Opening
HOST
Welcome back. Today we are on stabilization policy: how a central bank tries to keep output and inflation steady, here with a fixed rule for its interest rate. Could a robot run the Federal Reserve, or Fed, the central bank of the United States?
ECONOMIST
In fact, a recipe of one line, which looks only at inflation, has followed the Fed's interest rate quite well since 1960. Not always, though: in some years the Fed set its rate far below what the recipe gives.
HOST
So here is today's question. What happens to output and inflation when the central bank follows a rule?
ECONOMIST
By the end of this episode, you'll be able to do three things. First, explain why the aggregate demand curve slopes down and the aggregate supply curve, the firms' side, slopes up, each as a chain from cause to effect. Second, follow three events year by year: a jump in the fuel price, a lower inflation target and a wave of extra spending. And explain why lowering inflation costs a slump, however tough the central bank is. Third, describe how well a simple rule fits the Fed's interest rate, and explain why a believed inflation target makes low inflation cheap.
HOST
And we'll follow the chapter's mind map part by part?
ECONOMIST
Yes. The three parts are called A rule and one diagram, Three events, and Rules meet the data. Each part is a branch of the map. The first two branches have four leaves, or small topics, and the third has five.
A rule and one diagram
HOST
Part one of the map: A rule and one diagram. So far, the central bank chose its interest rate case by case. What changes now?
ECONOMIST
Now it follows a rule, a fixed recipe. Then the short-run model, our model of booms and slumps, the ups and downs of output, fits in one diagram with two curves. Where they cross gives this year's output and inflation.
HOST
So what's the rule?
ECONOMIST
Let's visit Islandia, our imaginary island country. Its central bank, the Bank of Islandia, has an inflation target of 2 percent. A point here is one percentage point, like going from 2 to 3 percent. For each point of inflation above the target, the Bank sets the real interest rate, the rate after taking out inflation, half a point above its normal level. That's the rate new machines and buildings earn. Below the target, it sets the rate below normal. This number, one half, is called the policy response.
HOST
The first leaf says a policy rule makes the AD curve slope down. AD means aggregate demand, total spending in the economy. Explain it with numbers.
ECONOMIST
Suppose inflation is 3 percent, one point above the target. The rule sets the real rate half a point above normal. So Harbor Boatworks, the island's boat builder, delays a new workshop, and islanders delay big purchases.
HOST
How much does spending fall?
ECONOMIST
Each point of higher real rate cuts spending by 2 percent of potential output. That's what the island makes when its workers and tools are used at a normal pace. So half a point cuts spending by 1 percent, and output falls to 1 percent below potential. That's the AD curve: the higher inflation is, the lower output is under the rule. The Bank wants this, because a weaker economy pulls inflation down later.
HOST
Wait. I learned that demand curves slope down because people buy less when prices are high. Isn't this the same thing?
ECONOMIST
A lot of students think that, but no. This curve is about the inflation rate, how fast prices rise, not about how high they are. And the slope comes from the Bank, not from shoppers: it sees high inflation, raises the real rate, and spending falls.
HOST
Next leaf: a tougher central bank, flatter AD. My guess is that a tougher bank makes the curve steeper. Tougher sounds steeper.
ECONOMIST
That's the natural guess, but it's the opposite. Take a bank twice as tough: its policy response is 1 instead of one half. Now one extra point of inflation raises the real rate by a full point, so output falls by 2 percent, not 1.
HOST
But why is that flatter?
ECONOMIST
In the diagram, output is on the horizontal axis and inflation on the vertical one. So when a small rise in inflation brings a big fall in output, the line is flat: a bank that fights inflation hard.
HOST
Next leaf: the Phillips curve is the AS curve. AS means aggregate supply. What is it?
ECONOMIST
It's the firms' side: how fast firms raise their prices when they produce more or less. Harbor Boatworks expects this year's inflation to be like last year's, and plans its prices that way. But in a boom, when output is above potential, it pays overtime and works its machines harder. Its costs rise faster, so it raises its prices faster than planned. When all firms do this, inflation rises above last year's rate. In a slump, or recession, when output is below potential, the opposite happens.
HOST
So in numbers?
