Fixed and Flexible Exchange-rates in Two Matching Models: Non-equivalence Results

There is a presumption that fixed and flexible (floating or market-determined) exchange-rate systems are equivalent if prices are flexible. We show that the presumption does not hold in two matching models of money. In both models, (i) currencies are the only assets and all trade is spot trade; (ii) the trades that directly determine welfare occur in pairwise meetings between buyers and sellers; and (iii) imperfect substitutability (including, as a special case, no substitutability) among currencies is a consequence of the trading protocol in those meetings. The two models are variants of the Lagos-Wright (2005) model and differ regarding the timing of the shock realizations relative to the centralized trade opportunities. One version has a speculative fringe. In it, the unique stationary (monetary) equilibrium under the fixed exchange-rate regime is one of a continuum of equilibria under a flexible exchange-rate regime. The other version has no speculative fringe. In it, there is a unique (monetary) stationary equilibrium under each exchange-rate regime and they differ.