Recipes and Economic Growth: A Combinatorial March Down an Exponential Tail

As Romer and Weitzman emphasized in the 1990s, new ideas are often combinations of existing ideas, an insight absent from recent models. In Kortum’s research around the same time, ideas are draws from a probability distribution, and Pareto distributions play a crucial role. Why are combinations missing, and do we really need such strong distributional assumptions to get exponential growth? This paper demonstrates that combinatorially growing draws from standard thin-tailed distributions lead to exponential growth; Pareto is not required. More generally, it presents a theorem linking the max extreme value to the number of draws and the shape of the upper tail for probability distributions.