Here's a conversation I had with /u/geerussell last night

geerussell [4:26 PM] As I stated before, you don't know the number. The only reason you'll say "it's not 20%" is because we're currently below 20% and no inflation monster. When it was 6, they said 5. When it was 5 they said 4. When it's 4... you get the picture. Worthess as a guide to policy, had nairu adherents held sway at any point in time we'd have higher unemployment for no good reason.

besttrousers [4:27 PM] Wait, how do you think people estimate NAIRU

geerussell [4:27 PM] Not that being consistently wrong is any deterrent to defenders of the faith.

besttrousers [4:27 PM] walk me through how you think people do it

geerussell [4:28 PM] Mostly looking at historical averages of UE and inflation.

besttrousers [4:28 PM] What do you mean "Looking at"?

geerussell [4:28 PM] Which word didn't you understand?

besttrousers [4:29 PM] I want you to draw out what you mean "Look at" *by "Look at" like are they just staring at the data? Why do people think that the NAIRU is closer to 4% than 20%?

geerussell [4:31 PM] Because actual moved, inflation didn't materialize, so a new guess was pulled out of the air. Good thing that goalpost is on wheels.

/u/geerussell's model of how policymakers think about the NAIRU, as I understand it, is that they always claim that NAIRU is in the [0,current unemployment at t=0] range. If current unemployment falls below the NAIRU estimate, you just recalculate it such that it is in the [0,current unemployment at t 1] range.

I think that there's a lot of people who effectively do think of the relationship between unemployment and inflation like that. We all recall people who were hyperventilating over hyperinflation around 2009. /u/geerussell is right to dismiss those people (which includes some prominent economists <glares at John Taylor, who should know better>.

However, I think that they way most economist think about NAIRU (and the way all economists should think about NAIRU) is more complicated. Moreover, I think that we (even you kids at home) can estimate NAIRU pretty easily using the available data - even if we are not currently at NAIRU.

Let's back up:

NAIRU is Non-Accelating Inflation Rate of Unemployment. The basic logic is that the Federal Reserve can decrease cyclical unemployment by increasing inflation (/inflation expectations), but it can't decrease frictional (people looking for jobs) or structural (people who can't get jobs) unemployment. Trying to decrease unemployment past NAIRU has no effect on unemployment, it just increases inflation.

NAIRU doesn't exist by itself - it's part of a broader framework we use to think about the relationship between unemployment and inflation. Specifically, the Phillips curve and the expectations augmented Phillips curve. The Phillips curve is just the correlation between unemployment and inflation. This can be useful for thinking about the relationship between unemployment and inflation in the short run, but is less useful over longer periods of time. If people expect high inflation next year, the inflation will not have any effect. The expectations augmented Phillips curve is a modification that accounts for this. It measures relationship between year-over-year changes in inflation (working on the assumption that people generally anticipate that inflation next year will be the same as inflation in the previous year).

This is important - the Phillips curve gives us information that allows us to estimate the NAIRU even when we are not currently at the NAIRU. Here's how Ball and Mankiw do it:

We use the Hodrick-Prescott Ž lter (Hodrick and Prescott, 1997). The HP Ž lter is a generalization of a linear time trend that allows the slope of the trend to change gradually over time. Formally, the HP Ž lter minimizes the sum of squared deviations between the trend and the actual series, with a penalty for curvature that keeps the trend smooth. If there were no penalty, the Ž lter would yield the original series; if the penalty were very high, it would yield a linear time trend.

To implement this procedure, we must choose two parameters. The Ž rst is the Phillips curve slope, a. In our results below, we use an a of 0.63, the slope coefŽ cient obtained from regressing D on unemployment and a constant. This value is consistent with conventional wisdom about the costs of disin ation (it implies that reducing in ation by one percentage point produces 1/0.63 5 1.6 point-years of unemployment). Reasonable variation in the assumed coefŽ cient has little effect on our conclusions.

The other parameter is the smoothing parameter in the HP Ž lter—the weight that the procedure gives to keeping the estimated U* smooth rather than Ž tting every movement in U* 1 (v/a). The choice of this parameter is largely arbitrary. In some ways, this is not surprising: as we noted earlier, the distinction between U* and v is not well deŽned. Most economists have the intuition that movements in U* are “smooth” and that v represents a different kind of high-frequency shift in the Phillips curve, but this intuition is too vague to have much practical import. In the analysis below, we experiment with alternative values of the HP smoothing parameter

Now, I know what you're thinking: "Why do I have to read this? The paper contributes nothing - not even an opinion or belief - on any of the substantive questions about calculating the NAIRU for someone who is unfamiliar with advanced macroeconomics. One can speculate about the purposes for which this paper was written - a Nobel Prize in Economics? - but obviously it is not an attempt to engage with non-researchers in discussion of research strategies."

I'm just a plain country applied microeconomist, so here's an easier way to estimate NAIRU without all that mucking around with HP filters:

• Graph a scatter plot of change in inflation vs. unemployment (say for the previous ten years)
• Find the line of best fit
• Calculate the point at which the line cross the horizontal axis - that's the estimated NAIRU!

Here's what you get if you look at the last 10 years of data (2008-2017). The line crosses the horizontal axis when unemployment is 4.36 - pretty close to actual unemployment (4.35)!

Here's a table of NAIRU estimates using this method since 2000

Note that NAIRU is currently close to unemployment - but that hasn't been the case earlier.

This isn't a fool proof method (ie, 2015 is weird because those particular 10 observation show a slope very near 0!). What you really want is something that gives more weight to recent observations, but doesn't discount old observations entirely. But simplicity can be a virtue.