How different are Monetary Unions to national economies according to prices?

Not that different. Based on a unique dataset of semi-annual microeconomic price levels of goods and services across and within countries for 1990:1-2018:2, we show that time-series volatility and cross-sectional dispersion of law-of-one-price deviations is similar for pairs of cities within the same country and within the European Monetary Union. Our empirical analysis reveals that inflation and nominal exchange rate volatility/dispersion across locations have a positive impact on the volatility/dispersion across locations of law-of-one-price deviations across the globe. Furthermore, dispersion of law-of-one-price deviations across goods falls when the relative inflation rate between these locations rises, suggesting that the degree of price adjustment in individual product markets within a country has an international component shaped by international trade and arbitrage considerations. According to this measure of price integration, economies within the monetary union are half-way to the level of integration characterizing national economies. Moreover, monetary union membership reduces the volatility of law-of-one-price deviations, taking member countries more than half-way towards the volatility levels characterizing national economies.