A study on the impact of high-quality openness on China’s economic growth based on mathematical statistics

Since the reform and opening up, China has relied on factor-driven, investment-driven and foreign trade-driven to promote rapid economic growth [1]. However, the traditional economic growth mode is facing serious challenges with the ever-changing international environment and the transformation of the domestic economy to high-quality development [2]. The marketization process is an important driving force to promote the domestic macro-cycle. It can effectively break down various market barriers, promote the free flow of commodities and factors, and enhance the vitality and attractiveness of the domestic market [3-4]. Opening up to the outside world is an important part of the domestic and international double cycle [5]. A high level of opening to the outside world helps to broaden the international market space of the Chinese economy. The process of marketization and opening up to the outside world support and promote each other, and together constitute an important support and guarantee for the new development pattern [6-7]. Meanwhile, from the perspective of institutional determinism, although factors such as technological innovation, economies of scale, education and capital accumulation are important, the deep-seated driving force of economic growth stems from institutional change and innovation. In particular, the reform and opening up in 1978, as the most far-reaching institutional change on China’s economy, its successful experience and far-reaching impact has provided us with valuable insights [8-9]. This further highlights the significant theoretical and practical value of studying the impact of the marketization process and opening-up on the factor efficiency of economic growth [10].

China’s opening up has entered a new stage since the 2018 Central Economic Work Conference proposed “promoting the transformation from commodity and factor flow-based opening to system-based opening, including rules”. Institutionalized openness is the institutionalization of openness and the formulation of stable and standardized rules and systems for openness [11-13]. Institutional openness is centered on optimizing the domestic system and docking the international high-standard rules to promote the efficient flow of factors of production, and to better promote the flow of resources and optimize resource allocation by improving the quality of the system and eliminating institutional barriers [14-15]. The open platform set up by China, which is expected to become a regional growth pole and radiate the economic development of neighboring cities under the premise of improving the quality and scale of its own economic development, is the highland of system reform and the carrier of system-oriented opening and becomes into an important part of the country’s development in the stage of system-oriented opening [16-18].

While social development is gradually moving towards the stage of maturity, the green and sustainable development of the economy needs to rely more on the improvement of economic efficiency [19-20]. As China’s economy is transitioning to the stage of high-quality development, the efficiency-driven development model has become an urgent need at this stage [21-22]. Combined with the recent international focus on carbon emissions, the issue of green and sustainable high-quality economic development will be the focus of future research, and economic efficiency is an important dimension reflecting high-quality economic development [23-24]. Meanwhile, in the context of globalization, the high-quality development of inland areas is not only an important part of China’s comprehensive modernization, but also a key part of achieving coordinated regional development. Among them, as the frontier of China’s opening to the outside world, the construction of its open platform and the improvement of its economic efficiency play a pivotal role in promoting the high-quality development of inland areas [25-26].

Current studies exploring the relationship between trade openness and national economic growth generally agree that trade openness has a positive effect on the economic growth of the country, but a few studies hold the opposite view. Among these positive studies, Keho, Y in a multivariate analytical framework with capital stock, labor and trade openness as regressor variables examined how trade openness affects the economic growth of Côte d’Ivoire, and found that trade openness contributes to the economic growth of the national society, while revealing that trade openness and capital are complementary [27]. Alam, M. M et al. conducted a relevant study combining the autoregressive distributed lag (ARDL) approach and related intermediate estimators including pooled mean group (PMG), mean group (MG), and dynamic fixed-effects (DFE) instruments, which elucidated that economic growth, trade openness, and technological advancement have a positive impact on the long-term applicability of renewable energy in a country [28]. Kong, Q et al. examined the association between China’s openness to the outside world and the country’s economic growth in the context of exchange rate fluctuations, and the study pointed out that trade openness contributes to the high-quality growth of the country’s economy in both short-term and long-term perspectives, and that the effect is characterized by significant regional heterogeneity and non-linear thresholds [29]. It is known that the economic development of externally oriented countries will be more advantageous based on the current literature related to trade openness and economic growth. Huchet-Bourdon, M et al. confirmed that countries exporting high-quality and innovative products have a more significant trend of economic growth in a further study on the impact of trade openness on the economy [30]. Raghutla, C’s empirical analysis shows that trade openness positively affects economic growth and states that there is a bidirectional causality between economic growth and inflation and a unidirectional causality between economic growth and trade openness and also between economic growth and trade finance development [31]. All of the above studies affirmed that foreign trade liberalization has a positive effect on national economic growth, and also studied the specific paths and logical mechanisms of foreign trade liberalization affecting economic growth from the perspectives of export products, regional differences, etc. While some researchers do not believe that foreign trade liberalization will necessarily have a role in the country’s economy. Zaman, M et al. studied the economic development of countries along the Belt and Road based on a two-step system of GMM technology and found that FDI and gross capital formation have a significant positive effect on the economic growth of the countries along the Belt and Road, while IT exports and trade liberalization do not have a significant effect on their economic growth [32]. It is therefore necessary to conduct in-depth analysis and research on how trade openness affects economic growth in order to uncover the underlying logic and path of foreign trade affecting economic growth.

