The Taylor rule vs. the Fed (repost)

Being new to writing articles on LinkedIn, I posted my first article as a PDF file. Some of my friends noted that it would have been better to have it as LinkedIn post. I am using the opportunity that today the FOMC announced their decision to keep interest rates constant in order to post my first article properly. If you have already read the one from October 5, there is nothing new in this one. Here we go:

The Taylor rule vs. the Fed: Higher-for-longer or a Hard Landing

Over the past two years, monetary policy discussions have taken (again) center stage in the world of investing, policymaking, politics, and our everyday life. After jumping to 7-8%, inflation has now moderated to around 3-4%. But these values are still above the inflation target of around 2% set by most central banks, and therefore we expect that central banks around the world will maintain high interest rates until inflation returns to the target level.

So, will the Fed raise interest rates one more time in 2023? How much longer do we have to live with interest rates above 4-5%? In a series of articles, I plan to bring data and various tools to analyze the current situation and address these questions.

The first article in the series asks a simple question: What should be the level of the interest rate set by the central bank? To be transparent from the beginning, there is no simple answer to this question. Piles of academic papers and newspaper articles document that the range of opinions can be wide and volatile. I will start with a simple benchmark, called the Taylor rule, and eventually I will expand the conversation to include other perspectives on this question.

How does monetary policy work? Most central banks in advanced economies will state explicitly that their objective is to keep the rate of inflation at or below 2%. To meet this objective when faced with high inflation, central banks raise interest rates that in turn raise borrowing costs. This leads to a decline in demand from firms and households, and therefore alleviates the pressure on prices to increase. In other words, inflation falls. When inflation is below the 2% target, central banks lower interest rates to stimulate demand.

In 1993, John Tylor from Stanford University proposed a rule that captures this logic into a simple formula. The rule states that the central bank rate should be set to the sum of three simple components: the equilibrium nominal rate (ENR), the deviation of inflation from its target multiplied by an appropriate positive coefficient, and a measure of the slack in the economy (GAP), i.e., the difference between actual output and what the economy can produce without generating inflationary or deflationary pressures. If inflation is on target, then we can think of this “ideal” level of output as the Goldilocks economy – it is neither too hot, nor too cold.

We can represent the Taylor rule in this simple form:

Central Bank target rate = Equilibrium rate + A*(Inflation – 2%) + B*GAP

The equilibrium interest rate turns out to be important in understanding monetary policy rules, and I will devote an entire article to discuss it in detail.

The coefficients “A” and “B” capture how aggressively the central bank reacts to the inflation rate and to the output gap, respectively. Usually, “A” is set to 1.5 and “B” is between 0.5 and 1. This means that if inflation increases by 1%, the target rate should go up by 1.5%. If the economy goes into overeating mode and the GAP is +1%, i.e., actual output is above potential, the CB will raise interest rates by 0.5% to 1% (depending on the coefficient). The gap variable is in the rule as it is another way to capture when the economy might enter an overheating zone or a recessionary episode.

To illustrate how this works, I will follow the literature and set A = 1.5, B = 1 and ENR = 3% (again, we will discuss this in detail in another article). Today, most estimates of the US output gap are around 0.5% and US core inflation is at about 3.8%.[1] For the US central bank rate, called the federal funds rate, these numbers imply:

FFR target = 3% + 1.5*(3.8%-2%) + 1*0.5% = 6.35%

So, if these were the right parameters and values for the key variables, the interest rate should be at 6.35%. The Federal Reserve Bank of Atlanta has created a Taylor Rule Utility, where you can select various parameters and see how the Taylor rule performs over time. Here is the result of constructing the Taylor Rule values since 1985 and plotting them against the actual federal funds rate.

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The thin red line plots the actual federal funds rate, while the thick blue line is the result of plugging in the relevant numbers in the formula above. There is one more parameter that I have used here – I assume that the Fed does not jump to the target implied by the rule right away, as this may create too much volatility and potentially be damaging for the economy. To create the blue line, I have assumed that the Fed moves slowly to the prescribed rate by putting a weight of 2/3 on the interest rate from the last quarter and one-third weight is assigned to the prescribed target.

It is quite impressive how well the prescription fits the actual rate. All major swings in the fed funds rate in the 1980s, 1990s and early 2000s are remarkably close to the rate implied by the Taylor rule. One notable exception is the 2009 – 2016 period when the rule prescribes negative interest rates, but the Fed decided to keep rates at what is considered the “effective lower bound” of about 0.15%. In many communications, the Fed has explained why they did not want to set negative interest rates.

There is another notable discrepancy between the two series. While the rule suggested that interest rates should increase to about 2.5-3% in 2021, the Fed kept them at zero. It is not clear what would have happened if the Fed raised rates slowly in 2021 to react early on to the increase in inflation. By now, many observers have noted that this was a mistake, and we will discuss why the Fed stuck with the lower rates for a longer period. It is worth pointing out that 2021 was the first time since 1985 when the Fed was more dovish than the rule. In the past, if there were discrepancies between the actual and the prescribed rates, almost always the case would be that the Fed has chosen a tighter policy than what the rule would suggest.

The Taylor rule is a mechanical formula to calculate the interest rate that is supposed to bring inflation down to 2%. It does omit a lot of other important variables like credit market conditions and a myriad of other variables that enter the decision-making process. Still, in my view it is a useful starting point for a discussion. Deviations of the federal funds rate from the prescription ought to be analyzed and justified. One may decide to look for another rule that hopefully will better fit the performance of the Fed, and indeed there are plenty of rules out there. The June 2023 report of the Board of Governors described several of those rules (pp. 44-47). Interestingly, all these rules point to a big gap between the actual rate and the rate that would have been consistent with a tighter control of inflation.

So where are we today? In 2022 the Fed quickly caught up with the Taylor rule prescriptions, and as of November it follows it quite closely. The most recent reading of the Taylor rule is 5.42%, while the average effective rate as of August 15 was 5.26% (the rule is updated on a quarterly basis and the last observation is from August). The last few observations in this chart suggest that even though the Fed has finally caught up with the rule, the rule rates keep climbing up. The prescribed target rate without smoothing is slightly above 6%, which implies that there could be another hike. But given that the Fed funds rate is already above the inflation rate, it puts pressure on inflation to go down.

The Fed is facing a tradeoff: faster disinflation may lead to a recession, but it will eradicate inflationary pressures and, after peaking this year, the Fed will push down interest rates quickly in 2024. On the other hand, the desire for a soft landing may require “higher-for-longer” interest rates of around 5% – 6%. Barring any significant shocks, these rates will drive inflation down, albeit slowly. If the current values of key variables remain roughly the same in the next few weeks, the Taylor rule indicates that rates should go up to 5.62%. I doubt this will prompt the Fed to increase rates at the next meeting on October 31/November 1.

[1] I use core inflation because the Fed and many other central banks consider this to be a better target than the overall (headline) inflation. Core inflation excludes volatile components like energy and food prices. The reason for targeting core is that the volatile components in the headline inflation may lead to a volatile reaction by the central bank, which in turn will introduce higher volatility in the economy through central banks interest rates.