Lecture: Inflation, the Phillips Curve & Expectations
Lecture script · about 15–20 minutes spoken · Week 12
Opening
Here's a question worth asking out loud. Can a country buy fewer people out of work by putting up with prices that rise a little faster? And if it can, does the deal last?
Think about who lives inside that question. A line cook at a busy restaurant watches the menu prices climb and wonders how big a raise to ask for. A shop owner is setting next year's prices for haircuts. A nursing student is weighing two job offers in a town where every clinic seems to be hiring. Jobs and prices are pulling on all three of them at once.
Here's where we are. In Week 3, Measuring Inflation & Unemployment, you learned to compute the inflation rate and the unemployment rate, and you sorted unemployment into frictional, structural, and cyclical. In Week 6, Business Cycles & Short-Run Fluctuations, you saw that expected inflation shifts short-run aggregate supply. And in Weeks 9 through 11 you built the money supply and traced how the Fed's bond trades reach output. In this lecture we ask what all that money does over the long haul.
Here's the plan. I'll put inflation and unemployment on one diagram and read the trade-off between them. Then we'll find the natural rate of unemployment, watch expectations shift the whole curve, and see why the trade-off fades. After that we'll switch to a simple money equation and test what extra money does in the long run. We'll finish with an honest debate about how fast to bring inflation down. Every number in this lecture is illustrative, built for this course, not real data.
1. The short-run Phillips curve
Start with something you've seen. When help-wanted signs fill every window, employers compete for workers. They raise pay to win them. Then firms pass those higher costs on in their prices. When jobs are scarce, raises shrink and prices climb more slowly.
Economists put that pattern on one picture. Along the bottom, the horizontal axis, runs the unemployment rate, in percent. Up the side, the vertical axis, runs the inflation rate, also in percent. The curve slopes down from the upper left to the lower right.
Here's the term. The short-run Phillips curve is a downward-sloping curve with the unemployment rate on the horizontal axis and the inflation rate on the vertical axis. It shows that in the short run lower unemployment tends to come with higher inflation for a given level of expected inflation.
It carries a name from history. A. W. Phillips published a study in 1958 that found an inverse relationship between unemployment and the rate of change of money wages, using United Kingdom data for 1861 to 1957. Inverse means that when one rises, the other tends to fall.
Now the course's own curve. It passes through two points. At the first, unemployment is 4 percent and inflation is 6 percent. At the second, unemployment is 6 percent and inflation is 2 percent. Going from the first point to the second, unemployment rises and inflation falls. That's the downward slope, in numbers.
Pause and try this. On the course's curve, which point has the tighter job market, and what inflation comes with it?
Picture the curve before you answer.
Here's the answer. The point with 4 percent unemployment has the tighter job market, and it comes with 6 percent inflation. Fewer people looking for work means faster-rising pay and prices.
2. Reading the trade-off forwards
Suppose leaders want fewer people out of work. On this curve, that choice has a price tag, and the price is paid in inflation.
Here's the term. The inflation–unemployment trade-off is the short-run pattern in which pushing unemployment lower tends to bring higher inflation, and accepting higher unemployment tends to bring lower inflation; it holds along one short-run Phillips curve and fades once expected inflation adjusts.
Let's size it. Moving from 6 percent unemployment to 4 percent is a fall of two percentage points. Over the same move, inflation rises from 2 percent to 6 percent, a rise of four percentage points. Divide the change in inflation by the change in unemployment, and the slope is negative 2. In words, each point less unemployment comes with two points more inflation along this curve.
One small habit helps here. A point is one percentage point. Going from 6 percent to 4 percent is a fall of two percentage points, not a fall of 2 percent.
Now notice what kind of move this is. The curve itself didn't change. The economy slid from one point on it to another. That's a movement along the curve, the same habit you used on aggregate demand in Week 5. A shift of the whole curve is a different event, and it's coming up in section 4.
Here's a trap I want you to see coming. People sometimes say the trade-off backwards: "higher unemployment comes with higher inflation." It feels right, because both sound like bad news. But along one short-run curve, they move in opposite directions.
Pause and try this. A classmate writes, "On the short-run curve, unemployment and inflation rise together." Is that right?
Check the two points again before you decide.
Here's the answer. No, it's backwards. Along one short-run curve they move in opposite directions: 4 percent unemployment sits with 6 percent inflation, and 6 percent sits with 2 percent.
