Semiparametric Causality Tests Using the Policy Propensity Score

Abstract

Time series data are widely used to explore causal relationships, typically in a regression framework with lagged dependent variables. Regression-based causality tests rely on an array of functional form and distributional assumptions for valid causal inference. This paper develops a semi-parametric test for causality in models linking a binary treatment or policy variable with unobserved potential outcomes. The procedure is semiparametric in the sense that we model the process determining treatment -- the policy propensity score -- but leave the model for outcomes unspecified. This general approach is motivated by the notion that we typically have better prior information about the policy determination process than about the macro-economy. A conceptual innovation is that we adapt the cross-sectional potential outcomes framework to a time series setting. This leads to a generalized definition of Sims (1980) causality. We also develop a test for full conditional independence, in contrast with the usual focus on mean independence. Our approach is illustrated using data from the Romer and Romer (1989) study of the relationship between the Federal reserve's monetary policy and output.