**The current situation, and puzzling inertia**

A third of a percent is a lot less than eight percent. The usual wisdom says that to reduce inflation, the Fed must raise the nominal interest rate by more than the inflation rate. In that way the real interest rate rises, cooling the economy.

At a minimum, then, usual wisdom says that the interest rate should be above 8%. Now. The Taylor rule says the interest rate should be 2% (inflation target), plus 1.5 times how much inflation exceeds 2%, plus the long run real rate. That means an interest rate of at least 2+1.5x(8-2) = 11%. Yet the Fed sits, and contemplates at most a percent or two over the summer.

This reaction is unusually slow by historical precedent, not just by standard theory and received wisdom. The graph above shows the last episode for comparison. In early 2017, unemployment got below 5%, inflation got up to and just barely breached the Fed's 2% target, and the Fed promptly started raising interest rates. Inflation batted around the Fed's 2% target. March 2022 unemployment is 3.6%, lower than it has been since December 1969. No excuse there.

The 2017 episode is curious. The Fed seems to regard it as a big failure -- they raised rates on fear of inflation to come, and inflation did not come. I would expect a self-interested institution to loudly proclaim success: They raised rates on fear of inflation to come, just enough to keep inflation right at target without starting a recession. They executed a beautiful soft landing. The Fed has never before been shy about "but for us things would have been much worse" self-congratulation. The event sparked the whole shift to the Fed's current explicit wait-and-see policies.

The Fed's current inaction is even more curious if we look at a longer history. In each spurt of inflation in the 1970s, the Fed *did, *promptly, raise interest rates, about one for one with inflation. Look at the red line and the blue line, through the ups and downs of the 1970s. Not even in the 1970s did the Fed wait a whole year to do *anything*. Interest rates rose just ahead of inflation in 1974, and close to 1-1 with inflation from 1977 to 1980. Today's Fed is much, much slower to act than the reviled inflationary Fed of the 1970s. And that Fed had unemployment on which to blame a slow response. Ours does not.

The conventional story is that the 1970s 1-1 response was not enough. 1-1 keeps the real rate constant, but does not raise real rates as inflation rises. Only in 1980 and 1982, as you see, when the interest rate rose substantially above inflation and stayed there, did inflation decline. You have to repeat *that* experience, conventional wisdom goes, to squash inflation.

**What are they thinking?**

What is the Fed thinking? There is a model that makes sense of actions. Let's spell it out and see if it makes sense.

Here are the Fed's forecasts for the next year, taken from the March 16 projections. (I plot "longer run" as 2030. The Fed's "actual" is end of 2021 quarterly PCE inflation, 5.5%, where my previous graph uses monthly CPI inflation and ends in March, giving 7.9%. I'll use 5.5% in the rest of this discussion.)

As you see, this forecast scenario is dramatically different from a repetition of 1980. The remarkable fact about these forecasts is that *the Fed believes inflation will almost entirely disappear all on its own, without the need for any period of high real interest rates.*

An astute reader will notice that I have written of the "real" interest rate as the nominal interest rate less current inflation. In fact, the real interest rate is the nominal interest rate less expected future inflation. So we might excuse the Fed's inaction by their belief that inflation will melt away on its own; and their view that everyone else agrees. But the Fed's projections do not defend that view either. Expected inflation is higher, just not so much as past inflation; real rates measured by nominal rates less expected future inflation remain negative throughout until we return to the long-run trend.

By any measure, real rates remain negative and inflation dies away all by its own. Why?

*shock*, no matter its nature, does not necessarily lead to a one-time

*inflation*. When the shock ends, the inflation does not necessarily end.

**Modeling the Fed**

*once a shock is over, inflation stops, even if the Fed does not do much to nominal interest rates.*This is the "Fisherian" property. It is not the property of traditional models. In those models, once inflation starts, it will spiral out of control unless the Fed promptly raises interest rates, inflation will spiral out of control.

This being a blog post, I'm going to use the simplest possible model: A static IS curve and a Phillips curve. (Fiscal Theory of the Price Level Section 17.1.) The three equation model behaves the same way, but takes much more algebra to solve. The model is \begin{align} x_t &= -\sigma ( i_t -r - \pi^e_t) \\ \pi_t &= \pi^e_t + \kappa x_t \end{align} There are two variants: adaptive expectations \[\pi^e_t = \pi_{t-1}\] and rational expectations \[\pi^e_t = E_t \pi_{t+1}.\] Adaptive expectations captures traditional views of monetary policy, and rational expectations captures the Fisherian view, which--the point--accounts for the Fed's view.

