This paper focuses on the estimation of carbon shadow price (CSP) by applying the by-production (BP) model within a nonparametric framework. The extended BP model ensures the meaningful shadow price estimation and linkages between the sub-technologies that define production and pollution activities. We focus on the instance of the Fare-Grosskopf-Lovell index that is important for empirical analysis due to its non-radial nature. The model is applied to China's industrial sector, which has undergone considerable development in recent decades. Data from 1998 to 2017 are used for the analysis, and the results suggest that the eastern region performs the best. In general, the CSP has been increasing in all regions, suggesting that cleaner energy has been introduced into the energy mix. Further promotion of the renewables would result in a decline in the CSP. The comparative analysis is carried out to check the effects of the axioms on the resulting estimates of the CSP.