A salient feature of financial dollarization, arguably the one that causes most concern to policymakers, is its persistence: even after successful macroeconomic stabilizations, dollarization ratios often remain high. In this paper we argue 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 a simple model when agents differ in their ability to process information, which turns out to be enough to generate persistence upon aggregation. We provide empirical evidence that is consistent with this claim.