The model's equilibrium condition is\[\pi_{t}=-\sigma\kappa ( i_{t}-r)+\left( 1+\sigma\kappa\right) \pi_{t}^{e}.\] With adaptive expectations \(\pi_{t}^{e}=\pi_{t-1},\)the equilibrium condition is\[\pi_{t}=(1+\sigma\kappa)\pi_{t-1}-\sigma\kappa( i_{t}-r).\] With rational expectations, the equilibrium condition is\[E_{t}\pi_{t+1}=\frac{1}{1+\sigma\kappa}\pi_{t}+\frac{\sigma\kappa}{1+\sigma\kappa}(i_{t}-r).\] Now, fire up each model, start out at \(i_1=0.33%\), \(\pi_1=5.5%\), put in the Fed's interest rate path, and let's see what inflation comes out.

Rather than take the interest rate path as given and see what model produces the Fed's inflation forecast given that interest rate path, let's ask the opposite question of our two models: What interest rate path does it take to produce the Fed's inflation forecast? Just solve the equilibrium condition for the interest rate\[i_t = r+\frac{1+\sigma\kappa}{\sigma\kappa}\pi^e_t - \frac{1}{\sigma\kappa}\pi_t.\] Then use the Fed's inflation forecast for \(\pi_t\) and \(pi^e_t\), either one period ahead or one period behind.

**Really, a Fisherian Fed?**

The proposition that once the shock is over inflation will go away on its own may not seem so radical. Put that way, I think it does capture what's on the Fed's mind. But it comes inextricably with the very uncomfortable Fisherian implication. If inflation converges to interest rates on its own, then higher interest rates eventually raise inflation, and vice versa.

I have squared this circle by thinking there is a short run negative effect of interest rates on inflation, which central banks normally use, and a much longer run positive effect, which they generally don't exploit. Such a short-run negative effect can coexist with rational expectations, though this little model does not include it. So, relative to my priors, the surprise is that the Fed seems to believe so little in the (short-run) negative effect, and the Fed seems to think the Fisherian long run comes so quickly, i.e. that prices are so flexible.

Why might the Fed have come to this view? Perhaps, as I have argued elsewhere ('Michelson-Morley etc," and FTPL Chapter 22), the clear lessons of the zero bound era have sunk in. The adaptive expectations model works in reverse too: If you wake up in mid-2009 with 1.5% deflation and zero interest rate, turn off the shocks, then the adaptive expectations model predicts a deflation spiral. It did not happen. The rational expectations model makes sense of that fact. Perhaps the Fed has also lost faith in the power of interest rate hikes to lower inflation. Or perhaps the negative effect comes with a recession, which the Fed wishes to avoid, and would rather wait for a longer-term Fisherian stabilization. That part of 1980 is less attractive for sure!

Do I believe all of this? I struggle. (Ch. 5.3 of FTPL has a long drawn out apologia.) I also admit that my view of a very long run Fisher effect and a short run negative effect comes as much from trying to straddle economists' priors as it does from a heard-hearted view of theory and data. My "beliefs" are still colored by the vast opinion around me that thinks this temporary effect is larger, more reliable, and longer-lasting than anything I've seen in models I have worked out. Maybe I'm not being courageous enough to believe my own models, and the Fed is!

**The Fed may be right**

Bottom line: In the chorus of opinion that the Fed is blowing it, this post acknowledges a possibility: The Fed may be right. There is a model in which inflation goes away as the Fed forecasts. It's a simple model, with attractive ingredients: rational expectations. There is also a model, more likely in my view, that inflation persists and goes away slowly, because prices are stickier than the Fed thinks, as outlined in my last post. There is also some momentum to inflation, induced by some backward looking parts of pricing which could lead to inflation still increasing for a while before the forces of these simple models kick in. But, the key, inflation does not spiral away as the standard model suggests. If inflation does not spiral away, despite sluggish interest rate adjustment, we will learn a good deal. The next few years could be revealing, as were the 2010s. Or, we may get more bad shocks, or the Fed may change its mind and sharply raise rates to replay 1980, interrupting the experiment.

As with the last post, this is all an invitation to address the issue with much more serious and quantitatively realistic models. Include output and employment as well. What model does it take to produce the Fed's impulse-response function?

