Multi-dimensional research and quantitative evaluation of export potential of Dezhou smes to Central Asia based on multi-level regression model under the background of China-Kyrgyzstan-Uzbekistan Railway

With the social and economic development, the position of small and medium-sized enterprises (SMEs) in the national economy has gradually risen, so SMEs have received great attention from governments, and the understanding of SMEs has become more in-depth [1]. The development of SMEs has a greater contribution to providing jobs [2], absorbing labor [3], and increasing economic growth [4]. The contribution to the improvement of the economy is manifested in the promotion of the increase of the total economy, optimization of industrial structure, development of foreign trade, and improvement of the living standard of the residents [5-7]. In addition, small and medium-sized enterprises provide a large number of supporting services for large enterprises and promote cooperation between large enterprises [8-9]. All of the above has become an important motive for the government to support and develop SMEs.

Recently, the signing ceremony of the intergovernmental agreement between the three countries of the China-Kyrgyzstan-Uzbekistan railroad project was held in Beijing. The railroad project starts from Kashgar, Xinjiang, China, and enters Uzbekistan through Kyrgyzstan, and is expected to extend to West and South Asia in the future [10]. The completion of the railroad will greatly promote the connectivity between the three countries, and also become a key to China’s land transportation and logistics corridor [11-12]. Kyrgyzstan and Uzbekistan are the core areas of the Silk Road Economic Belt [13-14]. Kyrgyzstan and Uzbekistan are underdeveloped countries, with agriculture as the mainstay industry, a single industrial structure, and a weak industrial base, and are currently unable to have the ability to start and develop large-scale enterprises [15-18]. Influenced by the reality of Kyrgyzstan and Uzbekistan’s poor development of large enterprises, the entry of Chinese SMEs will become an inevitable choice to promote local economic growth, which creates favorable space for the export development of domestic SMEs [19-22]. frontier gravity model and the trade inefficiency model as the main research tools, this paper quantitatively evaluates the trade potential of small and medium-sized enterprises (SMEs) exporting from Dezhou to the five Central Asian countries in the context of the China-Kyrgyzstan-Uzbekistan Railway. First, the trade status quo of China’s exports to the five Central Asian countries is analyzed, and then relevant variables are set and an initial model is constructed. Then, the model is tested and corrected to obtain the final model, and the influencing factors of the export trade of Dezhou SMEs to the five Central Asian countries are analyzed. Finally, on the basis of analyzing the trade efficiency of Dezhou SMEs exporting to the five Central Asian countries, it realizes the measurement of their trade potential and the space for potential enhancement.

2

Analysis of the current situation of China’s export trade to the five Central Asian countries

Before analyzing the export potential of Dezhou SMEs in Central Asia in the context of the China-Kyrgyzstan-Uzbekistan Railway, this paper explores the current trade situation of China’s exports to the five Central Asian countries.

2.1

Scale of exports

China’s exports to the five Central Asian countries from 2013 to 2023 are shown in Figure 1. From the point of view of trade scale, China’s exports to the five Central Asian countries in 2013-2023 show significant growth, China’s exports to the five Central Asian countries in 2013 amounted to 21.302 billion U.S. dollars, and in 2023 it will be 61.754 billion U.S. dollars, and the scale of the exports nearly doubled nearly two times, especially in the period of 2020-2023, the scale of which is rapidly growing, with an average annual growth rate of 44.88%.

2.2

Export market share

China’s exports to the five Central Asian countries from 2013 to 2023 and its share of the total are shown in Table 1, the values in the table are in billion dollars. From 2013 to 2023, China’s exports to Kazakhstan in general show a significant upward trend, the export value of $24.834 billion in 2023, compared with the export value in 2013 more than doubled, but the market share of the market shows a downward trend. China’s exports to Kyrgyzstan show a significant overall increase, to $19.746 billion in 2023, compared to $4.358 billion in 2013, and its market share of Kyrgyzstan also shows an overall increase. China’s exports to Uzbekistan will be $12.447 billion in 2023, compared to $2.601 billion in 2013, nearly quadrupling in a decade. China’s export market share to Tajikistan and Turkmenistan is relatively small.

Table 1.

China’s exports to the five Central Asian countries from 2013 to 2023

Country	2013	2015	2017	2019	2021	2023
Kazakhstan	113.67	80.09	102.35	114.35	130.87	248.34
Kazakhstan	53.36%	48.58%	51.44%	46.60%	48.22%	40.21%
Kyrgyzstan	43.58	35.94	50.24	58.63	63.76	197.46
Kyrgyzstan	20.46%	21.80%	25.25%	23.89%	23.49%	31.97%
Tajikistan	18.54	18.06	13.27	15.16	15.85	37.39
Tajikistan	8.70%	10.96%	6.67%	6.18%	5.84%	6.06%
Turkmenistan	11.22	8.41	3.89	4.24	5.01	9.88
Turkmenistan	5.27%	5.10%	1.95%	1.73%	1.85%	1.60%
Uzbekistan	26.01	22.36	29.23	53.1	55.93	124.47
Uzbekistan	12.21%	13.56%	14.69%	21.60%	20.60%	20.16%
Total	213.02	164.86	198.98	245.39	271.42	617.54
Total	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%

2.3

Export product mix

A comparison of China’s exports to the five Central Asian countries in the top five product categories in 2013 and 2022 is shown in Table 2. From 2013 to 2022, China’s exports to Kazakhstan consist of 3,442 types of products, and the product categories have basically remained stable, with clothing, footwear, toys, camcorders, and cameras dominating the top five products exported to Kazakhstan. China’s exports to Kyrgyzstan are more than 2,600 kinds of products, and the product categories are slowly increasing, in the top five exports of products, mainly clothing and footwear and other textile products. China’s exports to Tajikistan showed rapid growth during this period, nearly doubling in assortment, with textiles, steel, body parts and lighting fixtures dominating the top five export categories. China’s exports to Turkmenistan numbered over 1,300 product categories, and the number of product categories is slowly increasing, with steel pipes, rubber tires, and agricultural equipment dominating the top five export categories. China’s exports to Uzbekistan showed rapid growth during this period, with steel, vehicles, primary chemicals, cameras and camcorders dominating the top five export categories. While China’s top five exports to Uzbekistan in 2013 were essentially steel, its top five exports in 2022 have shifted considerably, with a gradual shift to primary chemicals and vehicles, as well as cameras and camcorders.

