Growth is rare historically, with short expansions interspersed with long p
eriods of stasis. We examine how well this can be explained by a general cl
ass of Schumpeterian growth models that treat development as a progress thr
ough a space of commodities, from simple to more complex foods. This proces
s of sequential innovation in a partially ordered network of commodities is
called linkage formation. The central result of this article is that Schum
peterian growth models exhibit generic threshold behavior. Below a critical
probability of linkage formation, development gradually ceases. Above the
critical probability, innovation continues with probability one.