I recently ran in to a lovely paper by Neil White at Amherst, “The new Keynesian Price Puzzle: Reinterpreting Inflation Dynamics.” This post is closely related to my last one on the Lucas Phillips curve and that line of work.
“ policy. On the left you can see how the Federal Funds Rate responds to a shock. Conceptually, suppose the Fed wakes up one day, raises interest rates, and then keeps interest rates persistently high following the pattern shown in the left hand graphs.”
I don’t understand this, is it the fed funds rate responding to a shock (first sentence) or is the change in the funds rate itself the shock (second sentence)?
My paper shows that, based on 50 years of data, a consistent 12-18 month precursor to inflation is something I call the Domestic Liquidity Ratio, real M2/realGDP. When money supply is in balance with economic activity, inflation is ALWAYS under control. I also demonstrate that raising interest rates can be a precursor to inflation and that there is no evidence that raising interest rates cures it. The spike in my ratio in 2020 matches perfectly 2021-2022 inflation.
The center for financial stability publishes them. They also have more data on user costs and so on, but you have to email them if you want more than their Divisia aggregates.
Conceptually, this makes to me. If you raise rates, eventually this cost increase is going to work its way into what we pay for goods and services (i.e., inflation). Businesses may absorb some of the cost increase, but consumers will also pay their share, eventually.
Why then would the rate of price growth eventually flatten or decline? Again, from a behavioral standpoint it makes sense as consumer ability to absorb price increases is not infinite and at some point, purchasing activity (absent wage increases and/or governmental assistance) has to decline. At this point, producers and sellers are likely to find ways to reduce their costs and either stabilize or reduce prices in order to retain customers.
The whole point of raising rates has been to reduce demand in order bring down the rate of inflation, right?
A famous quote from Sherlock Holmes, “ It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.” All comments I’ve read are theoretical. I just looked at the data. In my talk I graph five series, only one of which is real (CPI adjusted) Federal Funds rate, and compare those to inflation rate. You are hard pressed to pick which is the real data that causes inflation to subside. That’s what I mean by “no evidence.”
1. What happens when you use your new model instead of the textbook NK model?
2. Martin Uribe (2022) had this paper identifying long-run vs short-run interest rates shocks. Permanent changes being conflated with transitory ones in interest rates is another possible resolution of the puzzle. It would be nice to see something like that too, but you’d need to include this in the theory to compare cleanly. It doesn’t resolve your point that the mechanism isn’t the aggregate demand story we invoke — but it might change the sign.
3. You can basically eliminate the price puzzle if you use a Divisia monetary aggregate (Keating et al., 2019). Nothing says the fundamental surprise needs to match the policy instrument. Josh Hendrickson also has a paper with Ronald Mau (2022) where they show a particular rule for monetary policy is equivalent to a particular money demand, so you can write the same NK model both ways. Like fiscal policy, money demand is always there even if they didn’t write it down.
I know the point you’re making here is to raise the possibility that conventional wisdom is just ignoring what data and theory has been screaming at us for years. Still, a price puzzle is far from necessary.
Alain Paquet and Christian Barette (2024) also have a cool TVP-VAR extension that look at this Christiano et al. (1999) type of analysis with Divisia money really carefully:
I thought the commonly told story is that interest rate hikes lead to falling inflation with long and variable lags. The story isn't really about the price level per se. The IRFs in Stock and Watson's paper are in terms of inflation, not the price level. The interest rate shock leads to falling inflation after about a year or two (consistent with White's paper after taking into account the higher frequency).
If you cumulate the inflation IRFs, you get the log price level response (so, the % change in the price level), so you can transform the IRFs of inflation into prices and vice-versa if you want to see it one way or another.