Table 2.

The top five categories of products exported by China to the Central Asian countries

Country	2013				2022
Country	Product category quantity	Product code	Amount ($100 million)	Share (%)	Product category quantity	Product code	Amount ($100 million)	Share (%)
Kazakhstan	3442	870423	1.88	1.65	3410	620193	3.82	2.16
		730420	2.10	1.85		847193	3.82	2.16
		730519	2.48	2.18		950390	5.09	2.88
		640299	5.06	4.45		620293	6.41	3.63
		847120	6.57	5.78		852520	6.63	3.76
Kyrgyzstan	2608	611030	1.41	3.24	2725	620462	5.14	4.64
		630260	1.62	3.72		611030	5.72	5.17
		540752	1.85	4.25		620193	6.81	6.15
		600192	2.04	4.68		640299	6.87	6.20
		521019	2.37	5.44		620293	10.49	9.47
Tajikistan	1483	630260	0.48	2.59	2659	940540	0.44	1.85
		730830	0.49	2.64		621210	0.53	2.23
		640510	0.52	2.81		870899	0.62	2.61
		610423	0.60	3.24		721070	0.71	2.99
		701339	0.64	3.45		640299	0.95	4.00
Turkmenistan	1398	841510	0.29	2.59	1624	510820	0.17	2.35
		842139	0.35	3.12		852810	0.21	2.90
		848180	0.39	3.48		401120	0.24	3.32
		847120	0.44	3.92		300220	0.28	3.87
		730420	0.96	8.56		860210	0.36	4.97
Uzbekistan	2232	721049	0.68	2.61	3341	852810	0.95	1.19
		730420	0.68	2.61		870323	0.96	1.20
		721070	0.75	2.88		390760	1.15	1.44
		730511	0.76	2.92		870390	1.48	1.85
		730519	1.94	7.46		852520	2.66	3.33

3

Empirical Analysis of the Factors Influencing the Exports of Small and Medium-sized Enterprises to Central Asia in Dezhou

On the basis of the current situation of China’s export trade to the five Central Asian countries, this paper comprehensively applies the stochastic frontier gravity model and the trade inefficiency model to analyze the relevant factors affecting the export trade of small and medium-sized enterprises (SMEs) from Dezhou to Central Asia.

3.1

Theoretical models

3.1.1

Stochastic Frontier Gravity Modeling

The stochastic frontier analysis (SFA) method [23] was originally used to analyze the technical efficiency problem in the production function in the following form: (1) $T_{i j t} = f (X_{i j}, β) \exp (v_{i j t} - u_{i j}), u_{i j} \geq 0$ ${T_{ijt}} = f\left( {{X_{ij}},\beta } \right)\exp \left( {{v_{ijt}} - {u_{ij}}} \right),{u_{ij}} \geq 0$ (2) $\ln T_{i j t} = \ln f (X_{i j}, β) + v_{i j t} - u_{i j}, u_{i j t} \geq 0$ $\ln {T_{ijt}} = \ln f\left( {{X_{ij}},\beta } \right) + {v_{ijt}} - {u_{ij}},{u_{ijt}} \geq 0$

Where T_ijt denotes the real export trade volume from country i to country j in period t. X_ijt denotes the natural factors acting on bilateral trade volume in the stochastic frontier analysis method, such as GDP per capita, market size, geographical distance and other variables. β is the vector of coefficients to be estimated. v_ijt is the stochastic disturbance term, obeying the normal distribution $N (0, σ_{v}^{2})$ $N\left( {0,\sigma_v^2} \right)$. u_ijt is the trade inefficiency term, obeying the half-normal distribution or truncated half-normal distribution, and v_ijt do not affect each other, because u_ij is usually assumed to be non-negative, so u_ijt represents the trade resistance caused by the artificial exogenous variables other than the natural factors in the stochastic frontier gravity model, and the impact of these artificial exogenous variables on trade will be estimated by the trade inefficiency model.

The formula for calculating trade potential is shown below: (3) $T_{i j t}^{*} = f (X_{i j t}, β) \exp (v_{i j t})$ $T_{ijt}^* = f\left( {{X_{ijt}},\beta } \right)\exp \left( {{v_{ijt}}} \right)$

Equation (3) in $T_{i j t}^{*}$ ${T_{ijt}}^*$ for the trade potential, said t period i countries to j countries in the ideal state, that is, trade without any resistance to the optimal state can be achieved, this ideal state in real life usually does not exist, because the reality of trade will always exist in the trade resistance, big or small.

