Causal Effects of Monetary Shocks: Semiparametric Conditional Independence Tests with a Multinomial Propensity Score
Macroeconomists have long been concerned with the causal e§ects of monetary policy. When the identiÖcation of causal e§ects is based on a selection-on-observables assumption, non-causality amounts to the conditional independence of outcomes and policy changes. This paper develops a semiparametric test for conditional independence in time series models linking a multinomial policy variable with unobserved potential outcomes. Our approach to conditional independence testing is motivated by earlier parametric tests, as in Romer and Romer (1989, 1994, 2004). The procedure developed here is semiparametric in the sense that we model the process determining the distribution of treatment ñ the policy propensity score ñbut leave the model for outcomes unspeciÖed. A conceptual innovation is that we adapt the crosssectional potential outcomes framework to a time series setting. This leads to a generalized deÖnition of Sims (1980) causality. A technical contribution is the development of root-T consistent distribution-free inference methods for full conditional independence testing, appropriate for dependent data and allowing for Örst-step estimation of the propensity score.