The long and variable lag is a common story. Milton Friedman famously used this phrase decades ago and early SVARs such as those featured in Christiano, Eichenbaum and Evans' 1999 handbook chaper tended to fit this expectation. Price puzzles are common in these types of SVARs, though not always very large or statistically significant, but the responses of price variables tend to be very persistent. You can get similar features using more recent methods like the sign restrictions such as in Arias, Caldara and Rubio-Ramirez (2019, here: https://www.sciencedirect.com/science/article/pii/S0304393218303908).
That being said, as I told professor Cochrane in his post on his 'Lucas Philips Curve' paper, that's not an unambiguous feature of the data. Some SVARs that rely on high-frequency instruments will produce a *jump* in the inflation rate (a statistically significant response at h=0), consistent with standard theory.
People are debating monetary policy because it's important, yet extremely complicated to evaluate in practice: all central banks spend millions of dollars making their policy extremely endogenous (and predictable)! Also, if professor Cochrane's musing in this post is right and monetary policy should produce positive responses for nominal rates and inflation, then the problem is even harder. As Christian Wolf (2020) pointed out (https://www.aeaweb.org/articles?id=10.1257/mac.20180328), monetary policy shocks are presumably tiny, accounting for only a small share of the variation in most of the macro data and that makes them hard to identify. However, he mentions that it's also a rare shock in our theories that really robustly predicts opposite sign response in inflation and nominal rates.
The paper should have used a standard "error correction model" here to cancel out the relationship at the levels.
It should be obvious that long-run prices will increase or decrease almost 1:1 with the money supply. You simply can't predict inflation without bringing into account changes (or expected changes) in the money supply, and controlling for the level of the money supply.
This is so obvious, I have trouble imagining a realistic reason why economists are so allergic to connecting money supply with inflation. Is there some conspiracy?
In any case, there are always two main reasons why prices go up: restriction of supply or boost to demand. Same goes with debt and the implied interest rates. If there's a sudden boost in demand to borrow, rates will go up, and if there's a sudden restriction in people willing to lend, that will also boost rates.
There are a few essential things that will balance out to net an increase or decrease in rates: 1. Borrowers being in a bad economic state (especially if optimistic about the future) will boost borrowing and rates. 2. Borrowers expectation to be in a bad economic state in the future will actually reduce borrowing and rates. 3. Lenders being in a bad state or expecting a future bad state will reduce lending and raise interest rates.
Prices are the net of the following dynamics: 1. Increase in borrowing for consumption will increase prices (until the debt needs to be paid off, and then it will decrease prices by the same amount. 2. Expansion of the money supply. 3. Technology that decreases prices.
That's pretty much it.
The reason why interest rates don't correspond to inflation is because inflation is the net effect of a few things that can offset each other. An increase in rates doesn't always correspond with an increase in net-dollars borrowed. It could be the result of lenders being more restricted or borrowers become more pessimistic. We also have the change in money supply effects. If the government prints and spends, this will drive up rates and prices, but if the government is merely offsetting pessimism, the net effect could go either way.
In other words, the paper could be improved by including in the model:
where, the superscript e on the variables π(t) and x(t) indicates the conditional expectation of the variable at time t.
This equation can be obtained by simple algebraic manipulation of the differential equation version of the simple two-equation NK model.
By assuming that x(t) ≡ x°, a constant, N. White obtains the relation
d(πᵉ(t)) = ρ∙i(t)∙dt – κ∙x°∙dt (2)
in which the infinitessimal change in the conditional expectation of the rate of inflation is directly proportional to the nominal rate of interest. This then gives the result he reports in his paper.
The assumption he makes is restrictive. If the assumption is removed, then we have equation (1) in which the conditional expectation of the rate of inflation is negatively proportional to the sum of the conditional expectation of the infinitessimal differential of output gap, d(xᵉ(t)), and the current output gap, x(t), and positively proportional to the nominal rate of interest, i(t).
As N. White relates in his paper, the conventional expectation is that an increase in the real rate of interest, r(t), depresses excess demand and increases savings thereby increasing the output gap in the short term. The effect should be evident in the raw data.