The formula for calculating trade efficiency is shown below: (4) $T E_{i j t} = \frac{T_{i j t}}{T_{i j t}} = \frac{f (X_{i j t}, β) \exp (v_{i j t} - u_{i j t})}{f (X_{i j t}, β) \exp (v_{i j t})} = \exp (- u_{i j t})$ $T{E_{ijt}} = \frac{{{T_{ijt}}}}{{{T_{ijt}}}} = \frac{{f\left( {{X_{ijt}},\beta } \right)\exp \left( {{v_{ijt}} - {u_{ijt}}} \right)}}{{f\left( {{X_{ijt}},\beta } \right)\exp \left( {{v_{ijt}}} \right)}} = \exp \left( { - {u_{ijt}}} \right)$

Equation (4) in TE_ijt is the trade efficiency, is the reality of the true level of trade T_ijt and the ideal state of the trade potential T_ijt^* of the quotient, TE_ijt is the exponential function of u_ijt, according to the value of TE_ijt, and then measure the gap between the reality of the state of the trade under study and analysis and the potential for trade. When u_ijt = 0, TE_ijt = 1, there is no trade resistance in such trade, i.e., the ideal state of trade is reached and the frontier level of trade is realized. When u_ijt > 0, TE_ijt ∈ (0, 1), there is trade resistance in such a trade state, which is more in line with the reality, and at the same time, when the trade resistance is large, it causes the trade efficiency to be low, and when the trade resistance is small, the trade efficiency is kept at a high level.

The stochastic frontier gravity model can be expressed by the formula as: (5) $u_{i j t} = {\exp [- η (t - T)]} u_{i j}$ ${u_{ijt}} = \{ \exp [ - \eta (t - T)]\} {u_{ij}}$

In equation (5), exp[− η(t − T)] ≥ 0 and u_ij follow a truncated half-normal distribution, and η is the parameter to be estimated to test for time variability, reflecting the trend of u_ij over time.

As can be seen from equation (5), if η > 0, it reflects that u_ijt gradually decreases over time, i.e., the trade environment continues to improve, trade friction tends to weaken: if η < 0, it reflects that u_ijt gradually increases over time, i.e., the trade environment continues to deteriorate, trade friction plus huge. If η = 0, u_ijt is fixed in both the long and short run, the model is transformed into a time-invariant stochastic frontier model.

3.1.2

Models of trade inefficiency

The trade inefficiency model is constructed to study the impact of trade resistance on trade efficiency generated by various anthropogenic exogenous variables, and the model can be estimated by a one-step method, u_ij in the specific form: (6) $u_{i j t} = α' Z_{i j} + ε_{i j}$ ${u_{ijt}} = {\alpha^\prime} {Z_{ij}} + {\varepsilon_{ij}}$

The meaning of the variables in the formula is that α is the vector of coefficients to be estimated, Z_ijt is the human exogenous variable affecting u_ijt, ε_ijt is the random error term, and the one-step method is to regress all the variables affecting the trade efficiency at the same time, so substituting Eq. (6) into Eq. (2) can be obtained: (7) $\ln T_{i j t} = \ln f (X_{i j t}, β) + v_{i j t} - (α' Z_{i j} + ε_{i j t})$ $\ln {T_{ijt}} = \ln f\left( {{X_{ijt}},\beta } \right) + {v_{ijt}} - \left( {\alpha^ \prime {Z_{ij}} + {\varepsilon_{ijt}}} \right)$

The meaning of the variables in the formula is that u_ijt obeys a truncated half-normal distribution with mean α′Z_ij, and that u_ijt and v_ij do not affect each other.

3.2

Model Setting and Description of Variables

3.2.1

Stochastic Frontier Gravity Model Setting

In order to estimate the trade potential of Dezhou SMEs exporting to Central Asia under natural variables, this paper constructs a model as shown in equation (8) to carry out the study: (8) $\begin{array}{rcl} I n E X P_{i j t} & = & β_{0} + β_{1} P C G D P_{i j} + β_{2} P C G D P_{p} + β_{3} I n P O P_{i t} \\ + β_{4} I n P O P_{j t} + β_{5} I n D I S_{i j} + β_{6} X_{i j} + V_{i j t} - u_{i j t} \end{array}$ $\begin{array}{rcl} InEX{P_{ijt}} &=& {\beta_0} + {\beta_1}PCGD{P_{ij}} + {\beta_2}PCGD{P_p} + {\beta_3}InPO{P_{it}} \\ &&+ {\beta_4}InPO{P_{jt}} + {\beta_5}InDI{S_{ij}} + {\beta_6}{X_{ij}} + {V_{ijt}} - {u_{ijt}} \\ \end{array}$

In the model set up in this paper, subscript i denotes Chinese SMEs in Dezhou and subscript j denotes the five Central Asian countries. In equation (8), the explanatory variable EXP_ij denotes the export value of the SMEs in Dezhou to the j countries in period t. The explanatory variables are those in the classical trade gravity model. 1)

where PCGDP_it and PCGDP_ji denote the per capita GDP of China and j countries respectively in period t, reflecting a country’s degree of economic development, demand level characteristics and factor endowment, etc., which are usually considered to be positively correlated with EXP_ij.

2)

POP_it and POP_ji denote the total population of Dezhou and j China in period t, representing the size of the domestic and export markets, respectively, and are usually assumed to be positively correlated with EXP_ij.

3)

DIS_ij represents the geographic distance between the capitals of China and j Dezhou, where an increase in geographic distance increases the cost of moving goods in trade and is expected to be EXP_ij negatively correlated.

4)

X_ij is a variety of other factors, including the common border BORD_ij, common language LANG_ij, etc. Given the stochastic frontier gravity model is more strict on the functional form requirements, whether to introduce the above factors will be determined by the likelihood ratio test.

