| Summary: | By observing the disturbance of indicators, models, and samples variability to the robustness of low carbon performance evaluation, the importance of random errors and heterogeneity of sample data is clarified. The carbon footprint joint total factor productivity conceptual framework is proposed in this study, then we apply it to a food production system in a region of China to reasonably judge the carbon footprint performance level of peasant households. With regard to the single-output production frontier, the internal method changes did not cause significant changes in the level of crop production technical efficiency in the deterministic and stochastic estimation strategies respectively. Although the results of partial low-carbon economic technical efficiency are consistent in the two estimation strategies, a significant difference is obvious for the low-carbon technical efficiency; The total low-carbon economic technical efficiency is significantly different between deterministic non-parametric slacks-based measure and parameterized random distance function estimation strategies under the framework of the multi-output production frontier; Ultimately, the total factor productivity including the carbon footprint of the food system in our research area close to the technical level of the industry, as well as the technical efficiency of the sample is at an efficient level.
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