Mediation analysis in recursive systems of distributed-lag linear regressions

Recursive systems of linear regressions is a consolidated methodology for mediation analysis, allowing to determine causal effects of interest in a closed form based on the regression coefficients. In a dynamic perspective, distributed-lags can be added to each regression in order to represent causal effects persisting over several periods. However, mediation analysis in the dynamic case is challenging, because causal effects depend on the time lag, and a general procedure to compute their lag distribution based on the regression coefficients is currently missing. In this paper, we formalize the rules to perform mediation analysis in recursive systems of distributed-lag linear regressions, here called Distributed-lag Linear Recursive Models (DLRMs). Firstly, mediation analysis is based on the Directed Acyclic Graph (DAG) representation of the DLRM, then a DAG-free algorithm is proposed to improve computational efficiency. Our DAG-free algorithm is applied to a DLRM representing the impact pathways of agricultural research expenditure towards poverty reduction in rural areas.