Terms of Trade Economic Model (ToTEM) is the main projection and policy analysis model of the Bank of Canada. This is a large-scale general equilibrium macroeconomic model that currently includes 356 equations and unknowns. In the paper, we construct and calibrate a “baby ToTEM” (bToTEM) – a scaled down version of ToTEM that has 55 equations and unknowns, including 26 state variables. Our impulse response analysis shows that bToTEM preserves the key features of ToTEM. Importantly, bToTEM is tractable under global nonlinear solution methods, while ToTEM is analyzed exclusively by the Bank of Canada using a first-order perturbation method. In our policy experiments, local and global solutions differ dramatically. First, in the context of bToTEM, we analyze the role of large negative foreign demand shocks in the recent episode of an effective lower bound (ELB) on nominal interest rates in Canada, and we find that the timing and duration of the ELB episodes varies significantly depending on the solution method used. Second, we explore the effect of an increase in the inflation target on the Canadian economy, and we find that this policy has a substantial economic cost under nonlinear solutions, while such a cost is absent under linear solutions. Our analysis is an important step toward the development of a nonlinear framework for analyzing large-scale central bank models.