I wouldn't rely on the proffered mathematical models as presented. Experience in the 2022 through the first quarter of 2025 does not lend support to N. White's thesis. Perhaps it is different this time, but color me skeptical.
Isn’t plugging initial inflation into the simple NK model the same as making a whole new model? In the NK model, initial inflation (i.e., first period) is endogenous; it is a jump variable (hence indeterminacy in the model without some assumptions about policy). Assuming an initial inflation value is inconsistent with the model (price setters set the first period’s prices - the researcher cannot set them on their behalf). Solving a price indeterminacy problem by just assuming a price outcome you like, is not a valid solution in this model imo.
Btw didn’t Romer and Romer interpret the longer-run drop in the price level after the temporary interest-rate increase, as a refutal of the price puzzle? (Interest rate up, prices down with a lag).
I mean, am I the only one to notice the widely different scale used in the third column of plots compared to the second one? There may be qualitative resemblance, but claiming that the NK model is consistent with the VAR responses seems a bit exaggerated.
It's extremely important that we understand what causes inflation and what policies can effectively prevent it. It is not helpful to invent data-mined models that produce specious, if elegant results.
In spring, 2022, the Fed started raising interest rates, ultimately raising Fed Funds from zero to over 5%. CPI has dropped from 8% to 2% today. Does Mr White really think the Fed should have CUT rates in 2022? I can find dozens of examples that falsify his hypothesis. What am I missing here?
Well, in April 2022, the real fed funds rate was negative 7 1/2% and inflation was rising. In April 2024, the real rate was positive 1% and inflation was dropping. That doesn't prove causation - nothing does - but it is the result I would expect. https://charles72f.substack.com/p/aint-nothin-but-a-party
Increased interest rate payments from the Fed to commercial banks were fiscally expansionary and could have kept inflation higher than it would have otherwise been. In 2022 the Fed paid 102.4B in interest payments to banks thanks to the higher rate. And in 2023 the Fed paid 281.1B.
A few hundred billion here, a few hundred billion there—eventually you're talking about real money.
Hello! Do you know that you are the only person (other than myself, though there must be many others) to realize that, unlike pre-2020, when the Fed RAISES interest rates these days, it actually SUPPLIES reserves and therefore LOOSENS monetary policy. I don't understand why more "experts" don't understand this, but there you have it. I really don't understand the impact this might have, but it certainly complicates money policy, especially if the Fed itself doesn't understand, which would not surprise me.
Actually, I am attending the MMT conference at Bard College next week. While, in my opinion, MMT has serious flaws, at least they don't assume away the banking system as conventional economists do.
“ policy. On the left you can see how the Federal Funds Rate responds to a shock. Conceptually, suppose the Fed wakes up one day, raises interest rates, and then keeps interest rates persistently high following the pattern shown in the left hand graphs.”
I don’t understand this, is it the fed funds rate responding to a shock (first sentence) or is the change in the funds rate itself the shock (second sentence)?
“The Fed always explains its actions as a re-
sponse to economic events. It never says “we
added another half percent just for the heck of
it.” Perhaps there are no true shocks.”
From an AER paper published a while back…it’s worth a read.
Here’s the money quote from that same AER paper:
The two high-frequency shocks give quite
different answers about inflation. The results for
the one-month Eurodollar shocks agree with
those based on the the CEE shocks that mone-
tary policy has nearly no effect on inflation. The
regression shock shows a large, though dubi-
ously significant, increase in inflation following
a shock. However, the standard errors are large
enough that we basically conclude that there is
no inflation response. This is also troubling.
Federal funds shocks should lower inflation, but
as in larger samples, there is no evidence that
they do so.
Both you and the authors of that paper know full well that this is exactly what you should expect to find if the fed is actively stabilising inflation
My paper shows that, based on 50 years of data, a consistent 12-18 month precursor to inflation is something I call the Domestic Liquidity Ratio, real M2/realGDP. When money supply is in balance with economic activity, inflation is ALWAYS under control. I also demonstrate that raising interest rates can be a precursor to inflation and that there is no evidence that raising interest rates cures it. The spike in my ratio in 2020 matches perfectly 2021-2022 inflation.