3.2.2

Modeling trade inefficiencies

In this paper, artificial exogenous factors such as tariffs and trade agreements are introduced into the trade inefficiency model to estimate the trade resistance between the two countries’ trade, based on which the trade inefficiency model is constructed as shown in equation (9) [24]. In-depth analysis of exogenous variables of China Dezhou SMEs’ export trade inefficiency to Central Asian countries along the China-Kyrgyzstan-Uzbekistan railroad, and a one-step method is adopted to estimate Eq. (9). Namely: (9) $\begin{array}{rcl} u_{i j t} & = & α_{0} + α_{1} T A F_{j t} + α_{2} I N F_{j t} + α_{3} S H P_{j t} + α_{4} E O C_{j t} + α_{5} T F_{j t} \\ + α_{6} W T O_{i j t} + α_{7} F T A_{i j t} + ε_{i j t} \end{array}$ $\begin{array}{rcl} {u_{ijt}} &=& {\alpha_0} + {\alpha_1}TA{F_{jt}} + {\alpha_2}IN{F_{jt}} + {\alpha_3}SH{P_{jt}} + {\alpha_4}EO{C_{jt}} + {\alpha_5}T{F_{jt}} \\ &&+ {\alpha_6}WT{O_{ijt}} + {\alpha_7}FT{A_{ijt}} + {\varepsilon_{ijt}} \\ \end{array}$

In equation (9), the explanatory variable u_ijt is the trade inefficiency term, which measures the magnitude of the trade resistance of various man-made exogenous variables to the exports of Dezhou SMEs to Central Asia. The explanatory variables are explained as follows: 1)

Explanatory variable TAF_jt is the share of import tariffs on products from importing countries in national tax revenues, which measures the tariff level of the importing country, and the higher tariff level of the importing country increases the cost of exporting the products of small and medium-sized enterprises in Dezhou and adversely affects the improvement of the efficiency of exporting their products, which is expected to be positively correlated with u_ijt.

2)

INF_jt is the quality of trade and transportation infrastructure indicators, reflecting the degree of improvement of the transportation infrastructure of the countries along the route, if the importing country has good transportation infrastructure, it will help the import of Dezhou SMEs’ products, which is expected to be negatively correlated with u_ijt.

3)

Liner transportation connectivity index $(S H P)$ $\left( {SHP} \right)$ reflects the degree of connectivity between countries and the global shipping network, the importing country has a convenient shipping connectivity network, can reduce the export cost of Dezhou small and medium-sized products, is expected to be negatively correlated with u_ij.

4)

The efficiency of customs clearance procedures $(E O C)$ $\left( {EOC} \right)$ reflects the speed of customs clearance and the simplicity of customs procedures in importing countries, and the simplicity of customs clearance procedures in importing countries can help to improve the export efficiency of Dezhou SMEs’ products, which is expected to be negatively correlated with u_ijt.

5)

The degree of trade freedom $(T F_{j t})$ $\left( {T{F_{jt}}} \right)$ reflects the height of international trade barriers, belonging to the economic system factors, the greater the value of freedom, the more frequent trade between the two countries.

6)

WTO_ijt is a dummy variable indicating whether the importing country is a member of the WTO. If it is, it is assigned a value of 1, if it is not, it is assigned a value of 0. If the two countries are members of the same trade organization, it is conducive to promoting the trade of products between the two countries, and it is expected to be negatively correlated with u_ijt.

7)

FTA_ijt is a dummy variable indicating whether China has signed free trade agreements with countries along the route. In this paper, FTA_ijt refers to whether it is a member of the Shanghai Cooperation Organization (SCO), if it is, the value is 1, if it is not, the value is 0. The signing of a free trade agreement will help to reduce the export tax rate of the products of small and medium-sized enterprises (SMEs) in Dezhou and improve the export efficiency of the products of SMEs in Dezhou to the countries along the Sino-Japanese-Ukraine Railway, and it is expected to be negatively correlated with u_ig.

3.3

Sample size and data sources

Export value of Dezhou SME products is derived from the Monthly Statistical Report on Agricultural Products of the Ministry of Commerce of China. Per capita GDP and population totals are from the World Bank WDI database, with per capita GDP in real terms in constant 2010 dollars. The DIS data are derived from the CEPII distance database, with the data being the straight-line geographic distance between the capitals of the two countries.

In addition, data on TF (trade freedom), TAF (import tariffs as a share of national tax revenues), INF (trade and transportation infrastructure quality indicators) and EOC (efficiency of customs clearance procedures) were obtained from the World Bank WDI database. Data on SHP (Liner Shipping Interoperability Index) are from the United Nations Conference on Trade and Development Report (UNCTAD database). The data on the membership of WTO the liner shipping industry is obtained from the official website of WTO the liner shipping industry. Data on FTA (free trade agreements with China) are from the official website of the Ministry of Commerce of the People’s Republic of China.

3.4

Empirical results and analysis

In this section, we first conduct correlation analysis and multiple covariance test on the proposed selection variables, and conduct applicability and robustness test on the relevant variables in the SFA model and the trade inefficiency model to explore the influencing factors of SMEs’ export trade in Dezhou to the countries along the Sino-Japanese-Ukraine Railway.

3.4.1

Model testing

1)

Correlation analysis

In this paper, the correlation analysis of each variable is carried out first [25]. The results of the correlation test between the variables using Python software are shown in Figure 2. Among them, POP and DIST are logarithmized, and PCGDP and POP are the product of the corresponding variables between China and the trading partner countries along the route. The results show that the correlation between geographic distance (DIS) and the level of infrastructure (INF) of the trading partner countries, and the correlation between trade freedom (TF) and the free trade agreement (FTA) of the trading bilaterals is relatively high, respectively 0.65 and 0.61, but the absolute value is less than 0.7, which is a low correlation, and thus it is judged that there is no serious correlation between the variables.

2)

Multicollinearity test

On the basis of determining that there is no serious correlation between the variables, this paper further confirms whether there is multicollinearity between the variables through the Variance Inflation Factor (VIF), and the results of the Variance Inflation Factor test are shown in Table 3. The results show that the maximum VIF value is the logarithmic value of geographic distance (InDIS) 3.263, which is less than the critical value of 10, therefore, it is determined that there is no multicollinearity problem among the variables.

