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The Econometrics of Utility Transferability in Dyadic Network Formation Models

Joseph Marshall

Abstract

This paper studies how to estimate an individual's taste for forming a connection with another individual in a network. It compares the difficulty of estimation with and without the assumption that utility is transferable between individuals, and with and without the assumption that regressors are symmetric across individuals in the pair. I show that when pair-specific regressors are symmetric, the sufficient conditions for consistency and asymptotic normality of the maximum likelihood estimator that assumes transferable utility (TU-MLE) are also sufficient for the maximum likelihood estimator that does not assume transferable utility (NTU-MLE). When regressors are asymmetric, I provide sufficient conditions for the consistency and asymptotic normality of the NTU-MLE. I also provide a specification test to assess the validity of the transferable utility assumption. Two applications from different fields of economics demonstrate the value of my results. I find evidence of researchers using the TU-MLE when the transferable utility assumption is violated, and evidence of researchers using NTU-model-based estimators when the validity of the transferable utility assumption cannot be rejected.

The Econometrics of Utility Transferability in Dyadic Network Formation Models

Abstract

This paper studies how to estimate an individual's taste for forming a connection with another individual in a network. It compares the difficulty of estimation with and without the assumption that utility is transferable between individuals, and with and without the assumption that regressors are symmetric across individuals in the pair. I show that when pair-specific regressors are symmetric, the sufficient conditions for consistency and asymptotic normality of the maximum likelihood estimator that assumes transferable utility (TU-MLE) are also sufficient for the maximum likelihood estimator that does not assume transferable utility (NTU-MLE). When regressors are asymmetric, I provide sufficient conditions for the consistency and asymptotic normality of the NTU-MLE. I also provide a specification test to assess the validity of the transferable utility assumption. Two applications from different fields of economics demonstrate the value of my results. I find evidence of researchers using the TU-MLE when the transferable utility assumption is violated, and evidence of researchers using NTU-model-based estimators when the validity of the transferable utility assumption cannot be rejected.

Paper Structure

This paper contains 23 sections, 11 theorems, 32 equations, 2 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Transferable Utility (TU) Model
  3. Non-Transferable Utility (NTU) Model
  4. Contribution
  5. Properties of the NTU-MLE
  6. With Symmetric Regressors
  7. Identification
  8. Consistency
  9. Asymptotic Normality
  10. With Asymmetric Regressors
  11. Identification
  12. Consistency
  13. Asymptotic Normality
  14. Other Model Extensions
  15. Testing for Utility Transferability
  16. ...and 8 more sections

Key Result

Theorem 1

Consider the NTU model with $\rho = 0$ and $W_{ij} = W_{ji}$ for all pairs $ij$. If (1a) $\Theta$ is bounded and convex and $\beta_0 \in \text{interior}(\Theta)$, (1b) $X_i$ is i.i.d., and (1c) $\mathbb{E} [W_{ij} W_{ij}']$ exists and is nonsingular, then the NTU-MLE, $\hat{\beta} = \argmax_{\beta \

Figures (2)

  • Figure 1: Visualizing the Gap in the Literature
  • Figure 2: Specification Test Power Curves

Theorems & Definitions (16)

  • Theorem 1: Consistency with Symmetric Regressors
  • proof
  • Theorem 2: Asymptotic Normality with Symmetric Regressors
  • proof
  • Proposition 1
  • proof
  • Theorem 3: Consistency with Asymmetric Regressors
  • proof
  • Theorem 4: Asymptotic Normality with Asymmetric Regressors
  • proof
  • ...and 6 more