Any thoughts on using Divisia aggregates vs simple sum aggregates for this? Usually, standard theory looks better with Divisia.
I did not find any Divisia money data records for the US in FRED. do you know of a source?
The center for financial stability publishes them. They also have more data on user costs and so on, but you have to email them if you want more than their Divisia aggregates.
Thank you
If you reference "your paper" you should include a link to it...
http://www.discenza.com/discenza-Inflation.pdf
Conceptually, this makes to me. If you raise rates, eventually this cost increase is going to work its way into what we pay for goods and services (i.e., inflation). Businesses may absorb some of the cost increase, but consumers will also pay their share, eventually.
Why then would the rate of price growth eventually flatten or decline? Again, from a behavioral standpoint it makes sense as consumer ability to absorb price increases is not infinite and at some point, purchasing activity (absent wage increases and/or governmental assistance) has to decline. At this point, producers and sellers are likely to find ways to reduce their costs and either stabilize or reduce prices in order to retain customers.
The whole point of raising rates has been to reduce demand in order bring down the rate of inflation, right?
JC, you sure you want to be posting these? Looks like a hack
A famous quote from Sherlock Holmes, “ It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.” All comments I’ve read are theoretical. I just looked at the data. In my talk I graph five series, only one of which is real (CPI adjusted) Federal Funds rate, and compare those to inflation rate. You are hard pressed to pick which is the real data that causes inflation to subside. That’s what I mean by “no evidence.”
A few things come to mind:
1. What happens when you use your new model instead of the textbook NK model?
2. Martin Uribe (2022) had this paper identifying long-run vs short-run interest rates shocks. Permanent changes being conflated with transitory ones in interest rates is another possible resolution of the puzzle. It would be nice to see something like that too, but you’d need to include this in the theory to compare cleanly. It doesn’t resolve your point that the mechanism isn’t the aggregate demand story we invoke — but it might change the sign.
3. You can basically eliminate the price puzzle if you use a Divisia monetary aggregate (Keating et al., 2019). Nothing says the fundamental surprise needs to match the policy instrument. Josh Hendrickson also has a paper with Ronald Mau (2022) where they show a particular rule for monetary policy is equivalent to a particular money demand, so you can write the same NK model both ways. Like fiscal policy, money demand is always there even if they didn’t write it down.
I know the point you’re making here is to raise the possibility that conventional wisdom is just ignoring what data and theory has been screaming at us for years. Still, a price puzzle is far from necessary.
Keaton 2019? Link?
Link to Hendrickson and Mau: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4287978
Sorry. It's Keating, Kelly, Smith and Valcarcel (2019). Here:
https://onlinelibrary.wiley.com/doi/full/10.1111/jmcb.12522
Alain Paquet and Christian Barette (2024) also have a cool TVP-VAR extension that look at this Christiano et al. (1999) type of analysis with Divisia money really carefully:
https://chairemacro.esg.uqam.ca/wp-content/uploads/sites/146/Barrette_Paquet_Sept2024_wp.pdf
I thought the commonly told story is that interest rate hikes lead to falling inflation with long and variable lags. The story isn't really about the price level per se. The IRFs in Stock and Watson's paper are in terms of inflation, not the price level. The interest rate shock leads to falling inflation after about a year or two (consistent with White's paper after taking into account the higher frequency).
If you cumulate the inflation IRFs, you get the log price level response (so, the % change in the price level), so you can transform the IRFs of inflation into prices and vice-versa if you want to see it one way or another.