*Update *The next post has a better title, "is the Fed New-Keyenesian" and adds unemployment forecasts.

**Code **

**(**Not pretty, but it documents my pictures.**) **

clear all

close all

%Fed data from https://www.federalreserve.gov/monetarypolicy/fomcprojtable20220316.htm

years = [2017 2018 2019 2020 2021 2022 2023 2024 2030]';

actual = [1.9 2.0 1.5 1.2 5.5 NaN NaN NaN NaN ]';

UpperRange = [ NaN NaN NaN NaN 5.5 5.5 3.5 3.0 2.0]';

UpperCentral =[ NaN NaN NaN NaN 5.5 4.7 3.0 2.4 2.0]';

MedianForecast =[NaN NaN NaN NaN 5.5 4.3 2.7 2.3 2.0]';

LowerCentral= [NaN NaN NaN NaN 5.5 4.1 2.3 2.1 2.0]';

LowerRange =[ NaN NaN NaN NaN 5.5 3.7 2.2 2.0 2.0]';

% I added last actual to the forecasts

%Interest rates

rate_years=...

[2022 2023 2024 2030]';

rates = [...

3.625 0 2 2 0;

3.375 0 1 2 0;

3.125 1 2 1 0;

3.000 0 0 0 2;

2.875 0 3 3 0;

2.625 1 3 2 0;

2.500 0 0 0 5;

2.375 3 4 3 1;

2.250 0 0 1 6;

2.125 2 1 2 0;

2.000 0 0 0 1;

1.875 5 0 0 0 ;

1.625 3 0 0 0;

1.375 1 0 0 0];

mean_rate_forecast = (sum(rates(:,1)*ones(1,4).*rates(:,2:end))./sum(rates(:,2:end)))';

x = load('pcectpi.csv');

x = x(x(:,2)==10,:); % use 4th quarter for year

pceyr = x(:,1);

pce = x(:,4);

x = load('fedfunds.csv');

x = x(x(:,2)==12,:); % use 4th quarter for year

ffyr = x(:,1);

ff = x(:,4);

rate_years = [2021; rate_years];

mean_rate_forecast = [ff(end); mean_rate_forecast];

figure;

hold on;

plot(years, actual, '-r','linewidth',2);

plot(pceyr,pce,'-r','linewidth',2)

plot(years, MedianForecast, '-ro','linewidth',2);

plot(rate_years,mean_rate_forecast,'-bo','linewidth',2);

plot(ffyr,ff,'-b','linewidth',2)

plot([2021.5 2021.5],[-1 10],'-k','linewidth',2);

plot([2010 2030],[0 0],'-k')

axis([2017 2030 -1 6])

text(2018,5.5,'Actual \leftarrow','fontsize',20)

text(2022,5.5,'\rightarrow Forecast','fontsize',20);

text(2022,1,'Fed Funds','color','b','fontsize',20);

text(2022.5,4,'Inflation','color','r','fontsize',20);

ylabel('Percent')

print -dpng actual_and_forecast.png

% Theory

sig = 1;

kap = 0.5;

r = 0.5;

T = 10;

tim = (1:10)';

it = 0*tim;

it(1:5) = mean_rate_forecast;

it(6:end) = it(5);

pita = it*0;

pitr = it*0;

pita(1) = 5.5;

pitr(1)= 5.5;

for t = 2:T

pita(t) = (1+sig*kap)*pita(t-1) - sig*kap*(it(t)-r);

pitr(t) = 1/(1+sig*kap)*pitr(t-1)+sig*kap/(1+sig*kap)*(it(t-1)-r);

end;

figure;

hold on

plot(tim+2020,it,'-b','Linewidth',2);

plot(tim+2020,pita,'-r','Linewidth',2);

plot(tim+2020,pitr,'-vr','Linewidth',2);

plot([tim(1:4)+2020; 2030],MedianForecast(end-4:end),'--r','linewidth',2);

plot([2021.5 2021.5],[-1 10],'-k','linewidth',2);

axis([2020 2030 0 10])

text(2022.5,8,'Inflation, adaptive E','color','r','fontsize',20)

text(2026,1.7,'Inflation, rational E','color','r','fontsize',20)

text(2022,4.5,'--Inflation, Fed forecast','color','r','fontsize',20)

text(2021.8,1,'Fed funds, Fed forecast','color','b','fontsize',20)

