Drivers of Economic Growth of the Nizhny Novgorod Region: Modeling GRP Using Data from Twin Regions

Problem statement

In recent years, the Russian economy has faced unprecedented sanctions pressure from a number of developed countries. In these conditions, it is extremely important both at the level of the country and individual regions to determine the potential for economic growth and import substitution. To understand the available opportunities, it is necessary to study resources, their dynamics and efficiency in terms of their impact on the main production indicators (primarily gross regional product), as well as trends in the development of regions in retrospect. It is important to develop adequate approaches to its modeling, allowing assessing the impact of supply, demand, macroeconomic and institutional environment factors on its level and dynamics to identify past trends and dependencies of gross regional product.

One of the problems of modeling the regional economy is the shortness of time series based on annual indicators, i.e. insufficient observations. This is especially true for Russian regions, for which the period of market history lasts just over three decades. Moreover, before the 1998–1999 crisis, the economy was in a transitional state, developed according to other trends, and the statistics of that time are incomplete. Therefore, at present modeling is possible and appropriate based on the 2000– 2022 data. But this time interval also has its own structural breaks, mainly related to the 2008–2009 and 2014–2015 crises, the 2020 pandemic and the beginning of the SMO in 2022. In addition, due to the active development of the military and civilian sector in recent years, the economy of most regions has completed its Keynesian stage; it has become labor deficient and is in an overheated state, i.e. in a state of full employment. This means that previous trends cannot be unambiguously extrapolated to the future, which limits the forecasting possibilities. Meanwhile, the main trends of regional economies due to the rigidity (inflexibility) of sectoral, technological and institutional structures, the effects of state and path dependence remain relatively unchanged, which makes their study relevant and valuable for further analysis.

The aim of our research is econometric modeling and analysis of the gross regional product of the Nizhny Novgorod Region based on pooled time series and spatial sampling by regions of the same cluster as the Nizhny Novgorod Region.

To achieve this aim, we solved the following tasks: 1) to identify a cluster of regions similar to the Nizhny Novgorod Region in terms of GRP per capita, sectoral structure of the economy and development trends; 2) to establish the indicators that can explain the change in GRP of regions belonging to the same cluster as Nizny Novgorod region and the lags of their influence; 3) to model the region’s GRP based on panel data; to establish the nature and degree of influence of supply, demand, macroeconomic conditions and individual tools of fiscal and monetary policy on it.

Literature review

A number of studies by Russian and foreign authors are devoted to modeling and forecasting regional indicators. They used different approaches. ARIMA models (AutoRegressive Integrated Moving Average) are often used for modeling GRP and its subsequent shortterm forecasting (Peng, 2023; Jijo, 2025). The advantage of such models is the possibility to take into account previous development trends and changing volatility of the modeled indicator. In ARIMA models, the current GRP depends on its own historical trends, but exclude the factors affecting it (changing resource and demand constraints, macroeconomic conditions and regulatory tools). Therefore, a more advanced approach is the one based on the construction of ARIMAX models – with the inclusion of a number of exogenous variables (Ugoh, 2021; Haydier et al., 2023). An important limitation of both approaches, however, is the need for a large number of observations. Models of this type are better realized on high-frequency, usually monthly data, but for many socio-economic indicators official statistics do not provide them. In addition, such data often contain seasonal and institutional components.

In the case of modeling GDP, GRP and other socio-economic indicators, it is objectively necessary to operate with short time series, which does not allow taking into account all the many factors affecting them. In addition, factors often show multicollinearity. To solve these problems, foreign researchers use the principal components analysis, which allows creating composite variables through the first principal components, covering the largest variance of attributes (Dias et al., 2015; Zhemkov, 2021). In Russian studies, the problem of shortness of time series was solved in a different way – by including all or some regions with similar indicators in the sample. The selection criteria were the size of GRP, and dummy variables were introduced for regions with different levels of GRP or independent regressions were constructed (Ivchenko, 2019).