3. The natural rate and the long-run curve
Some unemployment never goes away, even in a strong economy. A new graduate takes a few weeks to find the right job. A worker whose trade was replaced by a machine needs time to retrain. That leftover unemployment has a name.
Here's the term. The natural rate of unemployment is the unemployment rate that remains when the economy produces at potential output, made up of frictional plus structural unemployment with no cyclical unemployment; it is written u-star, the letter u with a small star.
In the course's economy, the natural rate sits midway between the two short-run points. Add 4 and 6 to get 10, and halve it to get 5 percent. The first point sits one percentage point below the natural rate, and the second sits one percentage point above it.
Now picture a second line, rising straight up from 5 percent on the unemployment axis.
Here's the term. The long-run Phillips curve is a vertical line at the natural rate of unemployment, showing that once expected inflation has caught up, unemployment returns to the natural rate whatever the inflation rate, so there is no lasting trade-off.
Why straight up? In the long run, people's expectations catch up with the inflation they live through. They set wages and prices to match it. Then inflation stops surprising anyone, and unemployment drifts back to its natural rate.
This is the natural-rate argument, the case associated with Milton Friedman and Edmund Phelps. It says policy can hold unemployment below the natural rate only until people come to expect the higher inflation it brings. After that, unemployment returns to the natural rate at a higher inflation rate. Friedman made the case in 1968 and Phelps in 1967.
An honest caveat. The 5 percent is this course's illustrative number, and the real natural rate can't be seen directly. Economists argue about its size. They don't argue about the shape. The long-run curve is vertical, and that's an agreed result.
Pause and try this. Someone sketches the long-run Phillips curve with a gentle downward slope. What's wrong with the sketch?
Think about what the long run removes.
Here's the answer. The long-run curve has no slope. It's a vertical line at the natural rate, so a slope would bring back the very trade-off the long run takes away.
4. Expectations shift the short-run curve
Go back to the line cook. She earns 20 dollars an hour, and she expects prices to rise 6 percent this year. To keep up, she asks for a 6 percent raise, which takes her to 21.20 dollars an hour. If she gets only 2 percent while prices rise 6 percent, her real wage falls by about 4 percent. So next time she bargains harder, and so do her coworkers.
That's why the short-run curve is drawn for a given level of expected inflation. When people expect more inflation, they build it into wages and prices. The whole short-run curve shifts up. Every unemployment rate now comes with more inflation than before.
Now let's run the story that matters most this week. Suppose policy holds unemployment at 4 percent, one percentage point below the natural rate. On the original curve, that buys 6 percent inflation. For a while, it looks like a good deal: fewer people out of work.
Then expectations catch up. Workers and firms come to expect 6 percent, and they build it into wages and prices. The short-run curve shifts up. Unemployment drifts back to 5 percent, and inflation stays at 6 percent. Policy bought higher inflation and the same unemployment once expectations caught up.
You've met this force before. In Week 6, higher expected inflation shifted short-run aggregate supply left. Same event, different diagram. On one, prices rise and output slips back toward potential. On the other, the curve climbs and unemployment slips back toward the natural rate.
Here's the classic error. People read the short-run curve as a permanent menu, as if a country could order 4 percent unemployment with 6 percent inflation and keep it forever. But the menu itself moves whenever expected inflation moves.
Pause and try this. Policy holds unemployment at 4 percent, and people come to expect 6 percent inflation. Where does the economy end up in the long run?
Hold on to the vertical line.
Here's the answer. It ends at 5 percent unemployment with 6 percent inflation. Unemployment returns to the natural rate, and the higher inflation stays.
5. The quantity equation
Now let's switch from jobs to money. Picture a street fair. The organizers sell 300 dollars of tokens. A visitor spends a token at a food stall. The stall owner spends it at a craft booth. The craft seller buys a lemonade. By the end of the day, the stalls have rung up 1,500 dollars of sales with the same 300 dollars of tokens. Each token changed hands 5 times.
That turnover has a name. The velocity of money is the number of times an average dollar is spent on final goods and services in a year, found as nominal output divided by the money supply and written V.
And it lives inside one equation. The quantity equation is the identity M times V equals P times Q. It says the money supply times the number of times each dollar is spent equals the price level times real output, the nominal value of what the economy produces. Here M is the money supply, and imports keep their own label, IM, so the two never collide. P is the average price of one unit of real output. Q is real output.
Let's run the course's numbers. The money supply is 500 dollars, and velocity is 4. Multiply them, and total spending is 2,000. Real output is 1,000 units. Divide 2,000 by 1,000, and the price level is 2. You can also run it the other way. Divide the 2,000 of nominal output by the 500 of money, and velocity comes out to 4.
