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

Jie Gao

Jie Gao

School of Economics, Shanghai University of Finance and EconomicsShanghai, China
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Gao, Jie
  
24 mar 2025
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Pubblicato online: 24 mar 2025
Ricevuto: 10 ott 2024
Accettato: 03 feb 2025
DOI: https://doi.org/10.2478/amns-2025-0726
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© 2025 Jie Gao, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

Economic openness and GDP
Economic openness and GDP

Figure 2.

Economic openness and GDP growth
Economic openness and GDP growth

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

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

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

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

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 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
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Scienze biologiche, Scienze della vita, altro, Matematica, Matematica applicata, Matematica generale, Fisica, Fisica, altro
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