In a stunningly original paper Gojko Barjamovic, Thomas Chaney, Kerem A. Coşar, and Ali Hortaçsu use the gravity model of trade to infer the location of lost cities from Bronze age Assyria! The simplest gravity model makes predictions about trade flows based on the sizes of cities and the distances between them. More complicated models add costs based on geographic barriers. The authors have data from ancient texts on trade flows between all the cities, they know the locations of some of the cities, and they know the geography of the region. Using this data they can invert the gravity model and, triangulating from the known cities, find the lost cities that would best “fit” the model. In other words, by assuming the model is true the authors can predict where the lost cities should be located. To test the idea the authors pretend that some known cities are lost and amazingly the model is able to accurately rediscover those cities.
Here from the paper is more detail. Each step is an accomplishment and the final product is something completely unexpected. Bravo!
Our first contribution is to extract systematic information on commercial linkages between cities from ancient texts. To do so, we leverage the fact that the ancient records we study can be transcribed into the Latin alphabet, allowing all texts to be digitized and parsed. We automatically isolate, across all records, the tablets which jointly mention at least two cities. We then systematically read those texts, which requires an intimate knowledge of the cuneiform script and Old Assyrian dialect of the ancient Akkadian language that the records are written in. Taking individual source context into account, this analysis relies exclusively upon a subset of records that explicitly refer to journeys between cities and distinguishes whether the specific journey was undertaken for the purpose of moving cargo, return journeys, or journeys undertaken for other reasons (legal, private, etc.).
Our second contribution is to estimate a structural gravity model of ancient trade. We build a simple Ricardian model of trade. Further imposing that bilateral trade frictions can be summarized by a power function of geographic distance, our model makes predictions on the number of transactions between city pairs, which is observed in our data. The model can be estimated solely on bilateral trade flows and on the geographic location of at least some cities.
Our third contribution is to use our structural gravity model to estimate the geographic location of lost cities. While some cities in which the Assyrian merchants traded have been located and excavated by historians and archaeologists, other cities mentioned in the records can not be definitively associated with a place on the map and are now lost to us. Analyzing the records for descriptions of trade and routes connecting the cities and the landscapes surrounding them, historians have developed qualitative conjectures about potential locations of several of these lost cities. We propose an alternative, quantitative method based on maximizing the fit of the gravity equation. As long as we have data on trade between known and lost cities, with sufficiently many known compared to lost cities, a structural gravity model is able to estimate the likely geographic coordinates of lost cities. Our framework not only provides point estimates for the location of lost cities, but also confidence regions around those point estimates. For a majority of the lost cities, our quantitative estimates come remarkably close to the qualitative conjectures produced by historians, corroborating both such historical models and our purely quantitative method. Moreover, in some cases where historians disagree on the likely location of a lost city, our quantitative method supports the conjecture of some historians and rejects that of others.