Causal Data Fusion for Panel Data without a Pre-Intervention Period

Traditional panel-data causal inference frameworks, such as difference-in-differences and synthetic control methods, rely on pre-intervention data to estimate counterfactual means. However, such data may be unavailable in real-world settings when interventions are implemented in response to sudden events, such as public health crises or epidemiological shocks. In this paper, we introduce two data-fusion methods for causal inference from panel data in scenarios where pre-intervention data are unavailable. These methods leverage auxiliary reference domains with related panel data to estimate causal effects in the target domain, thereby overcoming the limitations imposed by the absence of pre-intervention data. We demonstrate the efficacy of these methods by deriving bounds on the absolute bias that converge to zero under suitable conditions, as well as through simulations across a variety of panel-data settings. Our proposed methodology renders causal inference feasible in urgent and data-constrained environments where the assumptions of existing causal inference frameworks are not met. As an application of our methodology, we evaluate the effect of a community organization vaccination intervention in Chelsea, Massachusetts on COVID-19 vaccination rates.

💡 Research Summary

The paper tackles a pressing gap in causal inference for panel data: the inability of standard Difference‑in‑Differences (DiD) and Synthetic Control (SC) methods to operate when no pre‑intervention observations exist for the treated unit. This situation frequently arises in emergency contexts—such as the rapid rollout of COVID‑19 vaccines—where interventions are deployed immediately and researchers lack any baseline data. To overcome this limitation, the authors propose two data‑fusion approaches that combine information from a primary “target” domain (the setting where the causal effect is of interest) with an auxiliary “reference” domain that contains related panel data.

The first approach, called Equi‑Confounding Data Fusion, extends the DiD logic by assuming that the unobserved confounding bias affecting the treated unit’s potential control outcome in the target domain is identical to the bias affecting the analogous outcome in the reference domain. Two versions are presented: a linear version (Assumption 2) and a logarithmic version (Assumption 3) for multiplicative scales. Under these assumptions, the average treatment effect on the treated (ETT) ψ₀ can be expressed as a simple difference between the treated unit’s observed outcome and the reference outcome, adjusted by the average difference across control units. The authors prove unbiasedness of the estimator ˆψ_eq₁ (Theorem 1) and, for the logarithmic case, derive explicit bias bounds (Theorem 3, Corollary 2) that shrink as the number of control units J grows and as dependence among controls weakens (τ(J)→0). The bias analysis requires bounded outcomes and a weak dependence condition, but does not demand independence between target and reference outcomes.

The second approach, Synthetic Control Data Fusion, adapts the SC framework to the two‑domain setting. The key idea is to construct a synthetic control for the treated unit using weighted combinations of control units in the reference domain, while simultaneously imposing a “domain‑balance” constraint that forces the same weighted combination to serve as a synthetic control in the target domain. This yields a constrained linear program that determines non‑negative weights summing to one, ensuring that the synthetic control reproduces the reference outcome and, by the equi‑confounding assumption, also approximates the unobserved counterfactual in the target domain. The resulting estimator ˆψ_SC = Y₁ – Σ w_i F_i is shown to be consistent when the assumptions hold.

The authors complement the theory with extensive simulations covering linear and nonlinear time‑unit interaction structures, varying noise levels, and different numbers of control units. Across all scenarios, both fusion methods exhibit markedly lower absolute bias and mean‑squared error than naïve DiD or SC applied without pre‑intervention data.

A real‑world application evaluates a community‑organization vaccination outreach in Chelsea, Massachusetts. The target domain consists of COVID‑19 vaccination rates among the Hispanic sub‑population; the reference domain consists of vaccination rates among the Black sub‑population in the same cities, which were not directly targeted by the outreach. Assuming the outreach had no effect on the Black rates (satisfying the equi‑confounding condition), the fusion methods estimate a roughly 12 percentage‑point increase in Hispanic vaccination attributable to the community effort, providing actionable evidence for policymakers.

Strengths: (1) Introduces a novel, theoretically grounded solution to a practically important problem; (2) Provides clear identification conditions and finite‑sample bias bounds; (3) Demonstrates robustness through simulations and a compelling empirical case.

Limitations: The equi‑confounding assumption is strong and may be violated if the reference outcome is indirectly affected by the intervention or shares different unobserved shocks. The bias bounds rely on a large pool of control units; performance may degrade with few controls. The current formulations are limited to linear or log‑linear relationships, leaving nonlinear dynamics unaddressed.

Future Directions: (i) Develop sensitivity‑analysis tools to assess the plausibility of equi‑confounding; (ii) Incorporate machine‑learning techniques to model nonlinear relationships between domains; (iii) Extend the framework to multiple treated units and multiple reference domains; (iv) Design hybrid methods that blend partial pre‑intervention data (when available) with the proposed fusion approach.

Overall, the paper makes a substantial methodological contribution, opening the door for credible causal inference in urgent, data‑constrained settings where traditional panel methods fail.