This paper evaluates whether an estimated, structural, small open economy model of the Canadian economy can account for the substantial influence of foreign-sourced disturbances identified in numerous reduced-form studies. The analysis shows that the benchmark model - and a number of variants which include a range of market imperfections - imply cross-equation restrictions that are too stringent when confronted with the data, yielding implausible parameter estimates. While appropriate choice of ad hoc disturbances can relax these cross-equation restrictions and therefore capture certain properties of the data - for instance, the volatility and persistence of the real exchange rate - and yield plausible parameter estimates, this success is qualified by the model’s inability to account for the transmission of foreign disturbances to the domestic economy: less than one percent of the variance of output is explained by foreign shocks.