Is There A Relationship Between Inflation And Unemployment?

Or, old fogey downloads data, finds a negative relationship, a.k.a. the Phillips Curve…

Much was made of the meeting of minds of AOC and Larry Kudlow regarding the Phillips Curve, to wit (from Bloomberg):

… Ocasio-Cortez said many economists are concerned that the formula “is no longer describing what is happening in today’s economy” — and Powell largely agreed.

“She got it right,” Kudlow told reporters at the White House later on Thursday. “He confirmed that the Phillips Curve is dead. The Fed is going to lower interest rates.”

Well, since I’ve been teaching the Phillips Curve for lo these thirty odd years, I thought I’d check to see if I’d missed something. First, it’s important to remember that while we talk about the negative relationship between inflation and unemployment, or the positive relationship between inflation and output, the actual model we use is the expectations augmented Phillips curve including input price shocks. My preferred specification is:

πt = πet + f(ut-4 – un,t-4) + θzt

Where π is 4 quarter inflation, πe is expected inflation, u is official unemployment rate, un is natural rate of unemployment [ so (u-un) is the unemployment gap], and z is an input price shock, in this case the 4 quarter inflation rate in import prices. Each of these series is available from FRED; using the FRED acronyms, PCEPI for the personal consumption expenditure deflator, MICH for University of Michigan’s 1 year inflation expectations, UNRATE for unemployment rate, NROU for natural rate of unemployment, and IR for import prices.

Estimate this relationship using OLS over the 1987-2019Q2 period (first two months of 2019Q2 used to proxy for Q2). This sample period, after accounting for lags, spans the “Great Moderation”.

One obtains:

πt = -0.19 + 0.74πet – 0.18(ut-4 – un,t-4) + 0.15zt

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