# Tag Archive for 'Taylor'

### Deriving the New Keynesian Phillips Curve (NKPC) with Calvo pricing

The Phillips Curve is an empirical observation that inflation and unemployment seem to be inversely related; when one is high, the other tends to be low.  It was identified by William Phillips in a 1958 paper and very rapidly entered into economic theory, where it was thought of as a basic law of macroeconomics.  The 1970s produced two significant blows to the idea.  Theoretically, the Lucas critique convinced pretty much everyone that you could not make policy decisions based purely on historical data (i.e. without considering that people would adjust their expectations of the future when your policy was announced).  Empirically, the emergence of stagflation demonstrated that you could have both high inflation and high unemployment at the same time.

Modern Keynesian thought – on which the assumed efficacy of monetary policy rests – still proposes a short-run Phillips curve based on the idea that prices (or at least aggregate prices) are “sticky.”  The New Keynesian Phillips Curve (NKPC) generally looks like this:

$\pi_{t}=\beta E_{t}\left[\pi_{t+1}\right]+\kappa y_{t}$

Where $y_{t}$ is the (natural) log deviation – that is, the percentage deviation – of output from its long-run, full-employment trend and $\beta$ and $\kappa$ are parameters.  Notice that (unlike the original Phillips curve), it is forward looking.  There are criticisms of the NKPC, but they are mostly about how it is derived rather than its existence.

What follows is a derivation of the standard New Keynesian Phillips Curve using Calvo pricing, based on notes from Kevin Sheedy‘s EC522 at LSE.  I’m putting it after this vile “more” tag because it’s quite long and of no interest to 99% of the planet.