Another frequently used approach to modeling GDP and GRP is the construction of production functions in which gross product depends on labor, capital, investment and other factors. One of the most popular is the Cobb – Douglas production function (Malkina, 2015; Vavilova, Zerari, 2024; Baranov et al., 2023); it is the power-type function, which is transformed into a linear form by logarithmization, which makes it possible to apply the least squares method for its estimation. An alternative option is the construction of the R. Solow model, which can also be based on the Cobb – Douglas function, but it takes into account a limited number of factors. For example, in (Kutyshkin, 2021) the one-sector R. Solow model of economic growth is applied to simulate the gross regional product of the Yamal-Nenets Autonomous Area. There are other types of production functions, such as the function with Constant Elasticity Substitution (CES), which allows taking into account the changing relationships between factors. Due to its nonlinearity, its estimation presents certain difficulties, but sometimes methods of approximate linearization are used (Cheremukhin, Gruzdev, 2022).

The choice of the most adequate production function for modeling GRP of this or that region is an independent research task. For example, the article (Skuf’ina, Baranov, 2017) addressed the question of finding the optimal production function when modeling GRP of the regions of the North and the Arctic. The following alternatives were considered: 1) multiplicative production function; 2) Cobb – Douglas power function; 3) production function with constant elasticity of substitution. The authors concluded that the CES function is better for four of the fifteen regions under consideration and the Russian Federation as a whole, the Cobb – Douglas function is better for one region, and no function is suitable for eight regions.

There are also other approaches to modeling GRP and GDP. For example, the article (Kuznetsov, Kuligin, 2022) develops a model of gross regional product based on the finite-time scheme of the integro-differential equation using economic and mathematical methods.

One of the advanced and rather time-consuming ways of GRP modeling is a structured approach based on separate modeling of industries or sectors of the economy and subsequent synthesis of the results. The application of such an approach allowed (Eremin, 2024) determining the potential for increasing the GRP of the Novgorod Region by changing the structure of investment, taking into account the calculated multipliers for different types of industries. Another paper (Dubovik et al., 2022) uses regression modeling and the Box – Cox transformation to estimate the contribution to GRP of the Bryansk Region of three major industries – agriculture, manufacturing, wholesale and retail trade. Some studies are devoted to modeling complex economic systems with the identification of the leading sector of the regional economy – a specific industry according to OKVED (Afanas’ev, Gusev, 2023).

Another variant of the structured approach to modeling the regional product involves separate modeling of demand (consumption, investment, government purchases and net exports) and supply components and bringing them together (Lombardini, 2024) or modeling the behavior of individual types of economic entities and then synthesizing them into a single model (Jokubaitis et al., 2021).

When modeling gross product, in addition to the lack of data, authors face the problem of changing methods of calculating indicators, which often makes statistical data incomparable (Mikheeva, 2022). To solve this issue, either recalculation of indicators according to new methodologies, which is a non-trivial task, or use of correction factors or introduction of dummy variables for new periods is used.

An important research task is the selection of factors affecting GRP. Researchers are guided by both basic provisions and concepts of economic theory and available data. The final selection of variables is made on the basis of their significance, multicollinearity, etc. testing. Usually, fixed assets, fixed capital investment, employment or labor costs are considered as factors affecting GRP. For example, in (Crespo–Cuaresma et al., 2010) using Bayesian model averaging (BMA) for a class of quantile regressions, it is shown that the main determinants of real GRP growth in EU countries with country fixed effects are fixed capital investment, labor skills and initial gross domestic product per capita, but the influence of these factors is distinctive in different quantiles. Using panel data for European countries, the work (Ghosh, Samanta, 2021) tested GRP models of different specifications: with random, fixed effects, cross-sectional data and with heteroskedasticity. The model with random effects showed the best result. The authors concluded that such indicators as investment, change in labor force and budget surplus have forecasting power for GDP.