ECONOMIST
This year's inflation is last year's, plus a push from a boom, plus any shock, like a jump in the fuel price. The slope of this curve says how strongly prices react. Say last year's inflation was 2 percent, output is 1 percent above potential, and the slope is 1. Then this year's inflation is 3 percent. Higher output goes with higher inflation, so the AS curve slopes up. And because it's built on last year's inflation, it shifts whenever inflation changes, which drives all of part two.
HOST
Last leaf of this part: the steady state, output at potential and inflation on target. Why there?
ECONOMIST
A steady state is a resting point, so inflation must stop changing. The AS curve says that happens only when output is at potential and there's no shock. So the output gap, the distance between output and potential, is zero. And the rule pushes output away from potential whenever inflation is off target. So inflation must be on target, at 2 percent, however tough the Bank is.
HOST
So in part one we saw two curves with two stories. AD slopes down because the Bank fights inflation, and AS slopes up because firms charge more in a boom. At rest, they cross where output is at potential and inflation is on target.
ECONOMIST
Next branch: what happens when something pushes Islandia away from that resting point.
Three events
HOST
Part two of the map: Three events. The first leaf is an inflation shock, with stagflation. What's the shock?
ECONOMIST
Islandia's boats burn fuel. Suppose the fuel price jumps, and for one year it adds 2 points to inflation. If output stayed at potential, inflation would jump from 2 to 4 percent. But the rule fights inflation above target with a slump.
HOST
So where is Islandia in year one?
ECONOMIST
Each percent of output below potential pulls inflation back by one point. And the rule makes the slump as large as the rise in inflation. So, with our numbers, the fuel's push of two points is shared. One point shows up as higher inflation, at 3 percent. The other is held back by a slump: output 1 percent below potential. That's stagflation, a slump and rising inflation at the same time. The United States had it after the oil shocks of the 1970s.
HOST
Next leaf: the gap halves every period. Here a period is a year. The fuel price is back to normal in year two, so I'd guess inflation drops right back to 2 percent.
ECONOMIST
That's the tempting answer, but no. Firms now expect last year's 3 percent, one point above the target, so the AS curve stays high. The Bank still sees inflation above target and keeps a slump going, which pulls inflation down only part of the way. In year two, inflation is 2.5 percent, and output is half a percent below potential.
HOST
So each year the distance to the target is cut in half?
ECONOMIST
Yes, with our numbers, for both: the inflation gap, how far inflation is from target, and the output gap. So a one-year shock leaves a slump that lasts many years.
HOST
Next leaf: disinflation from 4 percent to 2 percent costs 2 percent of a year's output. What's a disinflation?
ECONOMIST
Lowering inflation permanently. Say Islandia's target, and its inflation, have been 4 percent for years. Now the Bank lowers the target to 2 percent.
HOST
But firms still expect 4 percent.
ECONOMIST
Exactly, and under the new rule that's too high. So the Bank raises the real rate. In year one, inflation falls only to 3 percent, halfway, and output is 1 percent below potential. Then both gaps are cut in half each year. Let's add up the lost output step by step. Year one: 1 percent below potential. Year two: half of that, 0.5 percent.
HOST
Year three, half again, 0.25. So far that's 1.75.
ECONOMIST
Right. Each new year adds half of what is still missing to reach 2. So the total gets closer and closer to 2 percent of one year's output. That's the price of lowering inflation by 2 points.
HOST
But a tough bank would finish faster. So surely it pays less.
ECONOMIST
A lot of people believe that, but in this model it's wrong. A tough bank causes a deeper slump that ends sooner. A gentle bank causes a milder slump that lasts longer. Both lose 2 percent of a year's output. Here's why. With the Phillips curve's slope of 1, each percent of output below potential, held for one year, takes one point off inflation. Inflation must fall by 2 points, so the slumps must add up to 2.
HOST
Last leaf: demand boom, up to 4 percent inflation, then a slump. What starts it?
ECONOMIST
A wave of optimism. Islanders spend more, by 2 percent of potential output, for nine years. In year one, half of the push goes into output and half into inflation: output is 1 percent above potential, and inflation is 3 percent.
HOST
And then Islandia goes back to where it started, like after the fuel shock?
