Monetary Policy & Inflation | US
Inflation – The Fed’s ‘Unpleasant Arithmetic’
- By Sam van de Schootbrugge
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- 8 min read
Summary
- A new NBER working paper by Stanford University’s John Cochrane sets out the ‘unpleasant arithmetic’ facing the Fed in its battle to curb inflation.
- In his view, the Fed’s slow inflation response is not outlandish or incoherent. Rather, it reflects their belief that inflation expectations are anchored.
- Also, raising rates more than currently projected will only lower inflation today at the cost of more inflation tomorrow.
- The only way to reduce inflation is via a coordinated fiscal and monetary response that involves prolonged austerity and higher interest rates.
Introduction
Why is the Fed reacting so slowly to inflation when price stability is its primary mandate? It is unprecedented. Even in the 1970s, the Fed never waited a whole year or let inflation get 8% above the Federal Funds rate. Has it misperceived the scale of the task at hand, just as it failed to forecast the emergence of the highest inflation in 40 years?
A new NBER working paper tries to decipher what model the Fed is using for its macroeconomic projections to help rationalise their slow reaction. What does such a model require, and, under these assumptions, how long will inflation last? Most importantly, though, how will the Fed’s current interest rate path alter the inflation trajectory?
The Fiscal Origins of Inflation
According to the paper, ‘the underlying source of the current inflation is straightforward’. Contrary to the reigning supply-shock theory, he believes it was the ‘fiscal helicopter drop’ that caused it. The US government printed about $5tn in stimulus checks, equivalent to 25% of GDP or 30% of government debt.
This large accumulation of debt manifests itself as an increase in aggregate demand. Per month, the cash injections were roughly three times greater than income. In the words of Larry Summers, ‘it’s perhaps not surprising that that’s led to an overflow of demand, which has generated inflation’.
Analytically, we can use the following rule of thumb to show the link between fiscal policy and inflation. If you multiply the deficit by roughly 1.5 and compare it with a reasonable estimate of the GDP gap (I use the sixth order polynomial), it is evident a large spike in inflation was coming (Chart 1).
The Fed’s Reaction Function
Whether fiscal policy or supply constraints drove inflation, there is no denying the Fed has reacted slowly. Being behind the curve can itself have inflationary consequences – negative real rates actually boost inflation! To avoid such a spiral, a Taylor-rule style interest rate rule would theoretically require the Fed Funds rate to be at 8%.
Despite this, the Fed’s March 2022 projections show inflation will almost entirely abate without the Fed Funds rate exceeding 3% (Chart 2). So, has the Fed made a policy mistake? Or is there a sensible view of the world in which the Fed’s slow reaction does not affect inflation? It is the latter, according to the paper.
How We Perceive Inflation
The key lies in how individuals perceive inflation. Is inflation today a function of yesterday’s inflation (adaptive expectations)? Or are we forward-looking beings who make projections of tomorrow’s inflation based on what we know today (rational expectations)?
There is a subtle difference. Under adaptive expectations, output is high when inflation is high relative to past inflation, i.e., inflation is increasing (today is higher than yesterday). Under rational expectations, output is high when inflation is high relative to expected future inflation, i.e., inflation is high but decreasing (today is higher than tomorrow).
If we are forward looking and believe the Fed’s rhetoric, we should expect inflation to return to its lower long-run level. And so, rather than spiralling out of control because of negative real rates, inflation will naturally decline. In the extreme, the only reason the Fed would raise rates under the rational expectations theory is to alleviate some of the inflation pain in the short run – but this does not come free, as we explain later.
What Is the Fed’s Current View?
Cochrane runs a simple model under the two assumptions (Charts 3a & 3b). He finds the rational expectations model can almost perfectly replicate the official Fed projections (Chart 3b).This means that the Fed thinks inflation is high, but it is decreasing because expectations tomorrow are for lower inflation.
Having established the type of model the Fed is using, the paper shows the Fed Funds rate needed to attain the Fed’s projected path for inflation (Chart 4). It turns out that interest rates can stay low, and indeed lower than the Fed projects. And that path is perfectly consistent with unemployment slowly reverting to the natural rate – a soft landing.