This study constructs economic openness evaluation indexes including trade openness, foreign cooperation, real tariff rate, service openness, production openness, investment openness and financial openness. The data of economic openness and GDP from 2009 to 2023 are collected for empirical analysis. First, the co-integration theory is applied to establish a co-integration regression model for each measure of China’s economic growth and economic openness. Second, the co-integration regression is done on China’s overall economic openness and economic growth. Then, an error correction model is built for China’s overall economic openness and economic growth. Finally, Granger causality test is conducted to verify the causal relationship between China’s overall economic openness and economic growth.

2

An empirical study of high-quality openness and China’s economic growth

Since the reform and opening up, China’s economic openness has been greatly improved, and the level of China’s openness to the outside world has shown a very strong upward trend in both its breadth and depth. In order to explore the impact of high-quality openness on China’s economic growth, this paper establishes a model to empirically analyze the relationship between China’s economic openness and economic growth.

2.1

Introduction to the empirical model

When modeling time series, economic variables are often assumed to be smooth. However, most economic time series data are actually not smooth. If the simple linear regression is performed directly on the unstable time series data, it will produce “pseudo-regression” phenomenon and makes the analysis results unable reflect the authenticity. Therefore, the co-integration theory is used to determine the smoothness before the regression analysis of economic variables [33].

2.1.1

Smoothness test for time series

In this paper, the ADF unit root test is chosen to test the smoothness of the time series for three models:

Model 1 (no constant, no trend term): (1) $Δ Y_{t} = δ Y_{t - 1} + \sum_{i = 1}^{p} λ Y_{t - i} + μ_{t}, t = 1, 2, \dots, T$

Model 2 (with constant, no trend term): (2) $Δ Y_{t} = α + δ Y_{t - 1} + \sum_{i = 1}^{p} λ Y_{t - i} + μ_{t}, t = 1, 2, \dots, T$

Model 3 (with constant, trend term): (3) $Δ Y_{t} = α + β t + δ Y_{t - 1} + \sum_{i = 1}^{p} λ Y_{t - i} + μ_{t}, t = 1, 2, \dots, T$

The specific steps of the ADF test are as follows:

Step 1: Estimate model 3. At the given significance level of the ADF critical value, if parameter δ is zero, it proceeds to step 2. Conversely, it means that the series ${Y_{t}}$ does not have a unit root and is smooth, then the test ends.

Step 2: Assuming δ = 0, at the given significance level of the ADF critical value, if parameter β is zero, then it means that series ${Y_{t}}$ does not contain a time trend term, and goes directly to step 4. Instead, proceeds to step 3.

Step 3: Apply the general t distribution to test δ = 0. If parameter δ is significantly none-zero, then series ${Y_{t}}$ does not have a unit root, being smooth, and the test ends. Conversely, it means that sequence ${Y_{t}}$ has a unit root and is non-smooth, then the test is over.

Step 4: Estimate model 2. At the given significance level of the ADF threshold, if parameter δ is significantly zero, proceed to the next step. If parameter δ is significantly non-zero, then sequence ${Y_{t}}$ does not have a unit root and is smooth, end of test.

Step 5: At a given significance level of the ADF threshold and δ = 0, if parameter α is significantly non-zero, it indicates that sequence ${Y_{t}}$ contains a constant term, then goes to step 3. Conversely, goes to the next step.

Step 6: Estimate model 1. At the given significance level of the critical value of the ADF, if parameter δ is significantly zero, then sequence ${Y_{t}}$ has a unit root and is non-stationary, and the test is over. If parameter δ is significantly non-zero, sequence ${Y_{t}}$ does not have a unit root, being smooth, and the testing process is over.

2.1.2

Co-integration test for time series

For the test of this co-integration relationship, it can be mainly categorized into two kinds of the Engle-Granger (EG) two-step method and the Johansen maxium likelihood test according to the different test objects.