3)

Applicability test

After verifying that there is no multicollinearity among the variables, this paper adopts the likelihood ratio test to test whether there is a trade inefficiency term in the export trade of Chinese SMEs from Dezhou to the countries along the China-Kyrgyzstan-Uzbekistan Railway, as well as whether there is a time-varying characteristic. In addition, it is also necessary to test whether the two introduced dummy variables (i.e., common language and common border) are significant to determine the basic form of the stochastic frontier gravity model. Similarly, this paper tests seven variables in the trade inefficiency model to determine the final form of the model. (1)

Likelihood Ratio Hypothesis Testing for the Stochastic Frontier Gravity Model

The original hypotheses and test results of the four types of likelihood ratio tests for the SFA model are shown in Table 4.

In this hypothesis test, the original hypothesis should be rejected when the LR statistic is greater than the 1% chi-square critical value. The results of the study show that the first three tests are rejected, indicating that the existence of trade inefficiency factors is time-varying. Therefore, the study should adopt the time-varying SFA model. Meanwhile, the hypothesis of not introducing a common border variable is rejected, so the variable should be introduced in the model. Whereas, the hypothesis test of not introducing the common language variable fails the test and therefore the variable should not be introduced in the model. Therefore, the basic form of the model is: (10) $\begin{array}{rcl} I n E X P_{i j t} & = & β_{0} + β_{1} P C G D P_{i t} + β_{2} P C G D P_{j t} + β_{3} I n P O P_{i t} \\ + β_{4} I n P O P_{j t} + β_{5} I n D I S_{i j} + β_{6} B O R D_{i j} + V_{i j t} - u_{i j t} \end{array}$ $\begin{array}{rcl} InEX{P_{ijt}} &=& {\beta_0} + {\beta_1}PCGD{P_{it}} + {\beta_2}PCGD{P_{jt}} + {\beta_3}InPO{P_{it}} \\ &&+ {\beta_4}InPO{P_{jt}} + {\beta_5}InDI{S_{ij}} + {\beta_6}BOR{D_{ij}} + {V_{ijt}} - {u_{ijt}} \\ \end{array}$

(2)

Hypothesis testing of likelihood ratio of trade inefficiency model

The results of the hypothesis tests for the seven variables in the trade inefficiency model are shown in Table 5.

All seven hypothesis tests conducted in Table 5 rejected the original hypothesis, indicating that each variable has a significant effect on the trade inefficiency term. Therefore, the final form of the model is: (11) $\begin{array}{rcl} I n E X P_{i j t} & = & β_{0} + β_{1} P C G D P_{i t} + β_{2} P C G D P_{j t} + β_{3} I n P O P_{i t} + β_{4} I n P O P_{j t} \\ + β_{5} I n D I S_{i j} + β_{6} B O R D_{i j} + v_{i j t} - [- η (t - T) (α_{0} + α_{1} T A F_{j t} \\ + α_{2} I N F_{j t} + α_{3} S H P_{j t} + α_{4} E O C_{j t} + α_{5} T F_{j t} + α_{6} W T O_{i j t} \\ + α_{7} F T A_{i j t} + ε_{i j t})] \end{array}$ $\begin{array}{rcl} InEX{P_{ijt}} &=& {\beta_0} + {\beta_1}PCGD{P_{it}} + {\beta_2}PCGD{P_{jt}} + {\beta_3}InPO{P_{it}} + {\beta_4}InPO{P_{jt}} \\ &&+ {\beta_5}InDI{S_{ij}} + {\beta_6}BOR{D_{ij}} + {v_{ijt}} - \left[ { - \eta \left( {t - T} \right)} \right.\left( {{\alpha_0}} \right. + {\alpha_1}TA{F_{jt}} \\ &&+ {\alpha_2}IN{F_{jt}} + {\alpha_3}SH{P_{jt}} + {\alpha_4}EO{C_{jt}} + {\alpha_5}T{F_{jt}} + {\alpha_6}WT{O_{ijt}} \\ &&+ {\alpha_7}FT{A_{ijt}} + \left. {\left. {{\varepsilon_{ijt}}} \right)} \right] \\ \end{array}$

Table 3.

Test of variance inflation factor

Variables	VIF	1/VIF
PCGDP	1.524	0.656
InPOP	1.798	0.556
BORD	1.915	0.522
LANG	2.382	0.420
InDIS	3.263	0.306
TAF	1.241	0.806
INF	2.518	0.397
SHP	2.065	0.484
EOC	1.859	0.538
TF	1.752	0.571
WTO	1.603	0.624
FTA	1.731	0.578

Table 4.

Results of SFA model applicability test

Original hypothesis	Constraint model	Unconstrained model	LR	1% critical value	Conclusion
There are no trade inefficiencies	-1542.36	-1076.43	985.92	9.34	Refuse
Non-efficient terms do not have time variability	-571.24	-502.49	120.45	10.61	Refuse
The variable BORD is not introduced	-471.28	-505.64	-82.47	10.48	Refuse
The variable LANG is not introduced	-541.35	-516.03	57.24	10.48	Can’t refuse

Table 5.

