Research Article 
Corresponding author: Elizaveta V. Martyanova ( elizaweta.martyanowa@yandex.ru ) © 2023 Nonprofit partnership “Voprosy Ekonomiki”.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BYNCND 4.0), which permits to copy and distribute the article for noncommercial purposes, provided that the article is not altered or modified and the original author and source are credited.
Citation:
Martyanova EV, Polbin AV (2023) General equilibrium model with the entrepreneurial sector for the Russian economy. Russian Journal of Economics 9(2): 109133. https://doi.org/10.32609/j.ruje.9.105790

This paper proposes a general equilibrium model with the entrepreneurial sector for the Russian economy. The novelty of the model lies in several points. First, the model is a small open economy. Second, it includes the entrepreneurial sector. Third, the model reflects the main features of the Russian economy. Five experiments were conducted, for which steady states and transitions were computed. These experiments included: (1) an export price shock, (2) redistribution of government consumption between the corporate and entrepreneurial sectors, (3) relaxation of collateral requirements, (4) a credit rate subsidy for entrepreneurs, (5) VAT for entrepreneurs. The export price shock results in lower entrepreneurial output due to higher wages in the short run, but in the long run the positive effects of increased demand and assets lead to higher output. Increased government consumption of entrepreneurial goods leads to a reallocation of resources from the corporate sector to the entrepreneurial one. The relaxation of collateral requirements leads to a sharp increase in entrepreneurial investment and capital and a decline in the number of entrepreneurs, which means that they become bigger. The credit rate subsidy leads to an increase in capital in the entrepreneurial sector, and then in output. The cost of subsidies leads to a decrease in lumpsum transfers, but this does not lead to a significant change in household consumption. The introduction of a valueadded tax on entrepreneurial goods leads to a redistribution of resources from the entrepreneurial sector to the corporate one, lower household consumption and higher GDP.
general equilibrium, entrepreneurship, heterogeneous agents.
Small and mediumsized enterprises play an important role in the economy: they are a source of employment and economic growth, as well as one of the important factors in adapting the economy to internal and external changes. Support of small and mediumsized enterprises is considered one of the priorities of government policy in Russia. Thus, in 2016, the Strategy for the Development of Small and Medium Entrepreneurship in the Russian Federation for the period up to 2030 was approved. In addition, the national project “Small and mediumsized enterprises and support for individual entrepreneurial initiatives” is being implemented as part of the execution of the Decree of the President of the Russian Federation No. 204, dated May 7, 2018. Therefore, the task of developing economic and mathematical tools to assess the consequences of economic policy and macroeconomic shocks on the dynamics of the main indicators of small and medium enterprises in Russia seems relevant.
General equilibrium models are a key tool for macroeconomic analysis in economic research. Examples of research on general equilibrium models for the Russian economy include
The purpose of this paper is to develop a general equilibrium model with the entrepreneurial sector for the Russian economy. The proposed model differs from the developed models in the spirit of
The present paper is close to a number of studies.
The article is organized as follows. Section 2 presents the model. Section 3 describes the calibration of the model parameters. Section 4 describes the policy experiments. Section 5 discusses the results. The last section concludes.
The model is a small open economy. This implies that the interest rate and prices of imported and exported goods are exogenous. The model economy consists of households, which may be entrepreneurs or hired workers, the corporate sector, the intermediary sector, the government, and the oil and gas sector.
The trade structure of the model is shown in Fig. 1. There are two sectors of production of goods and services in the economy: the entrepreneurial sector and the corporate sector.
The corporate sector consists of larger firms and is characterized by diversified risk and anonymous operations. The corporate sector is divided into nontradable and exportable sectors. The nontradable sector produces goods Y_{t}^{N}, which are then consumed domestically. Government consumption of nontradable goods is exogenous and is denoted by G_{t}^{c}. The exportable sector produces goods Y_{t}^{E}.
The entrepreneurial sector consists of households that decided to become entrepreneurs in the previous period. They implement their own entrepreneurial project, the success of which depends on the decisions and entrepreneurial abilities of the owner, who is limited in borrowing depending on accumulated assets.
