# Instantaneous Inflation

From a new working paper by Jan Eeckhout (UPF Barcelona), h/t Torsten Slok:

Current practice to measure inflation for monetary policy uses the average annual inflation rate. When inflation changes fast, whether increasing or decreasing, the annual average rate is biased towards data from too far in the past and conveys the true price level with six months delay. I propose to use instantaneous inflation as a more adequate measure of the price change. The measure trades off noise in the data with the precision of the instantaneous price change. Using the latest inflation numbers, it shows that instantaneous inflation in the US and the Eurozone is back to the target of 2% and that the high inflation period is over. This is not so for the UK, Japan and Australia.

Note that this is related to the debate we have had on this blog about the relative merits of 12 month inflation (or some people’s desire to use 17 or 18 month annualized inflation), 3 month or 1 month. 12 month overweights older data, 1 month is too noisy. The figure below shows the conventional 12 month (blue), and one month (or month-on-month) as black circles.

Using a polynomial kernel with weight a=4 (the conventional measure is 0, i.e., equal weighting to each monthly inflation rate), the author obtains the red line, which he terms “instantaneous inflation”. (See Figure B1.a in the paper for a graph showing how more recent observations are more weighted than older, relative to the simple 12 month change, a=0).

The author notes:

I find that the smoothed inflation in December 2022 is at 2%, the inflation target (see Figure 1, where a = 0 corresponds to the traditional measure and a = 4 corresponds to the instantaneous inflation measure with bandwidth parameter 4… The traditional [year-on-year] measure of inflation in December instead is 6.5%.

## 54 thoughts on “Instantaneous Inflation”

1. Macroduck

Nice idea and clearly right, in theory. Can it be shown that this approach would work in practice, that it could have provided useful information in the past? In other words, can it be demonstrated that this approach would have improved earlier policy decisions?

The author concludes that “The optimal weight is a function of how much variability there is in the data.” Can a decision rule be identified to pick the optimal weight?

2. Paweł Skrzypczyński

Non-parametric estimation is always a nice idea. The measure with a = 4 resembles the 3-month annualized rate which seems very good to analyze short-term trends and gauge turning pionts of 12-month rates.

1. Menzie Chinn Post author

Pawel Skrzypczynski: Thanks for the link. Furman and I share the same predeliction for using 3 month annualized, as a compromise between trend and noise. Although there’s no (or little) science to that. As pointed out in the paper, the weight and bandwidth should depend on the amount of noise in the series.

3. pgl

Current practice to measure inflation for monetary policy uses the average annual inflation rate. When inflation changes fast, whether increasing or decreasing, the annual average rate is biased towards data from too far in the past and conveys the true price level with six months delay. I propose to use instantaneous inflation as a more adequate measure of the price change. The measure trades off noise in the data with the precision of the instantaneous price change.

This is the point Alan Blinder recently made. I might mention a term such as the first derivative but that would likely get pretend lawyer Rick Stryker all fussing and forgetting his prime directive of excusing Trump’s treason.

1. Anonymous

TDS is real.

Everything – annualized, real-time, instantaneous, spontaneous, FIFO/LIFO, or otherwise – was better when Trump was President.

Convince me tom the contrary.

4. pgl

‘instantaneous inflation in the US and the Eurozone is back to the target of 2% and that the high inflation period is over.’

If one takes SA CPI over the past 6 months, it has increased by 0.9%. So if one annualizes this – one gets 1.8%. Something I have noted a few times.

“Note that this is related to the debate we have had on this blog about the relative merits of 12 month inflation (or some people’s desire to use 17 or 18 month annualized inflation)”

Ah yes – the Bruce Hall trick. But note he got 13.3% by using 17 months excluding the last 6 months and doing it with NSA data. And he found it too hard to annualize his bogus calculation. And in comment after comment he tried to justify his nonsense by blaming me for his stupidity? OK I’m guilty of pointing out the many flaws in his pathetic excuse for an analysis.

