Several academics and practitioners have pointed out that inflation follows a seemingly exogenous statistical process, unrelated to the output gap, leading some to argue that the Phillips curve has weakened or disappeared. In this paper, we explain why this seemingly exogenous process arises, or, in other words, why it is difficult to empirically identify a Phillips curve, a key building block of the policy framework used by central banks. We show why this result need not imply that the Phillips curve does not hold—on the contrary, our conceptual framework is built under the assumption that the Phillips curve always holds. The reason is simple: if monetary policy is set with the goal of minimizing welfare losses (measured as the sum of deviations of inflation from its target and output from its potential), subject to a Phillips curve, a central bank will seek to increase inflation when output is below potential. This targeting rule will impart a negative correlation between inflation and the output gap, blurring the identification of the (positively sloped) Phillips curve. We discuss different strategies to circumvent the identification problem and present evidence of a robust Phillips curve in US data.

中文翻译：

---

最优通货膨胀和菲利普斯曲线的识别

一些学者和从业者指出，通货膨胀遵循一个看似外生的统计过程，与产出缺口无关，导致一些人认为菲利普斯曲线已经减弱或消失。在本文中，我们解释了为什么会出现这种看似外生的过程，或者换句话说，为什么难以凭经验确定菲利普斯曲线，这是中央银行使用的政策框架的关键组成部分。我们展示了为什么这个结果不需要暗示菲利普斯曲线不成立——相反，我们的概念框架是在菲利普斯曲线始终成立的假设下建立的。原因很简单：如果货币政策的目标是最大限度地减少福利损失（以通货膨胀与其目标的偏差和产出与其潜力的偏差之和来衡量），受菲利普斯曲线的约束，当产出低于潜在水平时，中央银行将寻求提高通货膨胀率。这一目标规则将在通胀和产出缺口之间产生负相关，模糊（正斜率）菲利普斯曲线的识别。我们讨论了规避识别问题的不同策略，并提供了美国数据中强大的菲利普斯曲线的证据。