The entrepreneurial sector produces goods Y_{t}^{nc}, which are then exported or consumed domestically. Government consumption of entrepreneurial goods is exogenous and is denoted by G_{t}^{nc}. Goods between domestic consumption and exports are allocated based on a function with constant elasticity of transformation (CET):
where D_{t}^{nc} is the consumption good produced by the entrepreneurial sector for the domestic market; X_{t}^{nc} is export of entrepreneurial goods; α_{e} is the export share parameter in CET function; ρ is the transformation parameter.
From the entrepreneur’s profit maximization problem, we can derive the optimal ratio between exports X_{t}^{nc} and domestic sales D_{t}^{nc}:
where p_{t}^{e} is the price for exported goods (excluding goods of the oil and gas sector); pd_{t}^{nc} is the price for domestic consumption of goods produced in the entrepreneurial sector.
Given the CET function, the aggregate price of entrepreneurial goods p_{t}^{nc} is given by:
The consumption tax in the model is a counterpart to the valueadded tax in Russia. The consumption tax is imposed on domestically produced goods and imported goods that are used for final consumption, but it is not imposed on investment goods, entrepreneurial goods, exported goods and government consumption goods. To reflect this, two Cobb–Douglas functions are introduced: one for consumption goods and one for investment goods.
Entrepreneurial goods for domestic consumption C_{t}^{nc}, nontradable consumption goods C_{t}^{c} and imported goods C_{t}^{M} are aggregated into homogeneous domestic consumption good C_{t} based on the Cobb–Douglas function:
where ω_{1} is the share of the entrepreneurial sector in the production function; ω_{2} is the share of the corporate sector in the production function.
The objective is to minimize costs:
s.t. (4)
where τ_{t}^{nc} is the tax on entrepreneurial goods; p_{t}^{N} is the price of corporate nontradable goods; and p_{t}^{M} is the price of imported goods. In the baseline scenario τ_{t}^{nc} is equal to zero since entrepreneurial goods are not subject to consumption tax. However, this tax allows us to analyze the macroeconomic effects of a hypothetical tax reform, if the entrepreneurial sector is subject to VAT. The price of consumption goods p_{t}^{C} is equal to ((1 + τ_{t}^{nc})pd_{t}^{nc})^{ω}^{1} ((1 + τ_{t}^{C})p_{t}^{N})^{ω2} ((1 + τ_{t}^{C})p_{t}^{M})^{1– ω1 – ω2}.
From the problem of cost minimization, we can derive the demand for entrepreneurial consumption goods:
the demand for nontradable consumption goods:
and the demand for imported consumption goods:
Entrepreneurial investment goods I_{t}^{nc}, nontradable investment goods I_{t}^{c} and imported investment goods I_{t}^{M} are aggregated into homogeneous domestic investment good I_{t} based on the Cobb–Douglas function:
The price of investment goods is set as follows:
From the problem of cost minimization, we can derive the demand for entrepreneurial investment goods:
the demand for nontradable investment goods:
and the demand for imported investment goods:
The production function of the nontradable sector is a Cobb–Douglas function:
where Y_{t}^{N} is the output of the nontradable sector; K_{t}^{N} is the capital stock in the nontradable sector; α is the output elasticity of capital; A_{t}^{N} is total factor productivity in the nontradable sector; L_{t}^{N} is labor input in the nontradable sector.
Corporate firms own capital, so they make decisions about the amount of capital and labor they hire based on the problem of maximizing market value:
where r_{t+i} is the interest rate in the (t + i)th period; τ^{K}_{t+s} is the profit tax in the (t + i)th period; τ^{wf}_{t+s} is the social contributions rate; w_{t+s} is the wage rate; δ is the depreciation rate for capital.
The capital stock of firms in the nontradable sector evolves according to:
where ψ is the adjustment cost parameter. The quadratic term penalizes abrupt changes in capital, so firms will change investment gradually in response to shocks.
The problem of the exportable sector is set in a similar way. Firms make decisions about the amount of capital and labor inputs based on the problem of maximizing market value:
The capital stock of firms in the exportable sector evolves according to:
The household’s problem is a modification from
There is a continuum of infinitely living households of measure one. In the current period, agents choose their occupation in the next period, that is, whether they work for hire or run their own business. At the beginning of the period, each agent is randomly endowed with:
(1) labor productivity ϵ, which follows a Markov chain with a state vector ε = {ϵ_{1}, ..., ϵ_{N}_{ϵ}};
(2) entrepreneurial ability θ, which follows a Markov chain with a state vector Θ = {θ_{1}, ..., θ_{Nθ}}. This parameter shows how efficiently an agent can run the business.
