The research explores the intricate relationship between trade openness, foreign direct investment (FDI), capital formation, and industrial economic growth, particularly within the context of China's rapid economic expansion. While global consensus acknowledges the importance of FDI and trade openness as catalysts for economic growth, particularly in developing nations, the specific dynamics and interdependencies between these factors remain a subject of ongoing debate. China's remarkable economic growth, fueled by increased FDI inflows and trade openness, provides an ideal case study. However, this growth model has raised concerns about its sustainability, given its reliance on extensive capital, labor, and resource inputs. This research aims to address these questions by investigating the dynamic relationships between these four key variables in China, specifically examining whether trade openness and FDI contribute positively to industrial economic growth, and whether these factors synergistically enhance growth through mechanisms such as technological innovation.

Existing literature presents conflicting views on the impact of trade openness and FDI on economic growth. Some studies highlight the positive contributions of FDI, emphasizing productivity increases, technology spillovers, and talent cultivation. Others suggest that FDI's effect on growth may be contingent on macroeconomic stability and the presence of supportive policies. The impact of trade openness is similarly debated, with studies showing positive effects through technological diffusion and industrial development, while others find insignificant or negative impacts. Regarding China, research specifically examining the link between trade openness, FDI, capital formation, and industrial economic growth is limited. Existing studies often adopt broader national or regional perspectives, neglecting the industrial sector-specific implications of foreign trade and FDI.

This study employs the Autoregressive Distributed Lag (ARDL) approach to analyze the long-run and short-run dynamics between China's trade openness (TRO), foreign direct investment (FDI), capital formation (K), and industrial economic growth (IEG). The ARDL model is chosen for its ability to handle variables with different integration orders, making it suitable for the analysis of short time series data such as the one used here (1990-2021). The study uses data obtained from the World Bank and the National Bureau of Statistics of China. Control variables, including inflation rate, labor force, and technological innovation, are incorporated to account for potential confounding factors. The data is transformed into double logarithmic format to ensure a more regular distribution and mitigate heteroskedasticity. Unit root tests (ADF and PP) are conducted to determine the stationarity of the variables. The ARDL bounds test is applied to investigate the existence of long-run co-integration relationships. The optimal lag length is determined using information criteria (AIC, SC, HQ, etc.). Once co-integration is confirmed, long-run coefficients are estimated using the ARDL model. A Vector Error Correction Model (VECM) is then constructed to analyze the short-run dynamics and the speed of adjustment to long-run equilibrium. Robustness tests (CUSUM and CUSUMSQ) are performed to assess the stability of the ARDL model.

The ARDL bounds test confirms the existence of a long-run co-integration relationship between IEG, TRO, FDI, and K. Long-run analysis reveals a positive and statistically significant relationship between FDI and IEG, supporting the notion that FDI inflows contribute to industrialization and economic growth. A 1% increase in FDI is associated with a 0.071% increase in IEG. Conversely, IEG positively impacts FDI. The long-run effects of industrial economic growth on trade openness and capital formation are also significant and positive. However, a notable finding is the negative relationship between trade openness and industrial economic growth in the long run, although not statistically significant. In the short run, the error correction term (ECM) indicates that the model adjusts relatively quickly (within 1-2 years) to long-run equilibrium following shocks. Short-run analysis largely supports the long-run findings of positive relationships between the variables, with some exceptions: a small, insignificant negative effect of trade openness and capital formation on industrial economic growth. The control variables (labor, technological innovation, and inflation) also show significant impacts on the relationships between the variables, generally consistent with the long-run results. Robustness tests generally confirm the stability of the model, though some instability is detected in the trade openness and capital formation models.

The findings of this research provide valuable insights into the complex interplay of trade openness, FDI, capital formation, and industrial economic growth in China. The confirmed long-run co-integration and predominantly positive relationships between these variables support the theoretical expectations of synergy between trade openness, investment, and industrial development. The findings emphasize the importance of FDI in driving industrial economic growth and also underline the positive role of capital formation in fostering this growth. The unexpected negative relationship between trade openness and industrial growth in the long run warrants further investigation, possibly attributable to specific aspects of China's trade structure or policy. The short-run dynamics, largely mirroring the long-run relationships, enhance our understanding of the immediate impacts and the speed at which the system adjusts to equilibrium after any disturbances.

This study contributes to a deeper understanding of the dynamic interactions between trade openness, FDI, capital formation, and industrial economic growth in China. The findings highlight the long-run co-integration and predominantly positive relationships among these key variables. Policy implications include strengthening investment promotion strategies, expanding trade openness, and addressing regional imbalances in FDI and trade. Future research could explore the regional variations within China and delve deeper into the negative long-run relationship between trade openness and industrial economic growth. Further investigation of the impact of specific trade policies and industry characteristics would also enrich the understanding of these dynamics.

The study's main limitation lies in its focus on national-level data, which potentially obscures regional variations in the relationships between the variables. The relatively short timeframe (1990-2021) might also limit the generalizability of the findings. Furthermore, while control variables were included, unobserved factors could still influence the relationships examined. The use of a single econometric model (ARDL) might limit the perspectives offered; future research could consider alternative approaches.