Applicability test results of trade inefficiency model

Original hypothesis	Constraint model	Unconstrained model	LR	1% critical value	Conclusion
The variable TAF is not introduced	-178.48	-505.64	78.95	10.48	Refuse
The variable INF is not introduced	-178.48	-516.03	132.16	10.48	Refuse
The variable SHP is not introduced	-178.48	-140.57	74.59	10.48	Refuse
The variable ECC is not introduced	-178.48	-129.46	97.34	10.48	Refuse
The variable TF is not introduced	-178.48	-87.39	181.21	10.48	Refuse
The variable WTO is not introduced	-178.48	-116.58	124.68	10.48	Refuse
The variable FTA is not introduced	-178.48	-114.58	128.92	10.48	Refuse

3.4.2

Analysis of Factors Affecting Dezhou SMEs’ Exports to Central Asia

1)

Robustness test

In this section, the stochastic frontier gravity model is constructed, and the regression results of the OLS model, the random effects model (RE) and the time-invariant stochastic frontier gravity model are also comparatively analyzed to verify the robustness of the constructed model. The regression results are shown in Table 6. Where *, **, and *** indicate that the estimates of the regression coefficients passed the 10%, 5%, and 1% significant level tests, respectively.

According to the regression results, the parameter estimation symbols of each model are consistent, and the parameters of the SFA model are more significant, among which the value of γ of the time-invariant model is 0.857 and the value of γ of the time-varying model is 0.915, indicating that the trade inefficiency term plays a leading role in the impact of the export of Dezhou SMEs to Central Asian countries along the China-Kyrgyzstan-Uzbekistan railway, and the η is significantly positive (0.024>0) at the 1% level, reflecting that the effect gradually increases over time. In terms of LR statistics and parameter significance, the time-varying stochastic frontier gravity model has better estimation effect. Therefore, this model is used in this paper to study the influencing factors of Dezhou SMEs’ exports to Central Asian countries along the China-Kyrgyzstan-Uzbekistan Railway.

2)

Estimation results

The test above determines the reasonableness of the selection of variables and the robustness of the model, proves the existence of the trade inefficiency term and the inefficiency term is time-varying, so this paper estimates equation (11), and the results of parameter estimation are shown in Table 7. From the estimation results of the reference volume, LR = 117.241, γ = 0.675, indicating that the trade inefficiency term exists and has a significant impact, the overall regression effect of the model is better.

3)

Analysis of results (1)

Core variables

Level of economic scale. Both variables PCGDP_it and PCGDP_jt passed the test at 1% significance level and were positively correlated with the explanatory variables, which is consistent with the expectation, indicating that the larger the scale of domestic economic development in China and the countries along the China-Kyrgyzstan-Uzbekistan Railway, the more conducive to the expansion of the exports of SMEs from Dezhou, China, to the Central Asian countries along the route.

Population size level. Variables InPOP_it and InPOP_jt both pass the test at the 1% significance level with the expected signs, with variable InPOP_it having a negative sign and variable InPOP_jt having a positive sign. It indicates that the growth of China’s population size leads to an increase in the demand of the domestic market, thus suppressing exports. On the one hand, with the growth of China’s population size, the consumer demand in its domestic market is also gradually increased, SMEs are more inclined to meet the needs of the domestic market, reducing foreign exports, which will lead to a relative decrease in the export trade of Dezhou SMEs to Central Asian countries along the route. On the other hand, with the growth of China’s population size, labor costs and production costs are also gradually increasing, resulting in China’s competitiveness in the field of manufacturing declined, which will also lead to Dezhou SMEs to Central Asian countries along the route of the manufacturing industry export trade by a certain inhibition. The larger the population size of the importing country, the larger the market capacity, so selling products in such a market will be easier and potentially more cost-effective, which is conducive to expanding the export trade of SMEs in Dezhou.

Geographic distance. Variable InDIS_ij has a negative sign, which is consistent with expectations and passes the test at the 1% significance level, indicating that the more geographic distance, the more it will inhibit China’s manufacturing exports. The logistics cost and time cost of international trade transactions will rise with the increase of geographic distance, at the same time, there may be some cultural differences between countries with greater geographic distance, which may affect the market adaptability of the export products of Dezhou SMEs and reduce the competitiveness of the products. However, with the development of the logistics system, the transportation cost of international trade is gradually reduced, and the hindering effect of geographic distance on the export trade of SMEs in Dezhou is limited, so the SMEs in Dezhou need to broaden the logistics channels and develop corresponding export strategies according to the actual situation of different countries.

Common boundary. The sign of variable BORD_ij is positive, and passed the test at the 5% significance level, indicating that the impact of the common border in the trade of products between China and the five countries of Central Asia is positively correlated, the border makes the transportation distance of bilateral trade shorter, the cost of transportation is lower, and the cultural differences between the countries are relatively small, which makes it easy for the SMEs in Dezhou to export to the Central Asian countries along the route.

(2)

Trade inefficiency term impact variable

Importing country tariff level. Variable TAF_jt passes the test at the 1% significance level with a positive sign and a large coefficient, indicating that the tariff level of the importing country is an important factor restricting the exports of SMEs in Dezhou. Higher tariff levels will increase the trade costs of SMEs in Dezhou, reduce the price competitiveness of exported goods, and lead to a reduction in the scale of exports.

Level of transportation infrastructure development. The sign of the coefficients of variables INF_jt and SHP_jt are both negative, consistent with expectations, indicating that the improvement of transportation infrastructure between the import and export trade parties can effectively promote the exports of Chinese SMEs from Dezhou to the five Central Asian countries. Good infrastructure can reduce transportation costs, improve transportation efficiency, and facilitate the flow of logistics, which in turn promotes the development of trade activities. In addition, better infrastructure can also attract more foreign investment to the countries along the route, thus promoting local economic development and increasing the demand of the local market, thus stimulating the growth of exports from SMEs in Dezhou to the Central Asian countries along the route.

Customs clearance process efficiency. The coefficient of variable EOC_jt is negative in trade inefficiency and significant at the 1% level, which indicates that the efficiency of customs clearance procedures is negatively related to trade inefficiency. The higher the efficiency of product import clearance procedures in the importing country, the greater the hindering effect on the trade inefficiency term, and the more favorable to Dezhou SMEs’ exports to Central Asian countries along the route.

