Natural Output

Macro

Natural output $y_t^n$ is the level of output that would prevail if all prices were perfectly flexible — i.e., the RBC equilibrium output within the same New Keynesian Model.

Core intuition: The NK model has two “layers.” Strip away the nominal rigidities (Calvo Price), and you’re left with a standard RBC economy where markets clear perfectly. The output in that frictionless version is $y_t^n$. It moves only in response to real shocks (primarily technology $a_t$), not monetary shocks — because with flexible prices, money is neutral.

Why it matters: Natural output serves as the benchmark against which we measure the distortion caused by sticky prices. The output gap is defined as:

${\tilde{y}}_t=y_t-y_t^n$

This gap captures how far the actual economy deviates from where it would be without nominal frictions. It’s the key variable in the NKPC:

${\pi }_t=\kappa {\tilde{y}}_t+\beta E_t({\pi }_{t+1})$

and the Dynamic IS equation:

${\tilde{y}}_t=-\frac{1}{\sigma }(i_t-E_t[{\pi }_{t+1}]-r_t^n)+E_t({\tilde{y}}_{t+1})$

The key takeaway: Inflation isn’t driven by the level of output itself, but by how much output exceeds (or falls short of) its natural, flexible-price level. When ${\tilde{y}}_t>0$, real marginal costs are above their flexible-price level, putting upward pressure on inflation. The central bank’s job is essentially to close this gap — steering actual output toward $y_t^n$ — which simultaneously stabilizes inflation (this is the “divine coincidence” result).