$
(1)

The increase in production in relative terms in relation to the macroeconomic level is as followsFootnote 2:

$$G = \frac{s}{k},\quad {\text{where}}\quad s = \frac{I}{Y},$$
(2)

where G is GDP growth rate, I is investments (accumulation, savings), Y is GDP, and ΔY is GDP growth.

The value of the GDP savings rate (s) characterizes the scale of investment activity relative to the product, and the value of the incremental capital−output ratio (k) characterizes the qualitative side of the investment resource, indicating the amount of investment necessary to increase GDP by one unit.

The consistency of the parameters of Eq. (2) assumes that the increase in production in year t is generated by investments made in the same year (no lag). One methodological remark should be made regarding the calculation of the indicator of incremental capital−output ratio (k): in retrospective calculations, at the given GDP growth rates and savings rate, this indicator, according to (2), is calculated by the formula:

$$k = \frac{s}{G}.$$
(3)

As is known, the savings rate is calculated and published in statistics at current prices in annual terms. To estimate it on average over the period (1, τ), one can use various methods, each of which is not perfect. In fact, formula (4) is used:

$${{s}_{{1,\tau }}} = \frac{1}{\tau }\mathop \sum \limits_{t = 1}^\tau {{s}_{t}}.$$
(4)

As a result, everywhere below, the indicator of the incremental capital−output ratio is calculated according to the formula

$${{k}_{{1,\tau }}} = {{s}_{{1,\tau }}}~:\left( {{{{\left( {\frac{{{{Y}_{\tau }}}}{{{{Y}_{0}}}}} \right)}}^{{\frac{1}{\tau }}}} - 1} \right),\quad \tau = 1, \ldots ,T.$$
(5)

Let us dwell in more detail on the interpretation of basic expression (2). Acceleration of GDP growth rates in the forecast period can be achieved by increasing the savings rate s and (or) reducing the incremental capital−output ratio k. In terms of content, a decrease in the value of k relative to the base period means an increase in the return on a unit of additional capital. In other words, in the forecast period, the ratio of the effect of introducing new technological systems into production (increase in product calculated in prices) to expenditures (costs associated with their creation) is more favorable than a similar ratio in the base period; investment costs per unit of power are reduced. The involvement in production of technologies with a lower incremental capital−output ratio creates conditions for accelerating economic growth under a constant savings rate.

If the value of the incremental capital−output ratio increases, growth can be accelerated only by increasing the savings rate. The additional investments in this case actually (more than) compensate for their declining economic efficiency. It is possible that the increase in the product, calculated in physical (natural) indicators, during a unit of time starting from the introduction of new technically more advanced production systems is higher than in the base period.

Note that the value of the indicator of the incremental capital−output ratio, or rather, the opposite of it, can be interpreted in accordance with its nature as the actual return on a unit of additional capital only in the situation where aggregate demand is not limited (large enough); in conditions of lower demand, this indicator plays the role of a balancing parameter. This means that the correct interpretation of the indicator \({{k}_{{1,\tau }}}\) implies a period of observation sufficient to identify a stable situation-independent trend of macroindicators. This important remark must be kept in mind when assessing the specific values of the incremental capital−output ratio in the period of retrospective development.

Assessing the impact of the investment parameters on the social component of GDP and the consumption fund, we add to relation (2) the known balance

$$Y = I + C,$$
(6)

where C is the consumption fund.

Let us denote by\({{s}_{t}}~\) the savings rate in year t, and by \({{k}_{t}}\), the incremental capital−output ratio in year t. In continuous form, with the limiting decrease in the time step (\(\Delta t \to 0)\), the volume of investments in year t is calculated as follows:

$${{I}_{t}} = {{k}_{t}}Y_{t}^{'},$$
(7)

where\(Y_{t}^{'}\) is the time derivative of Y at point t.

