The Keynesian Perspective

This is Unit Nine of Principles of Macroeconomics, part two of two. Part one built the expenditure model and the multiplier. This part puts them to work on policy, and then shows what the model quietly leaves out. Carry the unit's idea to its payoff. The expenditure model gives the size of a policy move, and it gives it well. What it omits is the price level, and what it cannot see is expectations — and those two omissions are what the capstones here expose and what the units after this one restore. By the end you will compare a spending change with an equal tax change, tell a shift of the line from a rotation, size the policy that closes a gap, say why this model has no price level in it, and tell a movement along a Phillips curve from a shift of it.

Two entries comparing policies of the same size, and finding the one change that moves the multiplier itself.

Two policies, the same size.

MAC 0828 Spending Against an Equal Tax Change

Compare two policies in the course's economy, where the multiplier is two point five and the propensity to consume is nought point seven five. Government purchases enter expenditure directly, so raising them by a hundred billion shifts the line up by the full hundred and output rises by two hundred and fifty. A tax cut of a hundred billion reaches households as income, and they spend three quarters of it, so the line shifts by seventy-five and output rises by a hundred and eighty-seven and a half. The spending increase moves output by more, and the ratio between them is the propensity to consume. Do both a spending rise and an equal tax rise together and output changes by sixty-two and a half. In the simplest model, with no income tax and no imports, that last figure comes out at exactly the change in spending, and the balanced-budget multiplier is said to equal one. With an income tax in the economy it does not. The result equals one in a special case, not in general.

A change that moves the slope.

MAC 0829 Shift or Rotation

Classify a policy by what it does to the expenditure line. Some changes shift the line without changing its tilt, leaving the multiplier alone; one kind tilts it and changes the multiplier as well, and deciding which has happened comes before computing anything. A change in government purchases shifts the line by its own amount, and the slope is untouched. A change in autonomous taxes shifts it by the propensity to consume times the change, and again the slope holds. A change in the income tax rate is different: it changes how much of each extra dollar reaches households, so the line rotates, the slope changes, and the multiplier changes with it. Raising the rate flattens the line and shrinks the multiplier; cutting it steepens the line and enlarges it. When the line rotates, the new output must be computed with the new multiplier, and using the old one is an error the arithmetic will not reveal, because the answer still looks reasonable.

Three entries on the gaps as distances, the policy that closes them, and why that policy is smaller than the gap.

The gaps as distances.

MAC 0830 The Two Gaps, Measured

Unit eight named the two gaps; here they are distances. A recessionary gap is equilibrium output below potential GDP, and an inflationary gap is output above it. With equilibrium at six thousand seven hundred and fifty and potential at seven thousand, the recessionary gap is two hundred and fifty billion. The gap is the distance in output, not the policy needed to close it.

Sizing the policy.

MAC 0831 Sizing the Policy That Closes a Gap

Given a gap and a multiplier, the required change in spending is the gap divided by the multiplier, because the multiplier is what turns a change in spending into a larger change in output. Work it, then verify against the algebra rather than trusting the formula alone. The course's economy has a recessionary gap of two hundred and fifty billion and a multiplier of two point five, so the required change is a hundred billion. Verify: raising government purchases by a hundred lifts the autonomous total to two thousand eight hundred, and dividing by nought point four gives seven thousand, which is potential GDP. The two routes agree. A tax cut instead takes a larger cut, because only the propensity to consume of it is spent: about a hundred and thirty-three billion. An inflationary gap runs the same arithmetic in reverse. The model gives the size of the move, and assumes it arrives on time and that nothing else changes.

Why the policy is smaller.

MAC 0832 Why Closing a Gap Takes Less Than the Gap

Here the unit's governing idea is at work. That a two hundred and fifty billion gap closes with a hundred billion of spending is the point of the whole model, and it is not a trick. The extra spending does not stop when it is received: the firms that receive it pay workers and suppliers, whose incomes rise, and they spend a share on other firms, whose workers spend again. Each round is smaller, because at every round some money leaks out of the flow of spending on domestic output — saving takes a share, taxes take a share, imports take a share — and what is left circulates. Add the rounds and they converge on a total larger than the injection, and the ratio of total to injection is the multiplier. With a slope of nought point six, a hundred billion gives rounds of a hundred, sixty, thirty-six, twenty-one and a half, then about thirteen, eight, five. After ten rounds the additions are under two billion, and they sum to two hundred and fifty — the same figure the formula gives in one step. Running the rounds once is worth doing, because it is what stops the formula looking arbitrary. Three cautions. The multiplier works downward with equal force, so a collapse in confidence is magnified the same way, which is part of how a recession deepens. Its size is a tradeoff rather than a target: a high multiplier makes policy powerful but magnifies every shock, and a low one gives a steadier economy and weaker leverage, with no setting delivering both. And every number here assumes the price level holds still.

Three entries on what the model leaves out, ending with the trap in reading it literally.

How large they are in practice.

MAC 0833 How Large Are Multipliers in Practice

Measured multipliers are contested. Estimates vary with the kind of spending, the state of the economy, and the modelling assumptions. One study from two thousand and ten estimated a larger effect from spending than from tax cuts, and a Cleveland Fed commentary from two thousand and fourteen sets out why economists still disagree. The anchor's claim that certain tax cuts have a multiplier below one is one position, not a settled result.

