Andres Gomez-Lievano, Vladislav Vysotsky, and Jose Lobo. 7/15/2020. “
Artificial Increasing Returns to Scale and the Problem of Sampling from Lognormals.” Environment and Planning B: Urban Analytics and City Science.
Publisher's VersionAbstract
We show how increasing returns to scale in urban scaling can artificially emerge, systematically and predictably, without any sorting or positive externalities. We employ a model where individual productivities are independent and identically distributed lognormal random variables across all cities. We use extreme value theory to demonstrate analytically the paradoxical emergence of increasing returns to scale when the variance of log-productivity is larger than twice the log-size of the population size of the smallest city in a cross-sectional regression. Our contributions are to derive an analytical prediction for the artificial scaling exponent arising from this mechanism and to develop a simple statistical test to try to tell whether a given estimate is real or an artifact. Our analytical results are validated analyzing simulations and real microdata of wages across municipalities in Colombia. We show how an artificial scaling exponent emerges in the Colombian data when the sizes of random samples of workers per municipality are 1% or less of their total size.
Charles D Brummitt, Andres Gomez-Lievano, Ricardo Hausmann, and Matthew H Bonds. 1/8/2020. “
Machine-learned patterns suggest that diversification drives economic development.” Journal of the Royal Society Interface, 17, 162, Pp. 20190283.
Publisher's VersionAbstractWe combine a sequence of machine-learning techniques, together called Principal Smooth-Dynamics Analysis (PriSDA), to identify patterns in the dynamics of complex systems. Here, we deploy this method on the task of automating the development of new theory of economic growth. Traditionally, economic growth is modelled with a few aggregate quantities derived from simplified theoretical models. PriSDA, by contrast, identifies important quantities. Applied to 55 years of data on countries’ exports, PriSDA finds that what most distinguishes countries’ export baskets is their diversity, with extra weight assigned to more sophisticated products. The weights are consistent with previous measures of product complexity. The second dimension of variation is proficiency in machinery relative to agriculture. PriSDA then infers the dynamics of these two quantities and of per capita income. The inferred model predicts that diversification drives growth in income, that diversified middle-income countries will grow the fastest, and that countries will converge onto intermediate levels of income and specialization. PriSDA is generalizable and may illuminate dynamics of elusive quantities such as diversity and complexity in other natural and social systems.