Some studies include other factors in the production functions, in addition to the traditional ones. For example, in the paper (Ivchenko, 2019), in addition to the standard ones, the author studied such determinants of GRP as social expenditures in the regional budget, the current assets of enterprises and organizations, the balance of income and expenditures of enterprises and organizations, the indicator of purchasing power of the population of the region. In the article (Zhemkov, 2021) oil prices, real exchange rate, growth rates of the world economy and short-term and long-term interest rates on loans were used as factors for the formation of scenario indicators for modeling Russia’s GDP. In the article (Zazdravnykh, 2023), an important factor for the growth of real GRP was the rise of new companies and their entry into the regional market.

Sometimes models test the impact of a specific factor on GRP. An example is the work (Fedorova et al., 2020), which studied the impact of inbound tourist flows on GRP of regions and also found positive effects of investment in fixed capital in the previous year and the volume of paid tourist services. The work (Demidova, Kamalova, 2021) investigated the spatial factor concerning the regions’ economic development, and using the methods of spatial econometrics found the impact of neighboring regions on the growth of real GRP per capita adjusted for purchasing power parity.

Based on the previous studies, in this article, we use a whole pool of indicators that presumably affect GRP of the Nizhny Novgorod Region: resource, demand, macroeconomic and institutional. We solve the problem of short time series by identifying twin regions of the Nizhny Novgorod Region, which are similar to it in terms of a number of development indicators, which is a fundamentally new approach. We also use as a principal model the extended Cobb – Douglas production function including four types of variables and without restrictions on the scale effect, combining it with the distributed lag model to account for the influence of past values of the studied variables on the current GRP.

Selection of twin regions for modeling

As we have already noted in the literature review, the lack of data in time series severely limits the ability to model and forecast the performance of each specific region on the basis of its own values. At the same time, it is not quite correct to include all regions in the analysis due to their different sectoral and technological structures, achieved level of development and trends. Therefore, in this article we single out the regions that can serve as perfect twins of the Nizhny Novgorod Region, whose data are used to expand the panel sample.

We propose the formation of twin regions according to three criteria.

• 1 . Similar GRP per capita (based on 2022 data) in the k -th region (Y_k ) and in the Nizhny Novgorod Region (Y_N ). For this purpose, their absolute difference is determined:

• 2 . Similar sectoral structure (based on 2022 data). For its analysis, we used the shares in the gross value added of the following aggregated and combined types of economic activities:

• S1    – agriculture, forestry, hunting, fishing and fish farming;

• S2    – mining;

• S3    – manufacturing industries; provision of electric power, gas and steam; air conditioning; water supply; water disposal, organization of waste collection and utilization, pollution elimination activities;

• S4    – building;

• S5    – wholesale and retail trade; repair of motor vehicles and motorcycles;

• S6    – transportation and storage; activities of hotels and catering enterprises; activities in the field of information and communication;

• S7    – financial and insurance activities; real estate activities;

• S8    – professional, scientific and technical activities;

• S9    – administrative activities and related ancillary services; public administration and military security; social security;

SY,. = abs(Yk - Yn)        (1)

S10 – education; activities in the field of health care and social services; activities in the field of culture, sports, leisure and entertainment; provision of other types of services; activities of households as employers.

To assess the proximity of two sectoral structures, a similarity index to the Nizhny Novgorod Region (region N ) is calculated for each k -th region:

SSl_kN = 10 ^L^_kl - S „, ) 2 , (2) where:

S_ki — share of the i -th aggregated industry in the GVA of the k -th region;

• I    = 1Д0 ;

• 3.    Similar development trends of the regions. For this purpose, intertemporal correlations of all basic indicators of each k-th region with the Nizhny

  Novgorod Region are calculated on the basis of annual data for 2000–2022, and their simple average (Cor_kN ) is determined.

S_Ni — share of the i -th enlarged industry in the GVA of the Nizhny Novgorod Region.