EG two-step method:

The test steps of the EG two-step test method are as follows:

Step 1: Fixed order. That is according to the unit root test to get the order of the two variables single integer. If there is no unit root between the two variables, it is a smooth series, then the test ends. On the contrary, if the orders of single integer between two variables are not the same, it means that there is no co-integration relationship between two variables. If the orders of their single integers are the same, the test proceeds to the next step.

Step 2: Establish the regression equation. The regression equation (4) of the two variables is established and ordinary least squares (OLS) is used to get the residuals e_t for estimating the equilibrium error ε_t. (4) $y_{t} = α_{0} + α_{1} x_{t} + ε_{t}$

Step 3: Test the smoothness of the residual series e_t. If e_t is smooth, it means that there is a co-integration relationship between y_t and x_t. On the contrary, it means that there is no co-integration between y_t and x_t.

Johansen maxium likelihood test is referred to as Johansen method. It is a co-integration test on the regression coefficients of vector autoregressive model (VAR), which is mainly applied in the co-integration test on two or more variables [34].

Firstly, a VAR(q) model is built: (5) $y_{t} = L_{1} y_{t - 1} + L_{2} y_{t - 2} + \dots + L_{q} y_{t - q} + B x_{t} + ε_{t}, t = 1, 2, \dots, T$

where y_1t, y_2t, …, y_it are all first order single integer non-stationary variables. x_t is an exogenous variable with dimension q, which is used to represent deterministic terms such as constant and trend terms. ε_t represents a l -dimensional vector of random disturbances.

A differential transformation of the above VAR(q) model yields: (6) $Δ y_{t} = H y_{t - 1} + \sum_{i = 1}^{q - 1} Γ_{i} Δ y_{t - i} + B x_{t} + ε_{t}$

where $H = \sum_{i = 1}^{q} L_{i} - I$ , $Γ_{i} = - \sum_{j = i + 1}^{q} L_{j}$

The basic principle of Johansen co-integration test is the original first-order single integer variable y_t after one difference will become smooth variable Δy_t, so as long as Hy_t−l is smooth in the above equation, it means that there is a co-integration relationship between the original series, which is determined by the rank of the matrix H. Thus the co-integration test of y_t is converted to analyze the rank of the matrix H, and because the rank of the matrix H is equal to the number of its non-zero eigenvalues, the rank of the co-integration vectors and the co-integration relationship can be examined by examining the number of non-zero eigenvalues.

Assuming that the characteristic root of the matrix H is λ₁ > λ₂ > ⋯λ_n, the original and alternative hypotheses of the characteristic root trace test (Trace test) are: (7) $\begin{matrix} H_{r 0} : λ_{r + 1} = 0 \\ H_{r 1} : λ_{r + 1} > 0 \end{matrix}$

where r = 0, 1, …, n − 1. Then the corresponding test statistic is: (8) $Q_{r} = - T \sum_{i = τ + 1}^{n} \ln (1 - λ_{i})$

where Q_r is denoted as the characteristic root trace statistic, which is next analyzed for significance in turn.

When Q₀ is significantly not zero, then the original hypothesis of H₀₀(r = 0) is not rejected, i.e., it is considered that there are n unit roots in the matrix H and there is no co-integration in the original series y_t. When Q₀ is significantly zero, the original hypothesis of H₀₀(r = 0) is rejected, i.e., the original series is considered to have at least one cointegrating relationship and Q₁ should be tested. When Q₁ is significantly not zero, then does not reject H₁₀, that is, the original series have only a co-integration relationship, so that the test continues until does reject H_r0, then the original series have r co-integration relationships.

2.1.3

Error correction models

The error correction model is transformed from an autoregressive distributed lag model (ADL). Consider an ADL (1, 1) model: (9) $y_{t} = α_{0} + α_{1} y_{t - 1} + β_{0} x_{t} + β_{1} x_{t - 1} + u_{t}, t = 1, 2, \dots, T$

where u_t assumes that there is no autocorrelation or heteroscedasticity and that it follows a normal distribution with mean zero and variance σ². Subtracting y_t−1 from both sides of the above equation simultaneously and adding and subtracting β₀x_t−1 at the right side, the equation is transformed into: (10) $Δ y_{t} = α_{0} + β_{0} Δ x_{t} + (α_{1} - 1) y_{t - 1} + (β_{0} + β_{1}) x_{t - 1} + u_{t}$