Getting the price level back.

MAC 0834 From Expenditure to Aggregate Demand

Each expenditure line assumes one price level. Change the price level and the line moves, through unit eight's three effects, giving a different equilibrium output, and those pairs are the aggregate demand curve. A lower price level lifts the line and raises equilibrium output: one point on the curve. So a change in autonomous spending moves aggregate demand by the multiplier times the shift.

Where the price level went.

MAC 0835 Where Is the Price Level

The expenditure model has no price level and no supply curve in it. That is a deliberate simplification, and it creates a trap worth walking into on purpose. Read the model literally and it says output can be pushed to any level at all, because raising the expenditure line far enough puts the crossing anywhere you like. That reading is wrong, and it is wrong because the supply side binds: there are only so many workers, so much capital, so much technology and so much institutional capacity, and none of those appear in the model. So an inflationary gap is not a prediction that output will reach that level. It is a measure of how far spending exceeds what is needed to reach potential, and the excess comes out as a higher price level rather than as goods. Take the course's economy at potential, seven thousand billion, and add another two hundred billion of autonomous spending: the arithmetic puts the crossing at seven thousand five hundred, while unit eight's diagram says the economy is in the steep zone, so most of the movement lands on the price level. The expenditure model has given a correct measure of excess demand and an incorrect forecast of output, and both come from the same missing piece. Two cautions. Inflation is present here implicitly, through the gap, though the price level never appears in the equation — a model can carry a variable it never names. And the two models answer different questions: reach for the expenditure model for the size of a spending change, and for demand and supply when the question is what that change does to output and prices together.

Three entries on the tradeoff between inflation and unemployment, and what expectations did to it.

The curve, and where it came from.

MAC 0836 The Short-Run Phillips Curve

A nineteen fifty-eight study by A. W. Phillips of a century of British data found unemployment inversely related to wage growth, and extended to prices it became a curve trading inflation against unemployment. United States data through the nineteen sixties traced that shape, unemployment falling as inflation rose. A relationship holding for one decade in one country is a finding, not a law.

Reading movements on it.

MAC 0837 Along the Curve or a Shift

Classify a movement in inflation and unemployment as a movement along a short-run Phillips curve or a shift of it, and the test is which curve of unit eight's diagram moved. Aggregate demand moving along an unchanged short-run supply curve traces the Phillips curve. Short-run supply moving shifts the Phillips curve instead. A contractionary policy shifting demand left lowers output and the price level together, so unemployment rises and inflation falls: a movement along the curve. A sharp rise in energy prices shifts short-run supply left, so output falls while the price level rises and unemployment and inflation rise together — and no point on a single downward-sloping curve does that, so the curve itself has moved. Rising inflation means the price level is rising at an increasing rate, not merely rising; falling inflation means prices are still rising, more slowly. Reading falling inflation as falling prices turns a recovery into a deflation.

Why the tradeoff stopped holding.

MAC 0838 Why the Phillips Menu Failed

Through the nineteen sixties the curve was read as a menu: policymakers believed they could pick a combination of inflation and unemployment and use policy to reach it. The nineteen seventies destroyed that reading. Attempts to hold unemployment low produced higher unemployment and higher inflation at the same time, which no single downward-sloping curve permits, and the episodes of nineteen seventy-three to seventy-five and nineteen eighty to eighty-two are the clearest cases. Two things shift the curve, and both work by moving aggregate supply. The first is a supply shock, such as an economy-wide jump in energy prices. The second matters more: a change in what people expect inflation to be. The tradeoff holds while people expect stable prices and are caught out by rising ones; once they expect inflation and write it into wage agreements and price lists, short-run supply shifts left and the menu is gone. Trace it in three phases. Demand rises and the economy moves up an unchanged supply curve: prices run above what was expected when wages were set, real wages fall below what was intended, and inflation rises as unemployment falls. Then expectations catch up: workers negotiate for the price level they now expect, supply shifts left, output falls back and prices rise further, so unemployment and inflation rise together. Then policy responds to the new gap by raising demand again, output recovers and inflation falls. Each phase is a shift in one of two curves, and the loop is what decades of scattered data actually show. Three cautions. The short-run tradeoff survives all of this as a short-run relationship, which is why it is still taught and still tested; what failed was the claim that it offers a stable menu. Because expectations are one of the two shifters, the curve's position depends on beliefs about future policy, which policy itself changes. And this says nothing about the long run: whether the tradeoff exists at all once expectations have fully adjusted is unit ten's question, and it takes the whole unit.

Look at what you can now do. You can compare a spending change with an equal tax change, and say why the balanced-budget result equals one only in a special case. You can tell a shift of the expenditure line from a rotation, and remember that a rotation changes the multiplier itself. You can size the policy that closes a gap, dividing the gap by the multiplier, and verify it against the algebra. You can say why this model has no price level in it, and why that makes it a correct measure of excess demand and a wrong forecast of output. And you can tell a movement along a Phillips curve from a shift of it, by asking which curve of unit eight's diagram moved. Unit ten turns to what the neoclassical economists concluded from the same evidence.