How wrong could policymakers be when using linearized solutions to their macroeconomic models instead of nonlinear global solutions? This question became of much practical interest during the Great Recession and the recent zero lower bound crisis. We assess the importance of nonlinearities in a scaled-down version of the Terms of Trade Economic Model (ToTEM), the main projection and policy analysis model of the Bank of Canada. In a meticulously calibrated “baby” ToTEM model with 21 state variables, we find that local and global solutions have similar qualitative implications in the context of the recent episode of the effective lower bound on nominal interest rates in Canada. We conclude that the Bank of Canada’s analysis would not improve significantly by using global nonlinear methods instead of a simple linearization method augmented to include occasionally binding constraints. However, we also find that even minor modifications in the model's assumptions, such as a variation in the closing condition, can make nonlinearities quantitatively important.