Qingsong Pan (潘青松)

Research

Working Papers

1. Identification of Gross Output Production Functions with Nonseparable Productivity

   R&R · Review of Economic Studies

   Abstract

   We study nonparametric identification of gross-output production functions in which productivity enters nonseparably, relaxing Hicks neutrality, and use the framework to measure the bias of technical change. Under perfect competition, we extend Gandhi et al. (2020) (GNR) to identify output elasticities, and then impose an empirically motivated homogeneity restriction to obtain full identification of the technology. Under imperfect competition with revenue data, markups and returns to scale (RTS) are difficult to separately identify. We therefore calibrate RTS for point identification and show that the implied directions and relative magnitudes of technological bias are invariant to this calibration. Applying the framework to Chinese manufacturing firms (1998–2007), we find that technical change is predominantly capital-biased and least favorable to labor. Yet in the realized data, the marginal product of labor (MPL) rises the most over the decade. A decomposition resolves this apparent paradox: MPL growth is driven primarily by capital and materials deepening through factor complementarities rather than by productivity growth, whereas for capital and materials the opposite pattern holds. These findings point to biased technical change as a distinct force behind the pronounced factor deepening observed over this period.

2. Nonparametric Identification Using Timing and Information Set Assumptions with an Application to Non-Hicks Neutral Productivity Shocks

   with Daniel Ackerberg and Jinyong Hahn

   R&R · RAND Journal of Economics

   Abstract

   Recent studies in empirical industrial organization, both in production function and demand estimation, address endogeneity using assumptions regarding the time when agents chose endogenous variables and their information sets at those times. Using a control function framework, we show these assumptions can identify a nonparametric model with a nonseparable unobservable term. Moreover, the model's structure allows a relaxation of the strong support condition typical of control function approaches, which is empirically important in production function contexts. Our empirical application identifies nonseparable (non-Hicks-neutral) shocks in widely-used production datasets, revealing biased technological change consistent with prior literature, but in a distinct manner.

3. The Identification Power of μ-Strong Concavity Assumptions and Sensitivity Analyses

   Abstract

   This paper derives a set of partial identification results for the mean treatment response and the average treatment effect when the μ-strong concavity assumption is combined with the MTR or the MTR-MTS assumption. μ-strong concavity is a generalization of the usual concavity assumption and the parameter μ can be seen as a measure of the strength of concavity. By tuning the value of the parameter μ, a practitioner can conduct sensitivity analyses with respect to the concavity assumption. I illustrate my findings by reanalyzing the return to schooling example of Manski and Pepper (2000).

4. Markups, Marginal Costs, and Returns to Scale from Financial Statements

   Draft available upon request

   Abstract

   I generalize the Klette and Griliches (1996) framework beyond a CES demand system to a nonparametric demand system and beyond a Cobb–Douglas Hicks-neutral production function to a nonparametric, nonseparable production function. My method can be used to identify markups, returns to scale, and marginal costs from financial statements, while allowing for firm-level heterogeneity in all three objects. Applying this method to the Chinese food industry, I find that, relative to private firms, (i) SOEs exhibit lower productivity but also enjoy lower marginal costs; and (ii) SOEs operate under significantly stronger increasing returns to scale and charge higher markups. These findings contribute to a deeper understanding of SOE performance and help inform policies related to SOE reform.

5. Tracking Down the Unobserved Prices: A Constrained GMM Approach to Production Function Estimation

   with Daniel Ackerberg

   New draft coming soon · Slides upon request

   Abstract

   We show that the Klette–Griliches (1996) method, developed to consistently estimate returns to scale using financial statement data, is internally consistent only when a CES price index is employed. However, such a CES price index is rarely observed in practice. We propose a constrained generalized method of moments (GMM) estimator that treats the CES price index as an unknown parameter vector to be estimated, imposing the model-implied restrictions required for identification. Applying our approach to Chinese manufacturing data, we find robust evidence of markedly increasing returns to scale, substantially larger than those implied by existing methods.

Work in Progress

1. From Revenue to Production: Identification and Estimation

   with Vincent Mastantuno and Lixue Zhou

2. Shape-Restricted Production Functions: An Application to Allocative Efficiency

   with Daniel Ackerberg

   Abstract

   We propose a two-step nonparametric estimator of production functions. In the first step, we estimate the productivity shock from the input demand function using sieve MLE. In the second step, we estimate the production function using Bernstein polynomials after plugging in the estimated productivity shock. The use of Bernstein polynomials makes it easy to impose theory-based shape restrictions on the production function, such as monotonicity and concavity. With the shape restrictions, our second step is a disciplined convex programming (DCP) problem, which has attractive computational properties. Applying our estimator to commonly used production datasets, we find that, while the concavity restriction does not make much difference, imposing the monotonicity restriction can greatly reduce the dispersion of the estimated marginal productivity across firms, which implies much higher efficiency of resource allocation among firms.

Referee Service

• RAND Journal of Economics (x3)
• International Journal of Industrial Organization

Presentations

Invited Seminars

Western University (2023), McGill University (2023), University of Manchester (2023), Charles River Associates (2023), Peking University-Guanghua School of Management (2025), Peking University-PHBS (2025), Shanghai University of Economics and Finance (2025), Zhejiang University (2025), Hong Kong University of Science and Technology (2026).

Conferences

Texas Econometrics Camp (2023), Shandong University Summer Econometrics Conference (2024), Hong Kong University Firm and Industry Dynamics Workshop (2025), Econometric Society World Congress (2025), SUFE IO Conference (2026), EARIE (2026, scheduled).

Teaching