I develop and study a factor-augmented quasi-vector autoregressive (FAQVAR) model for economic policy analysis in tumultuous times. An observation-driven framework that exploits the information from the score of the model allows a maximum likelihood estimation. This multivariate FAQVAR model, which assumes a Student t error distribution, is robust to atypical observations such as the global financial crisis and the recent pandemic. The model outperforms the FAVAR moving average model because of the assumed heavy tails that capture the COVID-19 atypical data and other turbulent episodes. An empirical application to the U.S. economy assessing its monetary policy reveals that estimates and impulse responses are stable when considering the sample before and during COVID-19.