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How do political connections affect firm dynamics, innovation, and creative destruction? We extend a Schumpeterian growth model with political connections that help firms ease bureaucratic and regulatory burden. The model highlights how political connections influence an economy's business dynamism and innovation, and generates a number of implications guiding our empirical analysis. We construct a new large‐scale data set for the period 1993–2014, on the universe of firms, workers, and politicians, complemented with corporate financial statements, patent data, and election data, so as to define connected firms as those employing local politicians. We identify a leadership paradox: market leaders are much more likely to be politically connected, but much less likely to innovate. Political connections relate to a higher rate of survival, as well as growth in employment and revenues, but not in productivity—a …