For each of the three indicators of each k -th region ( SY_kN, SSI_kN, and Cor_kN), the rank among all regions is calculated, these ranks are summed and ranked again. Then, the regions with the lowest total rank are selected among all regions. These are the regions closest to the Nizhny Novgorod Region in terms of industry structure, level of development and trends. In other words, these are twin regions, whose indicators further participate in modeling.

Table 1 presents the selected regions and their indicators.

Regional GRP modeling

The region’s GRP modeling was conducted on a panel sample, including annual data on 16 regions of the Nizhny Novgorod cluster for 2000–2022. Initially, we tested 18 explanatory variables (for significance, multicollinearity, etc.), of which 12 variables were included in the final models¹. Table 2 presents them.

Table 1. Regions of the same cluster with the Nizhny Novgorod Region and their selection indicators

Region	Yk * (rubles)	Rank	SS kN *	Rank	Cor kN	Rank	Total rank
Nizhny Novgorod Region	739,125	1	0	1	1	1	1
Novosibirsk Region	693,656	9	1.456	22	0.705	2	2
Arkhangelsk Region	722,234	5	1.379	20	0.642	18	3
Vladimir Region	585,131	29	1.136	11	0.680	4	4
Chelyabinsk Region	673,545	14	1.292	17	0.644	16	5
Kaliningrad Region	715,359	6	1.582	27	0.639	19	7
Yaroslavl Region	623,525	25	0.665	2	0.620	25	7
Kaluga Region	647,307	21	1.427	21	0.661	12	8
Rostov Region	556,629	33	1.333	18	0.672	8	10
Sverdlovsk Region	816,092	16	0.690	3	0.568	40	10
Tver Region	516,489	39	0.938	7	0.651	15	11
Kostroma Region	480,120	46	1.135	10	0.673	7	13
Tula Region	674,432	13	2.123	41	0.668	9	13
Leningrad Region	822,794	19	1.258	16	0.581	34	16
Moscow Region	901,231	30	1.200	15	0.632	24	16
Ryazan Region	566,113	32	1.007	8	0.601	29	16
* Data for 2022.

Table 2. Indicators for modeling the regional economy and their designations

Variable	Designation	Variable	Designation
Gross regional product (million rubles)	GDP	Gratuitous receipts to the consolidated budget of the constituent entity of the Russian Federation from other levels of the budgetary system (million rubles)	BR_transfers
Investments in fixed capital (million rubles)	Invest	Expenditures of the consolidated budget of the constituent entity of the RF (million rubles)	BE
Value of fixed assets at the end of the year (million rubles)	Assets	Expenditures of the consolidated budget of the constituent entity of the RF on the national economy (million rubles)	BE_econ
Average annual number of employed persons (thousand people)	Employ	Expenditures of the consolidated budget of the constituent entity of the Russian Federation on the social sphere* (million rubles)	BE_soc
Average monthly per capita cash income of the population (rubles)	Income_pc	Brent crude oil price (U.S. dollars per barrel)	Brent
Consolidated budget revenues of a constituent entity of the RF (million rubles)	BR	Average annual key interest rate of the Bank of Russia (%)	Rate
Own (tax and non-tax) revenues of the consolidated budget of the constituent entity of the RF (million rubles)	BR_own	U.S. dollar to Russian Ruble exchange rate (rubles/ U.S. dollar)	USD
* Expenditures on the following socio-cultural activities were summarized: education, health care, culture, physical culture and sports, and social policy.

A distributed lag model, ADL(q,k), was selected based on assumptions about the lag effects of a number of variables:

yt = ^ + Et=i Xj=0 bkj*k t-j + ^t, where:

• ( i = 1, k ) — exogenous variable number;

• ( j = 17q ) — lag of exogenous variable x_{k t-} j .

It is worth noting that models of this type can be built not only for time series, but also for panel data interpreted as pooled time series. The autoregressive distributed lag (ARDL) model can be used as an alternative and more advanced model. Its advantage is a more successful solution to the problem of autocorrelation of residuals and sometimes hetero-scedasticity. However, the coefficients in such a model will no longer reflect the full impact of the factors concerning the production function and therefore are less interpretable.