Combining the third and fourth terms at the right side of the above equation into one term and utilizing $α_{0} = k_{0} (1 - α_{1})$ , $β_{0} + β_{1} = k_{1} (1 - α_{1})$ , it yields: (11) $Δ y_{t} = β_{0} Δ x_{t} + (α_{1} - 1) (y_{t - 1} - k_{0} - k_{1} x_{t - 1}) + u_{t}$

Then the above equation is known as the error correction model, where $(y_{t - 1} - k_{0} - k_{1} x_{t - 1})$ describes the long-run relationship between x_t and y_t, while $Δ y_{t} = β_{0} Δ x_{t} + (α_{1} - 1) (y_{t - 1} - k_{0} - k_{1} x_{t - 1})$ describes the short-run relationship between x_t and y_t. The $(α_{1} - 1) (y_{t - 1} - k_{0} - k_{1} x_{t - 1})$ in the equation is the error correction term, which reflects the short-term deviation of y_t from the long-run equilibrium level at the moment of t. Since the absolute value of α is less than one, the coefficient of the error correction term must be negative, indicating that the error correction term has an inverse correction mechanism for Δy_t in the short run.

2.1.4

Granger causality test

The term causality refers to the dependence between variables, where the variable of the outcome is determined by the variable of the cause, and changes in the cause variable cause changes in the outcome variable [35].

Granger causality test requires the estimation of the following regression model: (12) $M o d e l 1 : y_{t} = \sum_{i = 1}^{q} α_{i} x_{t - i} + \sum_{j = 1}^{q} β_{j} y_{t - j} + μ_{1 t}$ (13) $M o d e l 2 : x_{t} = \sum_{i = 1}^{s} λ_{i} x_{t - i} + \sum_{j = 1}^{s} δ_{j} y_{t - j} + μ_{2 t}$

where it is assumed that white noise μ_1t and μ_2t are uncorrelated.

Model 1: Null hypothesis H₀ : α₁ = α₂ = ⋯ = α_q = 0.

Model 2: Null hypothesis H₀ : δ₁ = δ₂ = ⋯ = δ_s = 0.

If the null hypothesis of model 1 is rejected and the null hypothesis of model 2 cannot be rejected, then x is the Granger cause of y. If the null hypothesis of model 2 is rejected and the null hypothesis of model 1 cannot be rejected, y is the Granger cause of x.

In order to test that x is the Granger cause of y, the steps of the Granger causality test are as follows: 1)

Do a regression of the current y on all the lags and whatever other variables (if they exist), i.e., a regression of y on the lag y_t−1, y_t−2, ⋯, y_t−q of x and the other variables, to get the constrained sum of squares of the residuals RSS_R.

2)

Do the regression with lag x, i.e., add lag x to the previous regression equation, which is an unconstrained regression, and the resulting regression yields the unconstrained sum of squares of residuals RSS_U.

3)

The null hypothesis is H₀ : α₁ = α₂ = ⋯ = α_q = 0, i.e., the lag term x does not belong to this regression.

4)

To test this hypothesis, we use the F test, i.e.: (14) $F = \frac{(R S S_{R} - R S S_{U}) / q}{R S S_{U} / (n - k)}$

It follows an F distribution with degrees of freedom q and (n − k). Here n is the sample capacity, q is equal to the number of lag terms x, i.e., the number of parameters to be estimated in the constrained regression equation and k is the number of parameters to be estimated in the unconstrained regression. 5)

If the value of F calculated at the selected level of significance (α) exceeds the critical F_α value, the null hypothesis is rejected, indicating that x is the Granger cause of y.

6)

Similarly, to test whether y is the Granger cause of x, the above steps can be repeated by replacing variables y and x with each other.

2.2

Indicators and data

Regarding the indicators for measuring economic openness, this paper combines relevant literature to take trade openness, degree of external cooperation, effective tariff rate, service openness, production openness, investment openness and financial openness [36] as the seven major indicators of China’s comprehensive economic openness. Here the data of China for a 15 year period from 2009 to 2023 are selected for measurement and the explanation of the seven indicators is as follows:

Trade openness (X₁): Import and export trade has long been one of the troika of China’s economic growth. For a long time, China has been in a surplus position in world trade, and import and export trade contributes to China’s economic growth to a high degree according to the previous studies on trade openness literature. In this paper, the measurement standard of trade openness is the ratio of the total domestic import and export amount (USD billion) to the gross domestic product (GDP) (USD billion) in the calendar year, where GDP is converted to USD denomination by the median price of the RMB-dollar exchange rate in the calendar year, ignoring the influence of the price factor.

