Research on the relationship between government subsidies, R&D investment and high-quality development of manufacturing industry

Taking the mixed cross-sectional data of large and medium-sized industrial enterprises in Shanghai from 2014 to 2021 as the research sample, this paper empirically analyses the impact of government subsidies and R&D investment on the high-quality development of the manufacturing industry. First, the quantile regression model is established to analyse the relationship among the three factors, and the asymmetric linear loss function is introduced to obtain the point estimation of quantile. According to the Moivre–Laplace limit theorem, the asymptotic distribution is obtained; the sample quantile function is calculated and the fitting residual of quantile regression is used to estimate the asymptotic covariance matrix. The model was tested by goodness-of-fit criterion; it can more comprehensively describe the characteristics of distribution, so as to get a comprehensive conclusion. The experimental results show that: with increase of the quantile, the advantage gradually increases. Medium-sized enterprises have a less significant ‘inverted U’ relationship at 0.8, while large enterprises have a more significant ‘U’ relationship at 0.2–0.5. It can effectively reduce the estimation deviation and reduce the root mean squared error, so as to improve the estimation accuracy.