The model was based on the Cobb – Douglas production function, which was transformed into a linear form by logarithmization. Thus, in the above formula all variables were represented in logarithmic form. Optimal lags for exogenous variables were chosen taking into account the significance of the coefficients in the regressors and the requirements of the model to the normality of residuals.

The Wald test indicated the presence of group heteroskedasticity in the fixed effects model, while the Breusch – Pagan test indicated the presence of heteroskedasticity in the residuals of the random effects model. Also, autocorrelation in the residuals was found in both cases. To eliminate heteroscedasticity as much as possible, the models were estimated using iterative weighted least squares method with selection of weights based on maximization of the likelihood function. Table 3 presents the modeling results and the corresponding tests.

All presented in Table 3 models are significant by Fisher’s criterion, coefficient estimates are significant by Student’s criterion (and for most at the p-value < 0.001 level). The residuals are normally distributed. According to the variance of residuals (S.E. of regression), all models have high predictive power.

Table 3. ADL models of regional GRP: maximum likelihood estimates with group heteroscedasticity; dependent variable ln GDP, 16 cross sections, 352 observations

	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6
	Coefficient (standard error), significance
const	–1.456 (0.185)***	–0.975 (0.196)***	–1.226 (0.155)***	–1.326 (0.150)***	–1.268 (0.135)***	–1.399 (0.148)***
In Investt	0.132 (0.016)***	0.147 (0.017)***	0.147 (0.015)***	0.143 (0.015)***	0.129 (0.015)***	0.145 (0.015)***
In Assetst-1	0.102 (0.014)***	0.099 (0.015)***	0.092 (0.014) ***	0.097 (0.014)***	0.104 (0.013)***	0.110 (0.014)***
In Employt	0.460 (0.026)***	0.495 (0.024)***	0.437 (0.024)***	0.455 (0.024)***	0.449 (0.021)***	0.474 (0.023)***
In Income_pct-1	0.202 (0.027) ***	0.210 (0.027) ***	0.181 (0.026) ***	0.199 (0.025)***	0.204 (0.022) ***	0.210 (0.024)***
In BRt	0.175 (0.029)***	-	0.129 (0.030)***	0.104 (0.031)***	-	-
In BR_ownt-1	0.297 (0.038)***	0.293 (0.032)***	0.254 (0.036)***	0.259 (0.036)***	0.368 (0.029)***	0.324 (0.030)***
In BE_econt-1	-	0.026 (0.013)**	-	-	-	-
In BE_soct-1	–0.107 (0.034)***	-	-	-	-	-
In Brentt	0.167 (0.018)***	0.127 (0.016)***	0.149 (0.018)***	0.150 (0.018)***	0.152 (0.017)***	0.163 (0.018)***
In USDt	0.463 (0.025)***	0.454 (0.024)***	0.460 (0.024)***	0.460 (0.024)***	0.452 (0.023) ***	0.474 (0.024)***
In Ratet	-	–0.051 (0.019)***	-	-	-	-
Л In Ratet	–0.078 (0.018)***	-	–0.077 (0.018)***	–0.078 (0.018)***	–0.072 (0.017)***	–0.084 (0.018)***
Д In BRt	-	-	-	-	0.323 (0.039)***	-
Д In BEt	-	-	-	0.151 (0.045)***	-	0.204 (0.043)***
Л In BE_soct	-	0.152 (0.050)***	0.097 (0.050)**	-	-	-
Log-likelihood	447.176	433.023	444.604	447.595	462.765	443.686
Akaike criterion	–829.853	–844.045	–867.209	–873.191	–905.530	–867.371
Schwarz criterion	–855.440	–801.545	–824.709	–830.691	–866.894	–828.735
Hannan-Quinn	–872.353	–827.132	–850.296	–856.278	–890.155	–851.996
S.E. of regression	0.076	0.080	0.076	0.077	0.074	0.078
χ 2 test / Chi-square(15) p - value 1 )	46.381	45.373	45.580	48.738	56.170	52.671
	4.625e-005	6.686e-005	6.200e-005	1.933e-005	1.134e-006	4.373e-006
χ 2 test / Chi-square(2) p - value 2)	0.536	0.129	0.185	0.733	2.766	1.203
	0.765	0.938	0.912	0.693	0.251	0.548

Note: value *** p - value < 0.01; ** p - value < 0.05.

