Understanding the Math behind Recent Inflation Trends

Monday, December 11, 2023

Following the release of a recent monthly Consumer Price Index (CPI) report, I noticed some conflicting headlines among news stories. Here are just a few:

Inflation sped up
Inflation nudged up
Inflation was up slightly
Biggest jump in inflation in over a year
Good news on inflation despite jump in gas prices
Inflation ticked up for 2^nd consecutive month
High gas prices push up inflation, but prices overall are slowly moving in the right direction
Gasoline lights up US consumer inflation; underlying trend steadily improving
The CPI Was Hot

So, you might wonder, which is correct? Was the CPI hot, did it nudge up, or is it steadily improving? The answer lies in the way you look at the numbers. Let’s have some fun with math.

We’ll start by looking at the 1-month change in the CPI for all items, known as the “headline” CPI. As seen in the following chart, inflation rose 0.6 percent in August and 0.4 percent in September. So, prices were up in September, but up less than in the prior month. Was this good news or bad news? Let’s dig deeper.

Spikes in specific categories, rather than broader price movements, can have a large effect on monthly changes, so it’s important to look at what drove the overall change. In this case, the 0.6-percent increase in August was largely driven by a big increase in gasoline prices, which are often volatile. Gasoline prices rose more than 10 percent in August but only about 2 percent in September.

Editor’s note: Data for this chart are available in the table below.

Note that when we focus on monthly changes, we generally use seasonally adjusted data. Some price movement occurs simply due to the time of year. For example, prices tend to fall (or at least increase less) in November and December because of holiday sales and other factors. Using seasonally adjusted data allows us to see price change that isn’t just normal seasonal variation.

A common barometer of inflation is to look at the yearly change—how much higher are prices today than they were a year ago. This often gets a lot of attention, as it did in the summer of 2022, when the annual change reached 9 percent—the highest in 40 years. Similarly, the annual change got a lot of attention earlier in 2023 when it dropped rapidly, as the following chart shows.

Editor’s note: Data for this chart are available in the table below.

Consider, for example, the annual changes for February 2023 and March 2023. The 12-month change from February 2022 to February 2023 was 6.0 percent, but it fell to 5.0 percent for the period from March 2022 to March 2023. However, the monthly change in March 2023 was positive, a 0.3-percent increase. The decrease from 6.0 percent to 5.0 percent was mainly because a large 1-month increase from February to March 2022 of 1.3 percent is now outside the 12-month window. The base of the 12-month period is now the higher March 2022 index, which gives us a smaller 12-month change.

The movement in the 12-month change from one month to the next depends not only on price change this month but on the price change for the same month a year ago. Whether the 12-month change for September 2023 is higher than the one for August 2023 depends on whether the monthly change from August to September 2023 was larger than the change from August to September 2022. In this case, they were about the same; the September 2022 and September 2023 increases were both 0.2 percent (not seasonally adjusted). So, the 12-month change remained stable at 3.7 percent. It is possible for the 12-month change to rise even if prices fall over the month (and vice versa)!

So, if the 1-month change can be influenced by an unusual spike in a particular item, and the 12-month change is influenced by the base effect, are there other ways to assess the recent trends in inflation? One approach is a 3-month moving average, which focuses on the most recent data but avoids short-term spikes. In the chart below, we see less volatility in recent months than we see in the 1-month changes. The inflation rate was largely steady for several months in 2023, with a slight increase in the most recent months.

Editor’s note: Data for this chart are available in the table below.

Another approach is to focus on the index numbers, rather than the percent change. In simple terms, the monthly calculation of the CPI yields an estimate of the price level relative to a base period. For most CPI indexes, the base period is 1982–84. The index number, compared with the prior month’s number, results in the 1-month percent change that you see in news headlines. Similarly, comparing the index number from one year to the next provides the 12-month percent change. But looking just at the index numbers provides a different perspective.

Editor’s note: Data for this chart are available in the table below.

One thing you notice from the chart of index numbers is that the line continues to go up. Prices tend to continue to rise, sometimes slowly, sometimes quickly. For those of you who still remember high school geometry, you will notice that the slope of the line changes, consistent with the higher and lower rates of inflation.

Maybe you want to consider inflation over a longer period, like since the same month 5 years ago or since the Mets last won the World Series. The index numbers can help with that as well. In August 2018, the index for the CPI stood at 252.146 as compared with 307.026 in August 2023. Some quick math reveals a change of about 22 percent over 5 years. Going waaaay back to when the Mets took the series in 1986 (I’ll use August just to make the math easier), the index number was 109.7, and the change over those 37 years was 179.9 percent. We even have an inflation calculator so you can pick your own favorite date (like your birth month or some other special occasion) and find how much prices have changed since then.

But, perhaps the trend in inflation is not the focus you need. Another way to look at price change is to consider the impact. For instance, you can compare price increases to increases in workers’ earnings to find out if earnings are keeping up with inflation. The BLS real earnings data do just that by comparing the average hourly earnings (from the Current Employment Statistics program) to the CPI. When earnings rise faster than inflation, real earnings are positive. In contrast, if inflation exceeds earnings growth, real earnings are negative.

