Business cycle models with sticky prices and endegenous firm entry make novel predictions on the transmission of shocks through the extensive margin of investment. This paper tests some of these predictions using a vector autoregression with model-based sign restrictions. We find a positive and significant response of firm entry to expansionary shocks to productivity, aggregate spending, monetary policy and entry costs. The estimated response to a monetary expansion does not support the monetary policy transmission mechanism proposed by the model. Insofar as firm startups require labour services, wage stickiness is needed to make the signs of the model responses consistent with the estimated ones. The shapes of the empirical responses suggest that congestion effects in entry make it harder for new firms to survive when the number of startups rises.