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Identification and Estimation of Production Function and Consumer Demand Function under Monopolistic Competition from Revenue Data

Chun Pang Chow, Hiroyuki Kasahara, Yoichi Sugita

Abstract

We establish nonparametric identification of production functions, total factor productivity (TFP), price markups, and firms' output prices and quantities, as well as consumer demand, using firm-level revenue data, without observing output quantity, in a monopolistically competitive environment with a fully nonparametric demand system. This result overturns the widely held view -- formalized by Bond, Hashemi, Kaplan, and Zoch (2021) -- that output elasticities and markups are not nonparametrically identifiable from revenue data without quantity information. Under the additional restriction that demand satisfies the homothetic single-aggregator (HSA) structure of Matsuyama and Ushchev (2017), we further nonparametrically identify the representative consumer's utility function from firm-level revenue data. This new identification result enables counterfactual welfare analysis without parametric assumptions on preferences. We propose a semiparametric estimator that is feasible for standard firm-level datasets under a Cobb--Douglas production specification. Monte Carlo simulations show that the estimator performs well, while treating revenue as output induces substantial bias. Applying the estimator to Chilean manufacturing data, we reject the CES specification in favor of HSA, and find that market power reduces welfare by approximately 3%--6% of industry revenue in the three largest manufacturing industries in 1996.

Identification and Estimation of Production Function and Consumer Demand Function under Monopolistic Competition from Revenue Data

Abstract

We establish nonparametric identification of production functions, total factor productivity (TFP), price markups, and firms' output prices and quantities, as well as consumer demand, using firm-level revenue data, without observing output quantity, in a monopolistically competitive environment with a fully nonparametric demand system. This result overturns the widely held view -- formalized by Bond, Hashemi, Kaplan, and Zoch (2021) -- that output elasticities and markups are not nonparametrically identifiable from revenue data without quantity information. Under the additional restriction that demand satisfies the homothetic single-aggregator (HSA) structure of Matsuyama and Ushchev (2017), we further nonparametrically identify the representative consumer's utility function from firm-level revenue data. This new identification result enables counterfactual welfare analysis without parametric assumptions on preferences. We propose a semiparametric estimator that is feasible for standard firm-level datasets under a Cobb--Douglas production specification. Monte Carlo simulations show that the estimator performs well, while treating revenue as output induces substantial bias. Applying the estimator to Chilean manufacturing data, we reject the CES specification in favor of HSA, and find that market power reduces welfare by approximately 3%--6% of industry revenue in the three largest manufacturing industries in 1996.
Paper Structure (70 sections, 16 theorems, 244 equations, 7 figures, 10 tables)

This paper contains 70 sections, 16 theorems, 244 equations, 7 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Identification
  3. Setting
  4. Identification in a Parametric Example: Generalized CES Demand with Heterogeneity
  5. Step 1: Identification of the Demand Shocks
  6. Step 2: Identification of Control Function and TFP
  7. Step 3: Identification of Production Function, Markup, and Demand Function
  8. The Identification under Normalization
  9. Nonparametric Identification
  10. Step 1: Identification of the Demand Shocks
  11. Step 2: Identification of Control Function and TFP
  12. Step 3: Identification of Production Function, Markup, and Demand Function
  13. Comparison to Existing Identification Approaches
  14. Extensions to Alternative Settings
  15. Fixing Normalization across Periods
  16. ...and 55 more sections

Key Result

Proposition 1

Under Assumptions A-0, A-1, A-data, and assu: revenue monotonicity hold, $\phi_{t}(\cdot)$ and $u_{it}$ are identified.

Figures (7)

  • Figure 1: Production Function Estimation with ACF on Revenue Data and Quantity Data
  • Figure 2: Production Function and Demand System Estimation with Revenue Data
  • Figure 3: True and estimated TFPs and Markups for first 20 MC Simulations
  • Figure 4: Observed revenue vs. fitted revenue from Step 4
  • Figure 5: Rank of demand shock from Step 1 vs. Step 4
  • ...and 2 more figures

Theorems & Definitions (30)

  • Proposition 1
  • Proposition 2
  • proof
  • Remark 1: Support Requirements and Persistence
  • Proposition 3
  • proof
  • Corollary 1
  • Remark 2
  • Proposition 4
  • Proposition 5
  • ...and 20 more