The heterogeneous impact of market size on innovation: evidence from French firm-level exports

We analyze how demand conditions faced by a firm impacts its innovation decisions. To disentangle the direction of causality between innovation and demand conditions, we construct a firm-level export demand shock which responds to aggregate conditions in a firm's export destinations but is exogenous to firm-level decisions. Using exhaustive data covering the French manufacturing sector, we show that French firms respond to exogenous growth shocks in their export destinations by patenting more; and that this response is entirely driven by the subset of initially more productive firms. The patent response arises 3 to 5 years after a demand shock, highlighting the time required to innovate. In contrast, the demand shock raises contemporaneous sales and employment for all firms, without any notable differences between high and low productivity firms. We show that this finding of a skewed innovation response to common demand shocks arises naturally from a model of endogenous innovation and competition with firm heterogeneity. The market size increase drives all firms to innovate more by increasing the innovation rents; yet by inducing more entry and thus more competition, it also discourages innovation by low productivity firms.