Methodological Evaluation and Proxy Variable Selection in TFP Estimation: Evidence from China’s Provincial and Industrial Data (1998–2022)

Total factor productivity (TFP) is crucial for evaluating technological innovation, yet its accurate measurement remains challenging due to diverse methodologies. Notably, the selection of proxy variables in control function approach (CFA) significantly influences TFP estimation, yet existing studies have failed to clarify the criteria for proxy variable selection, particularly at meso and macro levels. This study employs a comprehensive methodological framework integrating significance, robustness, and comparative analyses to assess TFP estimation methods, addressing prevalent misconceptions. We utilize data sourced from 30 Chinese provinces across three major industries over the period 1998–2022, and conduct TFP calculations employing theoretically comparable methods. Our findings reveal significant discrepancies among methods, emphasizing the impact of proxy variable selection on TFP outcomes. This study finds that while CFA shows comparable performance to traditional production function approach (PFA) in terms of goodness-of-fit and significance (it does not verify the first level of Hypothesis 1 set forth in this study), it excels in reducing TFP estimation volatility (it verifies the second level of Hypothesis 1 set forth in this study). Crucially, proxy variable selection significantly impacts TFP results. We provide empirical norms for proxy variable selection at macro and meso levels, although Hypothesis 2 was not fully validated, offering a standardized framework to enhance TFP measurement accuracy and robustness: energy input is superior for lowly heterogeneous subjects, whereas intermediate input is preferable for those with high heterogeneity, offering valuable implications for policymakers and researchers.