We study unofficial dollarization, i.e., the use of foreign money alongside the domestic currency, in an environment where spatial separation and limited communication create a role for currency and banks arise endogenously to provide insurance against liquidity preference shocks. Unofficial dollarization has been a common phenomenon in emerging market economies during high inflations. However, successful disinflations have not necessarily been followed by dedollarization. In particular, Argentina, Bolivia, Peru, Russia, and Ukraine remained highly dollarized long after the inflation rate was reduced to single digits. We refer to this phenomenon as a "dollarization hysteresis paradox." It has also been observed in these economies that higher inflation has a negative impact on output and financial intermediation, that dollarization and capital flight adversely affect capital accumulation, and that post-stabilization output growth is impeded by dollarization. This paper presents an overlapping-generations model with random relocation of agents between two locations that explains the dollarization hysteresis paradox and several other stylized facts. The key link between inflation, dollarization, and capital accumulation in the model is that high inflation undermines financial intermediation, which leads to the adoption of a less efficient production technology. As a result, it is possible for economies to become stuck in low output "development traps," where the marginal product of capital is the same as the return from holding dollars. In such an environment, we show how dollarization can preclude further capital accumulation, even in the presence of successful inflation stabilization policies. We complement previous work on dollarization by allowing the "hard" currency to compete with domestic capital as a store of value instead of focusing on either currency substitution (where the use of a "hard" currency replaces the domestic currency as a medium of exchange) or official dollarization (where the domestic currency is abandoned altogether and replaced with the US dollar). We assume that in the first period of life, agents inelastically supply labor and receive the competitive market wage. A given fraction of agents will be relocated to another location, and they can take only domestic currency with them. Competitive banks arise endogenously in this environment to insure against liquidity (relocation) shock. They issue demand deposits and hold portfolios of domestic currency and the capital market assets, which may include productive capital and dollars. There are two different productive technologies that banks can invest in. The first one is a primitive autarkic technology that they can use directly. The second one is an advanced technology that requires the use of a financial center. The financial center is a profit-maximizing natural monopoly. Its profit depends positively on the scale of intermediation and production. Our model predicts that an increase in inflation will reduce the capital stock, output and the scale of intermediation. If inflation is low enough, the financial center makes a positive profit, and the advanced technology is used. However, when inflation exceeds a certain threshold, the profit of the center falls below zero, and it shuts down. Hence competitive banks switch to the inefficient autarkic technology. Even though the capital stock falls, the marginal product of capital falls as well due to the switch in technology. This creates the possibility of a "dollarization trap," in which dollars are held as a store of value alongside the autarkic productive capital. The arbitrage condition between the return on dollars and the marginal product of capital determines the capital stock and output. A subsequent disinflation does not affect this arbitrage condition, and thus has no effect on capital accumulation. Therefore, as long as the economy gets stuck in the dollarization trap during a high inflation episode, a successful stabilization of inflation is followed neither by dedollarization nor by output recovery.