1) Likelihood ratio test for group heteroscedasticity using cross-sectional analysis. Null hypothesis: units have common error variance.

2) Test for normality of residuals. Null hypothesis: the residuals are normally distributed.

The best model is selected based on the maximum of the log likelihood function, the minimum of the Akaike, Schwartz, and Hannan – Quinn information criteria. Model 5 satisfies these criteria. However, it is inferior to all other models by the criterion of normality of residuals. According to this criterion, the best model is Model 2.

Meanwhile, the chosen method of model estimation did not allow completely overcoming heteroscedasticity in the residuals. To eliminate it, we additionally constructed the ARDL model (autoregression with distributed lag), which differs from ADL models by including lag values of the endogenous variable. Table 4 presents it.

The constructed ARDL model meets all quality criteria, moreover, it lacks heteroskedasticity and autocorrelation in the residuals. The signs at variables and their relative influence generally correspond to ADL models. Meanwhile, all the coefficients at exogenous variables are lower in absolute value because their influence was distributed to the lag variables In GDPt-1 and In GDPt-2. And hence, they cannot be interpreted as measures of factor elasticities in the production function. Meanwhile, this model fulfills a control function in our study: the compatibility of its substantive results with ADL models allows proceeding further to the interpretation of the results obtained on the basis of the traditional production function.

In general, the constructed models correspond to the main provisions of economic theory. First of all, GRP of the regions of Nizhny Novgorod cluster depends on the available production resources (labor — In Employ_t , capital — available fixed assets at the beginning of the period — In Assets_t-1 ) and their change in the current period (level of investment in fixed capital — In Invest_t ).

Table 4. ARDL model of GRP of the region: maximum likelihood estimations taking into account group heteroscedasticity; dependent variable ln GDP , 16 cross sections, 352 observations

	Coefficient	Standard error	p–value	Value
const	–0.371	0.092	< 0.0001	***
In GDPt-1	0.610	0.050	< 0.0001	***
In GDPt- 2	0.084	0.038	0.0277	**
ln Investt	0.081	0.010	< 0.0001	***
In Employt	0.142	0.013	< 0.0001	***
In BR_ownt-1	0.106	0.027	< 0.0001	***
In Brentt	0.110	0.012	< 0.0001	***
In USDt	0.237	0.021	< 0.0001	***
A In Income_pct	0.213	0.057	0.0002	***
A In Ratet	–0.046	0.015	0.0024	***
A In BRt	0.261	0.033	< 0.0001	***
Log-likelihood	548.223
Akaike criterion	–1074.445
S.E. of regression	0.050
χ 2 test / Chi-square(15) 1	21.130		0.133
χ 2 test / Chi-square(2) 2	2.493		0.287
Note. Value *** p - value < 0,01; ** p - value < 0,05. 1)    Likelihood ratio test for group heteroscedasticity using cross-sectional analysis. Null hypothesis: units have common error variance. 2)    Test for normality of residuals. Null hypothesis: the residuals are normally distributed.

