Latest / Monetary Policy Explained with Fexingo: Central Banks, Money Supply, and Interest Rates / How Central Banks Use the Taylor Rule: A Real-World Case
Transcript
- Lucas: So we've talked a lot about the tools central banks use — QE, forward guidance, standing facilities. But we've never really talked about the formula that, in theory, tells them where interest rates should be. Luna: The Taylor Rule. I've seen the equation — it looks simple enough. But does the Fed actually follow it, or is it more of a reference point? Lucas: It's definitely a reference, not a rigid rule. But it's worth understanding because it frames almost every policy debate. The rule was proposed by economist John Taylor in 1993. The basic idea is that the central bank should set the nominal fed funds rate equal to the neutral real rate plus inflation, plus weights on how far inflation is from target and how far output is from potential. Luna: Right — so it's a formula that tells you: if inflation is above target, raise rates. If the economy is weak, lower them. But the coefficients matter a lot, don't they? Lucas: They do. Taylor originally suggested a weight of 0.5 on the inflation gap and 0.5 on the output gap. So if inflation is one percentage point above target, you raise rates by half a point more than the neutral rate would suggest. If output is one point below potential, you lower them by half a point. The idea is to lean against the wind without overreacting. Luna: And where does the neutral rate come from? That's the elusive 'r-star' that we keep hearing about. Lucas: Exactly. R-star — the neutral real rate — is the rate that neither stimulates nor restrains the economy when it's at full employment and inflation is at target. It's not observable. You have to estimate it. The Fed's current estimate is around 0.5 to 1.0 percent in real terms. Add the 2 percent inflation target, and you get a nominal neutral rate around 2.5 to 3 percent. That's the baseline before you add the Taylor adjustments. Luna: So let's plug in some real numbers. It's June 2026. Core PCE inflation is running at about 2.1 percent — just a touch above target. The output gap is positive — maybe 0.8 percent above potential. What does the Taylor Rule say the fed funds rate should be? Lucas: Okay, let's do the math. Let's assume the Fed's estimate of r-star is 0.7 percent. The inflation rate is 2.1 percent, so the inflation gap is plus 0.1 percentage points. The output gap is plus 0.8 percent. Using Taylor's original coefficients: the prescribed nominal rate would be 0.7 plus 2.1, which is 2.8, plus 0.5 times 0.1 — that's 0.05 — plus 0.5 times 0.8 — that's 0.4. So 2.8 plus 0.05 plus 0.4 equals 3.25 percent. Luna: Huh. The actual fed funds rate today is about 3.75 percent. So the rule says rates should be 3.25 — meaning the Fed is actually tighter than the rule suggests. That's interesting. Lucas: It is. But that depends on which version of the Taylor Rule you use. Some economists argue the coefficients should be larger. For example, if you use a coefficient of 1.0 on the inflation gap — which some hawks prefer — the prescribed rate jumps to 3.65 percent. Much closer to where we are. Others argue the output gap coefficient should be higher too. Luna: So the rule is really sensitive to assumptions. That's why central bankers don't just follow it mechanically. Lucas: Right. And if walking through the economy with us has made something click, it's worth mentioning that this show stays ad-free thanks entirely to listener support. If you find yourself using the Taylor Rule at a dinner party — or even just nodding along — you can help us keep this going at buy me a coffee dot com slash fexingo. We keep it simple because we think you do too. Luna: Yeah, it's genuinely just a small way to say the show matters to you. No pressure, but we appreciate it. Lucas: So back to the math. The Taylor Rule also has a more modern variant that uses the core PCE inflation rate and the output gap from the Congressional Budget Office's estimate of potential GDP. That version — called the Taylor 1999 rule — uses a higher weight on the output gap and tends to prescribe even lower rates during recessions. Luna: Let's go back to the 2008 financial crisis. If you ran the Taylor Rule in 2009, what would it have said? Lucas: It would have said the fed funds rate should be deeply negative — like negative 5 or 6 percent. Of course, the Fed couldn't go below zero easily, so they had to use QE and forward guidance instead. That's a classic example of the rule pointing to a policy that's not feasible, which is a big criticism. Luna: So the rule assumes that interest rates can go anywhere, but in reality there's the zero lower bound. Lucas: Exactly. And that led to modifications. Some economists proposed a 'balanced approach' rule that puts more weight on the output gap when rates are near zero. Others suggested using a 'difference rule' that focuses on the change in the output gap rather than the level, to avoid prescribing unrealistically low rates. Luna: There's also the criticism that the Taylor Rule doesn't account for financial stability risks. Before 2008, the rule suggested rates should have been around 3 to 4 percent in 2005-2006, which is roughly where they were. But many argue that ignoring the housing bubble was a mistake. Lucas: That's a huge debate. John Taylor himself argues that the Fed kept rates too low in 2003-2005, fueling the housing bubble. He says if they had followed his rule, rates would have been about 1.5 percentage points higher, and the bubble might have been smaller. But critics say the rule would have been too restrictive and could have caused a recession earlier. Luna: So it's not a perfect tool, but it's a useful benchmark. Let's talk about how the Fed actually uses it in 