ylabel('Percent')

print -dpng inflation_forecast.png

% plot needed interest rate

tim = (1:12)';

it = 0*tim;

pit = [MedianForecast(end-4:end);MedianForecast(end)*ones(7,1)];

ita = it*0;

itr = it*0;

for t = 2:size(tim,1)-1

ita(t) = r+ (1+sig*kap)/(sig*kap)*pit(t-1) - 1/(sig*kap)*(pit(t));

itr(t) = r+ (1+sig*kap)/(sig*kap)*pit(t+1) - 1/(sig*kap)*(pit(t));

end;

ita(1) = NaN;

itr(1) = NaN;

figure;

hold on

plot(tim+2020,pit,'-r','Linewidth',2);

plot(tim+2020,ita,'-b','Linewidth',2);

plot(tim+2020,itr,'-vb','Linewidth',2);

plot(tim+2020,0*tim,'-k');

plot(rate_years,mean_rate_forecast,'--bo','linewidth',2);

plot([2021.5 2021.5],[-1 10],'-k','linewidth',2);

axis([2020 2030 -0.5 9])

text(2023.5,8,'Needed rate, adaptive E','color','b','fontsize',20)

text(2022.5,0.5,'Needed rate, rational E','color','b','fontsize',20)

text(2026,1.5,'Inflation, Fed forecast','color','r','fontsize',20)

text(2026,4,'--Rate, Fed forecast','color','b','fontsize',20)

ylabel('Percent')

print -dpng needed_rate.png

One thing to add to the 1980s-2020s history lesson:

ReplyDeletehttps://fred.stlouisfed.org/series/FDEFX

Fiscal "consolidation" did not really begin until about 1990 when the bulk of the Reagan tax cuts were reversed and defense spending was put on a glide path downward.

One thing I would say is that nominal rates really do matter for the actions of investors.

ReplyDeleteConsider if you owned an apartment building worth 100million, and at a 60% LVR you had 40million in equity and 60million debt.

Now if the apartment building returned before finance 6% on the 100million = 6million .

Let's say interest rates are a 2.0% margin above the fed funds rate. And that inflation was previously 3.0% but increased to 8.0% over a year.

If their interest bill goes from 2.1% to 7.1% due to a 5.0% rise in the FFR.

Their financing costs increase from 1.26million to 4.26million.

The real rate is still -0.9% in both cases. Yet their net operating income after financing has been squeezed from 4.74mil to 1.74mil.

And their cash return on their equity falls from 4.74/40 = 11.85% to 1.74/40 = 4.35%.

Yes their rents will now be inflating 8.0% a year. But the increased nominal interest costs in the short term will cause far more damage and risk to their situation then the small benefit of negative real rates.

Even if theoretically, held for an infinite amount of time, these should actually generate the same result (the cash return has moved into the capital gains / inflation of the property price).

Hi, John! Thanks for sharing! Your post is enlightening, as always.

ReplyDeleteThank you for writing all this out and working through it, spelling out the assumptions. It's a little hard to read through not being familiar with the models and without all of the parameters defined. Pulling it out from the text:

ReplyDeletepi = Inflation

i = interest rate

k = price-stickiness parameter

I don't see sigma defined in the post, in your textbook though the notation glossary says.

Ïƒ. Intertemporal substitution elasticity, e.g. xt = Etxt+1 − Ïƒ (it − EtÏ€t+1).

And you discuss r=0.5, but don't explain what it is. In the textbook

r = A constant or steady state real rate of return

With this explanation 0.5 did not make a whole lot of sense to me unless it's 0.5% given you represent the interest rate inflation that way. This is a dumb question, but why is it pi = 5.5 rather than pi = 0.055? Is everything including the other parameters scaled to be 1 = 1% so it's arbitrary?

Finally, as I was just finishing this comment I noticed in 17.1 of your textbook you have the final part of the rational expectations equation as just i and not (i-r). I'm assuming in the textbook that's real inflation = i-r or something like that? At any rate the code explicitly uses the r parameter so the rest of this precedes from the equations in the post.

Looking more closely at the rational expectations model what's odd is that the stickier prices are the *faster* inflation converges to i-r (with pi / (1 + pi * k) for the prior period then the prior inflation becomes less relevant and inflation converges faster as k in the denominator gets larger). It's extremely counter-intuitive that stickier prices *increase* the rate of conversion to the steady state. What's odd about that it that as a comparative static it's true *regardless* of the current rate of inflation. So I think this is the mechanical reason why you had to make prices stickier to get inflation to come down in this model more quickly.

