General Equilibrium Model of Arbitrage Trade and Real Exchange Rate Persistence

Modelling of the physical characteristics of goods and geography can explain both the puzzling persistence and volatility in the deviations of the international relative prices and the real exchange rate (the PPP persistence puzzle). In a two-country, three-good general equilibrium model, arbitrage firms trade goods across borders using a linear transportation technology. Distance and product weights (their physical mass) determine the costs to arbitrage trade, while the differences in the endowments between countries create profitable trading opportunities. Tradability of goods is endogenous, in that only goods with a deviation from the law of one price in excess of their trade cost are traded. The adjustment of prices across borders is non-linear, with heterogeneous thresholds that depend positively on the weight of a product and distance { an empirical regularity. Aggregation of the law of one price deviations implies a smooth threshold non-linearity in the real exchange rate, justifying a reoccurring finding in the recent empirical literature. When stochastic endowments follow an AR(1) process calibrated to match the quarterly HP-filtered US and EU GDPs, and the aggregate trade costs consume 1.7% of the GDP, the half-life of deviation in the real exchange rate matches the persistence found in the data. A model with quadratic adjustment costs in the volume of trade is also capable of creating real exchange rate volatility, and so can explain the PPP puzzle entirely as a trade phenomenon.