Degree of external cooperation (X₂): In recent years, with the expansion of China’s foreign investment and the strengthening of its participation in the infrastructure construction of countries around the world, the number of Chinese outbound workers has shown an increasing trend, reflecting the further strengthening of China’s foreign economic cooperation, the degree of external cooperation can better reflect the role of the world economy on China’s participation in the construction of the global economy, so this paper utilizes foreign labor service cooperation as the degree of external cooperation. The number of people outside at the end of the year (people)/the total population of the country (people) and plus the total amount of foreign contracted engineering contracts (USD billion)/the annual GDP (USD billion) are calculated.

Effective tariff rate (X₃): The effective tariff rate reflects the impact of a country’s tax rate on its economic openness. Since China’s accession to the World Trade Organization (WTO) in 2001, China has produced a set of scientific tariff subjects under the WTO’s cooperation framework in line with the world standard. The tariff level has a significant impact on China’s import and export trade, and the numerous literatures on the tariff level are largely consistent. This paper uses the ratio of total tariff revenue (USD billion) to total import and export (USD billion) as a measure of the actual tariff rate, which is the overwhelmingly adopted standard.

Services openness (X₄): Trade in services itself is part of import and export trade. This paper is based on the convenience of discussion, a more detailed measure of the openness of the integrated economy, singled out, services openness is measured by using the balance of payments in the current account of services credits plus debits and then divided by the total amount of credits and debits in the current account in China’s balance of payments. It reflects the proportion of trade in services in China’s balance of payments current account.

Production openness (X₅): Openness of production reflects the production capacity of Hong Kong, Macao, Taiwan and foreign-invested enterprises, and the level of their production capacity can reflect the quality of China’s economic openness. Here, production openness is measured by the capitalization of three-funded industrial enterprises and the total capitalization of industrial enterprises nationwide.

Investment openness (X₆): This paper adopts the sum of China’s net outward investment and the amount of China’s actual utilization of the foreign direct investment and then the ratio to GDP as the measure of investment openness.

Financial openness (X₇): Financial openness can reflect the breadth and depth of a country’s participation in the world’s financial sector. Openness in the world’s financial sector can better promote economic development, and plays a certain role in stabilizing a country’s economic. The calculation method of financial openness in this paper utilizes the ratio of the total credits and debits of investment income under the current account to the total debits and credits of the current account in China’s Balance of Payments Statement to determine the degree of financial openness. The data are selected from the time-series data of China’s Balance of Payments on the official website of the State Administration of Foreign Exchange.

3

Empirical analysis

Herein, we explores the relationship between GDP as an indicator of economic growth and various indicators of economic openness. According to the availability of data and the scope and nature of the issue under discussion, the time series data between 2009 and 2023 are selected from the issues of China Statistical Yearbook and the official website of China Bureau of Statistics. China’s GDP and its growth are analyzed and researched based on economic openness and their change trends from 2009 to 2023 are shown in Figure 1 and Figure 2, respectively. It can be clearly seen from the figures that the trends of economic openness, GDP and its growth are basically the same, except for the period between 2020 and 2022 duo to COVID-19 epidemic, and the highest economic openness reaches 0.34.

The relationship between economic openness and economic growth is further analyzed for co-integration. In order to prevent the generation of heteroskedasticity phenomenon and to avoid any negative impact on the results, the seven economic openness indicators, economic openness and GDP time series data identified in the previous section are logarithmized and denoted as LGX₁, LGX₂, LGX₃, LGX₄, LGX₅, LGX₆, LGX₇, LGF, and LGGDP, respectively. The software used for the analysis in this section is EVIEWS 13.0.

3.1

Stability test

Before conducting the co-integration test on the variables, the smoothness of the variables needs to be tested first. In this paper, the smoothness of the variables is tested using the ADF unit root test, and the test results are shown in Table 1. Herein, C and T denote the constant term and the time trend term, respectively, and P denotes the lag order used, which is determined by the AIC and SC minimum criterion. Δ denotes the first-order difference, and Δ² denotes the second-order difference. The critical values in the table are obtained from the data given by Mackinnon. Those with * denote critical values at 1% significance level, those with ** denote critical values at 5% significance level, and the rest are critical values at 10% significance level. After the test, it can be seen that all the original variable series are non-stationary with unit root, and the first-order difference series are stationary because the ADF test values of the original time series of all the variables are greater than the corresponding critical values, while the ADF test values of the first-order difference series are less than the corresponding critical values, indicating that the original variable series are all I(1) series, which meet the requirements of conducting the co-integration analysis. In the following, the relationship between the non-stationary series LGGDP and LGX₁, LGX₂, LGX₃, LGX₄, LGX₅, LGX₆, LGX₇, and LGF are analyzed for co-integration.

