Four Questions and Four Answers: US and Euro Area Core Inflation

Or why Jason Furman and I get different answers.

  • Is US core inflation faster than Euro Area, during the pandemic? Yes.
  • Was US core inflation faster than Euro Area, before the pandemic? Yes.
  • Is US core m/m inflation faster than Euro Area during the pandemic period, with statistical significance? No.
  • Did US core m/m inflation accelerate relative to Euro Area, with statistical significance? No.

A follow up to this post.

I examine US and Euro area inflation, month-on-month, using log differences of the price level. The Euro area HICP indices are seasonally adjusted using geometric X-12. Then define the annualized month/month inflation difference US vs. country i:

Take this variable and regress this object on a constant over the 2018M01-2020M01 period, and I obtain an estimate of 0.012, HAC standard error of 0.0025 (i.e., US core inflation exceeds Euro area core inflation by 1.2% on average). Then do the same regression on 2020M02-2022M03, to obtain an estimate of 0.019, HAC standard error of 0.0109. So, the difference between US and Euro area core inflation widens from 0.012 to 0.019, or 0.007 (0.7%).

How to calculate the difference in mean inflation differentials? One could do a t-test doing a manual calculation of the standard error (essentially a weighted average of the first and second standard errors). Or, I can just run the regression over the 2018-2022M03 period:

Where covidt is a dummy variable taking a value of 1 from 2020M02 onward.

The α coefficient is the pre-covid inflation differential between the US and country i; the β coefficient is the change in the inflation differential post-covid. (This diffs-in-diffs approach is to be preferred because the compositional aspects of the US series and the Euro Area HICP.)

Using HAC robust standard errors, I find that the estimated β coefficient is  0.007 for US-Euro Area (HAC robust standard error 0.011). The t-statistic for the null of zero on the β coefficient approach statistical significance at conventional levels. That’s partly because (in a mechanical sense), the variability of the differential in the pandemic period is so large.

Figure 1: Month-on-month core inflation differential between the US and Euro Area (black), calculated using log differences. Teal line is mean differential 2018-2020M1; red line is mean differential 2020M02-2022M03. Euro Area core HICP seasonally adjusted by author using geometric Census X-12. NBER defined peak-to-trough recession dates shaded gray. Source: BLS, Eurostat via FRED, NBER, and author’s calculations.

Now, why does Jason Furman get a big difference in his “Since Feb. 2020” category, vs “Feb. 2018 to Feb. 2020” in the Table below?

Source: Furman (2022).

After some number crunching, I think what’s going on is that Jason Furman calculates the growth rate before, and after, using the slopes of lines in Figure 2 below.

Figure 2: US core CPI, s.a. (black) and Euro Area HICP core seasonally adjusted (teal). Red arrows connect 2018M02-2020M02, 2020M03-2022M03 for US, green arrows for Euro Area. Euro Area core HICP seasonally adjusted by author using geometric Census X-12. NBER defined peak-to-trough recession dates shaded gray. Source: BLS, Eurostat via FRED, NBER, and author’s calculations.

As the slopes of the arrows steepen for both series, inflation rates are rising for both — but the US slope steepens more than the Euro Area slope.

Both approaches are “right”. If you want to focus on the last 3 months or last year, you should do what is done in Jason’s table. If you want to compare pre-pandemic and pandemic periods, you can do what is in the table (and implicitly Figure 2). But then you can’t do a statistical significance test, as I did.* Personally, I prefer the diffs-in-diffs in a regression context just because, well, that’s how I teach it in class.

*  There may be some deep issue, about whether the slopes approach treats the CPI or HICP as a I(0) variable, while the regression of inflation rates approach treats inflation as I(0), but I don’t quite have the energy to think about that right now.