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This paper examines a novel mechanism linking fertility and growth. There are three components to the model. First, increases in capital per worker raise women's relative wages, since capital is more complementary to women's labour input than to men's. Second, increasing women's relative wages reduces fertility by raising the cost of children more than household income. Third, lower fertility raises the level of capital per worker. This positive feedback loop generates a demographic transition: a rapid decline in fertility accompanied by accelerated output growth.
Galor et al. (Mon,) studied this question.