After the shocks are realized, agents make decisions about how much to consume and how much to save. Moreover, because there is no uncertainty between the realization of ϵ and θ shocks in the current and next period, households can also immediately choose an occupation in the next period. Households maximize expected lifetime utility:
where E_{t} is the conditional expectation operator evaluated at period t; β is the subjective discount factor; u (∙) is the utility function; j is the number of periods after period t. The household is subject to the budget constraint and the borrowing constraint, which depend on the occupation that the agent chose in the previous period.
The instantaneous utility function u (c_{t}) is a constant relative risk aversion (CRRA) function:
where σ is the coefficient of relative risk aversion.
The problem of the hired worker is given by:
subject to
a' ≥ 0, c ≥ 0, i ∈{0, 1}, j ∈{0, 1},
where V^{W} (a, ε, θ) is the value function of a hired worker, which depends on the stock of assets in the current period a, labor productivity ϵ and entrepreneurial ability θ; V^{E} (a', ϵ', θ', j') is the value function of an entrepreneur, which also depends on the choice of tax regime j: “income” (j = 0) or “income minus expenses” (j=1); i is a binary variable that is zero if the household will be an entrepreneur in the next period, and one if a hired worker, a', ϵ', θ', j' are the corresponding variables in the next period; Tr is lumpsum transfers (or lumpsum taxes if transfers are negative); τ^{wh} is payroll tax rate.
The production function of the entrepreneur is defined as:
where k is the capital invested in the entrepreneurial project; n is labor input; θ is the entrepreneurial ability of the household; v_{1} and v_{2} are the output elasticities of capital and labor, respectively.
As in (
where α is the output elasticity of capital in the corporate sector, and v = v_{1} + v_{2} ∈ (0, 1).
The problem of the entrepreneur is given by:
subject to
a' ≥ 0, c ≥ 0, i ∈{0, 1}, j ∈{0, 1},
where π^{E} is entrepreneurial profit; j is a binary variable reflecting the entrepreneur’s choice regarding the object of taxation.
It is assumed that at the end of each period the household that chose to be an entrepreneur in the next period also chooses the object of taxation I, which can be “income” (j = 0) or “income minus expenses” (j = 1). Thus, the profit of the entrepreneur is set as:
where the taxes T (I, j) paid by an entrepreneur with object of taxation I are set as:
τ_{t}^{nc,r} p_{t}^{nc}f (k, n, θ), if j = 0,
entrepreneurial capital is limited:
and interest rate on capital is given by:
where k and n are the capital and labor inputs that the entrepreneur invests in his project; τ_{t}^{nc,π} is the tax rate on profits; τ_{t}^{nc,r} is tax rate on revenue; d is the maximum leverage ratio; r_{d} is the borrowing rate for entrepreneurs; ϕ is the credit spread.
The intermediary sector is defined in the same way as in
Banks lend to the corporate sector at the riskfree rate r. The entrepreneurial sector borrows at the rate r_{d} = r + ϕ, where r is the riskfree deposit rate, and ϕ is the fixed cost per unit of borrowed funds. It is assumed that the cost ϕ is wasted, so it does not contribute to the overall equilibrium.
Entrepreneurs can borrow only up to a limit, which is an increasing function of household assets. Entrepreneurial ability θ is not observed by banks, so it does not affect the borrowing limit. It is assumed that the limit on assets for entrepreneurs is given by (1 + d)a/p^{I}, where a is household assets, and d is the maximum leverage ratio.
The production in the oil and gas sector is exogenous and is denoted by O_{t}. The entire volume of extracted oil and gas is exported at exogenous price p_{t}^{O}. The oil and gas sector pays the extraction tax τ_{t}^{O} p_{t}^{O} O_{t}.
