Download Notes Inflation and Interest Rates in the Medium Run

Notes Inflation and Interest Rates in the Medium Run Point of the class Math •
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manipulating an equation algebraically manipulating graphs Model building •
Using previous models to develop insight Economic concepts and intuition •
Determination of output, inflation and unemployment in the short‐run and the medium‐run Definitions •
Sacrifice ratio •
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Staggered wage contracts Point years of excess unemployment Homework Problems On the webpage. credibility •
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Facts [M]any of the hawks [people who think the Fed should do more to fight inflation] do not just differ in their outlooks [their
perceptions of future inflation], but in how monetary policy works. The conventional view, shared by Mr. Bernanke,
Donald Kohn, his influential vice-chairman, and their professional staff, is that monetary policy affects inflation via its
impact on the real economy.
Higher interest rates reduce demand relative to the economy’s potential to supply goods and services. Reduce it enough,
and unused slack will accumulate, forcing firms and workers to compete for scarce customers and jobs by lowering prices
and wages. The opposite happens when demand rises relative to supply.
This relationship is captured in the Phillips curve, which shows inflation falling when unemployment is above its natural
rate. In this view, it does not matter whether it is monetary policy or a credit crunch that raises unemployment: both put
downward pressure on inflation. What is more, Mr Bernanke and his colleagues reckon today’s low fed funds rate is
merely offsetting tighter financial conditions from the credit crunch.
The hawks, by contrast, think that unemployment and other measures of “economic slack” have limited bearing on the
transmission of monetary policy. Fed actions affect inflation primarily by altering inflation expectations. They worry that a
low funds rate in itself threatens to lift inflation, and rising unemployment and the credit crunch will do little to contain it.
The Economist, When hawks cry, Sep 11th 2008, http://www.economist.com/finance/displaystory.cfm?story_id=12209639 Model Building Building Blocks The medium run is defined as the period of time when inflation expectations and actual inflation are equal. The Phillips Curve is Okun’s Law is or Aggregate Demand‐Inflation curve is 1
So, for any given period, the level of output is determined by the amount of spending by households, firms, government, etc.; by the size of the money supply, and by the inflation rate. So the change in output be determined from year to year (in the short run and in the medium run) should •
by the change in the amount of spending (which we’ll ignore from now on); •
by the change in the size of the money supply •
by the inflation rate . ∆
, and ∆
∆
Nominal Money Growth Aggregate Demand Output Growth Okun’s Law Inflation Unemployment
Phillips Curve Putting the Building Blocks Together Medium Run 1. In the medium run, expectations of inflation are met, . By the Phillips Curve , this means that, unemployment equals the natural rate of unemployment, Medium‐run Phillips Curve This combines the Phillips Curve with the definition of the medium . run, u
2. In the medium run, output is at the natural level of output, . What determines the rate of growth of the natural level of output? The Solow Model (chapter 11) says that long‐run output growth depends on •
productivity growth greater availability of resources, particularly labor and capital 12
Trillions of $
Neither the rate of growth of money supply nor inflation play any role in medium‐run output growth. 11
10
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Real GDP
, then that has to be the growth rate of actual output. 2005
2003
2001
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2
1
Real GDP
The Aggregate Demand‐Inflation curve implies that at any point in time, output, money, and inflation are related: 2005
1995
0
2003
∆
5
growth rate, %
∆
Potential GDP
2001
∆
1999
natural level of output is growing at 1999
And if is growing, then has to be growing at the same pace. If the 1997
1995
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1997
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Potential GDP
However, in the medium run, the growth rate of (the natural level of) output does not depend on money growth or inflation. And money growth is exogenous. Then it must be the case that . inflation is fully determined by and by So at any point in time, the level of inflation is And in the medium run This combines the AD‐π curve with medium‐run economic growth, . Medium‐run inflation is determined by the rate of growth of the money supply and the growth rate of the natural level of output. Medium‐run inflation will be higher if money supply is growing faster; and it will be smaller if the natural level of output is growing more quickly. In other words medium‐run inflation will be o
o
. higher if the money supply grows more quickly ƒ In the medium run, the level of inflation is closely connected to the rate of growth of money supply. “Inflation is always and everywhere a monetary phenomenon” applies in the medium run. higher if the medium‐run supply of goods (the natural level of output) grows more . slowly Aggregate Demand at u
Medium run equilibrium is determined by the intersection of these two curves. Suppose that the growth rate of the natural level of output rises . Then, in the medium run, inflation should fall. Medium‐run Phillips Curve
A
Aggregate Demand at B
u
Examining the Result and Using the Model AS‐π Short Run in AD­AS The above implies that the monetary authority can pretty much pick its preferred level of inflation by changing the rate of growth of money supply. A Suppose the economy starts at the medium run. Call it equilibrium “A”. Then the Central Bank reduces : there’s a monetary contraction because the Central Bank slows down the pace at which it increases money supply. AD‐π The graph to the right illustrates one such situation. In 1978, the Fed reduced drastically the rate at which money supply grew. Money supply kept growing (the graph above), but much more slowly. If money demand doesn’t change, then interest rates will rise. This will reduce investment and equilibrium short‐run output growth, , shifting the AD‐π curve to the left. If the natural level output keeps growing at the same pace, the reduction in the growth rate of actual output leads to a recessionary gap . This raises unemployment above the natural rate of unemployment by Okun’s Law . Higher unemployment lowers , by inflation below expected inflation the Phillips Curve. The economy moves along the AS‐π curve to point “B”. Another way of seeing this is to say that because people are expecting an unrealistically high level of inflation, they are asking for relatively fast wage raises. Since firms can’t quite afford that (as they can’t raise prices that fast ‐ inflation is relatively low), some firms go bankrupt and/or lay workers off. As unemployment AS‐π B
