The causal interpretation of panel vector autoregressions

TL;DR

This paper explores how the interpretation of Panel Vector Autoregressions (PVAR) varies with the distribution of variables and introduces a method to identify average treatment effects under certain assumptions, enhancing causal analysis in panel data.

Contribution

It presents a novel causal interpretation framework for PVARs, linking them to treatment effects and residual assumptions, and offers a new identification method for interventions in panel data.

Findings

PVAR interpretation depends on the distribution of the causing variable.

Under no residual autocorrelation, PVAR can identify average treatment effects on the treated.

The method captures impacts of interventions on the innovation component of outcomes.

Abstract

This paper discusses the different contemporaneous causal interpretations of Panel Vector Autoregressions (PVAR). I show that the interpretation of PVARs depends on the distribution of the causing variable, and can range from average treatment effects, to average causal responses, to a combination of the two. If the researcher is willing to postulate a no residual autocorrelation assumption, and some units can be thought of as controls, PVAR can identify average treatment effects on the treated. This method complements the toolkits already present in the literature, such as staggered-DiD, or LP-DiD, as it formulates assumptions in the residuals, and not in the outcome variables. Such a method features a notable advantage: it allows units to be ``sparsely'' treated, capturing the impact of interventions on the innovation component of the outcome variables. I provide an example related to the evaluation of the effects of natural disasters economic activity at the weekly frequency in the US.I conclude by discussing solutions to potential violations of the SUTVA assumption arising from interference.