The production function of the oil and gas sector is the Leontief function:
where Y_{t}^{O} is the output of the oil and gas sector; ϕ_{1} and ϕ_{2} are the exogenous production parameters; L_{t}^{O} is labor input in the oil and gas sector; K_{t}^{O} is capital input in the oil and gas sector.
The optimal factor inputs are given by:
The government spends on goods of the corporate nontradable and entrepreneurial sectors, transfers to households, and interest on the government debt.
Government revenues consist of:
The budget constraint of the government is given by:
where T_{t}^{nc,r} are tax revenues from entrepreneurs who chose the “income” regime; T_{t}^{nc,π} are tax revenues from entrepreneurs who chose the “income minus expenses” regime; B_{t} is public debt in the tth period.
The dynamics of lumpsum transfers are given by:
where Tr_{ss} is the lumpsum transfers in the steady state (in scenarios where the steady state changes, the tax from the new steady state was taken as Tr_{ss}); ρ_{Tr} is the autoregression parameter for lumpsum transfers; γ_{Tr} is parameter of sensitivity of lumpsum transfers to the deviation of the debttoGDP ratio from the steady state ratio; debt_GDP_ratio is debtGDPratio in the steady state.
The state vector of each agent at the beginning of each period is given by s = (a, ϵ, θ, ξ), where a is assets; ϵ is labor productivity; θ is entrepreneurial ability; ξ ∈ {W, E_{1}, E_{2}} is occupation (hired worker or entrepreneur with one of two possible tax regimes). Let a ∈ A = R_{+}, ϵ ∈ ε, θ ∈ Θ, ξ ∈ Ξ. Then the state space is defined as S = A × ε × Θ × Ξ.
The stationary equilibrium in the given economy is value functions, decision rules {ξ_{t+}_{1}, c_{t}, a_{t+}_{1}, k_{t}, n_{t}}^{∞}_{t =} _{0}, prices {w, p^{nc}}, distribution of workers and entrepreneurs, tax structure, intermediaries and distribution of agents in the state space S, defined as Φ (s), s ∈ S, such that:
(1) The allocations { ξ _{t+}_{1}, c _{t} , a _{t+}_{1}, k _{t} , n _{t} } ^{∞}_{t =}_{0} solve the maximization problem for a household for given prices and lumpsum transfers (taxes).
(2) Factor prices satisfy the conditions for maximizing firm value in the corporate sector.
(3) The government budget satisfies the budget constraint and the lumpsum transfer dynamics equation.
(4) Banks in the intermediary sector receive deposits from households at the riskfree rate r and lend to the corporate sector at the riskfree rate r and the entrepreneurial sector at the rate r + ϕ, where ϕ is the credit spread.
(5) The goods market clears.
(6) The capital market clears.
(7) The labor market clears.
(8) The distribution of Φ is timeinvariant.
The values of the parameters, their descriptions and sources are presented in Table
Parameter  Description  Source 
σ = 2  Elasticity of marginal utility of consumption  
β = 0.90  Subjective discount factor  
r = 3%  Interest rate  
ω _{1} = 0.25  Share of the entrepreneurial sector in the production function  Calculations based on GDP by expenditure data 
ω _{2} = 0.48  Share of the nontradable sector in the production function  Calculations based on national accounts data 
A^{N} = A^{E} = 0.55  Total factor productivity in the nontradable and exportable sectors  The parameters are calibrated so that aggregate GDP equals 1 
α = 0.35  Output elasticity of capital  
δ = 0.11  Capital depreciation rate  
ψ = 1.20  Investment adjustment cost parameter 

γ_{G} = 0.18  Share of government spending in GDP  National accounts data 
ρ_{Tr} = 0.70, γ_{Tr} = 0.05  Parameters for the equation for lumpsum transfers  
debt_GDP_ratio = 0  DebtGDP ratio  
α_{e} = 0.1428  Parameter of the share of exports in the CET function in the entrepreneurial sector  
ρ = –0.15  Parameter transformation in the CET function in the entrepreneurial sector 

ε = {ϵ_{1}, …, ϵ_{Nϵ}}, P_{ϵ}  State vector and transition matrix for household labor productivity  
Θ = {0; θ_{1}} = {0, 1.05}, P_{θ}  State vector and transition matrix for entrepreneurial ability  
ν = 0.9  Parameter of the production function in the entrepreneurial sector  
d = 0.5  Maximum leverage ratio 

ϕ = 0.028  Credit spread  Bank of Russia^{a)}; data on the zerocoupon yield curve from the Moscow Exchange^{b)} 
The parameters σ, r, α were calibrated based on commonly used values in the literature. The elasticity of marginal utility of consumption σ generally takes values from 1 to 2. For example, σ equals 1 in
The discount factor is formulated in real terms since the model is of the neoclassical type. A value of 0.9 was chosen, which gives the closest value for consumptionGDP ratio. The calibration of its value is consistent with the foreign practice of calibrating this parameter in models of the corresponding class (see, for example
The maximum leverage ratio d was taken from
The parameters δ, A^{N} and A^{E} were chosen so that GDP = 1, as in
The share of investment in fixed capital (gross fixed capital formation) was approximately 21%, according to data on GDP by expenditure. According to data on fixed capital investment (excluding small businesses),^{4} as well as data on total investment, the share of exportoriented investment of the oil and gas sector was approximately 12% between 2017 and 2020.^{5} As for small and mediumsized businesses, the share of this sector’s investment in total investment in fixed capital was approximately 8%, according to Rosstat data.
