Running the gravity model in reverse to find lost ancient cities

The gravity model of trade or migration (which I have written about before here) must be one of the consistently best-performing empirical regression models (in terms of in-sample prediction, at least). The model is really simple too. In its simplest form, a gravity model suggests that the migration (or trade) flow between two regions is positively related to the 'economic mass' (proxied by population in the case of migration, or by GDP in the case of trade) of the origin and the economic mass of the destination, and negatively related to the distance between the two places. So really, you don't need a whole lot of data in order to run a gravity model (though you do need data on trade or migration flows).

The standard gravity model is based on known data such as the distances between countries (or regions, or cities). But what if you didn't know where the cities were (as might be the case for lost ancient cities), but you did know the size of the trade flows? Could you use the gravity model to triangulate the likely location of those lost cities, by estimating the distance from their trade partners? It turns out that yes, you can.

In what might be the most ingenious use of the gravity model I've ever seen, a new NBER Working Paper (ungated version here) by Gojko Barjamovic (Harvard), Thomas Chaney (Sciences Po), Kerem A. Coşar (University of Virginia), and Ali Hortaçsu (University of Chicago) does almost exactly that. The authors use a dataset of over 12,000 Assyrian tablets from 1930-1775 BCE, 2,806 of which contain mentions of mentions of multiple cities in Anatolia (modern-day Turkey). Of those tablets, 198 contain merchants' itineraries for 227 itineraries relating to travel between 26 cities (15 of which are known, and 11 of which are 'lost'). The authors explain the difference between known and lost cities, as:

‘Known’ cities are either cities for which a place name has been unambiguously associated with an archaeological site, or cities for which a strong consensus among historians exists, such that different historians agree on a likely set of locations that are very close to one another. ‘Lost’ cities on the other hand are identified in the corpus of texts, but their location remains uncertain, with no definitive answer from archaeological evidence. From the analysis of textual evidence and the topography of the region, historians have developed competing hypotheses for the potential location of some of those.

So, the authors use the data from the itineraries to construct a dataset of trade between known cities, and between known and lost cities. Using that dataset they then estimate a gravity model of migration, which provides an estimate of the distance elasticity of trade of about 3.8. That means that each 1 percent increase in distance between two cities reduced trade by about 3.8 percent. This is much higher than modern models of trade where the elasticity is usually about one, but given ancient trade was mostly by road (or by coastal shipping) and the roads were not high quality, that doesn't seem too unusual.

Next comes the really cool bit. They then use the distance elasticity measure to 'back out' estimates of the location of the lost cities. Their method even gives confidence bounds around the estimated point location of each lost city. They conclude that:

...[f]or 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.

Eyeballing the results from the maps though, the estimated location of the lost cities doesn't appear (to me) to be particularly close to the historians' qualitative estimates. However in spite of that, this is a very cool paper using the gravity model in a very novel way. Hopefully we see more of this in the future.

[HT: Marginal Revolution]