Trade freedom. Variable TF_jt represents the tariff and non-tariff barriers, i.e. the openness of trade. Its sign is negative, which is in line with the expectation, indicating that the higher the trade freedom of the importing country, the more favorable it is for Dezhou SMEs to export to Central Asian countries along the route.

International economic integration environment. The results show that whether to join the World Trade Organization (WTO) (WTO_ijt) and whether to sign a free trade agreement with China (FTA_ijt) selected in this paper have a negative impact on the trade inefficiency term, which indicates that the signing of a free trade agreement between the importing country and China can reduce the trade barriers, which is conducive to the expansion of SMEs’ exports in Dezhou. At the same time, accession to the WTO can also bring more trade opportunities to member countries and promote their economic development and growth, which is conducive to the export trade of SMEs in Dezhou.

Table 6.

Regression result

Variable	OLS	RE	SFA
Variable	OLS	RE	Time invariant	Time-varying
PCGDP_it	1.174***	0.895***	1.132***	0.984***
PCGDP_jt	0.886***	1.114***	0.998***	0.875***
InPOP_it	-11.208	-12.319***	-11.526***	-13.914***
InPOP_jt	1.257**	1.406**	0.683**	0.878***
InDIS_ij	-0.643***	-0.347	-0.012	-0.514***
BORD_ij	1.625***	1.434***	1.538***	1.296***
cons	231.742	265.839	273.824***	274.521***
μ	-	-	0.615	1.498
σ²	0.862	1.157	1.483	2.106
η	-	-	-	0.024***
γ	-	-	0.857	0.915
Logarithmic likelihood value	-	-	-501.365	-582.419
LR				154.257
Sample size	800	800	800	800

Table 7.

Parameter estimation result

	Variable	Coefficient	T-statistic
Random frontier gravity model	β₀	261.415*	28.436
	PCGDP_it	1.048***	-8.82
	PCGDP_jt	0.756***	26.034
	InPOP_it	-12.035***	-15.87
	InPOP_jt	0.765***	-2.538
	InDIS_ij	-0.514***	4.885
	BORD_ij	0.736**	-18.059
	η	0.021***	24.958
Trade inefficiency model	α₀	1.026***	-1.105
	TAF_jt	3.247***	-1.245
	INF_jt	-1.466***	-2.034
	SHP_jt	-0.518***	-2.653
	EOC_jt	-3.525***	-4.516
	TF_jt	-0.067***	-4.948
	WTO_ijt	-1.965**	-5.137
	FTA_ijt	-1.829*	-15.073
Reference quantity	σ²	1.584
	γ	0.675
	Logarithmic likelihood value	-1185.639
	LR	117.241

4

Trade Efficiency Analysis and Trade Potential Measurement of Small and Medium-sized Enterprises in Dezhou

After model testing and analyzing the influencing factors of SMEs’ exports to Central Asia in Dezhou, this chapter will measure the trade efficiency as well as the trade potential of all the panel data in the SMEs-Central Asia five-country export trade in Dezhou during the period of 2013-2023.

4.1

Trade efficiency analysis

According to the regression results of the stochastic frontier gravity model to derive the value of the trade efficiency of the product exports of Dezhou SMEs to the countries of the five Central Asian countries during the period of 2013-2023 is shown in Figure 3, the value of the trade efficiency interval for (0,1), the larger the value of the trade efficiency indicates that the current bilateral product trade efficiency is higher.

As can be seen from Figure 3, in the product trade of exports from SMEs in Dezhou to the five Central Asian countries in 2013-2023, the trade efficiency of product exports between SMEs in Dezhou and the five importing countries all show an upward trend. And the value of product export efficiency between SMEs in Dezhou and Kazakhstan is the one with the largest change and the fastest growth, followed by Kyrgyzstan, Tajikistan, Uzbekistan and Turkmenistan, where the slowest growth in trade efficiency value is Turkmenistan. This is also reflected in the selection of variables and the values of variables in the stochastic frontier gravity model. Turkmenistan has no border with China, the distance of its capital city is the farthest among the five Central Asian countries, and Turkmenistan is the only one among the five Central Asian countries that has not yet joined the Shanghai Cooperation Organization (SCO), and the free trade agreement with China has yet to be carried out.

4.2

Measuring trade potential

The value of trade efficiency of product export reflects the current trade status of the actual export of products from SMEs in Dezhou to the five Central Asian countries. The higher value of trade efficiency indicates that the trade efficiency between SMEs in Dezhou and the agricultural products importing countries is relatively good, and the influence of non-efficiency factors hindering bilateral trade is low, but it also indicates that the bilateral trade potential is low, and there is less space for expanding the trade potential. According to the regression results of the stochastic frontier gravity model in the previous section, in the product export trade of Dezhou SMEs to the five Central Asian countries during the period of 2013-2023, the value of trade efficiency with Kazakhstan has been the leading and fastest developing, growing from 0.2074 in 2013 to 0.7943 in 2023. At the same time, the trade efficiency value of product exports from SMEs in Dezhou to Turkmenistan has been at the bottom of the list, and there is almost not much added value in recent years. By analyzing the trade efficiency value, we can use equations (12)~(13) to measure the trade potential of products exported by SMEs in Dezhou to the five Central Asian countries during the period of 2013-2023, as well as the room for improvement of the trade potential. (12) $T P = \frac{A T V}{T E}$ $TP = \frac{{ATV}}{{TE}}$ (13) $T P I S = T P - A T V$ $TPIS = TP - ATV$

Where TP represents the value of trade potential, ATV represents the actual export value, TE represents the value of trade efficiency, and TPIS represents the room for improvement of trade potential.