Considering (7), the fundamental relation of interest to us can be written as a differential equation (similar to the Harrod–Domar model [11, 12]):

$$Y_{t}^{'} = \frac{{{{s}_{t}}}}{{{{k}_{t}}}}{{Y}_{t}}.$$
(8)

Then the dependence of the volume of the consumption fund Ct in the structure of GDP on the parameters \({{s}_{t}}\) and \({{k}_{t}}\) can be represented as

$${{C}_{t}} = (1 - {{s}_{t}}){{Y}_{0}}{{e}^{{\int {\frac{{{{s}_{t}}}}{{{{k}_{t}}}}dt} }}}.$$
(9)

Assuming a linear relation of the savings rate in time (\({{a}_{0}},~{{a}_{1}}\) are constants)

$${{s}_{t}} = {{a}_{0}} + {{a}_{1}}t,$$
(10)

as well as the invariance of the indicator of incremental capital−output ratio

$${{k}_{t}} = k,$$
(11)

we obtain in explicit form the analytical dependence of the volume of GDP and the consumption fund on the values of the investment parameters:

$${{Y}_{t}} = {{Y}_{0}}{{e}^{{({{a}_{0}}t + 0.5{{a}_{1}}{{t}^{2}})/k}}},$$
(12)
$${{C}_{t}} = \left( {1 - {{a}_{0}} - {{a}_{1}}t} \right){{Y}_{0}}{{e}^{{({{a}_{0}}t + 0.5{{a}_{1}}{{t}^{2}})/k}}}.$$
(13)

Relations (12) and (13) open opportunities related to the formulation and solution of a number of nontrivial problems. For example, at what constant values of k the following occur:

• an increase in the savings rate favoring stable growth of the product and the consumption fund;

• the savings rate reaching a level sufficient to at least maintain the scale of consumption achieved in the base period;

• an arbitrarily high savings rate no longer able to withstand a steady decline in the consumption fund.

The solution of these problems will make it possible to assess the parameters of the scale and dynamics of saving in the interests of growth that do not prevent (for a given specific capital requirement) an increase in consumption.Footnote 3

ANALYSIS OF RETROSPECTIVE DEVELOPMENT

The economic development of Russia during the entire post-Soviet period has been accompanied by an extraordinary variety of external and internal conditions. However, even against this motley background, the 1990s stand out—a transitional stage from one socioeconomic structure to another. This phase of development was distinguished by destructive avalanche-like processes in the economy, determined by a powerful combination of destructive circumstances, associated, first and foremost, with the collapse of the country.

Based on the methodological apparatus discussed above, a retrospective assessment of the relationship between macroeconomic dynamics in the Russian Federation and the factors that determine it—the savings rate and incremental capital−output ratio—will make it possible, to a certain extent, to justify the approach to factorial values in the forecast period. Note that the inclusion of the transition period in the general data series for the purpose of a systematic presentation of these values, in our opinion, is inappropriate since it can lead to significant distortions. Let us cite as a typical example the data concerning the savings rate (Fig. 1).

Fig. 1.
figure 1

Annual savings rate (Gross fixed capital formation), %.

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There are three subperiods with different characteristics of the dynamics of the savings rate: fall, growth, stabilization. However, a special (extreme) change in the savings rate, characterized by its unprecedented reduction from 31.8% to 14.4%, refers only to the period of 1989–1999. Numerical characteristics of growth factors and GDP dynamics in retrospect are presented in Table 1.

Table 1. Summary data on growth factors and GDP dynamics before and after the 2008–2009 crisis
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The postcrisis significant weakening of economic dynamics is primarily due to a sharp deterioration in the return on additional capital: the value of the incremental capital−output ratio increased from $2.9/dollar in 2001–2008 up to $19.9/dollar in 2009–2021. From the point of view of common sense, such a dynamic of the parameter seems implausible; thus, it is worth dwelling on this phenomenon in more detail. The point is that the development in the period 2001−2008 largely relied on the mobilization of a large amount of accumulated free capacity (more information below), and in this sense it was extremely “capital-saving.” At the same time, restrictions on the part of demand, primarily external and, to a certain extent, internal, were insignificant. After 2009, the situation changed qualitatively. Investment activity due to inertia and investment lags (formally) slightly increased, but the dynamics of production slowed down sharply due to constrained demand, the average annual GDP growth rate fell six times. In relation to the intensity of demand, the scale of supply, or rather the potential of newly created and reconstructed capacities, turned out to be excessive, redundant. The “capital-unsparing” nature of development outwardly (according to the laws of arithmetic) manifested itself in a sharp increase in the incremental capital−output ratio indicator. An even greater weakening of demand could lead to its rise, as they say, into the stratosphere. The form of relationship between the macroeconomic dynamics and the incremental capital−output ratio over 2001–2021 is shown in Fig. 2. The rising trend of cumulative macroeconomic dynamics in 2007−2008 was due to the increase in the savings rate and was supported by a reduction in the incremental capital−output ratio.