The depreciation rate δ was calibrated so that the share of corporate sector investment in GDP equals 0.168. Since production function in both sectors is Cobb–Douglas function, the optimal capital stock in the corporate sector is given by:
The law of motion of capital in the steady state is defined as:
Given (36–38), we get:
from where we can express δ:
Substituting the above calculated values of Y^{E} and Y^{N} by exogenous parameters α, r, τ_{K}, I^{c}̅ , we can calculate the parameter δ. Given δ, we can calculate the values of K^{N} and K^{E}.
The values of total factor productivities A^{N} and A^{E} in both sectors were calibrated so that Y^{N} and Y^{E} were equal to 0.54 and 0.11, respectively. Thus, there are four equations with four unknowns A^{E}, A^{N}, L^{E}, L^{N}:
The wage bill in the oil and gas sector was approximately 5% of the total wage bill in 2017–2021.
The share of the entrepreneurial sector ω_{1} and the share of the nontradable sector ω_{2} in the Cobb–Douglas function can be calibrated based on the equations:
The share of imports in GDP was approximately 21% according to national accounts data. As mentioned above, the share of goods produced by the entrepreneurial sector for the domestic market accounted for 17–18% of GDP. Domestic consumption output can be calculated as the sum of household final consumption and gross fixed capital formation. According to the national accounts data, its share in GDP was 0.73. Thus, the parameters ω_{1} and ω_{2} were calibrated at 0.25 and 0.48, respectively.
In
The transformation parameter in the CET function ρ was calibrated at –0.15 according to
We know from available data that the share of exports of SMEs in GDP was approximately 3%, and the share of SMEs in GDP was 20–22%. Given this data and the calibrated parameter ρ, the parameter α_{e} is approximately equal to 0.1428.
The share of government final consumption expenditures in GDP in 2011–2021 was stable, averaging around 18%. The exception was 2020, in which the share of government spending rose to 20%. Thus, government consumption in the model is set as a fixed share of nominal GDP:
where γ_{Gnc} + γ_{Gc} = γ_{G} = 0.18.
The target debttoGDP ratio was assumed to be 0. The autoregression coefficient for lumpsum transfers was calibrated at 0.7, and the sensitivity coefficient at 0.05. It is impossible to estimate the value of the parameters from the data due to the short time series and frequent changes in budget rules in Russia, so the parameters were calibrated based on partial equilibrium so that the model would generate satisfactory transition paths. For example, Fig. 2 shows the dynamics of fluctuations of transfers, public debt, and budget surplus in partial equilibrium after a 20% permanent increase in oil prices. For higher values of the parameter γ_{Tr}, the model generates periodic fluctuations. With the chosen parameters, the transitions of the fiscal sector indicators turn out to be reasonable. With a lower value, the national debt converges to its steady state in about 100 years.
Lump sum transfers, government debt, and budget surplus at different values of the rule parameters for transfers.
Source: Authors’ calculations.
