Bayesian Additive Regression Tree (BART) Models of Market Integration in the 19th-Century Trans-Atlantic Wheat Trade

Non-linear time series models are popular for the analysis of spatial market integration because they capture price behavior implied by the theory of arbitrage. Recent work considers fully flexible models based on linear combinations of unknown, smooth functions of the independent variables. We propose an alternative non-parametric approach using Bayesian additive regression trees (BART). BART represents the target function as a sum of many shallow regression trees, approximating complex, non-linear patterns without explicit specification of interactions. The BART-based model allows the speed of price adjustment to vary continuously with the size of the price differential, in contrast to models with a discrete number of thresholds, and avoids overfitting through Bayesian regularization. We demonstrate the approach in an application to trans-Atlantic wheat prices over the 19th century during what is widely acknowledged as the first era of globalization. The Anglo-American wheat trade was more highly integrated at the end of the century—supporting the Law of One Price—and certain markets were characterized by important non-linearities not adequately captured by threshold models.