ECONOMIST
Not while the optimism lasts. Inflation of 3 percent is above what firms expected, so next year they expect 3, and the AS curve shifts up. Inflation settles near 4 percent.
HOST
Why 4?
ECONOMIST
Inflation stops climbing only when output is back at potential. For that, the real rate must sit a full point above normal, to take away the extra 2 percent of spending. The rule does that only when inflation is two points above the target: 4 percent.
HOST
And when the optimism fades?
ECONOMIST
The extra spending is gone, but inflation is still near 4 percent, so the rule keeps the real rate high, and output drops to about 1 percent below potential. Inflation falls to about 3 percent. With output across and inflation up, the path is a loop that turns counterclockwise: both rise, then inflation rises as output falls, then both fall, then output recovers.
HOST
So does the boom at least leave Islandia with more output in total?
ECONOMIST
No. Inflation starts and ends at 2 percent. So, by the same reasoning as in the disinflation, the years above potential and the years below add up to zero. What's left is years of inflation above target. That's why central banks try to keep output at potential.
HOST
Still on this leaf: what drives all three events?
ECONOMIST
Sticky expectations, which are slow to change. Because firms expect last year's inflation, every shock fades slowly, and lowering inflation needs a slump. Each point of disinflation costs one divided by the Phillips curve's slope, in percent of a year's output. That's called the sacrifice ratio. With our slope of 1, it's 1 percent. If prices reacted only half as strongly to a slump, it would double.
HOST
So in part two we saw that a fuel shock brings stagflation, a lower target costs a slump, and a boom must be followed by one. For the fuel shock and the lower target, a tougher bank only changes the shape of the slump, not its total.
ECONOMIST
Next branch: does any of this match real central banks?
Rules meet the data
HOST
Part three of the map: Rules meet the data. The first leaf is the Taylor rule, with a correlation of 0.75. What is the Taylor rule?
ECONOMIST
The economist John Taylor suggested simple numbers for a rule like Islandia's. The normal real rate is 2 percent, the target is 2 percent, and the policy response is one half. But the Fed sets a nominal rate, the fed funds rate, which is the real rate plus inflation.
HOST
So at the target, the nominal rate is 2 plus 2, which is 4 percent?
ECONOMIST
Yes. Each point of inflation above the target adds one and a half points. The leaf writes this as 1 percent plus one and a half times inflation, which also gives 4 at the target.
HOST
Why one and a half? If inflation goes up 1 point, raise the rate 1 point. That should be enough.
ECONOMIST
It sounds like enough, but it isn't. Spending reacts to the real rate. A rise of one point only matches inflation, so the real rate stays the same, and nothing pulls inflation back. The extra half point, the policy response, raises the real rate.
HOST
And the 0.75?
ECONOMIST
That's a correlation, a measure of how closely two sets of numbers move together over time. One means perfectly together, and zero means they don't tend to move together at all. From 1960 to 2023, the Fed's rate and this rule have a correlation of 0.75: they move together most of the time.
HOST
And when didn't they?
ECONOMIST
From the late 1960s to 1980, the Fed's rate was well below the rule, and inflation climbed. After the financial crisis of 2008, it was below again, partly because a fuller version of the rule also cuts rates in a recession.
HOST
And more recently?
ECONOMIST
In 2021 and 2022, the Fed's rate was 6.7 points below the rule on average, while inflation jumped.
HOST
Next leaf: forecasts missed 2008 by up to 7.2 million jobs. But first, do the loops from part two show up in real data?
ECONOMIST
Yes, most clearly from 1960 to 1985. Booms raised inflation, and the high inflation of the 1970s was followed by deep recessions that brought it down.
HOST
And how do forecasts connect to rules?
ECONOMIST
If the Bank could see a wave of optimism, it could remove the extra spending with a higher interest rate, and skip the boom and the slump. Our rule waits until the shock shows up in inflation, because shocks are hard to see in time, even for professionals. Every three months, a survey asks professional forecasters to predict U.S. jobs. Around the Great Recession that followed the crisis, every one of their forecasts for a year ahead was too high. The one made in the third quarter of 2008 was too high by 7.2 million jobs, about 5 percent of all U.S. jobs.