As in
It is assumed that the process of income generation is described by a first order autoregression, which is then approximated by a discrete process based on the method proposed in
In papers that use general equilibrium models with the entrepreneurial sector, the transition matrix and the state vector for entrepreneurial ability are calibrated to reflect given moments of the distribution, since there are no suitable microdata or estimates. For example, in
Thus, an agent’s entrepreneurial ability can take two values: zero and some positive number θ_{1}. The transition matrix is of dimension 2 × 2, and the sum of the elements in each row must equal one.
That is, two more elements must be calibrated for the transition matrix. Thus, four parameters, namely the subjective discounting factor β, the parameter of the production function in the entrepreneurial sector ν, entrepreneurial ability θ_{1}, the transition matrix elements p^{θ}_{11} and p^{θ}_{22}, were calibrated so that the model reproduces the actual data from the Russian economy presented in Table
Description  Model, %  Data, %  Data source 
Share of household consumption in GDP  60  ≈ 50  GDP by expenditure data 
Share of entrepreneurs in the total employed population  10  5  RBC citing Sberbank^{a)}; Rosstat 
Share of entrepreneurs’ income  23.6  20–22  Rosstat 
Exit rate for entrepreneurs  18.8  15  Rosstat 
The transition matrix element p^{θ}_{22} strongly affects the exit rate from entrepreneurship, as it determines the loss of entrepreneurial ability. According to Rosstat,^{8} the official liquidation rate for organizations ranged from 9.8% to 17.2% in 2017–2022 with an average of 13.9%. Taking into account rounding, this parameter was calibrated at 15%. In
The second value of the transition matrix p^{θ}_{11} was calibrated so that the model reproduces the share of entrepreneurs in the total employed population. Thus, the transition matrix for entrepreneurial ability looks as follows:
The entrepreneurial ability parameter θ_{1} was calibrated so that in the baseline steady state the price of entrepreneurial goods approximately equals 1.
In the baseline scenario, all exogenous prices are set at 1, and tax rates are set at the same level as the corresponding rates in the Russian economy (see Table
Variable values  Variable description 
τ^{c} = 0.2  Consumption tax 
τ^{wh} = 0.13  Payroll tax 
τ^{wf} = 0.3  Social security contribution rate 
τ^{nc,r} = 0.06  Income tax rate for entrepreneurs who have chosen the “Income” regime (j = 0) 
τ^{nc,π} = 0.15  Income tax rate for entrepreneurs who have chosen the “Income minus expenses” regime (j = 1) 
τ_{t}^{K} = 0.2  Profit tax for corporate firms 
τ_{t}^{O} = 0.55  The average tax burden on oil and gas exports 
Scenario 1: export price shock. In the first scenario, oil prices increase by 20% and prices of export goods increase by 10%. This scenario can be interpreted as an increase in global business activity, which leads to an increase in demand for both oil and other exports.
Scenario 2: redistribution of government expenditures between the corporate and entrepreneurial sectors. As mentioned above, the share of government consumption in GDP is stable at around 18%. The baseline version of the model assumed that the government does not buy entrepreneurial goods, i.e., γ_{Gnc} = 0, γ_{Gc} = 0.18. The experiment 2 consisted of redistributing government spending between the corporate and entrepreneurial sectors: γ_{Gnc} = 0.03, γ_{Gc} = 0.15.
Scenario 3: relaxation of collateral requirements. This scenario consists of relaxing the credit constraint (29) for entrepreneurs, namely increasing the parameter d from 0.5 to 0.75. It is important to note that the model does not consider the possibility of default for entrepreneurs. An example of such a policy is the National Guarantee System, created to make access to credit for small and mediumsized enterprises easier.
Scenario 4: credit rate subsidy for entrepreneurs. This experiment consists of reducing the parameter ϕ by 0.01, that is, loans for entrepreneurs become cheaper. The government bears the costs of credit subsidies, which is reflected in its budget constraint. The cost is equal to the sum of entrepreneurial loans multiplied by 0.01.
Scenario 5: VAT for entrepreneurs. In this scenario, entrepreneurial goods are taxed at a rate τ^{nc} = 0.2, which is equivalent to imposing a valueadded tax on consumption goods of the entrepreneurial sector.
