Can news and noise shocks be disentangled?

Chahrour and Jurado (2018) have shown that news and noise shocks are observationally equivalent when the econometrician only observes a fundamental process and agents' expectations about it. We show that the observational equivalence result no longer holds when the econometrician observes a fundamental process and a noisy signal of it. Working with an RBC model with noise about TFP, we further show that, even if the signal is not directly observed by the econometrician, it can be inferred through its impact on other macroeconomic variables, since they are optimally chosen by agents conditional on all information, including the signal itself. In particular, we show that under these circumstances news and noise shocks can be exactly recovered in population. Our results demonstrate that news and noise shocks are not observationally equivalent for an econometrician exploiting all the information contained in standard macroeconomic time series.