5. Bruce Hall

… (or some people’s desire to use 17 or 18 month annualized inflation)

Still misinterpreting that… monthly yr/yr or (mo/mo)x12 gives a moving percentage, whereas the 18-month look was for the period. The moving numbers are not additive; the period number is cumulative. It is harder to get a cumulative inflation from moving yr/yr data because the denominator keeps changing. The moving numbers are not additive. A period that begins at a constant base point and then continues to extend each month answers the question, “How much more do things cost now than in (base point)?”

You want to refer to that as price level change. Okay, what’s inflation? Is it not anything more than the percent change in price levels for moving base points?

1. pgl

Why are you still chirping over a simple topic that you got so incredibly wrong in so many ways?

Look Brucie – we got that you are a complete moron years ago. We get you lie about what even you have said in the past all the time. Just relax as you do not have to work so hard to prove the obvious – Bruce Hall is the Dumbest Troll God Ever Created. Hands down!

2. Menzie Chinn Post author

Bruce Hall: You do know that (using logs) the cumulation of month-on-month nonannualized inflation gives you your desired “cumulated inflation” more properly price change relative to number, don’t you.

1. pgl

You just went way above the capabilities of Bruce’s favorite new website. Then again these clowns are apparently still in middle school.

2. Bruce Hall

So, you think that people in general understand inflation that way?
You do know that (using logs) the cumulation of month-on-month nonannualized inflation gives you your desired “cumulated inflation” more properly price change relative to number, don’t you.

When nearly all of the discussion (and government publications) represent inflation as yr/yr people are going to look at December’s number of 6.5% and think, “Inflation is still running pretty hot.” Economists should think about their audience and that doesn’t stop in the classroom or blog posts.

Publicized inflation (yr/yr)
June = 9.1%
July = 8.5%
August = 8.3%
September = 8.2%
October = 7.7%
November = 7.1%
December = 6.5%

It’s not enough to say “you don’t understand” when the government and the media are pushing those numbers. People don’t understand because a series with moving denominators for percentage calculations isn’t intuitive … even if you say “year over year”. If you say, for the first 18 months of Joe Biden’s administration, inflation raised the price of your purchase, on average, about 13%. And for the recent 6 months of his administration it has only be about 1%. There is a quick comparison of both time and momentum… and that there has been an abrupt change. The fact that so many people were mocking Biden for saying no inflation for 6 months is because all they hear and read about are annualized numbers. Very convenient for economists; not so communicative for the rest.

Sure, that’s not academic oriented or “conventional”, but go on the go around campus and tell the non-economics students that “(using logs) the cumulation of month-on-month nonannualized inflation gives you your desired “cumulated inflation” more properly price change relative to number” and see what kind of stares you get. Then go to a political gathering where people are discussing the “still high rate of inflation” and give that explanation and see what response you get. Yes, log scale is great for visually showing relative change for disparate absolute numbers, but that sort of esoteric knowledge (and for most it is esoteric) is not great for communicating reality in general.

1. pgl

Let me get this straight. If the morons at Fox and Friends believe something – it must be true? Damn – you are dumber than even Princeton Steve. Brucie – keep on chirping as the other kiddies at your preK school are laughing so hard at you!

3. pgl

the question, “How much more do things cost now than in (base point)?”

The question has been what is the inflation rate. You are representing something completely different. Even a 3 year old gets the difference but not Bruce Hall.

Could you PLEASE stop wasting our time and could you PLEASE stop embarrassing your poor mom? Damn!

1. Bruce Hall

Why do you believe that an annualize inflation rate is more informative than from a base point?

The government published an “inflation rate” of 6.5% in December. Is that more informative than saying there has only been 1% total inflation of prices since June? Even Joe Biden tried to explain that to people in August when he said no inflation, but the year/year rate was firmly entrenched so few were listening. Was he wrong?

You are not wrong is using yr/yr; you’re just not communicating the bigger picture.

1. pgl

Why do I believe that being honest with people is a virtue? Yea – we get you like in a MAGA world. Keep chirping Brucie boy. We are all snickering at you.

2. Bruce Hall

Why do you believe that an annualize inflation rate is more informative than from a base point?