Looking more closely at the adaptive version it seems like as k gets larger, i.e. prices get stickier then inflation spirals more quickly if r>i and deflation increases if i<r. In this model then when prices are extremely sticky you have inflation spirals, but if they're not less so.

What this brings me to substantively is that we know in practice people are resistant to nominal wage cuts so there is an asymmetry in price stickiness. You flagged that you had to assume a quite high price stickiness. My initial intuition was that if we incorporated the change in stickiness as a function of inflation that the lack of inflation at the zero lower bound could be explained, but that when prices are less sticky away from that bound that rapid inflation (particularly say hyper-inflation) would be hard to explain. Working though the equations though I'm not sure that's actually the case because in that instance like the comparative static predicts it would take *longer* for inflation to stabilize with less sticky prices, i.e. inflation would go on for longer. So the rational expectations model is not obviously broken by the nominal wage stickiness asymmetry, I think.

At any rate, I'd love to see more on how the price stickiness multipliers impact the models.

I like this post.

ReplyDeleteI would like to see a post on the Fed's balance sheet.

We live in a world of globalized capital markets, and money is a fungible commodity.

The world has about $450 trillion in assets (including property, equities, bonds).

So...the Fed sells or keeps its balance sheet. Any difference for global capital markets?

But...investors perceive the US federal government can obviously honor its debts. Interest payments are flowing back to the Fed and transferred to the Treasury.

Is there any harm in the Fed just sitting on its balance sheet?

The Bank of Japan? What say?

https://www.youtube.com/watch?v=71kXXqNTx-k&list=PLnVr2t8lPw8_xUBxu8caiJ3qKZ4MvA9DA

Delete"The Bank of Japan? What say?"

DeleteI say, as long as you are willing to accept price controls, like Japan, then go for it.

That guy on the Youtube link is brilliant.

DeleteModels are of great help in understanding, through simplifying and schematising: this is the reason why I myself devoted a significant part of my life to the study of macroeconomic models and models of asset pricing.

ReplyDeleteJohn's post, alongside his previous, provide us with a framework to better analyse the events currently evolving. I must add that, with reference to the facts discussed here, I am skeptical about the use of models.

This is explained by a sensation I have: women and men at the Fed are NOT referring to any specific model when taking their decisions. If that model existed, they would have explained more clearly their recent U-turns, and the U-turn about "transitory" in particular. They did not. They did not provide any explanation.

My guess is that, instead of referring to one, ore more, defined models of the economy, they are simply adapting, and hoping for the best, while trying to preserve and protect some very specific particular interests (against the interest of the whole of the society, as their mandate states).

Which is a problem. It is a problem, since it weakens the effectiveness of the policy, and reduces the probabilities of success. Futhermore, it is a problem for all economic agents, since they cannot "wait a few years": they have to take decisions today, using (along others) the informations provided by the Central Banks. Informations which, as of recently, have been of a very low quality, to say the least.

Conclusions: models alway provide a valuable contribution; in the case at hand, to measure the consistency (better: inconsistency) of policy makers' choices. And this is how personally read the two posts. Unemployment and output would be useful additions, alongside agents' incentives and asset prices.

Interesting viewpoint, thank you for posting it. Clearly we are all 'puzzled' by the feds inaction during this cycle. The question i have is whether the answer is much simpler. If the fed simply cannot raise rates above inflation (real not just cpi), as one would expect, because of the debt that is already in the system. Us gov debt around 30 trillion simply cannot be serviced in a prolonged high rate environment without exploding the deficit, especially at the time where other global players are loosing appetite for us debt. Also, tied to that could be the size of the feds balance sheet. All those mbs and treasuries were bought at a zero rate environment. Can they be sold without the fed taking a loss? If they cant then there cannot be any qt other than letting them mature, right? I know all of this is simplistic but it is stuck in my head so any help will be very much aporeciated. By reference when Volcker did his thing US debt to gdp was the lowest since wwii, so there was room to manoeuvre. Thanks !

