K-fold Cross-Validation and the Gravity Model of Bilateral Trade

This paper contributes to the gravity model literature by giving a side-by-side comparison of in-sample and out-of-sample data techniques, specifically k-fold cross-validation, to show the benefits of using out-of-sample data techniques when examining the gravity model of bilateral trade. This shifts the focus from sample uncertainty, which is limited within bilateral trade data, to model uncertainty, which poses a larger potential problem in this context (Varian, Journal of Economic Perspectives 28: 3–28, 2014). This research also begins addressing the implicit regularities that are often imposed upon the variables within the gravity model by examining possible interaction terms and various model specifications using the aforementioned k-fold cross-validation technique. The results indicate that the k-fold cross-validation method provides more robust models and prevents over-fitting the model with practically and statistically insignificant variables. Moreover, it finds strong evidence to suggest that the log specification of GDP and GDP per capita in the gravity model needs to consider raised powers of the variables in order to give the best predictive model and help avoid omitted variable bias. This change reduces the expected increases in bilateral trade of a currency union by almost 50 %, suggesting a large previously omitted variable bias within the model. Similar biases are revealed in the coefficient estimates for regional trade agreements and generalized system of preferences. © 2015, International Atlantic Economic Society.