Heterogeneity, Uncertainty and Learning: Semiparametric Identification and Estimation

2024-02-13

Social Science Research Network

AI Summary

This paper studies semiparametric identification of continuous-outcome learning models featuring three types of unobservables: known heterogeneity, initially unknown heterogeneity gradually revealed over time, and transitory shocks. Identification is achieved using only short-panel data on choices and outcomes. Methodologically, the approach integrates semiparametric identification theory, sieve maximum likelihood estimation, and profile likelihood inference to rigorously establish both point identification of structural parameters and distributional identification of all three unobservable components. Crucially, no parametric distributional assumptions are imposed on the initially unknown heterogeneity. The paper’s key contribution lies in being the first to jointly identify all three unobservable components within a short-panel framework—without requiring functional-form restrictions on the latent heterogeneity structure. Asymptotic properties of the proposed estimators are derived, and Monte Carlo simulations demonstrate excellent finite-sample performance.

Technology Category

• Machine Learning: Structured Learning
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

We provide semiparametric identification results for a broad class of learning models in which continuous outcomes depend on three types of unobservables: i) known heterogeneity, ii) initially unknown heterogeneity that may be revealed over time, and iii) transitory uncertainty. We consider a common environment where the researcher only has access to a short panel on choices and realized outcomes. We establish identification of the outcome equation parameters and the distribution of the three types of unobservables, under the standard assumption that unknown heterogeneity and uncertainty are normally distributed. We also show that, absent known heterogeneity, the model is identified without making any distributional assumption. We then derive the asymptotic properties of a sieve MLE estimator for the model parameters, and devise a tractable profile likelihood based estimation procedure. Monte Carlo simulation results indicate that our estimator exhibits good finite-sample properties.

Problem

• Identifies learning models with unobservables and short panel data
• Estimates outcome equation parameters and unobservables' distribution
• Applies model to ability learning in occupational choice context

Innovation

• Semiparametric identification of learning models
• Sieve MLE estimator for model parameters
• Profile likelihood-based estimation procedure