The long and variable lag is a common story. Milton Friedman famously used this phrase decades ago and early SVARs such as those featured in Christiano, Eichenbaum and Evans' 1999 handbook chaper tended to fit this expectation. Price puzzles are common in these types of SVARs, though not always very large or statistically significant, but the responses of price variables tend to be very persistent. You can get similar features using more recent methods like the sign restrictions such as in Arias, Caldara and Rubio-Ramirez (2019, here: https://www.sciencedirect.com/science/article/pii/S0304393218303908).
That being said, as I told professor Cochrane in his post on his 'Lucas Philips Curve' paper, that's not an unambiguous feature of the data. Some SVARs that rely on high-frequency instruments will produce a *jump* in the inflation rate (a statistically significant response at h=0), consistent with standard theory.
People are debating monetary policy because it's important, yet extremely complicated to evaluate in practice: all central banks spend millions of dollars making their policy extremely endogenous (and predictable)! Also, if professor Cochrane's musing in this post is right and monetary policy should produce positive responses for nominal rates and inflation, then the problem is even harder. As Christian Wolf (2020) pointed out (https://www.aeaweb.org/articles?id=10.1257/mac.20180328), monetary policy shocks are presumably tiny, accounting for only a small share of the variation in most of the macro data and that makes them hard to identify. However, he mentions that it's also a rare shock in our theories that really robustly predicts opposite sign response in inflation and nominal rates.
A well thought out reply, but ultimately I don't think it addresses my point.
My point is that if the theory is that X leads to delta_Y, then it doesn't necessarily mean that X leads to Y. Particularly in the short-term.
The paper should have used a standard "error correction model" here to cancel out the relationship at the levels.
It should be obvious that long-run prices will increase or decrease almost 1:1 with the money supply. You simply can't predict inflation without bringing into account changes (or expected changes) in the money supply, and controlling for the level of the money supply.
This is so obvious, I have trouble imagining a realistic reason why economists are so allergic to connecting money supply with inflation. Is there some conspiracy?
In any case, there are always two main reasons why prices go up: restriction of supply or boost to demand. Same goes with debt and the implied interest rates. If there's a sudden boost in demand to borrow, rates will go up, and if there's a sudden restriction in people willing to lend, that will also boost rates.
There are a few essential things that will balance out to net an increase or decrease in rates: 1. Borrowers being in a bad economic state (especially if optimistic about the future) will boost borrowing and rates. 2. Borrowers expectation to be in a bad economic state in the future will actually reduce borrowing and rates. 3. Lenders being in a bad state or expecting a future bad state will reduce lending and raise interest rates.
Prices are the net of the following dynamics: 1. Increase in borrowing for consumption will increase prices (until the debt needs to be paid off, and then it will decrease prices by the same amount. 2. Expansion of the money supply. 3. Technology that decreases prices.
That's pretty much it.
The reason why interest rates don't correspond to inflation is because inflation is the net effect of a few things that can offset each other. An increase in rates doesn't always correspond with an increase in net-dollars borrowed. It could be the result of lenders being more restricted or borrowers become more pessimistic. We also have the change in money supply effects. If the government prints and spends, this will drive up rates and prices, but if the government is merely offsetting pessimism, the net effect could go either way.
In other words, the paper could be improved by including in the model:
1. Money Supply
2. Net borrowing
3. Levels of household wealth & funds at lenders
4. Economic expectations
Neil White's result arises from the key assumption that x(t) ≡ x°, a constant.
Using the differential form of the simple two-equation NK model that:
– d(πᵉ(t)) = [(ρ/σ)∙d(xᵉ(t)) + κ∙x(t)∙dt] – ρ∙i(t)∙dt (1)
where, the superscript e on the variables π(t) and x(t) indicates the conditional expectation of the variable at time t.
This equation can be obtained by simple algebraic manipulation of the differential equation version of the simple two-equation NK model.
By assuming that x(t) ≡ x°, a constant, N. White obtains the relation
d(πᵉ(t)) = ρ∙i(t)∙dt – κ∙x°∙dt (2)
in which the infinitessimal change in the conditional expectation of the rate of inflation is directly proportional to the nominal rate of interest. This then gives the result he reports in his paper.