Fig. 2.
figure 2

Some characteristics of economic development on a cumulative basis (with 2000 as the base).

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The question arises: why is the indicator of the incremental capital−output ratio before the crisis significantly different from that after it? The point is that, by the end of the 1990s, for well-known reasons, significant amounts of unused capacities were accumulated in Russia, mostly by force. According to comparable Rosstat data on 77 types of industrial products, the average level of utilization of production capacities in industry as a whole by 2000 was 41.5%. By 2007–2008, due to the growth of export deliveries and the expansion of domestic demand, the average load reached approximately 56–58%, and since 2010 (for a noticeably wider range) it has fluctuated within 52–56%, without showing any noticeable changes.Footnote 4 In addition, after 2014, exports decreased markedly. This means that the relation of the volume of investments and the resultant increase in the product is sharply deteriorating relative to the precrisis situation.

FORECAST ESTIMATES

A few words about the methodology of the proposed approach. Introducing a single limiting resource, in this case investment, into the model allows one to measure the potential macroeconomic performance, unconstrained by any other supply and demand factors. In this case, the estimates of GDP growth rates obtained are not so much a forecast (as a probable development of events) but rather an idealized image of future development.

Labor resources in relation to models of economic growth are considered in the literature from two points of view. On the one hand, it is a factor of development through increased productivity, due to an increase in human capital; on the other hand, it is a limitation of growth. In applied models and economic reviews, labor resources most often act as limiting factors, a lack of which (primarily qualified personnel) does not allow full use of the created production potential and reduces the use of the available production capacities. To illustrate this thesis, let us turn to one of the World Bank reports on the Russian economy, published at the end of 2018. The last relatively calm pre-Covid period was chosen deliberately. In Russia, the slowdown in economic growth was due to “a shrinking potential labor force” [13], and further, “Growing working-age populations can lift potential growth” [13].

A short-term forecast for two or three years necessarily includes an assumption about intersectoral, in some cases, spatial, structural shifts that determine the macroeconomic dynamics. As for long-term foresight under conditions of global uncertainty, such a priori assumptions are not only impossible but rather, in our opinion, harmful. A well-known compromise could be the use of enlarged macroaggregates that implicitly consider the structural transformation of an economic system.

Any predictive scenario, regardless of the hypotheses concerning the control parameters, should, it seems, include three stages successively flowing into each other—evolutionary, structural transformation, and accelerated growth. There is no need to explain the content of each of these stages here. Table 2, in relation to one of the possible scenarios, proposes forecast estimates of GDP that follow from the assumptions (which are discussed below) regarding investment parameters in accordance with Eq. (2). Thus, a consistent increase in the savings rate is assumed. Its limiting value at the end of the forecast period approximately coincides with the level of the last years of the Soviet period.

Table 2. Some basic and forecast characteristics of the economic development of the Russian Federation by five-year stages
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Another assumption concerns the dynamics of the incremental capital−output ratio parameter. The key hypothesis here is formulated as follows: successive downward approximation during the forecast period from stage to stage, to the (unattainable) value of capital intensity recorded in 2001–2008, which was distinguished by a combination of extremely favorable external and internal conditions. Actually, the acceleration of development is mainly connected with these assumptions.

Note that the idea of the behavior of the incremental capital−output ratio indicator in the forecast period is based on the retrospective data for 2001–2021 and in this sense is quite realistic. It is assumed that its value in general for 2021–2035 is higher than the level of the retrospective period; however, at the final stage of accelerated development (2031–2035), it somewhat improves. At the same time, it is expected that, as the Russian economy adapts to international sanctions, the measure of uncertainty will decrease. This assumption in the forecast is implemented through a decrease in the interval of variation of the incremental capital−output ratio indicator.