The government published an “inflation rate” of 6.5% in December. Is that more informative than saying there has only been about 1% total inflation of prices since June? Even Joe Biden tried to explain that to people in August when he said no inflation, but the year/year rate was firmly entrenched so few were listening. Was he wrong?

You are not wrong is using yr/yr; you’re just not communicating the bigger picture. But if I’m wasting my time on you, I’ll stop replying to you.

1. pgl

Brucie – writing more and more stupid stuff does not make things better. You have proven yourself to be an utter embicile on this issue just as you are on every other issue. STOP WASTING our time with your idiotic babbling.

6. Ivan

How about a heat storage system with 0% loss. You convert the heat to chemical energy that has no storage loss over a long time period. Then you tap it right back out again when you need some heating (hot water). Not just a great way to collect waste heat energy but also to store excess (intermittent) solar and wind. Early states but something new with a lot of potential.

https://www.innovationnewsnetwork.com/pioneering-energy-transition-with-revolutionary-heat-storage-systems/28874/

7. Bruce Hall

I ran across this little site that does the calculations (although I don’t know if it uses SA or NSA CPI values.
https://www.usinflationcalculator.com/inflation/calculator-cumulative/

Plug in starting month, amount, and ending month. It is not the “conventional” look at inflation, but it certainly provides an “instantaneous” look. Note that these numbers would graph significantly different from figure 1 above if the base point is January 2021. It’s not that difficult.

One point, since the base point is constant and the calculations are cumulative, a graph would not return to a base point, but would continue to show the cumulative number as a relatively flat line from when the CPI values did not change much (6/22). It would answer two questions visually: how much more do things cost now than in X and have overall prices stopped increasing as fast… and when? Anyone could see that prices are about 13% … about (not going there again) … higher than 1/21, but have not increased much since 6/22. Annualized moving data, when graphed, is misleading visually and requires additional analysis to pinpoint the trend discontinuity and slope.

Think of stock price charts that show a trend, a break point, and another trend with a different slope. If you use moving 12-month changes, you will have a more difficult time reacting to price changes and have a misleading picture when the slope changes.

1. Menzie Chinn Post author

Bruce Hall: NSA.

Since there’s a box on the right hand top corner reporting the December value, which matches NSA value for December 2022 (FRED series CPIAUCNS).

1. pgl

That is because Bruce went back to his high schoolers who mislead him on what they were producing. Yea – they used BLS data for CPI but these high schoolers used NSA data and never told Brucie.

2. Bruce Hall

Yes, that is what was reported. Was inflation really running that hot? I think you’ll agree it was not. Good number for economists and media claiming the sky is still falling. Not so much about the past half year.

What I really find amusing is that I’m basically defending Joe Biden’s position that inflation has flattened and all of his buddies on this forum are going “whatabout 6.5%”.

1. pgl

“Yes, that is what was reported.”

Brucie – we told you 2 months ago that these high school clowns that run this website were using NSA data. And you STILL don’t get that they continue to mislead you. DAMN! YOU! ARE! DUMB!!!!

1. Bruce Hall

From BLS:

NEWS RELEASES
CPI for all items falls 0.1% in December as gasoline decreases
01/12/2023

In December, the Consumer Price Index for All Urban Consumers decreased 0.1 percent, seasonally adjusted, and rose 6.5 percent over the last 12 months, not seasonally adjusted. The index for all items less food and energy increased 0.3 percent in December (SA); up 5.7 percent over the year (NSA).
HTML | PDF | RSS | Charts | Local and Regional CPI

NEXT RELEASE
January 2023 CPI data are scheduled to be released on February 14, 2023, at 8:30 A.M. Eastern Time.
***

So those are “high school clowns that run this website”. Damn you are obtuse.

2. pgl

Bruce Hall
January 24, 2023 at 2:12 pm
From BLS:

No MORON – BLS is run by smart people. Your little website that you adore is run by clowns. Once again you think you are cute but no – you are both a liar and STUPID. Stop wasting our time with your idiocy and lies.

3. Bruce Hall

No MORON – BLS is run by smart people. Your little website that you adore is run by clowns. Once again you think you are cute but no – you are both a liar and STUPID.

