We use a dynamic factor model to provide a semi-structural representation for 101 quarterly US macroeconomic series. We find that (i) the US economy is well described by a number of structural shocks between two and six. Focusing on the four-shock specification, we identify, using sign restrictions, two non-policy shocks, demand and supply, and two policy shocks, monetary and fiscal. We obtain the following results. (ii) Both supply and demand shocks are important sources of fluctuations; supply prevails for GDP, while demand prevails for employment and inflation. (ii) Policy matters: Both monetary and fiscal policy shocks have sizeable effects on output and prices, with little evidence of crowding out; both monetary and fiscal authorities implement important systematic countercyclical policies reacting to demand shocks. (iii) Negative demand shocks have a large long-run positive effect on productivity, consistently with the Schumpeterian "cleansing" view of recessions.