The knowledge spillover theory of entrepreneurship (KSTE) claims that new ventures commercialize knowledge that incumbent firms leave unexploited, thereby linking entrepreneurship to economic growth. This paper studies the mathematical basis and empirical tests for the KSTE as provided in Acs et al. (2009). It is shown that the knowledge filter is absent; that entrepreneurial labour is idle; that the aggregation of individual start-up hazards is invalid; that the knowledge-filter interaction required by H2 is not established, while H3’s negative entry response is conditional on an inconsistently stated interpretation of the institutional parameter; and that the valuation condition is dimensionally inconsistent. Its empirical design further relies on a pooled correlation between R&D intensity and the knowledge stock that does not establish their within-country relationship, and on inference that does not account adequately for country-level dependence. The subsequent model of Acs and Sanders (2013) does not solve the central problem: by assuming that all ideas spill over, it removes the knowledge filter altogether. It is concluded that the KSTE is a promising narrative, not a theory.