ReplyDeleteHere is one potential solution:

Deletehttps://musingsandrumblings.blogspot.com/2019/09/the-case-for-equity-sold-by-u.html

"But it comes inextricably with the very uncomfortable Fisherian implication. If inflation converges to interest rates on its own, then higher interest rates eventually raise inflation, and vice versa." I'm not sure I understand this conclusion, John. According to your story, even the "Fisherian" Fed case is one in which the Fed has to raise the nominal rate permanently to bring inflation down permanently. (Obviously this means that higher real rates are also ultimately associated with lower inflation.) Am I misunderstanding you?

ReplyDeleteAlso, the Fed's inflation forecasts seem quite consistent with the 5 and 10 year breakeven inflation rates. Does those rates not supply support for the Fed's approach? (FWIW, My own view is that the Fed should hike more aggressively--and that it ought to have begun doing so sooner--but that it's a matter of another percentage point's worth or so in the next few quarters rather than of drastic hikes of the sort Summer and others claim to be be needed.)

Just one observation: One thing you are implicitly assuming is zero future shocks. But the reason why Fed and others expect inflation to drop is because there will be negative inflationary shocks in future months. Principle among those are car prices, which should decrease as production is no longer hampered supply chain issues, and that alone should amount for very large negative inflationary shock. Another example are oil prices, which are expected to decrease as geopolitical shocks unwind.

ReplyDeleteIn basic macro graph, decrease in AS increases prices, but reversal of that move lowers prices.

Don't overthink it. The Fed is being run by Ron Klain, not a banker nor an economist. A low grade political operative.

ReplyDeleteI suspect the Fed is tepid about raising rates because we have so much debt outstanding and are in the midst of passing a huge spending bill. I don't think the Fed is independent anymore, if it ever was.

ReplyDeleteSee Irving Fisher, Separation Thereom:

DeleteThe spending decision is independent of the financing decision.

With government, the financing decision allows for several choices:

1. Taxation

2. Borrowing

3. Printing / coining money

4. Sale of equity

Three of the four have nothing to do with the Fed.

I'm recalling from the dark days of economics blogs Krugman criticizing Kocherlakota for expressing his Fisherian stances, but my impression was later on Kocherlakota "switched sides". It was already a long time ago though back in the times before Covid, so my memory might be fuzzy and Kocherlakota is no longer on the Fed Reserve board of governors, so Im not sure how much of influence that line of thinking still remains.

ReplyDelete"A labor market view on the risks of a U.S. hard landing", Alex Domash & Lawrence H. Summers, NBER, WORKING PAPER 29910. DOI 10.3386/w29910. ISSUE DATE April 2022.

ReplyDeleteThe authors note that the current labor market is indicating an effective unemployment rate of 2%, with wage rate increases on the order of 6%/yr on average. They conclude that the FOMC will not be able to avoid a hard landing if it pursues efforts to bring the rate of inflation under control. Access to the article is limited to subscribers but NBER notes that visitors can download up to three working papers per year gratis.

A Fed that bases most of its bank capital requirements on that what’s perceived as risky is more dangerous to bank systems than what’s perceived safe, and much ignores misperceived credit risks or the unexpected, pandemic-war, can it model anything?

ReplyDeletehttp://subprimeregulations.blogspot.com/2019/03/my-letter-to-financial-stability-board.html

Try this for hard landing:

ReplyDeletehttps://fred.stlouisfed.org/series/W790RC1Q027SBEA

2020 4th Quarter - $4.7 Billion

2021 4th Quarter - $374.5 Billion

2022 4th Quarter - $766.7 Billion

Think that kind of growth rate is sustainable?

Even if it flat lines or slightly shrinks then all the other negative issues become more apparent (inflation, trade deficit, etc.).

Net domestic investment: Private: Domestic business (W790RC1Q027SBEA)

Deletein then-current nominal dollars:

Q4:2020 = $489 B (flat) your $4.7 B is ?

Q2:2019 = $727 B (rounded up)

Q1:2015 = $673 B (rounded down)

Q3:2007 = $526 B (rounded down)

Q4:2000 = $543 B (rounded up)

It doesn't look outlandish relative to historical (in then-current nominal dollars).

When divided by the Producer Price Index Total Mfg. "PPI-TM" Series (PCUOMFGOMFG)

["a" = (W790RC1Q027SBEA) , "b" = (PCUOMFGOMFG) and formula = "a/b*100"]

the annual NDI (constant $) values are (rounded):

Y2021: $338.5 B

Y2020: $248.6 B

Y2019: $312.6 B

Y2018: $346.4 B

Y2017: $290.3 B

Y2016: $278.9 B

Y2015: $311.2 B

Y2014: $323.7 B

...

