In this seminar, Nick Pretnar (University of California, Santa Barbara) will present the paper: 'One Production Function'.
We build a production function that can reconcile factor income shares and aggregate output in all stages of economic development using available data. The model can reconcile both Malthusian and Solow properties with respect to aggregate growth. Specifically, we show that, depending on the population growth rate versus the growth rate of aggregate productivity, Malthusian stagnation or Solow capital accumulation can occur. We characterise second-order properties regarding the effects of changes to population and productivity levels on the land, non-landed capital, and labor income shares. Generally, population growth leads to a growth in the share of aggregate income to land rents, as long as the population does not grow excessively fast. With excessively fast population growth, crowding causes the land share of income to decline, while workers’ share of aggregate income rises. With fast population growth the non-landed capital share of income could also rise despite zero capital accumulation. If both land/labor and capital/labor are complements and land is relatively more complementary with labor than non-landed capital, then incredibly fast population growth can actually lead to falling land rents, rising non-landed capital rents, and rising labor-income shares. Improving the efficiency of land utilisation always raises the land share of income at the expense of the labor share, all else equal. In a Malthusian setting with no growth in income per-capita, if the land share rises due to improved land efficiency, land owners receive increasing rents. In our setting a Solow economy is manifested when income per-capita grows because of non-landed capital accumulation. The key ingredient to Solow growth is improving the productivity of using non-landed capital.
After characterising the model’s growth properties, we estimate our one production function on factor-income share data for England and Wales from 1200-1860. Our best-fitting model is robust to growth properties from all eras of economic development in the 1200-1860 period. This is because our model, despite its nested CES structure, generates variable elasticities of substitution for land/labor, capital/labor, and land/capital. This is important because VES production is required to be able to generate the transitions between different economic eras that we observe (e.g., the Black Death, early development in the 1600s, and later industrial growth in the 1700s and 1800s). We conclude by discussing potential applications and extensions of the model to better understand the implications of modern industrial policy as oriented toward aggregate economic development.