Counterfactual Forecasting for Panel Data

TL;DR

This paper introduces FOCUS, a novel method for forecasting counterfactual outcomes in panel data with missing entries and latent factors, improving accuracy by leveraging time series dynamics.

Contribution

The paper proposes FOCUS, an extension of matrix completion that incorporates stochastic and deterministic factor dynamics for better counterfactual forecasting.

Findings

FOCUS outperforms existing benchmarks in autoregressive latent factor scenarios.

The method provides error bounds and asymptotic normality under standard conditions.

Empirical results on a mobile health study demonstrate practical effectiveness.

Abstract

We address the challenge of forecasting counterfactual outcomes in a panel data with missing entries and temporally dependent latent factors -- a common scenario in causal inference, where estimating unobserved potential outcomes ahead of time is essential. We propose Forecasting Counterfactuals under Stochastic Dynamics (FOCUS), a method that extends traditional matrix completion methods by leveraging time series dynamics of the factors, thereby enhancing the prediction accuracy of future counterfactuals. Building upon a consistent estimator of the factors, our method accommodates both stochastic and deterministic components within the factors, and provides a flexible framework for various applications. In case of stationary autoregressive factors and under standard conditions, we derive error bounds and establish asymptotic normality of our estimator. Empirical evaluations demonstrate that our method outperforms existing benchmarks when the latent factors have an autoregressive component. We illustrate FOCUS results on HeartSteps, a mobile health study, illustrating its effectiveness in forecasting step counts for users receiving activity prompts, thereby leveraging temporal patterns in user behavior.