In contrast to the very large literature on skill-biased technical change among workers, there is hardly any work on the importance of skills for the entrepreneurs who employ those workers, and in particular on their evolution over time. This paper proposes a simple theory of skill-biased change in entrepreneurial technology that fits with cross-country, historical and micro evidence. For this, it introduces two additional features into an otherwise standard occupational choice, heterogeneous firm model à la Lucas (1978): technological change does not benefit all potential entrepreneurs equally, and there is a positive relationship between an individual's potential payoffs in working and in entrepreneurship. If some firms consistently benefit more from technological progress than others, they stay closer to the frontier, and the others fall behind. Because wages rise for all workers, low-productivity entrepreneurs will then at some point exit and become workers. As a consequence, the entrepreneurship rate falls with income per capita, average firm size and firm size dispersion increase with income per capita, and "entrepreneurship out of necessity" falls with income per capita. The paper also documents, for two of the facts for the first time, that these are exactly the relationships prevailing in cross-country data. Quantitatively, the model fits the U.S. experience well. Using the parameters from a calibration to the U.S., the model also explains cross-country patterns quite well.