Bayesian Propensity Score-Augmented Latent Factor Models for Causal Inference with Time-Series Cross-Sectional Data

2026-03-26

AI Summary

This study addresses key challenges in causal inference with time-series cross-sectional data, where joint modeling of the treatment assignment mechanism and outcome model is difficult, and unobserved heterogeneity and confounding are hard to control. The authors propose a Bayesian latent factor model enhanced with propensity scores, which incorporates latent factor loadings into the treatment assignment mechanism and flexibly integrates propensity scores—such as through stratification—into the outcome model to effectively capture heterogeneity within propensity score strata. By jointly modeling propensity scores and latent factor structures within a unified Bayesian framework, the approach mitigates the feedback problem commonly encountered in traditional Bayesian propensity score analyses. Monte Carlo simulations demonstrate its strong finite-sample performance, and empirical application successfully identifies the causal effect of political connections on firm value.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose a Bayesian propensity score-augmented latent factor model for causal inference with time-series cross-sectional data. The framework explicitly models the treatment assignment mechanism by incorporating latent factor loadings, while the outcome model flexibly incorporates the propensity score, for example through stratification. Relative to existing approaches, the proposed method provides greater flexibility and captures additional heterogeneity across propensity-score strata, enabling more credible comparisons between treated and control units within each stratum. For estimation and inference, we adopt an approximate Bayesian procedure to address the model feedback problem common in Bayesian propensity score analysis. We demonstrate the performance of the proposed method through Monte Carlo simulations and an empirical application examining the effect of political connections on firm value.

Problem

• causal inference
• time-series cross-sectional data
• propensity score
• latent factor models
• treatment assignment

Innovation

• Bayesian causal inference
• propensity score stratification
• latent factor models
• time-series cross-sectional data
• model feedback problem