Y2007: $306.8 B

Y2006: $303.5 B

Y2005: $298.4 B

Y2004: $271.5 B

...

Y2000: $404.3 B

...

Y1988: $186 B

Y1987: $224 B

Y1986: $172 B

[source: https://fred.stlouisfed.org/graph/?g=O0Sa]

The constant $ time series NDI does not appear to suggest an outlandish deviation from historical NDI patterns.

PPI-TM index values: Q4:21 = 226.5, Q4:20 = 196.7, Q1:15 = 186.2, Q3:07 = 163.7, Q4:20 = 134.3 (Source: FRED series = PCUOMFGOMFG).

I find somewhat different numbers for the "rational expectations" model. I use the values of estimates for E_t{pi_(t+1)} appearing in the data lines following the comment line "%....monetarypolicy/fomcprojtable20220316.htm" and apply a symmetrical probability density for the quintiles "UpperRange", "UpperCentral", "MedianForecast", "LowerCentral", and "LowerRange" of 1/12, 1/4, 1/3, 1/4, and 1/12, respectively to obtain estimates of E_t{pi_(t+1)} for years 2022, 2023, and 2024, of 4.4%, 2.7%, and 2.3083%, respectively. I don't consider the "long run" (~ 2030) as being germane to the discussion.

ReplyDeleteI calculate the expected midpoint target FedFunds Rate from Figure 3.E. "Distribution of participants’ judgments of the midpoint of the appropriate target range for the federal funds rate or the appropriate target level for the federal funds rate, 2022-24 and over the longer run" from the FRB on-line publication "March 16, 2022: FOMC Projections materials, accessible version" (URL embedded in your blog article on this page) and use these calculated values for the expected interest rate, E_t{i_(t+n)} with n = 1, 2, 3 to determine the average inflation rate for each of the years 2022, 2023, and 2024 according to the rational expectations equilibrium equation (un-numbered equation (7) in the blog text). My calculations come up with the following estimates: (t = 2021)

Year 2022: E_t{pi_(t+1)} = 4.4% i_(t+1) = 1.93055 pi_(t+1) = 5.8847%

Year 2023: E_t{pi_(t+2)} = 2.7% i_(t+2) = 2.61111 pi_(t+2) = 2.9944%

Year 2024: E_t{pi_(t+3)} = 2.308% i_(t+3) = 2.58333 pi_(t+3) = 2.42078%

The estimates calculated and displayed immediately above are only good to 2 significant figures.

An appropriate criticism of this method is the reliance on the expectations of the future rate of inflation, i.e., E_t{pi_(t+1)}, E_t{pi_(t+2)}, and E_t{pi_(t+3)} and the FOMC participants' midpoint estimates of the future Fed Funds Rate for 2022, 2023, and 2024. As the March publication clearly demonstrates, the participants' estimates are subject to significant change from calendar quarter to calendar quarter.

"... the equilibrium condition for the interest rate" (the 8th equation in the body of the blog text) gives a negative value for i_(t+1) [t = 2021] using the values for the parameters "sig" = 1; "kap" = 0.5; and, "r "= 0.5%; from the code listing when pi_(t) = 5.5% and E_t{pi_(t+1)} = 4.4%. The computed value of i_(t+1) = -3.9%. Given FOMC policy, i_(t+1) = 0% would be selected.

The "adaptive expectations" model can be converted to a continuous time first-order ordinary differential equation, e.g., Ï€̇(t) = Ïƒ∙Îº·[ Ï€(t) – u(t) ] with u(t) = [ i(t) -r ] as the manipulated (or "control input") variable to drive the time rate of change of inflation, Ï€̇(t), to zero or to a negative quantity. If it is desired to arrest the increase in the rate of inflation, assuming an "adaptive expectations" model, one would set u(t) such that bracketed term in the O.D.E. is identically zero, i.e., set the manipulated variable, u(t) = [ i(t) -r ] , equal to the rate of inflation, Ï€(t), i.e., u(t) = Ï€(t) to obtain Ï€̇(t) = 0. [Note: Newton's convention for the time derivative of a variable is assumed for convenience.] The resulting rate of interest i(t) = u(t) + r is 6% when the rate of inflation Ï€(t) is 5.5% (year-end 2021). This rate of interest is surprisingly close to the "rational expectations" model's estimate of the rate of interest based on the FOMC data -- see the calculation results presented above for comparison.

