Estimation Bias in Production Functions Under Intelligent Manufacturing
WANG Wenbin, WANG Yongjin
Institute of International Organizations and the Global South Studies/The Laboratory for Economic Behaviors and Policy Simulation/School of Economics, Nankai University
Summary:
Total factor productivity (TFP) is a core indicator of firm performance and economic growth, and a key metric for evaluating technological progress and the effects of economic policies. The existing literature on the production function and productivity estimation largely rests on the assumption that the functional form of the production function is exogenously determined and stable. However, with the rapid advancement of intelligent manufacturing, this assumption is facing significant challenges. The defining feature of intelligent manufacturing is the substitution of machines for labor, which not only alters the ratio of capital to labor inputs but also makes the factor input share of firms endogenously determined by relative factor prices, factor-specific productivity, and the scope of substitution. In this context, continuing to rely on conventional methods to estimate production functions and TFP may lead researchers to mistake firms' endogenous adjustment of input choices for productivity changes. This, in turn, generates systematic bias and distorts the evaluation of technological progress, resource allocation efficiency, and industrial policy. Consequently, accurately estimating production functions and TFP in the context of intelligent manufacturing remains a critical theoretical and empirical challenge. To address this question, this paper develops a theoretical model with endogenous technology choice and proposes a new method for production function estimation. Relative to existing approaches, our method does not treat factor shares as exogenous constants. Instead, it explicitly incorporates firms’ endogenous technology choices, thereby allowing for more consistent identification of production function parameters and, in turn, more accurate measurement of TFP. We first assess the performance of the proposed estimator through Monte Carlo simulations. The results show that our method recovers the true parameters with relatively high accuracy, whereas conventional methods, namely the LP and ACF estimators, as well as the nonparametric GNR methods, exhibit significant bias. We then apply our method to Chinese manufacturing firms for the period of 1998 to 2013 to estimate production functions and TFP, and further examine the distribution, dynamics, and heterogeneity of productivity. We leverage data from this period because capital-labor substitution is not unique to the era of intelligent manufacturing; intelligent manufacturing mainly expands the range of substitution and reduces its cost. Therefore, if the gap between existing methods and our method is already substantial during the early stage of intelligent manufacturing, it will inevitably be magnified in periods when intelligent manufacturing is more pervasive. This paper yields several main findings. First, the Monte Carlo simulations show that both conventional and nonparametric methods suffer from sizable bias in estimating production functions. Second, our estimates indicate that manufacturing firms in China do exhibit substantial capital-labor substitution and that the production function is not of the standard Cobb-Douglas form, thereby validating the model specification. At the same time, capital productivity is generally higher than labor productivity, with the former being roughly two to three times the latter. This suggests that firms substitute capital for labor not only because relative prices change, but also because capital is more productive. Third, compared with conventional and nonparametric methods, our approach yields a substantially greater degree of within-industry productivity dispersion. This implies that existing methods seriously underestimate the true dispersion of productivity because they fail to account for firms’ endogenous technology choice. Fourth, the productivity decomposition shows that productivity growth in Chinese manufacturing over 1998 to 2013 was driven mainly by productivity improvements within incumbent firms, rather than by the extensive-margin contribution of firm entry and exit. Fifth, firm heterogeneity is pronounced: productivity differs substantially across ownership types, with non-state-owned firms outperforming state-owned firms on average. By contrast, productivity differences between exporters and non-exporters are not statistically significant. The contributions of this paper are fourfold. First,motivated by the fact that intelligent manufacturing fundamentally changes firms’ mode of production, we show that the existing production function estimation literature has overlooked the crucial role of endogenous technology choice. By building a theoretical model around this mechanism and proposing a new estimation strategy, we extend the literature on production function and productivity estimation. Second, we link intelligent manufacturing and automation to the problem of productivity measurement, showing that existing empirical studies on the effects of intelligent manufacturing may be contaminated by productivity mismeasurement. In this sense, this paper provides a new methodological foundation for reassessing the economic consequences of digital technologies and automation. Third, we show that ignoring endogenous technology choice leads to a systematic underestimate of within-industry productivity dispersion. This implies that existing estimates of resource misallocation may be overly conservative, and thus offers a new perspective for re-evaluating the extent of misallocation in Chinese manufacturing and the potential gains from improving allocation efficiency. Finally, our analytical framework is broadly adaptable. It is applicable not only to firm-level productivity analysis, but also to broader work on resource allocation, industrial policy, and general equilibrium analysis. This paper emphasizes several key policy implications. First, as intelligent manufacturing continues to deepen, neither academic research nor policy evaluation should continue to rely on conventional methods that assume an exogenous and invariant production function by default. Instead, both should explicitly take into account that firms adjust technology choices endogenously in response to input prices and technological conditions. Reliable inference on technological progress and policy effects requires accurate measurement of productivity as a prerequisite. Second, since productivity growth in Chinese manufacturing is driven mainly by efficiency gains within incumbent firms, while the reallocation effect across firms is negative, the next stage of reform should not only continue to support technological upgrading and intelligent transformation at the firm level, but also deepen market-oriented factor reforms so as to channel resources toward more efficient firms and improve allocative efficiency. Third, given the substantial productivity gap that remains across ownership types, continued reform of state-owned enterprises, together with better incentive design and resource allocation mechanisms, remains essential for raising aggregate productivity. This paper also offers several directions for future research. On the one hand, our estimation framework can be applied to more recent firm-level microdata to examine how endogenous technology choice affects production function estimation and productivity measurement in the context of the wider diffusion of artificial intelligence, industrial robots, and platform-based production. On the other hand, our framework can be combined with the measurement of resource misallocation to reassess thereal magnitude of allocative efficiency losses in Chinese manufacturing and even in services. More broadly, institutional features such as subsidies, tax incentives, credit constraints, and R&D policies can be incorporated into the model to study how they shape firms’ technology choices, the distribution of productivity, and industry dynamics.
王文斌, 王永进. 智能制造背景下的生产函数估计偏误[J]. 金融研究, 2026, 551(5): 40-58.
WANG Wenbin, WANG Yongjin. Estimation Bias in Production Functions Under Intelligent Manufacturing. Journal of Financial Research, 2026, 551(5): 40-58.
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