This paper delves into the relationship between the volatility of the capital market and economic growth within the broader framework of the macro capital market. By employing the Heston stochastic volatility model in tandem with macroeconomic theory, we aim to analyze the stochastic control problem between the allocation trajectory of macro-capital and economic fluctuations. Our mathematical analysis reveals that the influence of capital shifts on economic growth's volatility varies across different capital markets due to diverse risk levels inherent within the macro-capital market. To validate these mathematical findings, we embark on an empirical econometric analysis tailored to the nuances of China's capital market and its macroeconomic operations. This econometric exploration yields two primary insights: 1. Distinct components of China's capital market have varying influences on macroeconomic growth. 2. The structure of China's capital market, especially in its impact on macroeconomic development, exhibits imbalances and lacks optimal configuration.

This paper selects the panel data of 297 cities in China from 2003 to 2017 and analyzes the effects of government efficiency and innovation environment on the relationship between high-speed rail opening and economic growth from the perspective of government competition pressure and information flow by using the approach of difference-in-differences (DID). The findings are as follows: first, the opening of high-speed rail has a significant promoting effect on regional economic growth; second, government efficiency has negative impact on the relationship between high-speed rail development and economic growth, while the innovation environment has positive impact on this relationship; third, the moderating effects of government efficiency and innovation environment exhibit regional heterogeneity. This paper provides a new perspective from the perspectives of government competition pressure and information flow for understanding the impact of high-speed rail on the economy, offering insights for promoting the coordinated and sustainable development of the Chinese economy.