This paper incorporates diagnostic expectations and memory into a small open economy New Keynesian model estimated on quarterly data for New Zealand and Chile. The estimation uses survey data on expected depreciation as an observable to discipline the diagnostic parameters. The data favor diagnostic expectations with memory, where the weights on past news are hump-shaped, over rational expectations in both countries. Diagnostic expectations amplify volatility asymmetrically, raising the volatility of exchange rates and expected depreciation, while domestic volatility is slightly changed. Diagnosticity is higher in Chile, where this deviation also accounts for the survey movements that rational expectations attribute to measurement error. Overreaction lowers the slope of the Fama regression, and the slopes implied by the estimated models are consistent with those observed in both countries. Finally, the estimated degree of diagnosticity is robust to a Taylor rule that responds to the agents’ expected depreciation.