Pause and try this. Someone calls velocity a fudge factor, a number made up to force the equation to balance. How would you answer?
Think about how we got the 4.
Here's the answer. Velocity is measured, not made up. Divide the nominal value of output by the money supply: 2,000 divided by 500 gives 4, so each dollar changes hands 4 times a year.
6. Long-run neutrality of money
Here's a thought experiment. Suppose the money supply rises, and nothing real changes. Same workers, same machines, same know-how. More dollars are now chasing the same goods.
Let's run it. Raise the money supply 10 percent, from 500 to 550, and hold velocity and real output fixed. Total spending becomes 550 times 4, which is 2,200. Divide by the same 1,000 units of output, and the price level is 2.2. That's a rise of 10 percent, the same 10 percent as money. Real output stayed at 1,000.
Here's the term. Long-run neutrality of money is the result that, in the long run, a change in the money supply changes the price level and other nominal values but leaves real output and unemployment unchanged. And the quantity theory of money is the use of the quantity equation with velocity and real output held steady, which predicts that the price level changes in proportion to the money supply.
Notice how neatly this fits section 3. In the long run, money moves prices and leaves output and jobs where they were. On the Phillips diagram, that's the vertical line.
One honest caveat. Velocity doesn't always hold still, and unpredictable swings in velocity are one of the hazards of monetary policy. The fixed-velocity case is a model, not a promise.
Pause and try this. A classmate says, "The quantity equation proves money doesn't matter." What would you add?
Remember what you saw in Weeks 10 and 11.
Here's the answer. Money is neutral for real output in the long run, not in the short run. In Weeks 10 and 11, a bond purchase lowered the rate, raised investment, and shifted aggregate demand right, so output rose for a while.
7. Money growth, and how fast to bring inflation down
Most economies grow, so real output doesn't hold still either. One shortcut handles both kinds of growth at once.
Here's the term. The money growth rate is the percentage change in the money supply over a year; when velocity is stable, the inflation rate is approximately the money growth rate minus the growth rate of real output.
Let's use it. Money grows 8 percent a year, and real output grows 3 percent. Subtract, and inflation is about 5 percent. Of the 8 percent money growth, the extra goods absorb 3 percent, and the other 5 percent shows up in prices. It's an approximation, and it holds when velocity is stable.
Now tie the threads together. Steady money growth above output growth sets the inflation people come to expect. And expected inflation is the force that shifts the short-run curve up. So once inflation is high, a hard question follows. How fast should a central bank bring it down? Slowing money growth can mean, for a while, a slide down the short-run curve toward more unemployment.
Here's the Keynesian case, at full strength. Wages and prices are sticky, and expectations adjust slowly. A sharp squeeze would push unemployment well above the natural rate while expectations catch up, and that means real families losing real paychecks. A gradual path spreads out the pain.
Here's the classical and monetarist case, at full strength. Inflation in the long run is a monetary matter, so it ends only when money growth slows. A firm and believable commitment can bring expectations down faster, which shortens the painful stretch. A slow path risks letting high inflation settle in.
Both sides agree the long-run curve is vertical. They disagree about how fast expectations move, which is a question for evidence. And they weigh jobs now against stable prices later differently, which is a question of values. This course gives you both sides and leaves the verdict to the evidence and your own values.
Pause and try this. Money grows 8 percent and output grows 3 percent, but velocity starts falling. Is inflation more or less than about 5 percent?
Think about what slower spending does.
Here's the answer. Less. The shortcut holds only when velocity is stable, and if each dollar is spent less often, the same money growth brings less spending and less inflation.
Closing
Let me pull it together, in the order we built it. The short-run Phillips curve slopes down: lower unemployment comes with higher inflation. Reading it forwards, each point less unemployment costs two points of inflation on the course's curve, and a slide between points is a movement along it. The natural rate is frictional plus structural unemployment, 5 percent here, and the long-run curve stands vertical there. Expected inflation shifts the short-run curve up, so the trade-off is short-run only, never a permanent menu. The quantity equation says money times velocity equals prices times real output. With velocity and output fixed, a 10 percent rise in money is a 10 percent rise in prices. And inflation is about money growth minus output growth, when velocity holds still.
Next in this module come the slide deck, the Readings & Resources page, the lecture tutorial, the practice set, and the quiz. Next week opens a new unit, International Trade & Comparative Advantage, and asks why any country gains from trade at all.
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