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? Yes.
- Did US core m/m inflation accelerate relative to Euro Area during the pandemic period, 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.
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.
Update, 8pm Pacific: a formal estimate of differential trends in price level.
Define the dependent variable as the log relative US core CPI to Euro Area core HICP, and run the regression over the 2018-2022M03:
Adj-Rsq = 0.96, SER = 0.0040, N = 51, DW=0.71, bold denotes significance at 5% msl.
Using the estimates to fit the data, we get this picture.
Figure 3: Log ratio of US core CPI, s.a. to Euro Area HICP core seasonally adjusted (black). Fitted value using estimated equation (red). 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.
The series (either from 2000M12 or from 2018M01 onward) fails to reject the null hypothesis of unit root using ADF test, or DF-GLS test of Elliott-Rothenberg-Stock, but does reject the Kwiatkowski-Phillips-Schmidt-Shin trend stationary null. The extreme serial correlation (DW < R2) is suggestive of spurious correlation.