The most salient feature of financial dollarization, and the one that causes more concern to policy makers, is its persistence: even after successful macroeconomic stabilizations, dollarization ratios often remain high. In this paper we claim that this persistence is connected to the fact that the participants in the dollar deposit market are fairly heterogenous, and so is the way they form their optimal currency portfolio.We develop as simple model when agents differ in their ability to process information, which turns out to be enough to generate persistence up on aggregation. We find empirical support for this claim with data from three Latin American countries and Poland.