It makes sense to compare the calculated forecast characteristics with similar estimates obtained by the Ministry of Economic Development of Russia for the period 2022–2030. In accordance with the “accelerated adaptation” forecast scenario of this ministry, the GDP growth index by 2030 will not exceed 1.17 compared to 2021, and the nine-year average annual growth rate will be 1.76% [14, 15]. In our calculations, the average annual growth rate for the same period will be from 1.79 to 2.47%. Since the ministry is also developing inertial and stress scenarios, we can say with certainty that our vision of the medium term to 2030 is slightly more optimistic.Footnote 5 The Central Bank of Russia prepared a forecast for 2022–2025. In accordance with its baseline scenario, the volume of GDP, after the failures of a number of previous years, by 2025 will at best reach the level of 2021 (according to our calculations, it will slightly exceed this level).

No less important, perhaps even more important, than the dynamics of GDP is the forecast for the consumption fund. For this purpose, we use Eq. (13). The savings rate in 2020 was 0.218; by 2035 it is expected to reach 0.318. The forecast period is 15 years. Then the desired equation appears in the form

$${{C}_{t}}\, = \,(1\, - \,0.218\, - \,0.00667t)\,\,{{Y}_{0}}\,\,{{e}^{{(0.218t + 0.5\text{*}0.00667{{t}^{2}})/k}}}.$$
(14)

The dynamics of the summary indicators (with an average value of incremental capital−output ratio for the entire forecast period of 8.85) is shown in Fig. 3. It seems that by 2035 the consumption fund will grow by 37.3% compared to 2020, and with k = 12.2 (the average value in the first two stages), by 21.2%.

Fig. 3.
figure 3

GDP and consumption fund growth index, 2020, 1.0 (k = 8.85).

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RESULTS AND CONCLUSIONS

In accordance with our forecast calculations, the average annual GDP growth rates in the period 2021–2035 (2.6–3.3%), despite striking differences, primarily related to external conditions, approximately coincide with the dynamics in the retrospective of 2001–2021 (3.13%). It is worth dwelling on this collision in more detail. GDP growth rates for the first ten years of the forecast period will be 1.70–2.34%, and some acceleration is expected only by the final five years. The impetus for acceleration will be given at the stage of intensive structural transformation (2026–2030), when the savings rate in relation to the previous five years of evolutionary (extrapolative) development noticeably increases (by 5 p.p.).

The accelerated deployment of investments, at least by the second half of the 2020s, is the key to the entire predictive structure; we mean simultaneous major structural shifts within the investment complex and a new technological platform. It is assumed that the replacement and expansion of fixed capital with the involvement of the best technologies at the stage of intensive structural transformation will manifest itself in a reduction in the incremental capital−output ratio compared to the previous five years by more than half. This will require extraordinary effort.

During the years 2015–2020, in the structure of investment in fixed assets by type of economic activity, the share of coal, oil, and natural gas productionFootnote 6 was approximately 14–16% in total [17]. The significant decline in exports due to international sanctions and, consequently, the reduction in productionFootnote 7 will inevitably lead to the restriction and contraction of investment programs in these industries. A serious effort will be needed not only to compensate for the shortfall in investments but also to increase them significantly at the expense of modern capital-creating industries. Meanwhile, during the years 2015–2020, in the structure of investments in fixed capital by type of economic activity, the share of production of machinery and equipment (not included in other groups), including their repair and installation, was approximately 0.5%; information technology, production of computers, electronic and optical products, development of computer software, and consulting services in this area total 1.0% [17]. Of course, the Russian government, within the framework of the import substitution policy, is developing relevant promising fundamental programs and development projects. In particular, a preliminary concept of a new national project in the field of electronics has been prepared. Its implementation by 2030 may cost 3.19 trillion rubles [20]. However, if over the next three to four years this and many other ambitious projects, primarily in the field of investment engineering, are not prepared to the necessary extent for full-scale implementation, the forecasts of the Ministry of Economic Development and the Central Bank may turn out to be too optimistic.

Maintaining approximately the same ratio of per capita GDP in Russia over the past 10–12 years with the value of the corresponding indicator for the whole world was ensured mainly by rental incomes with a very modest value of the savings rate (21–22%). The results of the forecast calculations indicate that there is a fundamental opportunity to maintain the status quo, as well as to ensure in the Russian Federation the average annual GDP growth rate for the period up to 2035 at approximately 3%. The large-scale investments required for this should be focused not only on raising the savings rate to 26–27% in three to four years but also on simultaneously improving the quality of the investment resource and building production capacities on a new technological platform.