HOST
Next leaf: a credible target makes disinflation free. Free? Part two said it costs 2 percent of a year's output.
ECONOMIST
That was with firms that only look at the past. Credible means believed. Now suppose firms use all the information they have, including the target the Bank announces.
HOST
So Harbor Boatworks hears the new 2 percent target and believes it?
ECONOMIST
Yes, and it slows its price rises at once. Inflation falls straight from 4 to 2 percent, with output at potential, because no slump is needed to change what firms expect. If firms believe only half of the cut, they expect 3 percent, and the first-year slump is half as deep.
HOST
Then why doesn't every central bank announce a low target?
ECONOMIST
Because firms know about a temptation. Once prices are set, a central bank could surprise everyone with low rates and a quick boom. So firms don't fully believe a bank that is free to do it. That's why a bank gains by limiting its own freedom, with a rule, a clear target and a record of keeping promises.
HOST
Next leaf: the U.K. from 1997 to 2016. What's being measured?
ECONOMIST
The economist Ricardo Reis split British inflation since 1737 into periods of 20 years. For each one, he measured average inflation and its volatility, meaning how much it jumps around from year to year. The goal is 2 percent inflation with no jumping around.
HOST
And the period on the map came closest?
ECONOMIST
Yes. Those were the years when the Bank of England was independent of the government and had an inflation target. Inflation averaged 1.9 percent, and its volatility was only 1.1 points. No other period came as close to the goal.
HOST
Last leaf: rules or discretion? Discretion means deciding case by case, with judgment. So, back to our opening: should a robot run the Fed?
ECONOMIST
No. Shocks like the crisis of 2008 or the pandemic of 2020 need judgment that no simple rule has. That's why many central banks keep freedom in the short run, but promise a target for inflation in the long run. The U.S. adopted its 2 percent target only in 2012.
HOST
So in part three we saw that a simple rule fits the Fed's rate fairly well, with big misses. Shocks are hard to see in time, and being believed is what makes low inflation cheap.
ECONOMIST
Exactly. Let's sum up.
Wrap-up
HOST
Let's go back to our three goals. First, why does AD slope down and AS slope up?
ECONOMIST
AD: higher inflation, so the Bank raises the real rate, so spending and output fall. AS: higher output, so firms pay overtime, so they raise prices faster, so inflation rises.
HOST
Second, the three events. Each one brings a slump. For the fuel shock and the lower target, a tougher bank changes only how deep and how long the slump is, not its total.
ECONOMIST
Right, because sticky expectations keep inflation up until slumps bring it down. And third, a simple rule follows the Fed fairly well, and a believed target lets firms slow their price rises without a slump. So here is the big message. A central bank that follows a rule turns the short-run model of booms and slumps into one diagram with two curves that cross. Because expectations are sticky, every shock fades only slowly, and lowering inflation costs a recession. A believed target is what makes low inflation cheap.
HOST
Here's a question to think about. A new fuel shock hits Islandia, again adding 2 points to inflation for one year. The head of the Bank says: "I'll fight it twice as hard, so we lose less output in total." Is she right? And what would really make the shock cheaper?
ECONOMIST
Pause the episode and think about it for a moment.
HOST
Okay, we're back. What's the answer?
ECONOMIST
She's wrong about the total. Fighting twice as hard makes the first-year slump deeper, but shorter. The shock added a push of 2 points, and inflation must end at the target again. Each percent of output below potential for a year takes one point off, so the slumps still add up to 2 percent of a year's output.
HOST
And what would make it cheaper?
ECONOMIST
Prices that react more strongly to a slump would help, but no bank controls that. What a bank can build is credibility. If firms trust the target and don't raise their expectations after the shock, a much smaller slump is needed.
HOST
Where can students try all this themselves?
ECONOMIST
Open the chapter's Colab notebook to run each event. The Model Apps let you move the model's sliders with no code, and the Data Apps show the Taylor rule, the loops and British inflation.
HOST
And next time?
ECONOMIST
In Chapter 14, we add financial crises. We ask: why did the 2008 crisis cause such a deep slump, even though the Fed cut its rate to zero?
HOST
That's it for today. Thanks for listening, and see you next time.