Table 1.

The ADF unit root test results of each sequence

Variable sequence	Test form(C,T,P)	ADF statistics scale	Critical value	Conclusion	D.W.
LGGDP	(C,T,1)	-2.98648	-4.80008*	Nonstationary	2.34484
ΔLGGDP	(0,0,1)	-2.02126	-1.97403**	Smoothness	2.04473
Δ²LGGDP	(C,0,3)	-3.40168	-4.20006**	Smoothness	2.28614
LGX₁	(C,T,1)	-0.9395	-1.55929	Nonstationary	1.7654
ΔLGX₁	(C,T,3)	-1.09311	-0.9288	Smoothness	1.5562
Δ²LGX₁	(C,0,1)	-3.5074	-2.67972*	Smoothness	1.1445
LGX₂	(C,T,2)	-1.6916	-1.96996	Nonstationary	2.1460
ΔLGX₂	(C,T,1)	-5.3569	-1.30137	Smoothness	2.0217
Δ²LGX₂	(C,0,1)	-1.8197	-1.5774*	Smoothness	2.4514
LGX₃	(C,T,1)	-1.3057	-2.2505	Nonstationary	1.1004
ΔLGX₃	(C,T,1)	-4.2750	-1.80002**	Smoothness	1.2190
Δ²LGX₃	(C,0,2)	-3.5694	-2.01820*	Smoothness	2.1344
LGX₄	(C,T,1)	-2.39821	-2.7835	Nonstationary	1.6706
ΔLGX₄	(C,0,2)	-4.9464	-2.36258	Smoothness	1.9841
Δ²LGX₄	(C,0,3)	-4.5375	-1.08882*	Smoothness	2.1371
LGX₅	(C,T,3)	-1.6940	-2.663492	Nonstationary	1.7365
ΔLGX₅	(C,0,3)	-3.6487	-3.2392	Smoothness	2.1010
Δ²LGX₅	(C,T,2)	-1.6505	-1.24112*	Smoothness	2.3626
LGX₆	(C,T,4)	-1.60087	-2.6803	Nonstationary	2.4485
ΔLGX₆	(C,0,2)	-5.2887	-3.87252	Smoothness	2.1179
Δ²LGX₆	(0,0,2)	-5.7717	-2.92894*	Smoothness	1.8703
LGX₇	(C,T,1)	-1.2945	-1.53773	Nonstationary	1.6597
ΔLGX₇	(C,T,2)	-4.1444	-2.18508	Smoothness	1.4867
Δ²LGX₇	(C,T,1)	-3.18580	-2.5688*	Smoothness	1.1500
LGF	(C,T,1)	-3.26705	-4.88643*	Nonstationary	2.1357
ΔLGF	(0,0,3)	-3.09799	-2.77192*	Smoothness	2.1357
Δ²LGF	(C,0,3)	-3.71321	-3.14492**	Smoothness	1.9910

3.2

Co-integration tests

In this paper, Johansen method is used to conduct co-integration test between LGGDP and LGX₁, LGX₂, LGX₃, LGX₄, LGX₅, LGX₆, LGX₇, LGF, and then EG method is applied to analyze the co-integration between LGGDP and LGF.

The co-integration test of the variable LGGDP with LGX₁, LGX₂, LGX₃, LGX₄, LGX₅, LGX₆, LGX₇, LGF is conducted by using the maximum eigenvalue test of Johansen through EVIEWS 13.0, and the form of the test that includes the constant term and the time trend term should be applied when making the test. The test results obtained are shown in Table 2. That with * denotes the rejection of the original hypothesis at the 5% significance level. As can be seen from the test results, the original hypothesis of the number of covariates being zero is rejected at the 5% significance level, thus it can be known that there must be a co-integration relationship between the variables, that is to say, there is a long-term and stable equilibrium relationship between the indicators of economic growth and economic openness.

Table 2.