Well, pgl, your reference was pretty ambiguous and vague, so you get what you got. You still never specified what you meant by “your website” and when I referenced it. Of course not.

With regard to Yellen’s statements, here’s the interview. Basically, inflation is low, tax system is unfair to middle and lower income groups, we need to prioritize getting inflation lower. Read for yourself:
https://www.npr.org/2023/01/13/1148970513/prices-seem-to-be-easing-is-it-enough-for-the-fed-to-stop-raising-interest-rates

I’m still not sure why you want old uncle Joe saddled with complaints about high inflation after the last half of 2022 came in so low. Oh, wait, we must adhere to the rules: year over year only.

Jawohl! Wir haben das Reglement!

4. pgl

Bruce Hall wrote: “I’m still not sure why you want old uncle Joe saddled with complaints about high inflation after the last half of 2022 came in so low.”???

See how dishonest this troll is. He is now blaming ME for his insistence just before the election that Biden gave us high continuing inflation. Way to take responsibility for YOUR lies Bruce.

But yea – you did provide us a link to what Yellen really said to NPR. What she said was very sensible but a far cry from your cherry picked quotes. Damn Bruce – do you lie 24/7? I guess so.

2. pgl

Cumulative rate of inflation over 76%? Oh wait your high school clowns forgot to ANNUALIZE. The correct language is the cumulative increase in the price level. Come on Brucie – stop relying on high school clowns who are almost as dumb as you are.

You do know Excel can do these calculations too. Or did you never learn how to do Excel? Oh wait – FRED pulls the SA data for CPI all the way back to Jan. 1947 in Excel formats. Now try this calculation:

CPI for Dec. 2022 divided by CPI for Jan, 1947. You will get a huge increase. But no – it will not be the inflation rate.

3. pgl

“Anyone could see that prices are about 13% … about (not going there again) … higher than 1/21”

Let’s remember why this lying troll is hung up on how much CPI rose in the first year and a half of Biden’s Administration. This liar is trying to tell us the average household has seen real income fall by around 12.5% (yea I used SA not NSA data). But has nominal income not changed over this same period? I challenged Brucie to address this key issue two months ago. The lying coward has not so far so permit me.

I noted just yesterday that nominal GDP rose by 15%. So the simple arithmetic most 4 year olds get suggest real income INCREASED by 2.5% over this period.

We have told Bruce this fact over and over. But the liar he is – he still spews his intellectual garbage without addressing basic facts.

1. Bruce Hall

Oh, wow! pgl, you just fabricated a really big one. This liar is trying to tell us the average household has seen real income fall by around 12.5%

Kumquat! I did say that income was not keeping up with inflation so real income was falling, especially from 1/21 – 6/22. Are you the only one in the world disputing that?
Real average hourly earnings decreased 1.7 percent, seasonally adjusted, from December 2021 to
December 2022. The change in real average hourly earnings combined with a decrease of 1.4 percent in
the average workweek resulted in a 3.1-percent decrease in real average weekly earnings over this
period.

https://www.bls.gov/news.release/realer.nr0.htm

At least I cite references/sources. You might try that from now on.

1. pgl

Brucie wants us to believe he only cites BLS but he still refers to that high schooler website that uses NSA reporting without letting poor Brucie know that they have.

1. pgl

Poor little Brucie – caught in one lie after another. So he resorts to deny, deny, deny. BTW when nominal GDI rises by 15% and prices rise by 12.5% someone has seen an increase in real income. Or are you still struggling with preK arithmetic?

4. pgl

Hey Brucie – spend 15 minutes listening to that Peter Schiff video Dr. Chinn linked to. This dude may even be dumber than you are but I’m sure you will enjoy it.

8. AS

Dr. Eeckhout,
How does kernel forecasting differ from simple exponential smoothing or from Holt’s trend corrected exponential smoothing model? It would be instructive for a comparative example.

1. Menzie Chinn Post author

Anonymous: Isn’t this the same Peter Schiff who asserted “stats from BLS are BS”? And I thought Shadowstats was bad.

In this short piece, he claims (wrongly) the CPI is used in the calculation of GDP. He aslo cites some calculations he made for baskets of goods he selected, to compare against BLS CPI categories. I would *love* to see those spreadsheets.

