In this paper, we make the case that an argument for price-level targeting over inflation targeting need not to be based on some overly restrictive assumptions. We adopt a theoretical framework that deviates from the assumption of rational expectation, and that takes into account the cognitive limitations and a “trial and error” learning mechanism of the agents. The (im)perfect credibility of various monetary policies (e.g., a Taylor-type rule, strict domestic inflation targeting, strict consumer price index (CPI) inflation targeting, exchange rate peg, and domestic price-level and CPI-level targeting) may lead agents to react according to their expectation rules, and then create various degrees of booms and busts in output and inflation. Therefore, relaxing the rational expectation hypothesis has potential consequences for policy planning. We find that price-level targeting prevails over inflation targeting even under different expectation formation and even when the announced inflation target is not fully credible. The counterfactual analysis and sensitivity test confirm that CPI-level targeting is the most effective for improving social welfare and stability in an open economy. The business cycles induced by animal spirits are enhanced by strict inflation targeting.