Opponents of explicit inflation targeting (including ex-Chairman Greenspan) have argued that a commitment to a numerical inflation target is likely to reduce monetary policy flexibility, and hence increase output volatility. Our paper demonstrates that this claim may fail to account for the anchoring effect of explicit targets on expectations and wages—found in the data by a number of empirical studies. We do so in a novel, dynamic game theoretic framework with asynchronous moves that endogenizes the frequency of the private sector’s actions. We derive the conditions under which an explicit long-term inflation target makes the behaviour of private agents rationally inattentive and anchored. This is through enhancing monetary policy credibility, which leads private agents to reconsider expectations and wages less frequently to minimize the cost of processing information and/or wage negotiations. Such anchoring makes the policymaker’s interest rate instrument more effective in stabilization, giving it greater leverage over the real rate. This implies that an explicit inflation target may improve the variability tradeoff, i.e. shift the policy frontier inwards. It can therefore make both inflation and output less variable in equilibrium, unlike what inflation targeting sceptics argue. We show that our results are consistent with existing empirical evidence, and discuss them in light of the global financial crisis. The policy implication is that the Federal Reserve, the Swiss National Bank, the Bank of Japan, and the European Central Bank should be more explicitly committed to a long-run inflation target.