The Relation of Different Concepts of Causality Used in Time Series and Microeconometrics

Granger and Sims noncausality (GSNC), a concept frequently applied in time series econometrics, is compared to noncausality based on concepts popular in microeconometrics, program evaluation, and epidemiology literature (potential outcome noncausality or PONC). GSNC is defined as a set of restrictions on joint distributions of random variables with observable sample counterparts, whereas PONC combines restrictions on partially unobservable variables (potential outcomes) with different identifying assumptions that relate potential outcome variables to their observable counterparts. Based on the Robins' dynamic model of potential outcomes, we find that in general neither of the concepts implies each other without further (untestable) assumptions. However, the identifying assumptions associated with the sequential selection of the observables link these concepts such that GSNC implies PONC, and vice versa.