Divine coincidence

In economics, divine coincidence refers to the property of New Keynesian models that there is no trade-off between the stabilization of inflation and the stabilization of the welfare-relevant output gap (the gap between actual output and efficient output) for central banks. This property is attributed to a feature of the model, namely the absence of real imperfections such as real wage rigidities. Conversely, if New Keynesian models are extended to account for these real imperfections, divine coincidence disappears and central banks again face a trade-off between inflation and output gap stabilization. The definition of divine coincidence is usually attributed to the seminal article by Olivier Blanchard and Jordi Galí in 2005.

In a standard New Keynesian model consisting of a Calvo price and sticky wages on the supply side and both an Euler equation and the Taylor rule on the demand side, the so-called New Keynesian Phillips curve (NKPC) is the following:

where ${\displaystyle \pi _{t}}$ is current inflation, ${\displaystyle E_{t}[\pi _{t+1}]}$ is expected future inflation, ${\displaystyle y_{t}}$ is actual output, ${\displaystyle y_{t}^{*}}$ is natural output and ${\displaystyle (y_{t}-y_{t}^{*})}$ is the welfare-relevant output gap. This equation implies that the two goals of maintaining inflation stable and stabilizing the output gap do not conflict: if, for example, an increase in oil price affects natural output, then holding inflation constant will make actual output equal natural output. This implication, or property, is called "divine coincidence".

...
Wikipedia