The models assume that the rate of inflation, Ï€(t), is a unique measure of the change in the price level relative to some baseline price level. The typical definition is either P(t)/P(t-1) - 1 or log(P(t)/P(t-1)) -- the Naperian, or natural, logarithm generally being used for the purpose. Unfortunately, the price index used is not standardized. Furthermore, the measure of inflation can be "trimmed", have "volatile components removed", or otherwise be adulterated depending on the proclivity of the user's institution. Why is this germane? Well, a two-equation abridged model of an economy that focuses on forecasting "inflation" in future years will have different things to say depending on the definition of the measure of inflation. Why is that? The two-equation model, and its compatriot, the three-equation model, have cross-terms appearing in the equations. The stripped-down two-equation model has the expected inflation, Ï€áµ‰(t+1), appearing in the IS equation (eqn. #2 above) and the Phillips Curve equation (eqn. #3 above) has the output gap, x(t), appearing in it. The equations are linked. Now, if the definition of the price index differs (PCE, PCE-trimmed, PCE-median, or CPI, etc.) from model to model, then either the measure of the output gap must also differ or the parameter values must differ. For example, CPI-inflation is raging at 8%/yr at the end of 2021, whereas PCE-inflation is moving along at a sedate 5.5%/yr rate in the same period. If the output gap, x(t), is same (an assumption) in both models (CPI- or PCE- inflation) then the parameter values of sigma, kappa, and r must differ between the two models if the underlying economy is common to both. As long as we understand what the underlying price indices are and what the definition of the output gap is, motoring ahead with the analysis presents no difficulties. If not, then we're really not likely to make any considerable headway with the work. An final observation---the work is directed at discovering (a) the underlying model that the FOMC is apparently using, (b) whether that model is "Fisherian" in character, and (c) the evolutionary path of "inflation" going forward (once items (a) and (b) have been revealed). If we make a mistake in our assumptions going in, we get 'garbage' coming out the other side--the "GIGO" 'blue screen' effect we once in the distant past struggled with when computer punch cards were a 'thing'. I was reminded of this effect while reading the daily report ("Daily Digest") published online by the Bank of Canada which lists no less than four measures of the "rate of inflation" for Canada, viz., "Total consumer price index", "CPI-trim", "CPI-median", and, "CPI-common". Evidently, one measure of inflation is insufficient for the Governing Council to consider--it needs four props to decide the true measure of "inflation" in Canada. Wonders never cease, north of the 'Medicine Line'.

ReplyDeleteIsn't it a lot simpler? Once a short term supply shock passes, the natural interest rate goes back to negative. Standard rbc.

ReplyDeleteIf you write the three equation new keynesian model with iid shocks to the natural real interest rate and a nominal interest rate rule that does not respond to these shocks, inflation does not explode even though it spikes during a positive natural real interest rate shock. Actually, not only does inflation not explode, the price level does not even trend upwards - deflation offsets any inflation. This can be easily shown analytically by using the method of undetermined coefficients, as the output gap and inflation are easily seen to be linear functions of this iid shock to the natural real rate of interest.

ReplyDeleteI would argue that this is close to the current situation: temporary supply shock, with expected recovery, leads to a spike in the natural real rate. Once that temporary supply shock subsides, even with no change in nominal interest rates, the price level should return to its previous state.

Ok I was wrong about the price level returning to its previous level, there's a permanent effect on the price level. But the point that inflation does not explode when the initial spike is due to a (mean-reverting) shock to the natural rate, even with an unresponsive monetary policy, still stands.

ReplyDeleteFTPL predicts that a one-time fiscal shock leads to a one-time increase in the price level. Inflation will go away without a monetary policy response.

ReplyDeleteYet surely this is time inconsistent? Ex-ante, it is optimal for the monetary authority not to tighten given the temporary nature of the shock, and the Fisherian properties of the model. Yet ex-post, once the inflation shock arrives, tightening is indeed optimal, according to any Taylor Rule.

Agents under rational expectations would hence internalise this? FTPL assumes fiscal dominance, which makes the inflation shock permanent. Under fiscal dominance, an increase in interest rates will increase inflation, so if agents expect the monetary authority to tighten ex-post, they expect higher inflation. Hence, the initial temporary fiscal shock could lead to a permanent rise in inflation via these dynamics.