7.3 Intersectoral balance and economic forecasting model
The mathematical model allows assessing the total investment potential of the city, which is the sum of investment potentials related to various aspects of economic activity:
\[\begin{align*}
&IP = IP_{s} + IP_{CA} + IP_{FA} + IP_{R} &(24)
\end{align*}\]
where:
\(IP_{s}\) – investment potential by demand, associated with a possible increase in sales volumes of goods and services; \(IP_{CA}\) - investment potential related to possible growth in the profitability of using current assets; \(IP_{FA}\) - investment potential related to possible growth in the efficiency of using fixed assets; \(IP_{R}\) - investment potential related to possible growth in the efficiency of using material resources.
7.3.1 Investment potential by demand
For the calculation, industries are divided into two types based on sales localization:
- Industries with local sales – industries oriented towards the intra-city consumer. The volume of additional demand (market niche) is determined by the imbalance of local production and local final demand (consumption).
- Industries with regional sales – industries oriented both towards the intra-city consumer and consumers outside the city. The market niche for such industries is determined by the imbalance of production (capacity constraints) and the volume of demand in territories where delivery is economically feasible taking into account logistics costs.
Final consumption includes three components:
- Final consumption by households, the value of which is determined based on the total household expenditures in the city and the demand structure corresponding to the consumption structure for the RF obtained from the SNA.
- Final consumption by government bodies, determined based on total municipal budget expenditures and the consumption structure corresponding to the consumption structure for the RF obtained from the SNA.
- Final consumption by non-profit organizations, determined by the share of total final consumption of households and government bodies (determined according to the federal input-output table).
Intermediate consumption, formed by commercial organizations in the city, is determined by the proportion of revenue (output) of the city’s organizations. The specific consumption structure of the city’s industries, expressed by the resource consumption matrix, is determined by the proportion of revenue (output) of the city’s organizations.
In the “retail trade” industry, output (production) is determined as the value of the trade margin, i.e., the difference between the sale price of goods and their purchase price.
Investment potential by demand is determined based on market niche volumes as follows:
\[\begin{align*}
&IP_{s}=(C- YdL)*J =(C-RVN)*J*T^{*} &(25)
\end{align*}\]
where:
\(C\) – market niche (by internal and cross-border types of demand)
\(RVN\) – output volume
\(J\) – sales profitability
\(T^{*}\) – standard payback period of investments, defaulted to 7 years
7.3.1.0.1 Private efficiency by types of capital
To calculate investment potentials by efficiency, separate efficiency components are determined.
Efficiency of fixed assets is determined by the formula:
\[\begin{align*}
&E_{FA}=RVN/FA &(26)
\end{align*}\]
where:
\(FA\) - fixed assets (assets)
The efficiency function for fixed assets is an indicator of asset turnover. In other words, reducing the volume of fixed assets required to produce a unit of output is a component of technical progress.
Efficiency of current assets is determined by the formula:
\[\begin{align*}
&E_{CA}=CA/Пч &(27)
\end{align*}\]
where:
\(CA\) - current assets (working capital)
\(Пч\) - net profit
The efficiency function for current assets is an indicator of turnover for working capital. In other words, increasing the volume of profit required per unit of current assets is a component of technical progress.
Efficiency of resource costs is determined by the formula:
\[\begin{align*}
&E_{R}=RVN/R &(28)
\end{align*}\]
where:
\(R\) - costs of material resources
The efficiency function for natural resource costs is an indicator of specific resource costs. In other words, reducing the volume of natural resources required to produce a unit of output is a component of technical progress.
7.3.1.0.2 Calculation of investment potentials by efficiency
Potential calculation by efficiency factors is performed by calculating the deviations of the values of the corresponding efficiency factors from the median value for the industry across all cities and years of statistical observations.
Potentials for fixed assets are determined as follows:
\[\begin{align*}
&IP_{FA}=(-E_{FA}+\widehat{E_{FA}})*FA*J*T^{*} &(29)
\end{align*}\]
Potential for current assets:
\[\begin{align*}
&IP_{CA}=(E_{CA}-\widehat{E_{CA}})*CA*T^{*}*G &(30)
\end{align*}\]
where:
\(G\) - rate of attracting current assets
Potential for resource use:
\[\begin{align*}
&IP_{R}=(-E_{R}+\widehat{E_{R}})*R*J*T^{*} &(31)
\end{align*}\]
where the \(\widehat{\ \ \ }\) symbol means median calculation (quantile).
