This paper examines the effects of the COVID-19 pandemic on stock returns, CDS and economic activity in the US and the five European countries (the UK, Germany, France, Italy, and Spain) which have been most affected. The sample period covers the dates from the first confirmed COVID-19 cases in these countries to February 19, 2021. Specifically, we estimate first benchmark linear VAR models and then, given the evidence of parameter instability, TVP-VAR models with stochastic volatility which are ideally suited to capturing the changing dynamics in both financial markets and the real economy. The empirical findings can be summarised as follows. The linear VAR responses of electricity consumption (a proxy for real economic activity) to a one-standard-deviation shock to the number of COVID-19 cases are statistically insignificant, except for France, whilst the CDS ones are positive and significant only in a few periods, and there are very mixed results for those of stock returns. As for the TVP-VAR results, these indicate that COVID-19 cases had a negative and significant effect on economic activity in all countries in the early stages of the pandemic (especially in Italy), and a positive one on CDS at the same time (with cross-country differences). Finally, the negative impact on stock markets was felt only initially and it had tapered off by mid-April 2020.