The assumption he makes is restrictive. If the assumption is removed, then we have equation (1) in which the conditional expectation of the rate of inflation is negatively proportional to the sum of the conditional expectation of the infinitessimal differential of output gap, d(xᵉ(t)), and the current output gap, x(t), and positively proportional to the nominal rate of interest, i(t).
As N. White relates in his paper, the conventional expectation is that an increase in the real rate of interest, r(t), depresses excess demand and increases savings thereby increasing the output gap in the short term. The effect should be evident in the raw data.
I wouldn't rely on the proffered mathematical models as presented. Experience in the 2022 through the first quarter of 2025 does not lend support to N. White's thesis. Perhaps it is different this time, but color me skeptical.
Isn’t plugging initial inflation into the simple NK model the same as making a whole new model? In the NK model, initial inflation (i.e., first period) is endogenous; it is a jump variable (hence indeterminacy in the model without some assumptions about policy). Assuming an initial inflation value is inconsistent with the model (price setters set the first period’s prices - the researcher cannot set them on their behalf). Solving a price indeterminacy problem by just assuming a price outcome you like, is not a valid solution in this model imo.
Btw didn’t Romer and Romer interpret the longer-run drop in the price level after the temporary interest-rate increase, as a refutal of the price puzzle? (Interest rate up, prices down with a lag).
I mean, am I the only one to notice the widely different scale used in the third column of plots compared to the second one? There may be qualitative resemblance, but claiming that the NK model is consistent with the VAR responses seems a bit exaggerated.
PLEASE HELP!
It's extremely important that we understand what causes inflation and what policies can effectively prevent it. It is not helpful to invent data-mined models that produce specious, if elegant results.
In spring, 2022, the Fed started raising interest rates, ultimately raising Fed Funds from zero to over 5%. CPI has dropped from 8% to 2% today. Does Mr White really think the Fed should have CUT rates in 2022? I can find dozens of examples that falsify his hypothesis. What am I missing here?
Look at real fed funds rate then show me cause and effect.
Well, in April 2022, the real fed funds rate was negative 7 1/2% and inflation was rising. In April 2024, the real rate was positive 1% and inflation was dropping. That doesn't prove causation - nothing does - but it is the result I would expect. https://charles72f.substack.com/p/aint-nothin-but-a-party
Increased interest rate payments from the Fed to commercial banks were fiscally expansionary and could have kept inflation higher than it would have otherwise been. In 2022 the Fed paid 102.4B in interest payments to banks thanks to the higher rate. And in 2023 the Fed paid 281.1B.
A few hundred billion here, a few hundred billion there—eventually you're talking about real money.
https://www.federalreserve.gov/newsevents/pressreleases/other20230113a.htm#:~:text=January%2013%2C%202023-,Federal%20Reserve%20Board%20announces%20Reserve%20Bank%20income%20and%20expense%20data,to%20the%20Treasury%20for%202022&text=The%20Federal%20Reserve%20Board%20on,of%20%2458.4%20billion%20in%202022.
https://www.federalreserve.gov/newsevents/pressreleases/other20240112a.htm
Hello! Do you know that you are the only person (other than myself, though there must be many others) to realize that, unlike pre-2020, when the Fed RAISES interest rates these days, it actually SUPPLIES reserves and therefore LOOSENS monetary policy. I don't understand why more "experts" don't understand this, but there you have it. I really don't understand the impact this might have, but it certainly complicates money policy, especially if the Fed itself doesn't understand, which would not surprise me.
Yeah I find it perplexing too. I’ve only even heard MMT economists mention this.
Actually, I am attending the MMT conference at Bard College next week. While, in my opinion, MMT has serious flaws, at least they don't assume away the banking system as conventional economists do.
No way! I’ll be at the conference too. See you there I guess
See you there!
Thinking of that infamous Stephanie Kelton Jason Furman interaction on Twitter lol