Output elasticities and inter-factor substitution: Empirical evidence from the transportation sector of Shanghai

As a major consumer of fossil fuels, the transportation sector in Shanghai presents a wide range of problems, including air pollution, noise, and traffic congestion. This study aims to explore the energy substitution effect based on a trans-log production function to evaluate the contribution of each input factor to sectoral output, and reveal the substitution possibilities between capital, labor, and energy. To deal with a multicollinearity problem, we adopt ridge regression to obtain the coefficient of each variable under the appropriate penalty value. The bootstrap method is used for making statistical inferences, and the 95% confidence interval is obtained with 1000 bootstrap samples. The empirical results demonstrate the following. (1) The output elasticities of capital (0.13–0.15), labor (0.24–0.25), and energy (0.43–0.48) are positive and show an increasing trend over the study period. (2) The substitution elasticity between labor and energy is the highest among the input factors (around 1.0095), with a slight decreasing trend. (3) The substitution elasticity between energy and capital ranges from 1.0018 to 1.0021, and the substitution elasticity between capital and labor is infinitely close to 1.