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Peer effect analysis with latent processes

Vincent Starck

Abstract

I study peer effects that arise from irreversible decisions in the absence of a standard social equilibrium. I model a latent sequence of decisions in continuous time and obtain a closed-form expression for the likelihood, which allows to estimate proposed causal estimands. The method avoids linear-in-means regression by modeling the (possibly unobserved) realized direction of causality, whose probability is identified. I provide identification and estimation results under two settings, several networks and one large network, while allowing for various forms of peer effect heterogeneity. Under (strong) data requirements, it is possible to separate endogenous, contextual, and correlated effects while allowing for full heterogeneity and maximum likelihood methods where parameters lend themselves to standard inference.

Peer effect analysis with latent processes

Abstract

I study peer effects that arise from irreversible decisions in the absence of a standard social equilibrium. I model a latent sequence of decisions in continuous time and obtain a closed-form expression for the likelihood, which allows to estimate proposed causal estimands. The method avoids linear-in-means regression by modeling the (possibly unobserved) realized direction of causality, whose probability is identified. I provide identification and estimation results under two settings, several networks and one large network, while allowing for various forms of peer effect heterogeneity. Under (strong) data requirements, it is possible to separate endogenous, contextual, and correlated effects while allowing for full heterogeneity and maximum likelihood methods where parameters lend themselves to standard inference.

Paper Structure

This paper contains 9 sections, 5 theorems, 49 equations, 3 tables.

Table of Contents

  1. Introduction
  2. Causality, stochastic process, and likelihood
  3. Setup and causal peer effect parameters
  4. Stochastic process and unconfoundedness
  5. Likelihood
  6. Identification
  7. Asymptotic Theory
  8. Identification under block structure
  9. Identification under sparsity

Key Result

Proposition 1

Unconfoundedness of timings is equivalent to independence of latent partial times.

Theorems & Definitions (21)

  • Remark 1: Beyond binary outcomes
  • Definition 1: Stochastic process
  • Proposition 1
  • Example 1
  • Example 2
  • Example 3
  • Theorem 2
  • Example 4
  • Remark 2: 2 people example
  • Remark 3: Computation
  • ...and 11 more