Since all variables in the models are represented in logarithmic form, the coefficient estimates in ADL-models are interpreted as elasticities of GRP with respect to the corresponding exogenous variables, i.e. they show by what percentage GRP will change if this variable changes by 1%, all other things being equal. For example, a 1% change in investment in fixed capital in the current period presumably results in a 0.129–0.147% increase in GRP, ceteris paribus. And a 1% increase in employment leads to a 0.437–0.495% increase in GRP. This result is consistent with the findings of a number of other studies (Kutyshkin, 2021; Baranov et al., 2023), which also found a greater sensitivity of GRP of Russian regions to labor than to capital. At the same time, other studies have demonstrated that the coefficients of output elasticity with respect to labor and capital are different depending on the region under consideration and the period of study (Vavilova, Zerari, 2024; Skufyina, Baranov, 2017). Our result indicates the labor intensity of production in the regions of the same cluster as the Nizhny Novgorod Region (which includes regions with developed manufacturing industry) and the high significance of the problem of staff shortage under the current technological structure of the economy.

The results of modeling proved that the availability of financial resources plays an important role in increasing production in the region. The source of financial resources can be both own, budgetary, and borrowed funds. The volume, as well as the structure of revenues and expenditures of regional budgets play an important role in the regional development. In particular, the constructed models demonstrated the positive influence on the region's GRP of the consolidated budget revenues of the RF constituent entities in the current period (In BRt) and own (tax and non-tax) revenues of the consolidated budget of the RF constituent entities in the past period (InBR_ownt-1). The models also showed the average positive impact on the GRP of budget expenditures on the national economy in the past period (In BE_econt-1) and negative impact of budget expenditures on the social sphere in the past period (In BE_soct-1). At the same time, the increase in social expenditure in the current period compared to the past period (△ In BE_soct) proved to have a positive impact on the current GRP. This can be explained by the fact that social payments are an important component of the income of poorer people, who have a higher propensity to consume. In addition, social expenditures form the revenue of relevant industries and spheres of activity, contribute to the improvement of the human capital quality. The obtained result slightly corrected the estimate of the effects of social expenditures, which was previously exclusively positive (Ivchenko, 2019). This may be due both to the fact that in our case the amount of social expenditures was considered as the total amount of various spendings, and to the peculiarities of the sample of regions and modeling approaches.

As it would be expected, the models showed a positive impact of past period household income ( In Income_pc_t-1 ) on current period GRP, which is also consistent with the findings of other authors (Ivchenko, 2019; Arpitha et al., 2025). This means that, on average, in the period under consideration, regional production in the Nizhny Novgorod Region cluster depended on consumer demand, i.e., historically, regional economies were rather on the Keynesian than neoclassical segment of the supply curve.

In the constructed models, the average annual rate of the Bank of Russia ( In Rate_t ) and especially its change ( △ In Rate_t) showed a significant negative impact on the GRP of the region. Thus, the conclusion previously obtained for the Nizhny Novgorod Region (Malkina, Vinogradova, 2024) is applicable to the whole cluster. The Bank of Russia raises the interest rate to fight inflation, but the side effect of this is a slowdown in economic growth. Under tight monetary policy, nominal GRP decreases both in terms of inflationary and real components, which was reflected in the obtained coefficients.

Finally, all models showed a direct dependence of the region’s GRP on two weakly controlled macroeconomic parameters – the price of Brent oil and the exchange rate of the U.S. dollar to the Russian ruble. These parameters also turned out to be predictors in the models of Russian GDP presented in the article (Zhemkov, 2021).

Revenues from the oil sector spread throughout the Russian economy, feed the budget system, and create multiplier effects, so the impact of oil price on production in different regions (not only extractive, but also manufacturing) is positive. At the same time, the positive impact of oil price on GRP indicates a significant and permanent dependence of the Russian economy on the state of world oil markets, which, given the instability of these markets and sanctions restrictions on access to them by Russian producers, creates serious risks for regional development.

The U.S. dollar exchange rate to the ruble can be interpreted as a proxy for the price component of GRP. The exchange rate affects the prices of imported goods, the share of which in domestic consumption, according to various estimates, ranges from 24% to 40%. Via the pass-through effect, the exchange rate affects the prices of all goods. In addition, the depreciation of the national currency increases the price competitiveness of domestic production, promotes import substitution within the country and sales of domestic goods on foreign markets, as well as increasing the revenues of the budget system.