The Debate
The debate about the Fed’s approach therefore seems centred on how expectations are formed. The Fed believes in rational expectations, and New Keynesian models have been using this forward-looking behaviour since the 1990s. And over the last decade, the theory has held strong.
In the zero-lower bound era, many predicted deflationary spirals. They never happened. Interest rates stayed the same for years and could not move lower. Yet the deflation spiral never broke out. If inflation did not spiral downwards, why worry about inflation spiralling upwards?
Well, empirical evidence shows Phillips curves contain at least some backward-looking terms, which may also reflect wage indexation. It may also be that rational expectations are appropriate over long-term horizons, but in the short-run expectations are adaptive. There is also plenty of evidence that inflation expectations are not anchored.
The Fed’s Overly Optimistic Inflation Outlook
The idea that inflation will spiral out of control is not mainstream – most agree it will subside. So, how long will that take?
A fiscal policy shock equivalent to the one the US experienced is likely to have long-lasting effects. How long will depend on the size of the shock and on how ‘sticky’ prices are. According to Cochrane, the Fed’s inflation projections in Chart 2 are way off the mark.
Why? Future inflation will depend on how much of the initial increase in the deficit (30%) people expect to be paid back. With an inflation rate of 8%, people roughly expect 22% of the debt to be repaid in subsequent surpluses and the rest to be inflated away.
Using the Fed’s model of rational expectations, an 8% rise in inflation in the first year means that total inflation (i.e., the total eventual price rise) should be 20%. This means we have only experienced 40% of the cumulative inflation rise from the fiscal policy shock so far. Inflation is likely to continue for some time, contrary to the Fed’s optimistic view.
The Unpleasant Arithmetic Facing the Fed
Can the Fed lower inflation with policy rate changes? Yes, but with a caveat. And it is all because of the cause of inflation – the rapid rise in government debt.
The story refers to a pattern called ‘stepping on a rake’. A fiscal shock causes a boom in consumption and an upward jump in the inflation rate. This devalues the debt and can be thought of as that part of the debt that bondholders expect not to be paid back.
In response to higher inflation, the central bank increases the interest rate. Higher interest rates must be paid by higher surpluses, which increases the amount of government debt. If the government does not reduce its deficit, there is no getting away from the total cumulative impact of the fiscal policy shock on prices (Chart 5). The Fed cannot alter the fact that there must be some inflation now or later.
This identity is called the unpleasant interest-rate arithmetic. By raising interest rates in the short term, the Fed can shift the burden from short-term bondholders to long-term bondholders. But the cumulative impact on prices will be higher as a result. There is a trade-off: lower inflation today means higher inflation tomorrow.
If, for example, the Fed followed a Taylor-type rule under the rational expectations model, it could reduce inflation significantly today. However, it will also significantly increase the cumulative price changes over time relative to not increasing the interest rate at all (Charts 6a vs 6b). The total price rise would be three times greater. Therefore, the Taylor-rule only works to reduce the volatility of inflation caused by a fiscal policy shock, not the overall level.
The answer to reducing inflation in any meaningful way will require, according to the paper, an austerity programme. This austerity programme would have to span several years and total between $2tn and $4tn to dampen inflation.
Bottom Line
Cochrane provides a helpful framework for us to debate the strengths and weaknesses of the Fed’s policy. Clearly, the Fed feels inflation will subside on its own because expectations are anchored towards a much lower level. An inflation spiral is therefore out of the question.
If true, then the interest rate level will only influence the speed at which inflation subsides. Following a Taylor-rule will stabilise prices more quickly but at the cost of a larger cumulative price change. This may be optimal – people inherently prefer to smooth through shocks rather than experience extreme highs and lows.
Currently, however, the Fed appears to be steering closer towards higher inflation in the short term. This may be because it expects inflation to subside quickly. Its forecasts have been wrong before.
The paper concludes with a discussion on how US inflation can be reduced rather than moved around. This would require an austerity programme that must span several years and total $2-4tn. It also requires microeconomic reforms. It sounds unlikely, but it has been done before by the likes of New Zealand and Canada.
Sam van de Schootbrugge is a Macro Research Analyst at Macro Hive, currently completing his PhD in international finance. He has a master’s degree in economic research from the University of Cambridge and has worked in research roles for over 3 years in both the public and private sector.