Activation Costs, Fair Value, and Real Exchange Rate Adjustment

Models of real-exchange-rate adjustment are generally based on traded-goods arbitrage. We develop an integrated equilibrium model in which costly arbitrage operates through both goods and foreign-exchange markets. Goods arbitrage narrows traded-goods law-of-one-price gaps by changing the bilateral traded-goods price differential and hence the nominal fair-value benchmark. Financial convergence traders compare the quoted nominal rate with this common but uncertain benchmark, and progressively more capital is mobilised as the absolute fair-value gap grows. Because the real exchange rate’s deviation from its productivity-conditioned centre is identically the nominal fair-value gap, both channels act on the same state. Heterogeneous activation costs convert discrete individual decisions into smooth aggregate correction. Under transparent benchmark restrictions, aggregation and market clearing deliver the exponential smooth-transition autoregressive (ESTAR) law as an exact equilibrium outcome and impose identifying and testable restrictions on its location, outer response and shape. We take the model to nine sterling bilateral rates spanning up to two and a quarter centuries and estimate the seven stationary cases jointly by exact maximum likelihood. Five pairs support a productivity-conditioned equilibrium; three adjust towards it nonlinearly and two are adequately approximated as linear. Transition-selection tests support even adjustment where both tails are informative, and pairwise and joint Weibull tests retain the exponent-two benchmark. Across the productivity-anchored pairs, allowing the equilibrium centre to move reduces the average floating-regime half-life of a 1% shock from sixteen to seven years, while 20% shocks have half-lives of one to four years. The results recast real-exchange-rate persistence as the combination of a moving equilibrium and state-dependent corrective capacity.