Thus, for the regions belonging to the same cluster with the Nizhny Novgorod Region, i.e. twin regions, the dependence of GRP on the factors concerning demand, supply, fiscal and monetary policy tools, as well as a number of poorly controlled macroeconomic factors has been proved, the direction and degree of influence of these factors have been established.

Conclusion

In this paper, we have modeled GRP of the Nizhny Novgorod Region using the data of twin regions. The literature analysis has shown different approaches to modeling the main socio-economic indicators of the region: the construction of time series models such as ARIMA and ARIMAX, models with fixed and random effects based on panel data, the construction of production functions of various types, aggregated models. The choice of one or another model depends on the structure of the data. Important problems in modeling are also the choice of explanatory factors (based on theoretical concepts and available data) and overcoming the problem of shortness of time series.

The latter problem can be solved in different ways. In the present study, an approach to increase the number of observations by including data from twin regions in the model is proposed and implemented. Regions of the same cluster as the Nizhny Novgorod Region were selected according to three criteria: GRP per capita, similar sectoral structure of the economy, similar development trends. As a result, a panel sample of 16 industrialized regions with time series for 2000– 2022 was formed.

To model GRP of the cluster regions of the Nizhny Novgorod Region, the Cobb – Douglas production function with a distributed lag (ADL) was constructed, which was estimated by the method of iterative weighted ordinary least squares (OLS) with selection of weights based on maximization of the likelihood function. As a result, non-contradictory and partially complementary six models with high explanatory power were obtained. The models are significant by Fisher’s criterion, the estimates of all coefficients are significant by Student’s criterion, and the residuals of the models are distributed according to the normal law. To eliminate heteroscedasticity and autocorrelation of the residuals, they were supplemented by the construction of ARDL model, which led to the results that were consistent with ADL models.

The constructed models confirmed the greater dependence of GRP of the regions of the cluster under consideration on the labor factor than on the capital factor in the form of accumulated funds and current investments. This means that labor deficit imposes significant limitations on economic growth, the way to overcome it is the development of technological structures that contribute to increasing the capital intensity of national income and capital-labor ratio.

The positive impact on GRP of the state of the budget sphere of the region and the amount of support of the regional economy from the consolidated budget of the subject of federation is proved. At the same time, the ambiguous role of social expenditures has been established: on the one hand, their relatively large value is observed in regions with lower GRP, on the other hand, the increase in these expenditures can have a positive effect on the regional product through the formation of demand for the products of different sectors of the economy. Also, an important driver of economic growth in the region on the demand side is the increase in personal income, behind which, of course, there are other factors. A more precise determination of the relationship between population income and GRP requires the construction of more complex models with forward and backward linkages, probably based on a system of simultaneous equations.

In addition to fiscal policy tools, the models showed the negative impact of the key interest rate of the Bank of Russia and its increase on the GRP of the regions under consideration. Finally, they confirmed the persistent dependence of the economies of the regions under study on oil prices and the ruble-dollar exchange rate.

Thus, GRP of the regions of the same cluster as the Nizhny Novgorod Region is explained by resource, demand constraints, institutional and macroeconomic environment. The obtained results indicate the relative importance of these factors, the effectiveness of different measures of governance, reveal the weaknesses and growth reserves of regional economies. They can be useful in elaboration of a balanced regional development policy in Russian regions specializing in the manufacturing industry and having a sufficiently diversified sectoral structure, such as the Nizhny Novgorod Region.

Further research development is possible through the better specification of models, their construction using high-frequency data of other indicators, creation of structured models (modeling of GRP by types of economic activity or demand components), separate modeling of inflationary and real growth components, use of the principal component analysis to aggregate the influence of a larger number of variables. The refinement of models and approaches in the future will make it possible to develop more balanced approaches to short-term forecasting of GRP and other indicators of socio-economic development of regions.