2026. Lucas: The Fed publishes the Taylor Rule prescriptions in its Monetary Policy Report, but they explicitly say they don't follow any single rule. That said, many Fed officials — especially the more hawkish ones — refer to it in their speeches. For example, in the March 2026 FOMC minutes, several participants noted that the Taylor Rule would suggest a higher path for rates given the tight labor market. Luna: But the committee decided to hold rates steady at 3.75 percent. So discretion won over the rule in that meeting. Lucas: Right. And that's typical. The rule is more of a cross-check. If the Fed deviates significantly from what the rule says, they have to explain why. For instance, if inflation is temporarily high due to supply shocks, the rule would say raise rates, but the Fed might wait to see if it passes. That's exactly the debate we saw in 2021-2022. Luna: So the Taylor Rule is a normative model — it tells you what should happen — but the Fed uses a positive model that takes into account the specific circumstances. Lucas: Exactly. And there's also the issue of which rule to use. There are at least a dozen variants: the Taylor rule, the Taylor 1999 rule, the balanced approach rule, the first-difference rule, the inertial rule, and so on. Each gives a different prescription. So the Fed isn't ignoring all rules — they're choosing which one fits the current situation best. Luna: And the choice itself reveals their bias. A hawk will cite the rule that says rates should be higher. A dove will cite the one that says they're fine. It's almost like a Rorschach test. Lucas: That's a great way to put it. And it's not just the Fed. The European Central Bank, the Bank of England, the Bank of Japan — they all have their own versions. The ECB, for example, uses a Taylor rule with a weight on money growth, which is a nod to its Bundesbank heritage. Luna: Let's get into the nitty-gritty of the equation for a moment. The standard Taylor rule is: i = r) + 0.5(y - y is the neutral real rate, π is inflation, π is potential output. Lucas: That's the one. And note that the output gap is often measured as the percent deviation of real GDP from potential. If potential GDP is growing at 1.8 percent and actual GDP is at 2.6 percent, the gap is 0.8 percent. That's where we are now. Luna: One criticism of the rule is that it assumes the output gap can be measured accurately. But potential GDP estimates are notoriously unreliable and get revised constantly. The CBO's estimate of potential output in 2026 is quite different from what it was in 2020. Lucas: Absolutely. After the pandemic, there was a big debate about whether potential output had been permanently damaged. If your estimate of potential is too low, you think the output gap is smaller than it really is, and you keep policy too loose. That's a classic mistake. Luna: So the Taylor Rule is only as good as your inputs. Garbage in, garbage out. Lucas: Exactly. And that's why many economists now prefer a 'difference rule' — one that uses the change in the output gap rather than the level — because changes are measured more reliably than levels. That's what Janet Yellen advocated for when she was Fed chair. Luna: Let's talk about the 'first-difference rule' specifically. How does it differ? Lucas: The first-difference rule, proposed by John Taylor and others, sets the change in the federal funds rate equal to half the difference between actual inflation and target, plus half the difference between the growth rate of real GDP and the growth rate of potential. It doesn't depend on the level of the output gap at all — just the growth rate. That makes it more robust to measurement errors. Luna: So if inflation is at target and GDP is growing exactly at potential, the rate stays the same. It's purely a rule of thumb for adjustments. Lucas: Right. And it avoids the need to know r-star, which is a huge advantage. Many central banks have used this rule informally. But it also has a downside: it doesn't tell you the appropriate level of rates, only the direction of change. So if rates are too high or too low to begin with, the rule might keep them there. Luna: That's why you need both a level rule and a difference rule. The level rule gives you the destination; the difference rule tells you how fast to get there. Lucas: Exactly. And that's where inertial rules come in. Some models add a smoothing term — like only adjusting rates by 0.5 times the desired change per quarter — to avoid shocking markets. That's basically what the Fed does in practice. Luna: So the Taylor Rule isn't a single formula. It's a family of formulas, each with its own strengths and weaknesses. And the art of central banking is knowing which one to use when. Lucas: That's the best summary I've heard. And it's worth remembering that John Taylor himself never intended his rule to be followed mechanically. He wrote that it should be a 'benchmark for policy evaluation.' It's a way to check whether your decisions are consistent with a systematic approach. Luna: I think that's the key takeaway: the rule provides discipline. It forces central bankers to justify deviations from a transparent framework. And that's good for accountability. Lucas: Absolutely. So next time you hear a Fed official say 'the economy is evolving as expected,' you can think about the Taylor Rule and ask yourself: what would the formula say? And more importantly, why is the Fed doing something different? Luna: That's a great way to stay engaged. And maybe next time, we can talk about how the Taylor Rule applies in different countries — like the ECB with its one-size-fits-all challenge. Lucas: That'd be a good one. For now, we've covered the basics of the Taylor Rule, its variants, and how it's used in practice. Thanks for listening, and we'll see you next time.