Stationary equilibria were computed for all scenarios. The results are presented in Table
Variable  (1)  (2)  (3)  (4)  (5) 
Lumpsum transfer  14.1  0.8  –0.2  –0.7  15.2 
Price of entrepreneurial goods for the domestic market  9.6  1.8  –1.6  –0.7  –0.6 
Price of entrepreneurial goods  9.7  1.5  –1.4  –0.6  –0.5 
Household consumption  4.6  1.0  –0.2  0.0  –1.8 
Entrepreneurial output  1.9  11.5  1.4  0.7  –10.1 
Entrepreneurial labor  0.0  11.0  –0.1  0.1  –8.4 
Entrepreneurial capital  3.9  11.4  4.6  2.7  –10.4 
Number of entrepreneurs  2.5  0.5  –0.1  0.0  –1.8 
Entrepreneurial taxes  11.8  13.2  0.0  0.1  –10.5 
Entrepreneurial output for the domestic market  1.9  –1.0  1.4  0.7  –10.1 
Exports of the entrepreneurial sector  2.0  –1.3  1.7  0.8  –10.0 
Output in exportable sector  –5.6  –2.0  5.6  0.8  27.2 
Output in nontradable sector  1.9  –5.2  –0.1  0.0  2.1 
Capital in exportable sector  –3.0  –2.5  6.0  1.0  27.3 
Capital in nontradable sector  4.6  –5.6  0.3  0.2  2.3 
Labor in exportable sector  –6.9  –1.8  5.4  0.7  27.1 
Labor in nontradable sector  0.5  –4.9  –0.3  –0.1  2.0 
Price of investment goods on the domestic market  7.1  0.4  –0.4  –0.2  –0.1 
Price of consumption goods on the domestic market  7.1  0.4  –0.4  –0.2  4.5 
Wage rate  11.6  –0.2  0.2  0.1  0.1 
GDP  12.8  0.5  0.1  0.0  2.3 
Scenario 1: export price shock. In the first scenario, the entrepreneurial sector is influenced by three effects: the negative effect of the higher wage rate, the positive effect of an increase in lumpsum transfers and assets, and the positive effect of an increase in demand.
As can be seen in Fig. 3, the increase in wages leads to a decrease in entrepreneurial output by about 1% in the short run. In the long run, however, the positive effects exceed the negative effect, but output increases by only 2%. The number of entrepreneurs increases by about 2.5%. The price of entrepreneurial goods increases immediately after the reform and then decreases to a level that exceeds the initial level by 9.7%. This is explained by the fact that the nontradable sector is bearing the adjustment costs of investment, which does not allow it to increase production quickly in order to meet the increased demand in the domestic market.
Lumpsum transfers increase by about 14%, leading to an increase in household consumption. Output of the exportable sector declines by 5.6%, while output of the nontradable sector increases by about 2%. The domestic price for both consumption and investment increases by about 7%, following an increase in export prices. The wage rate increases by about 12%.
Scenario 2: redistribution of government consumption between the corporate and entrepreneurial sectors. In the baseline scenario, government consumption of entrepreneurial goods is 0% of GDP, and in the scenario 2 it is 3% of GDP. As can be seen in Fig. 4, the subsidy to entrepreneurs leads to an increase in output, capital, and labor in the entrepreneurial sector of 10% or more. At the same time, the number of entrepreneurs increases by only 0.5% compared to the baseline scenario, i.e., entrepreneurs grow in number on average.
Transitions for experiment 2 (redistribution of government expenditures).
Source: Authors’ calculations.
Household consumption increases by 1% in the long run. GDP decreases after the reform, while in the long run it increases insignificantly by about 0.5%. This can be explained by the fact that in the transition period there is a gradual reallocation of resources from the corporate sector to the entrepreneurial sector. Wages decrease immediately after the reform, and then increase to the level of the new steady state, which is lower than the initial one.
Scenario 3: relaxation of collateral requirements. As can be seen in Fig. 6, a decrease in the maximum leverage d leads to a sharp increase in investment and capital in the entrepreneurial sector. An increase in capital leads to an increase in output. It is important to note that the total number of entrepreneurs in the model economy declines in the long run. This is due to a decrease in the price of entrepreneurial goods, caused by a sharp increase in supply from the entrepreneurial sector. As can be seen in Fig. 5, the reform causes the “hump” of the distribution to become lower and the right tail of the distribution to become thicker. Thus, the share of entrepreneurs with more capital increases.