Johansen cointegral test results

Cointegral equation number r	Eigenvalue	Maximum eigenvalue statistics	5% threshold	P
r=0*	0.92128	89.2115	56.91319	0.000
r≤1	0.64216	48.3277	50.51985	0.0482
r≤2	0.87724	43.3356	44.3252	0.0988
r≤3	0.78896	33.1036	38.33901	0.0855
r≤4	0.59069	20.5844	31.85932	0.6561
r≤5	0.23903	14.7914	25.72421	0.7874
r≤6	0.41487	11.7042	19.38704	0.5705
r≤7	0.20406	8.7398	12.36498	0.2707

Accordingly, the standardized coefficients of co-integration obtained from the Johansen co-integration test method are shown in Table 3. A co-integration equation between LGGDP and LGX₁, LGX₂, LGX₃, LGX₄, LGX₅, LGX₆, LGX₇ is obtained from the standardized co-integration coefficient table: (15) $\begin{aligned} L G G D P & = 0.13124 L G X_{1} + 0.35014 L G X_{2} \\ + 0.34631 L G X_{3} + 0.05896 L G X_{4} \\ + 0.17763 L G X_{5} + 0.17365 L G X_{6} \\ + 0.09836 L G X_{7} - 0.05125 T R E N D \end{aligned}$

Table 3.

Normalized cointegral coefficient

LGX₁	LGX₂	LGX₃	LGX₄
0.13124	0.35014	0.34631	0.05896
(0.05552)	(0.04324)	(0.02124)	(0.02639)
LGX₅	LGX₆	LGX₇	@TREND(83)
0.17763	0.17365	0.09836	-0.05125
(0.03247)	(0.11469)	(0.02368)	(0.00247)

The coefficients of the co-integration equation show that the impact of each variable on economic growth is in line with the economic significance, which indicates that the degree of China’s foreign cooperation and the real tariff rate have the greatest impact on economic growth, and each 1% increase in the degree of foreign cooperation and the real tariff rate will cause the GDP to grow by 0.35014% and 0.34631%, respectively. Production openness, investment openness and trade openness have the second largest impact on economic growth, causing GDP to increase by 0.17763%, 0.17365% and 0.13124% respectively for every 1% increase in their rates. Financial openness and service openness have the least impact, as they cause GDP to grow by 0.09836% and 0.05896% per 1% increase. In conclusion, the various measures of economic openness have a strong contribution to economic growth.

In the following, the EG method is applied to conduct the co-integration test between China’s economic growth and the overall economic openness, i.e., the co-integration analysis of LGGDP and LGF.

Firstly, the co-integration regression of LGGDP and LGF is carried out by OLS method, and the obtained regression results are shown in Table 4. The resulting co-integration regression equation is obtained as: (16) $\begin{matrix} L G G D P = 12.0038 + 0.48532 L G F \\ t : (50.43528) (2.575134) \\ R^{2} = 0.173274, F = 2.724673 \end{matrix}$

Table 4.

Cointegral regression

Variable	Coefficient	Std.Error	t-Statistic	Prob.
LGF	0.48532	0.18846	2.57513	0.0231
C	12.0038	0.23800	50.43528	0.000
R-squared	0.17327	Mean dependent var		11.2052
Adjusted R-squared	0.10968	S.D. dependent var		0.39771
S.E. of regression	0.37527	Akaike info criterion		1.0012
Sum squared resid	1.83081	Schwarz criterion		1.09566
Log likelihood	-5.50939	Hannan-Quinn criter.		1.00025
F-statistic	2.72467	Durbin-Watson stat		0.27875
Prob(Wald F-stat.)	0.02307	Wald F-statistic		6.63132

The model fits better, the residual series of this equation is tested for smoothness by applying the ADF unit root test, and the results of the ADF test are shown in Table 5. The value of the ADF test statistic is -3.522055, which is smaller than the critical value of -2.006292 at the 5% significance level, and therefore it can be known that the residual series is smooth, and the above regression equation is a co-integration equation, i.e., LGGDP and LGF have a co-integration relationship, which means that there is a co-integration relationship between LGGDP and LGF. Through the co-integration coefficient, it can be seen that the overall economic openness has a very significant impact on economic growth, and every percentage point increase in the overall economic openness will cause GDP to increase by 0.48532 percentage points.

Table 5.

