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Revisiting the Identification of the Conduct Parameter in Homogeneous Goods Markets

Yuri Matsumura, Suguru Otani

TL;DR

This paper revisits the identification of the conduct parameter $\theta$ in homogeneous-good markets and argues that Lau's claim—non-identification iff the inverse demand is separable in demand shifters—is incomplete. It shows that identification hinges on the presence of demand rotation instruments, which can simultaneously alter the slope and intercept of the inverse demand, and it derives a precise necessary-and-sufficient condition for non-identification in terms of these instruments. The authors provide a constructive sufficient condition for non-identification via a transformation that keeps the equilibrium outcome invariant across competing conduct specifications, and they clarify the technical gaps in Lau's proof related to shifter dependence and differentiability. The results refine the theoretical underpinnings of the conduct-parameter method, clarifying when and how demand variation can identify competitive conduct and informing empirical practice, including firm-conduct tests and micro-foundations of the approach.

Abstract

We revisit the identification of the conduct parameter in homogeneous goods markets. Lau (1982) argues that the conduct parameter is not identified if and only if the inverse demand function is separable, except for a specific separable function. This result has been regarded as an extension of the result in Bresnahan (1982) to more general settings. However, we show that Lau's claim is incorrect and provide a new characterization of the non-identification. Our characterization shows that a demand function with demand rotation instruments is the necessary and sufficient condition for the identification of the conduct parameter. Therefore, our result properly generalizes the role of demand rotation instruments in identifying the conduct parameter, as highlighted by Bresnahan (1982), to more general settings.

Revisiting the Identification of the Conduct Parameter in Homogeneous Goods Markets

TL;DR

This paper revisits the identification of the conduct parameter in homogeneous-good markets and argues that Lau's claim—non-identification iff the inverse demand is separable in demand shifters—is incomplete. It shows that identification hinges on the presence of demand rotation instruments, which can simultaneously alter the slope and intercept of the inverse demand, and it derives a precise necessary-and-sufficient condition for non-identification in terms of these instruments. The authors provide a constructive sufficient condition for non-identification via a transformation that keeps the equilibrium outcome invariant across competing conduct specifications, and they clarify the technical gaps in Lau's proof related to shifter dependence and differentiability. The results refine the theoretical underpinnings of the conduct-parameter method, clarifying when and how demand variation can identify competitive conduct and informing empirical practice, including firm-conduct tests and micro-foundations of the approach.

Abstract

We revisit the identification of the conduct parameter in homogeneous goods markets. Lau (1982) argues that the conduct parameter is not identified if and only if the inverse demand function is separable, except for a specific separable function. This result has been regarded as an extension of the result in Bresnahan (1982) to more general settings. However, we show that Lau's claim is incorrect and provide a new characterization of the non-identification. Our characterization shows that a demand function with demand rotation instruments is the necessary and sufficient condition for the identification of the conduct parameter. Therefore, our result properly generalizes the role of demand rotation instruments in identifying the conduct parameter, as highlighted by Bresnahan (1982), to more general settings.

Paper Structure

This paper contains 29 sections, 9 theorems, 104 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Setting
  3. Conduct Parameter Model
  4. The Data Generation Process
  5. Definitions
  6. Main Result: Characterization of the Non-identification
  7. Lau's Claim
  8. Main Result
  9. Necessary Condition for the Non-identification
  10. Case: The denominators of $C_i$ and $D_i$ are zero for some demand shifters
  11. Case: The denominators of $C_i$ and $D_i$ are not zero
  12. Sufficient Condition for Non-identification
  13. Discussion
  14. Rethinking the role of demand rotation instruments:
  15. The technical problem in Lau's proof:
  16. ...and 14 more sections

Key Result

Corollary 1

The conduct parameter and the marginal cost are said to be identified if for any two distinct pairs of a conduct parameter and a marginal cost function, there exists a pair of demand shifters $\tilde{\bm{X}}^{d}$ and $\tilde{\bm{X}}^{s}$ where the equilibrium quantity $Q^e$ is different, that is, $h

Figures (1)

  • Figure 1: Intuition of the role of the demand rotation instrument and identification

Theorems & Definitions (14)

  • Remark 1
  • Definition 1
  • Corollary 1
  • Claim 1
  • Theorem 1
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Remark 2
  • ...and 4 more