Is the Fed Fisherian?

The current situation, and puzzling inertia

Inflation has been with us for a year; it is 7.9% and trending up. March 15, the Fed finally budged the Federal Funds rate from 0 to 0.33%, (look hard) with slow rate rises to come.

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?

Various Fed speeches and commentary I have read do not shed much light on this question. Much of the talk about inflation still revolves around a "supply" shock which will go away on its own. To my mind, it's evident that widespread inflation, including wage increases, comes from demand rather than supply, so I see a large fiscal shock. (See "Fiscal Inflation" and FTPL Ch. 21.)

But a one-time 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

So here is the question for today: The economy has been hit by a one-time shock, be it supply or fiscal. The shock is now over. So start your  model with 0.33% interest rate and 5.5% inflation, and no shocks. Does inflation melt away, or keep going? What implicit model lies behind the Fed's forecasts?

The Fed clearly believes that 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.

Here is the result. If we put the Fed's interest rate path in the adaptive expectations model, with no further shocks, and fire it up starting with a 5.5% inflation rate, inflation spirals away. This is a plausible model that Taylor, Summers, and other Fed critics may have in mind. On the other hand if we put the Fed's interest rate path in the rational expectations model, with no further shocks, and fire it up starting at a 5.5% inflation rate, inflation gently settles down. We obtain a path quite close to the Fed's inflation forecast. If you want to know "what model underlies the Fed forecast,"--how do we model the Fed's model-- the rational expectations version is a much better match.

To produce this graph, I used $$\sigma=1$$ and a price-stickiness parameter $$\kappa=0.5$$. (I also use r=0.5.) This is much less price stickiness than most estimates specify. The simulations of my last post used the full version (intertemporal IS) of this model, and had much more inflation persistence, among other things because I used a slightly more conventional $$\kappa=0.25$$ with stickier prices. Not only is the Fed rational-expectations, neo-Fisherian, it seems to believe that prices are surprisingly flexible!

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.

Using the adaptive expectations model, if the Fed wishes to see its inflation forecast come true, it needs an 8.5% interest rate, right now. (Starting at 5.5% inflation.) The resulting high real interest rate brings inflation back down again. But in the rational expectations model, the interest rate can stay low, indeed even a bit lower than the Fed's own projections. In any case, of these two very simple models, you can see which one fits the Fed's thinking, and matches Fed Governor's view of the appropriate interest rate with their view of how inflation will work out.

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

pceyr = x(:,1);

pce = x(:,4);

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(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(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