Re-Examining What We Can Learn About Counterfactual Results from Time Series Regression

McKay and Wolf (2023) describe a method for finding counterfactuals which only requires
that one know the impulse responses of shocks from a baseline structural model generating
the data. A key feature in their work is the use of news shocks. This an elegant piece of
theory and they indicate it can be applied empirically. We argue that one cannot recover the
impulse responses from data generated by the structural model when there are news shocks
as there are more shocks than observables in that case. We investigate an alternative
proposal whereby some off model variables are used to find the requisite impulse responses
and find that there are issues with doing that. Their theoretical result also relies upon the
baseline structural model only having monetary policy operating via the interest rate channel
so it excludes models that might be thought relevant for capturing data.