Transitions for experiment 3 (relaxation of collateral requirements).
Source: Authors’ calculations.
GDP increases sharply immediately after the reform because of the increased demand for investment from entrepreneurs, but in the new steady state it is slightly higher than the initial value, by 0.1%. The reform leads to a slight increase in household consumption in the short run, but in the long run consumption is lower by 0.2%. This is explained by a decrease in lumpsum transfers. It is important to note that, according to the construction of the model, it is impossible to consider the possibility of default, so the results of this experiment should be interpreted carefully.
Scenario 4: credit rate subsidy for entrepreneurs. As can be seen in Fig. 7, investment in the entrepreneurial sector rises to 10% immediately after the reform, as entrepreneurs need to build up the necessary amount of capital. Then investment gradually declines to the level necessary to maintain capital at the level of the longrun steady state. At the same time, the amount of labor increases slightly by 0.1%. The prices of entrepreneurial goods fall due to lower production costs. Entrepreneurial taxes increase by 0.5% immediately after the reform, and then decrease to a level that exceeds the initial level by 0.1%. This is explained by the fact that, on the one hand, the output of the entrepreneurial sector and the number of entrepreneurs increased, while production costs decrease, which increases the tax base. On the other hand, the price of entrepreneurial goods has declined monotonically throughout the transition, reducing entrepreneurial income.
Transitions for experiment 4 (credit rate subsidy for entrepreneurs).
Source: Authors’ calculations.
Lumpsum transfers decrease because of the additional costs of financing subsidies. Household aggregate consumption changed insignificantly: immediately after the reform, consumption declined by 0.06%, and in the long run it is lower than the value in the initial steady state by about 0.02%.
Scenario 5: VAT for entrepreneurs. The introduction of a tax on entrepreneurial goods used for final consumption leads to a 10% decrease in the entrepreneurial output. As can be seen in Fig. 8, the price of entrepreneurial goods decreases immediately after the reform, but then increases to a level that is 0.5% lower than the value in the initial steady state. The number of entrepreneurs declines by 1.8%.
Household consumption declines by 1.8% despite a 15.2% increase in lumpsum transfers. This can be explained, among other things, by the fact that the price of final consumption goods in the domestic market is increasing by 4.5%. The output of the corporate sector increases. Thus, output in the nontradable sector increases by about 2%, while output of the exportable sector increases by 27.2%. As a result, GDP increases by 2.3%, despite a decline in the entrepreneurial output.
The following conclusions can be drawn from the results of our study. This paper proposes a modification of the general equilibrium model with the entrepreneurial sector in the spirit of
Five scenarios were analyzed: (1) an export price shock, (2) redistribution of government consumption between the corporate and entrepreneurial sectors, (3) relaxation of collateral requirements, (4) a credit rate subsidy for entrepreneurs, (5) VAT for entrepreneurs. Steady states were computed for the baseline scenario and scenarios 1–5. The transition dynamics from the baseline steady state to each of the five proposed scenarios were computed.
In the short run, a wage rate increase after the export price shock leads to lower output in the entrepreneurial sector. However, in the long run, the positive effects of increased demand and assets exceeded this negative effect, leading to increased output in the entrepreneurial sector. The redistribution of government consumption between the corporate and entrepreneurial sectors leads to reallocation of resources from the corporate sector to the entrepreneurial sector. The relaxation of collateral requirements leads to a sharp increase in entrepreneurial investment and capital and a decline in the number of entrepreneurs, which means that entrepreneurs become bigger. The credit rate subsidy leads to an increase in capital in the entrepreneurial sector, and then in output. The cost of subsidies leads to a decrease in lumpsum transfers, but this does not lead to a significant change in household consumption. The introduction of a valueadded tax on entrepreneurial goods leads to a redistribution of resources from the entrepreneurial sector to the corporate sector, reducing household consumption and increasing GDP.
The study was supported by the Russian Science Foundation, grant No. 217810020.