Board of Governors of the Federal Reserve System

Figure 1. Canada common inflation

The figure displays a line graph representing the monthly 12-month inflation time series for Canada starting in January of 2016 and ending in August of 2021. In the figure, the solid black line with squares shows headline inflation, the solid red line with triangles shows the preferred measure of core inflation for Canada, the dashed red line shows the Bank of Canada’s own calculation for common inflation, and the solid purple line with open circles shows our calculation for Canada’s common inflation. Core inflation hovers around common inflation which tracks similarly to the Bank of Canada’s calculation. It demonstrates how core inflation can mean revert to common inflation.

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Figure 2. Euro area common inflation

The figure displays a line graph representing the monthly 12-month inflation time series for the euro area starting in January of 2016 and ending in August of 2021. In the figure, the solid black line with squares shows headline inflation, the solid red line with triangles shows the preferred measure of core inflation for the euro area, and the solid blue line with open circles shows our calculation for the euro area’s common inflation. Common inflation remains relatively stable while core inflation oscillates around it. It remained steady at or just below 1 percent during this period until the COVID-19 pandemic.

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Figure 3. Japan common inflation

The figure displays a line graph representing the monthly 12-month inflation time series for Japan starting in January of 2016 and ending in August of 2021. In the figure, the solid black line with squares shows headline inflation, the solid red line with triangles shows the preferred measure of core inflation for Japan, and the solid blue line with open circles shows our calculation for Japan’s common inflation. Common inflation has been hovering around zero since 2016 but core inflation contains more upward and downward volatility around zero.

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Figure 4. United Kingdom common inflation

The figure displays a line graph representing the monthly 12-month inflation time series for the United Kingdom starting in January of 2016 and ending in August of 2021. In the figure, the solid black line with squares shows headline inflation, the solid red line with triangles shows the preferred measure of core inflation for the United Kingdom, and the solid blue line with open circles shows our calculation for the United Kingdom’s common inflation. As headline and core inflation spike in 2017, common inflation increases at a gradual and smoother pace, emphasizing its ability to filter out short-term shocks.

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Figure 5. Brazil common inflation

The figure displays a line graph representing the monthly 12-month inflation time series for Brazil starting in January of 2016 and ending in August of 2021. In the figure, the solid black line with squares shows headline inflation, the solid red line with triangles shows the preferred measure of core inflation for Brazil, and the solid blue line with open circles shows our calculation for Brazil’s common inflation. Brazil’s common inflation has tracked closely with core inflation, acting as a smoother measurement with less short-term spikes.

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Figure 6. Mexico common inflation

The figure displays a line graph representing the monthly 12-month inflation time series for Mexico starting in January of 2016 and ending in August of 2021. In the figure, the solid black line with squares shows headline inflation, the solid red line with triangles shows the preferred measure of core inflation for Mexico, and the solid blue line with open circles shows our calculation for Mexico’s common inflation. In 2017, headline and core inflation had major spikes to which common inflation had a less extreme reaction. From 2018 on, common inflation has gradually increased with core inflation, staying close to the latter while acting as a smoother measurement.

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Figure 7. Decomposition of common inflation on the onset of the COVID-19 pandemic

This figure shows six bar graphs demonstrating the decomposition of core inflation into common and idiosyncratic inflation. The figure shows the results for Canada in the top left, the euro area in the top right, Japan in the middle left, the United Kingdom in the middle right, Brazil in the bottom left, and Mexico in the bottom right. The graphs show results from January 2020 to August 2021. The black line with dots overlayed on the bars shows 12-month core inflation for each month. The red bars show 12-month common inflation for each month, and the white bars stacked above or below the red bars show 12-month idiosyncratic inflation for each month. Core inflation is the preferred measure for each country, and common inflation is the calculated value derived from the DFM described in the paper. Idiosyncratic inflation is then calculated as core inflation minus common inflation for each month. For every country, the common inflation bars have gradual movements while the idiosyncratic bars can quickly switch from absolutely large to absolutely small and positive to negative, demonstrating how common inflation filters out these sporadic movements in core inflation.

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Figure 8. Power of common inflation in forecasting headline inflation

The figure contains two charts displaying our calculation of common inflation’s forecast power for each country. At each horizon, h, from 1 month ahead to 36 months ahead, we calculate forecast power by taking the root-mean-square deviation (RMSD) of two regressions. One where the preferred measure of core inflation predicts headline inflation h months ahead (RMSDcore) and the same regression where common inflation predicts headline inflation h months ahead. At each horizon we then divide RMSD by RMSDcore and multiply the result by 100. We call this the forecast power score for common inflation at horizon h. Since common inflation performs better when its RMSD is lower than core’s, a lower forecast power score is more desirable, with anything under 100 meaning common inflation had a better performance. We put a dashed black line at 100 to demonstrate this threshold.

On the left-hand side, we display forecast power scores from 1 month to 36 months ahead with the dashed brown line for the euro area’s common inflation, solid red line for Canada’s common inflation, dotted red line for the Bank of Canada’s calculation of common inflation, dashed (with smaller separation) blue line for the United Kingdom’s common inflation, and the dashed (with different sized dashes) green line for Japan’s common inflation. The euro area line hovers around 100, peaks around 12 months and troughs around 28 months. It is the only line that ever goes above 100. The Canada line decreases to 12 months and then has a sharp increase to 18 months where it is around 85. It then gradually decreases over time until 30 months where it increases slightly to the end of the horizon. The Bank of Canada line follows our Canada line but remains above it the entire time. The UK line gradually decreases from a little under 100 to below 80 (the lowest value of all the lines) from 1 to 28 months. At 28 months the UK begins to increase. The Japan line remains relatively stable just under 100 for the entire horizon. It has a slight trough at 12 months but increases until just before the end of the horizon.

On the right-hand side, we display forecast power scores from 1 month to 36 months ahead with the dashed green line for Mexico’s common inflation, and solid navy line for Brazil’s common inflation. Brazil starts around 100 and peaks above it at around 15 months. It then decreases to below 90 until 25 months where it stabilizes. Mexico starts around 100 and quickly drops to below 60 at around 20 months. It then increases at similar pace to 90 at 36 months.

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