This paper establishes the connection of exchange rates to macroeconomic fundamentals by estimating a small open-economy model for Canada. The model incorporates an endogenous interest rate spread on foreign bond holdings, enabling the modified uncovered interest rate parity (UIP) condition to exhibit a negative relationship between expected exchange rate depreciation and interest rate differentials, as observed in the data. Given the model's susceptibility to equilibrium indeterminacy, we estimate it using Bayesian methods that allow for both determinacy and indeterminacy of equilibrium. The results reveal that preference shocks to the household utility function are the primary drivers of exchange rate fluctuations, highlighting the connection between exchange rates and macroeconomic fundamentals. We further demonstrate that both allowing for indeterminacy and selecting a specific equilibrium representation from the data are essential for achieving this finding.