## What do they even want?: Inflation Edition

People were all excited last week when the CPI numbers were released because… the year-over-year rate of inflation did a whole lot of nothing. See below. The 12-month rate of inflation was practically constant. The 8.2% number was all over the headlines and twitter. We already know that news outlets don’t always report on the most relevant numbers. And I say that this is one of those times.

First of all, there is a problem with the year-over-year indicator. Well, not so much problem in the measure itself, but more a problem of interpretation. The problem is that the 12-month rate of inflation is the cumulative compound rate for 12 individual months. Each month that we update the 12-month inflation rate, we drop a month from the back of the 12-month window and we add a month to the front of the 12-month window. Below are both a graph and a table indicating the monthly rate of inflation and the 12-month periods ending in August 2022 (pink) and in September 2022 (green).

## AS-AD: From Levels to Percent

The aggregate supply & aggregate demand model (AS-AD) is nice because it’s flexible and clear. Often professors will teach it in levels. That is, they teach it with the level of output on one axis, and the price level on the other axis. This presentation is convenient for the equation of exchange, which can be arranged to reflect that aggregate demand (AD) is a hyperbola in (Y, P) space. Graphed below is the AD curve in 2019Q4 and in 2020Q2 using real GDP, NGDP, and the GDP price deflator.

The textbook that I use for Principles of Macroeconomics, instead places inflation (π) on the vertical axis while keeping the level of output on the horizontal axis. The authors motivate the downward slope by asserting that there is a policy reaction function for the Federal Reserve. When people observe high rates of inflation, state the authors, they know that the Fed will increase interest rates and reduce output. Personally, I find this reasoning to be inadequate because it makes a fundamental feature of the AS-AD model – downward sloping demand – contingent on policy context.

At the same time, I do think that it can be useful to put inflation on the vertical axis. Afterall, individuals are forward looking. We expect positive inflation because that’s what has happened previously, and we tend to be correct. So, I tell my students that “for our purposes”, placing inflation on the vertical axis is fine. I tell them that, when they take intermediate macro, they’ll want to express both axes as rates of change. I usually say this, and then go about my business of teaching principles.

But, what does it look like when we do graph in percent-change space?