1. pgl

That was 15 minutes of total BS. “I did not say all that money printing causes inflation. I said all that money printing IS inflation”. I’m surprised Trump did not put this clown on the FED.

2. Anonymous

I’m so old. I remember when the finest economics minds assured us inflation was “transitory.”

I didn’t say anything about Schiff’s perspicacity.

As usual, you grandees missed the point.

1. Menzie Chinn Post author

Anonymous: Well, I tend to quote approvingly people I believe are saying something insightful. Do I take from this Mr. Schiff is a contra-indicator for you?

3. pgl

‘To prove there are problems with the official CPI, Schiff calculated the price changes of a basket of 20 goods that consist of common household purchases. Schiff’s CPI basket of 20 goods included: eggs, new cars, milk, gasoline, bread, rent for a primary residence, coffee, dental services, potatoes, electricity, sugar, airline tickets, butter, store-purchased beer, apples, public transportation, cereal, tires, beef, and prescription drugs. From 1970 to 1980, the CPI rose 112% according to official statistics. During the same time period, the price of Schiff’s basket of 20 goods rose 117%. This leads to a difference of just 5% points.’

Now this is beyond stupid. But let’s be fair – Schiff may be a total moron but his little mistake here is something JohnH and Bruce Hall do routinely.

9. Bruce Hall

1/23
During an interview with NPR aired on Friday’s “Morning Edition,” Treasury Secretary Janet Yellen argued that inflation has been “quite low for the last six months or so,” but she wants to see “inflation come down to much lower levels” over the next year.

Yellen said, “Inflation has really been quite moderate, quite low for the last six months or so, importantly, because of lower energy prices. We continue to see improvement in supply chains. Goods prices have actually been falling. And some of the supply chain issues that pushed up the prices of goods and commodities, those have really turned around. Rent indexes continue to rise. But, really, we see those coming down substantially over the next six months or so.”

Later, host Michel Martin asked, “What’s going to be your metric of success for the year? If you and I were to speak at the same time next year, what will you consider your major accomplishments?”

Yellen responded, “My priorities would be to see inflation come down to much lower levels and to do that in the context of a job market that remains strong, with jobs readily available for people who want to work.”

So, while Yellen accepts that inflation has been quite low for the past six months(<1% cumulative; <2% annualized), she wants to "see inflation come down to much lower levels". What would be the "much lower levels" or has her thinking reverted to the 6.5% annual rate? Much confusion there? Well, we gotta hike those interest rates up some more because, you know, inflation is way too high.

1. pgl

Brucie – no link? Look by now even the MAGA trolls here know you are not an honest person. With no link there is every reason to believe you have taken Dr. Yellin’s comments out of context.

And don’t whine that I just called you a LIAR. After all – lying is your only talent.

1. pgl

“I just cut and pasted from an article”.

So you admit you cherry picked what she said. You are not only a liar and a moron. You’re a coward.

Now letting people know WHAT article. It is not hard. Oh but you are scared we will realize what a cherry picking troll you are if you do.

2. pgl

Well you finally did provide that NPR link. What Yellen said was sensible and a far cry from that cherry picked stuff you claimed. Look Bruce – we all know you are a serial liar. Get used to it.

10. AS

Regarding the 3-month annualized and the 1-month annualized forecast of future inflation, I used FRED series, PCEPILFE, starting 1959m01 and ending 2022m11. I annualized both the 3-month and the 1-month percentage changes. I then compared the 3-month (-12) and the 1-month (-12) forecasts with the Y/Y actual PCEPILE percent change and the PCEPILFE percent change lagged by 12 months using the EViews forecast evaluation function.

Assuming I made the correct calculations, the TheilU2 statistics are shown below. The lower the TheilU2 statistic the better the forecast. Generally, values less than 1.0 are desired, since using actual (-1) as a forecast produces a Theil U2 statistic of 1.0.

PCE3MOANNL(-12), Theil U2 = 5.4
PCE1MOANNL(-12), Theil U2 = 8.1
PCEPILFE_YY_PCT(-12),Theil U2 = 4.5