The structure of final consumption for households and municipal authorities does not depend on the volumes of real disposable income and budget income, respectively.
7.3.1.1 Assumptions used in calculations
The following assumptions were made when developing the Model:
- The matrices of intersectoral balance coefficients (a, b, e, l, p) change over time within the permissible error of statistical measurements.
- The dynamics of international export is not taken into account when building the model.
- The matrices of intersectoral balance coefficients (a, b, e, l) are the same for cities up to industry proportions (p).
- The specific volume of industry output is proportional to the specific volume of gross value added (GVA).
- The specific consumption of an industry corresponds to the specific consumption of the RF according to the SNA.
- Negative coefficients of the matrix multiplier characterize cross-border imbalances, i.e., the need for product imports. Negative output values obtained during calculations should be interpreted as the volume of imported products.
The scope of permissible application of the model for forecasting industry indicators is the medium-term period (up to 3 years), after which the MOB coefficient matrices must be refined using actual data.
7.3.1.2 Algorithm for carrying out calculations
Forecasting of industry indicators is performed in the following order:
- The Resources and Services Table, as well as the Table of Use of Goods and Services in basic prices from the System of National Accounts (SNA), are used as initial data. These tables contain information on 61 types of economic activity.
- The first step of calculations is the decomposition of these tables from 61 to 128 industries. Detailing is carried out based on the proportions of the revenue of 128 industries obtained from the balance sheets of Russian enterprises.
- Federal matrix coefficients of inter-industry balances are determined - a, e, b, l.
- Total output is determined for 128 industries (based on balance sheet data).
- Using the City System Dynamics Model, forecast series are built for the indicators of population and per capita income until 2030.
- Based on the data obtained in steps 4 and 5, output is calculated with detailing by 128 industries for the forecast period (until 2030).
\[
Q_{j i}^{t}=Q_{j i}^{t_{0}} \times\left(\frac{N_{j}^{t} \times \phi_{j}^{t}}{N_{j}^{t_{0}} \times \phi_{j}^{t_{0}}}\right)\ \ (32)
\]
7. The upper and lower values of the confidence corridor with a 95% confidence interval are determined.
\[
\delta=\mathrm{Z} \frac{\sigma}{\sqrt{n}} \ \ (33)
\]
where
\(Z\) - confidence coefficient. For 95% probability, it is 1.96;
\(\sigma\) - standard deviation;
\(n\) - sample size.
8. Based on the output data (by industry and city, obtained in step 6) and matrix coefficients, the absolute values of the matrices are found:
\(A\) - intra-industry consumption
\(Y\) - final consumption
\(L\) - total costs
\(E\) - output of goods and services
9. Based on the values of the matrix \(L\), the values for VGP (Gross City Product), GVA (Gross Value Added), Payroll, import and export of products to/from the city, as well as other economic indicators by industry, are calculated.
10. Medians are calculated for the following indicators:
- Return on fixed assets
\[
E F A_{i j}^{t}=\frac{R_{i j}^{t}}{F A_{i j}^{t}} \ \ (34)
\]
- Return on current assets
\[
E F L_{i j}^{t}=\frac{Пч_{i j}^{t}}{F L_{i j}^{t}} \ \ (35)
\]
- Return on material costs
\[
E M_{i j}^{t}=\frac{Пч_{i j}^{t}}{M_{i j}^{t}} \ \ (36)
\]
- Profitability of sales
\[
E sales_{i j}^{t}=\frac{Пч_{i j}^{t}}{R_{i j}^{t}} \ \ (37)
\]
11. In the next step, the investment potential is calculated.
12. After that, based on the values of the matrices \(A, Y, L\), the production and consumption of products by related industries are calculated.
13. Using data on implemented and planned projects in terms of investment and revenue, the output increments for 128 industries are determined.
14. Having obtained the output increments, we get the values of output indicators taking into account the increments from implemented and planned projects for all 128 industries within the investment scenario.