ADF test results

Augmented Dickey-Fuller test statistic		-3.522055
Test critical values	1% level	-2.937216
	5% level	-2.006292
	10% level	-1.598068

3.3

Error correction model

Herein, an error correction model is built for analyzing the short-term relationship between economic openness and economic growth. The previous co-integration analysis on the long-term impact of each economic openness indicator on economic growth has been performed. There is a long-term stable relationship between them, and the residuals of the model will be noted as: (17) ${\hat{ε}}_{t} = L N G D P - 0.48532 * L N F - 12.0038$

The following error correction model is built with $\hat{ε}$ as the equilibrium error and the regression results are: (18) $Δ L N G D P_{t} = 0.0904 - 0.003364 Δ L N F_{t} - 0.08485 {\hat{ε}}_{t}_{- 1}$

In the above regression equation, 0.0904 is the constant, -0.003364 is the regression coefficient of the degree of economic openness, and -0.08485 is the error term. All coefficients are calculated by statistical software.

In the long run, every 1% increase in the openness of China’s economy will raise economic growth by 0.48532%. In the short run, the openness of the Chinese economy has a minor impact on economic growth over the same period. This is less than the long-term equilibrium level of economic growth. When short-term fluctuations in China’s economic growth deviate from the long-term equilibrium, last year’s disequilibrium error will pull the disequilibrium back to the equilibrium level at a rate of 0.08485. The coefficient of the error correction term is negative, which is consistent with the reverse correction mechanism.

3.4

Granger Causality Test

From the results of the co-integration test, it can be seen that there exists a long-run equilibrium relationship as well as a short-run dynamic relationship between China’s economic growth and economic openness, but whether this relationship constitutes a causal relationship and what is the direction of the causal relationship need to be further verified. In this paper, the causality test proposed by Granger is used to solve this problem.

The Granger causality test is carried out using equation (14), and the test results are shown in Table 6. It can be seen that there is a unidirectional Granger causality between China’s economic openness and China’s economic growth, i.e., high-quality openness is the cause of promoting economic growth, while economic growth is not the cause of high-quality openness. This causal relationship is also highly significant (p=0.01422).

Table 6.

Granger causality test results

Null Hypothesis	Lag	F-Statistic	Probability
LGX1 does not Granger Cause LGGDP	1	6.12443	0.02121
LGGDP does not Granger Cause LGX1	1	0.92121	0.34241
LGX2 does not Granger Cause LGGDP	1	9.45274	0.01242
LGGDP does not Granger Cause LGX2	1	1.24537	0.12112
LGX3 does not Granger Cause LGGDP	1	6.45276	0.00152
LGGDP does not Granger Cause LGX3	1	0.45769	0.24241
LGX4 does not Granger Cause LGGDP	3	5.12445	0.01424
LGGDP does not Granger Cause LGX4	3	0.24207	0.34214
LGX5 does not Granger Cause LGGDP	4	4.27524	0.00124
LGGDP does not Granger Cause LGX5	4	3.21452	0.96113
LGX6 does not Granger Cause LGGDP	2	1.24577	0.31421
LGGDP does not Granger Cause LGX6	2	9.21425	0.01042
LGX7 does not Granger Cause LGGDP	1	6.45272	0.00142
LGGDP does not Granger Cause LGX7	1	0.45272	0.96341
LGF does not Granger Cause LGGDP	1	6.45212	0.01422
LGGDP does not Granger Cause LGF	1	0.45274	0.24242

4

Conclusion

The study explores the relationship between high-quality openness and China’s economic growth using techniques such as co-integration analysis and error correction modeling. The empirical analysis shows that: 1)

There is a long-term stable equilibrium relationship between economic openness and economic growth, and economic openness has a significant positive impact on economic growth, and every percentage point increase in overall economic openness will cause GDP to rise by 0.48532 percentage points.

2)

The promotion effect of economic openness on economic growth will deviate from the long-term level in the short term, but the reverse error correction mechanism will gradually bring it back to the long-term stable level.

3)

The causal relationship between economic openness and economic growth is unidirectional, and economic openness has a positive effect on China’s economic growth. It also reflects that high-quality openness can promote China’s economic growth.

Language:: English

Publication timeframe:: 1 times per year
Journal Subjects:: Life Sciences, Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics, Physics, other

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A study on the impact of high-quality openness on China’s economic growth based on mathematical statistics

Jie Gao

Published Online: Mar 24, 2025

Received: Oct 10, 2024

Accepted: Feb 03, 2025

DOI: https://doi.org/10.2478/amns-2025-0726

KeywordsCo-integration analysis, Error correction, Granger causality, China’s economic growth, High-quality openness

© 2025 Jie Gao, published by Sciendo

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

Keywords
Co-integration analysis, Error correction, Granger causality, China’s economic growth, High-quality openness