Editor’s note: Data for this chart are available in the table below.

As with price change, we can look at both monthly and yearly changes in real earnings. Monthly increases in real earnings from March through July 2023—meaning earnings were rising faster than prices—pushed the 12-month change in real earnings from negative to positive starting in May. Recent monthly declines in real earnings resulted in smaller 12-month increases.

As you can see, when it comes to assessing what’s going on with inflation, you have lots of choices. At BLS, our goal is to provide all the information, at high quality, so you can use that information to make decisions.

A special thanks to Steve Reed of BLS for his contributions to this blog post.

1-month percent changes, Consumer Price Index for all items, seasonally adjusted
Month	Percent
Jan 2022	0.6
Feb 2022	0.7
Mar 2022	1.0
Apr 2022	0.4
May 2022	0.9
Jun 2022	1.2
Jul 2022	0.0
Aug 2022	0.2
Sep 2022	0.4
Oct 2022	0.5
Nov 2022	0.2
Dec 2022	0.1
Jan 2023	0.5
Feb 2023	0.4
Mar 2023	0.1
Apr 2023	0.4
May 2023	0.1
Jun 2023	0.2
July 2023	0.2
Aug 2023	0.6
Sep 2023	0.4
Oct 2023	0.0

1-month and 12-month percent changes, Consumer Price Index for all items, not seasonally adjusted
Month	1-month percent change	12-month percent change
Jan 2022	0.8	7.5
Feb 2022	0.9	7.9
Mar 2022	1.3	8.5
Apr 2022	0.6	8.3
May 2022	1.1	8.6
Jun 2022	1.4	9.1
Jul 2022	0.0	8.5
Aug 2022	0.0	8.3
Sep 2022	0.2	8.2
Oct 2022	0.4	7.7
Nov 2022	-0.1	7.1
Dec 2022	-0.3	6.5
Jan 2023	0.8	6.4
Feb 2023	0.6	6.0
Mar 2023	0.3	5.0
Apr 2023	0.5	4.9
May 2023	0.3	4.0
Jun 2023	0.3	3.0
July 2023	0.2	3.2
Aug 2023	0.4	3.7
Sep 2023	0.2	3.7

3-month moving average percent changes, Consumer Price Index for all items, seasonally adjusted
Month	Percent
Mar 2022	0.8
Apr 2022	0.7
May 2022	0.8
Jun 2022	0.8
Jul 2022	0.7
Aug 2022	0.5
Sep 2022	0.2
Oct 2022	0.4
Nov 2022	0.4
Dec 2022	0.3
Jan 2023	0.3
Feb 2023	0.3
Mar 2023	0.3
Apr 2023	0.3
May 2023	0.2
Jun 2023	0.2
July 2023	0.2
Aug 2023	0.3
Sep 2023	0.4
Oct 2023	0.4

Consumer Price Index for all items, not seasonally adjusted (January 2020=100)
Month	Index
Jan 2020	100.000
Feb 2020	100.274
Mar 2020	100.056
Apr 2020	99.387
May 2020	99.389
Jun 2020	99.933
Jul 2020	100.438
Aug 2020	100.755
Sep 2020	100.895
Oct 2020	100.937
Nov 2020	100.875
Dec 2020	100.970
Jan 2021	101.400
Feb 2021	101.955
Mar 2021	102.677
Apr 2021	103.521
May 2021	104.351
Jun 2021	105.320
Jul 2021	105.827
Aug 2021	106.046
Sep 2021	106.334
Oct 2021	107.217
Nov 2021	107.744
Dec 2021	108.075
Jan 2022	108.984
Feb 2022	109.980
Mar 2022	111.448
Apr 2022	112.070
May 2022	113.306
Jun 2022	114.862
Jul 2022	114.849
Aug 2022	114.808
Sep 2022	115.055
Oct 2022	115.522
Nov 2022	115.405
Dec 2022	115.051
Jan 2023	115.970
Feb 2023	116.618
Mar 2023	117.004
Apr 2023	117.596
May 2023	117.892
Jun 2023	118.273
Jul 2023	118.498
Aug 2023	119.016

1-month percent change in real average hourly earnings for all employees, seasonally adjusted
Month	Percent change
Oct 2022	-0.1
Nov 2022	0.2
Dec 2022	0.3
Jan 2023	-0.2
Feb 2023	-0.1
Mar 2023	0.2
Apr 2023	0.1
May 2023	0.2
Jun 2023	0.3
Jul 2023	0.2
Aug 2023	-0.4
Sep 2023	-0.2
Oct 2023	0.2

12-month percent change in real average hourly earnings for all employees, seasonally adjusted
Month	Percent change
Oct 2022	-2.8
Nov 2022	-2.1
Dec 2022	-1.6
Jan 2023	-1.8
Feb 2023	-1.2
Mar 2023	-0.6
Apr 2023	-0.5
May 2023	0.2
Jun 2023	1.3
Jul 2023	1.0
Aug 2023	0.5
Sep 2023	0.5
Oct 2023	0.8