Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Identifying Behavioral Types

Christopher Kops, Paola Manzini, Marco Mariotti, Illia Pasichnichenko

TL;DR

This paper develops necessary and sufficient conditions for identifying the distribution of latent behavioral types from aggregate choice data, under minimal qualitative knowledge about how types map to alternatives. It shows that identifiability hinges on sufficient cross-type heterogeneity, formalized through combinatorial matchings between types and alternatives and through algebraic properties (nullspaces) of the type-level choice matrices. The authors introduce the type-state framework, deriving both matching-based and nullspace characterizations of generic and global identifiability, and extend the analysis to multiple choice occasions via tensor decomposition theory. Applications to vectors of characteristics and incomplete preferences illustrate the broad relevance and practical implications, including when aggregate data suffices to recover the underlying type distribution and, in some cases, the type-level probabilities themselves.

Abstract

We study identification in models of aggregate choice generated by unobserved behavioral types. An analyst observes only aggregate choice behavior, while the population distribution of types and their type-level choice patterns are latent. Assuming only minimal and purely qualitative prior knowledge of the process generating type-level choice probabilities, we characterize necessary and sufficient conditions for identifiability. Identification obtains if and only if the data exhibit sufficient cross-type behavioral heterogeneity, which we characterize equivalently through combinatorial matching conditions between types and alternatives, and through algebraic properties of the matrices mapping type-level to aggregate choice behavior.

Identifying Behavioral Types

TL;DR

This paper develops necessary and sufficient conditions for identifying the distribution of latent behavioral types from aggregate choice data, under minimal qualitative knowledge about how types map to alternatives. It shows that identifiability hinges on sufficient cross-type heterogeneity, formalized through combinatorial matchings between types and alternatives and through algebraic properties (nullspaces) of the type-level choice matrices. The authors introduce the type-state framework, deriving both matching-based and nullspace characterizations of generic and global identifiability, and extend the analysis to multiple choice occasions via tensor decomposition theory. Applications to vectors of characteristics and incomplete preferences illustrate the broad relevance and practical implications, including when aggregate data suffices to recover the underlying type distribution and, in some cases, the type-level probabilities themselves.

Abstract

We study identification in models of aggregate choice generated by unobserved behavioral types. An analyst observes only aggregate choice behavior, while the population distribution of types and their type-level choice patterns are latent. Assuming only minimal and purely qualitative prior knowledge of the process generating type-level choice probabilities, we characterize necessary and sufficient conditions for identifiability. Identification obtains if and only if the data exhibit sufficient cross-type behavioral heterogeneity, which we characterize equivalently through combinatorial matching conditions between types and alternatives, and through algebraic properties of the matrices mapping type-level to aggregate choice behavior.
Paper Structure (32 sections, 13 theorems, 73 equations, 1 figure)

This paper contains 32 sections, 13 theorems, 73 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Related literature
  3. Framework and definitions
  4. Characterizing identifiability of the type distribution
  5. Global identifiability
  6. The type-state framework
  7. Identifiability of the type distribution via matching
  8. Global identifiability
  9. Identification of the type distribution via nullspace conditions
  10. The $2\times2$ and $3\times3$ cases
  11. The general $r\times r$ case
  12. Multiple choice occasions and the identification of type-level choice probabilities
  13. General framework
  14. Type-state framework
  15. Applications
  16. ...and 17 more sections

Key Result

Theorem 1

The parameters in $\pi$ are generically identifiable if and only if there exists a matching $m:T\to X$. In addition, if a matching exists and it is unique, then the parameters in $\pi$ are globally identifiable. If no matching exists, then the parameters in $\pi$ are structurally non-identifiable.

Figures (1)

  • Figure 1: Choice problem in Example \ref{['example multiocc 1']}

Theorems & Definitions (63)

  • Definition 1
  • Definition 2
  • Theorem 1
  • proof
  • Remark 1
  • Example 1
  • Example 2
  • Theorem 2
  • proof
  • Example 3
  • ...and 53 more