The results of measuring the trade potential and the improvement space of trade potential of SMEs in Dezhou are shown in Table 8.

Table 8.

Potential value of export trade and potential improvement space

Country	Kazakhstan		Uzbekistan		Kyrgyzstan		Tajikistan		Turkmenistan
Year	TP	TPIS	TP	TPIS	TP	TPIS	TP	TPIS	TP	TPIS
2013	466.72	330.47	325.59	285.13	807.17	637.94	102.44	91.28	56.32	50.54
2014	501.49	356.45	268.05	247.18	778.91	618.18	169.38	145.79	56.33	44.94
2015	442.25	297.93	410.38	347.55	1170.64	899.65	307.71	260.92	53.37	51.01
2016	542.16	350.4	350.75	299.96	1620.68	1204.2	642.69	536.83	98.66	89.15
2017	538.15	319.11	463.53	408.53	1586.11	1156.74	285.62	239.51	101.41	88.91
2018	543.71	309.68	477.53	409.69	1539.82	1079.04	180.18	141.5	92.3	79.96
2019	578.77	285.51	355.39	302.99	1603.54	1014.14	409.39	332.24	104.83	79.89
2020	631.22	282.64	408.13	349.44	1301.5	838.87	201.12	158.71	115.81	102.25
2021	549.31	213.71	280.24	239.62	1255.95	765.72	117.58	85.79	91.16	79.21
2022	596.3	190.87	361.06	307.2	625.3	352.61	124	97.92	99.99	91.28
2023	582.85	136.19	386.9	319.95	949.51	499.5	321.43	238.77	78.15	71.12

From Table 8, it can be seen that in the product export trade of Dezhou SMEs to the five Central Asian countries from 2013 to 2023, the trade potential value of the product export trade of Dezhou SMEs with the five Central Asian countries and the space for potential enhancement from the overall performance of the first rising and then declining trend. And the ranking of product export potential value and potential improvement space in the table is: Kyrgyzstan>Kazakhstan> Uzbekistan>Tajikistan>Turkmenistan. The potential value of Dezhou SMEs with Kyrgyzstan rises from 807.17 in 2013 to peak at 1603.54 in 2019, and finally falls back to 949.51 in 2023. The potential value with Kazakhstan rises from 466.72 in 2013 to peak at 631.22 in 2020 and finally falls back to 582.85 in 2023. The potential value with Uzbekistan rises from 325.59 in 2013 to peak at 477.53 in 2018 and finally falls back to 386.90 in 2023. The potential value with Tajikistan rises from 102.44 in 2013 to peak at 642.69 in 2016 and finally falls back to 321.43 in 2023. The potential value with Turkmenistan rises from 56.32 in 2013 to peak at 115.81 in 2020 and finally falls back to 78.15 in 2023.

5

Conclusion

This paper comprehensively uses the stochastic frontier gravity model and the trade inefficiency model to explore the influencing factors of the export trade of Dezhou SMEs to the five Central Asian countries in the context of the China-Kyrgyzstan-Uzbekistan Railway, and quantitatively evaluates the potential of the export trade of Dezhou SMEs.

First of all, the analysis of the current situation of China’s export trade to the five Central Asian countries shows that: at present, China’s export trade volume to the five Central Asian countries shows a high growth trend. In terms of product structure, in the past ten years, China’s exports to the five Central Asian countries have been dominated by textiles, steel, rubber tires, vehicles and some digital products.

Secondly, per capita gross domestic product (PGDP), total population (POP), geographical distance (DIS) and common border (BORD), free trade agreement (FTA), trade freedom (TF) tariff level (TAF), efficiency of customs clearance procedures (EOC), liner shipping connectivity index (SHP), WTO, and indicators of trade- and transportation-related infrastructure (INF) are selected as explanatory variables. INF) as explanatory variables were modeled and analyzed, and the following research conclusions were drawn: 1)

In the main model of Dezhou SMEs’ export trade of products to the five Central Asian countries, China’s PGDP is positively correlated with the PGDP of the importing countries (five Central Asian countries), and the POP and BORD of the importing countries (five Central Asian countries) are positively correlated with the product trade flows, while China’s POP and the DIS between the bilateral capitals are negatively correlated with the trade flows. In trade inefficiency, the six variables of FTA, TF, SHP, EOC, WTO and INF have inhibiting effects on trade inefficiency, while the variable of TAF has promoting effects.

2)

From the analysis and measurement of trade efficiency and trade potential, the trade efficiency of SMEs’ exports to the five Central Asian countries in Dezhou from 2013 to 2023 shows an upward trend. And the value of product export efficiency between SMEs in Dezhou and Kazakhstan has the largest change and the fastest growth, followed by Kyrgyzstan, Tajikistan, Uzbekistan and Turkmenistan, of which the slowest growth in trade efficiency value is Turkmenistan. The trade potential of product exports between SMEs in Dezhou and Kyrgyzstan and the room for improvement of trade potential are the largest compared with the other four Central Asian importing countries, while the value of trade potential of product exports with Turkmenistan continues to be the lowest among the five Central Asian countries.

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Multi-dimensional research and quantitative evaluation of export potential of Dezhou smes to Central Asia based on multi-level regression model under the background of China-Kyrgyzstan-Uzbekistan Railway

Xingyuan Sun

Published Online: Sep 25, 2025

Received: Jan 05, 2025

Accepted: May 02, 2025

DOI: https://doi.org/10.2478/amns-2025-1015

KeywordsStochastic frontier gravity model, Trade inefficiency model, Trade potential, Five Central Asian countries

© 2025 Xingyuan Sun, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Stochastic frontier gravity model, Trade inefficiency model, Trade potential, Five Central Asian countries