This paper constructs a model with two structural equations: the Government budget constraint and a linear version of Cagan’s portfolio balance equation. The model contains a continuum of equilibria with “sunspot equilibria.” Closed forms for the solutions are found. Even though there is a continuum of equilibria, the model is overidentified econometrically, so that the model restricts time series data on price levels and currency stocks. We describe how the free parameters of the model can be estimated, including some parameters that serve to index particular members of the continuum of equilibria. The sunspot equilibria hold out some promise of explaining anomalies in the observed behavior of inflation and real balances during hyperinflations.