We introduce bounded rationality, along the lines of Gabaix (2020), in a canonical New Keynesian model calibrated to match Canadian macroeconomic data. We use the model to provide a quantitative assessment of the macroeconomic impacts of alternative monetary policy regimes—flexible inflation targeting (FIT), average-inflation targeting (AIT) and price-level targeting (PLT)—with an effective lower bound (ELB) constraint. First, our results suggest that the benefits of adopting history-dependent monetary policy regimes rely on two important assumptions: rational expectations and the central bank’s emphasis in stabilizing real variables such as the output gap. The macro-stabilization advantage of PLT disappears even for small deviations from rational expectations, and it is especially undermined when the central bank assigns a high weight on output volatility. Second, the presence of cost-push shocks, such as the ones global economies have experienced since the recovery from the pandemic, introduces important policy trade-offs that poses practical challenges which are best tackled using an AIT regime. Third, in choosing the optimal window width under the AIT regime, a central bank that assigns some emphasis on real sector stability needs to be mindful of expectation formation. If economic agents are sufficiently far from being rational, our simulations indicate that the optimal window is between 1 and 2.5 years.