AD‐π
rises, other firms are able to “convince” workers not to be so insistent and to accept lower wage raises. Inflation falls, but not as much as the decline in nominal money supply , so the real money supply contracts. Output doesn’t fall by a much as the decline in nominal money supply, but it does decline. AS‐π A B
AD‐π Medium Run in AD­AS C Over time, people realize what’s happening. As inflation turns out to be much lower than they expected (and unemployment much higher than normal), they begin to lower their expectations of inflation and their wage raise requests. First, they set their new so that it is equal to the actual . Firms recover profitability and are even able to lower their inflation rate ( ): AS shifts. A lower inflation rate means a higher level of real money supply, which leads to lower interest rates and higher output, moving along the AD curve. Eventually, inflation falls enough to bring output back to the natural level of output. The economy reaches a new medium‐run equilibrium at point “C”. If output returns to the natural level, it must be taht falls by as much as fell. In the medium run, output returns to the natural level of output and the disinflation is accomplished. That is how the economy moves from medium run to medium run. The Short Run Phillips Curve We can also think through this in terms of what happens to the Short Run Phillips Curve. The monetary authority engineers a monetary contraction, raising unemployment. As unemployment falls below the natural rate of unemployment, inflation falls. In time, as people realize that inflation is lower than they had expected, expected inflation falls. This causes the intercept of the Phillips Curve to become smaller, and the Phillips Curve shifts down. As the economy adjusts, output returns to the natural level of output and unemployment falls back to the natural rate of unemployment. Phillips Curve Phillips Curve A B C
u
u
The Short Run Phillips Curve plus AD­Okun’s Law A nice way of really seeing what happens is to combine the aggregate demand curve (solving for inflation; in the short run) with Okun’s Law, expressed in growth‐rate terms. In the medium run, and , and Okun’s Law is 0 on both sides. Okun’s Law only makes sense in the Short Run, so we can use it to study the short run. So, first, solve OL for . 1
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AD+OL
Then plug the result into AD 1
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u
This gives us a graph like the one to the right. We combine OL with AD and get a positive relation between unemployment and inflation: higher unemployment lowers output and increases inflation, for a given level of money growth. Remember that inflation is “too much money chasing too few goods”. What this OL+AD curve tells us is that a) if we don’t hire many workers, too few goods are produced; b) if too few goods are produced and the amount of money is the same, inflation will rise. (exogenously). This So, what happens when there’s a disinflation? The Central Bank lowers means that the AD+OL curve shifts down (as the intercept becomes smaller). If the economy’s short run equilibrium is where the Phillips Curve and AD+OL intersect, then inflation falls and unemployment rises. Notice inflation is above in the middle of a disinflation, but it’s always equal to . The reason for this is that, in the middle of a disinflation, . Eventually, lower inflation causes expected inflation to fall and the Phillips Curve shifts down. The economy returns to medium‐run equilibrium with unemployment at its natural rate, and inflation equal to . PC PC
AD+OL AD+OL A A B B C
u
u
The Medium Run Phillips Curve If we just look at medium‐run pictures (without bothering to think about the transition), the picture looks like this (remember Okun’s Law doesn’t work in the medium run, so we are just intersecting medium‐run PC with AD at ). Medium‐run Phillips Curve
A
Aggregate Demand at B
u
1. In the medium run, since the natural rate of unemployment hasn’t changed, the Medium‐
Run Phillips Curve is vertical at the same place. 2. In the medium run, the growth rate of the natural level of output, , hasn’t changed. But since the rate of growth of money supply, , is smaller, the medium‐run inflation rate is lower. Extending the Model How much does unemployment have to rise to bring inflation down? We can measure this by the “sacrifice ratio”. Consider the Phillips Curve Traditional Approach Suppose we want to change inflation by a particular amount. We know lowering inflation means increasing unemployment above the natural rate: that is, generating cyclical unemployment. How much? Label the desired change in inflation ∆ . ∆
∆
0. Then doesn’t change, ∆
If ∆
∆
∆
Then ∆
Suppose that 0.5, and we want to reduce inflation by 3 percentage points, ∆
3. Then 6 .
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unemployment has to be 6 percentage points above the natural rate during one year; or unemployment has to be 3 percentage points above the natural rate during two years; or unemployment has to be 2 percentage points above the natural rate during three years; or unemployment has to be 1 percentage point above the natural rate during six years. 1
∆
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Expectations and Credibility Robert Lucas and Thomas Sargent argued that if the monetary authority changes not only the rate of growth of money, but expectations of inflation (by telegraphing the future path of monetary policy, perhaps), it can reduce the sacrifice ratio significantly. If the Central Bank has enough credibility as an inflation fighter, it can bring inflation down with little pain. What if the announcement of the Central Bank’s plans is so credible that ∆
∆
∆
∆
falls immediately? ∆
∆
∆
We can see that the necessary cyclical unemployment will be less if expected inflation falls. So suppose that 0.5, and we want to reduce inflation by 3 percentage points, ∆
3, and falls 2. Then by 2 percentage points, ∆
∆
∆
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2 0.5
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unemployment has to be 2 percentage points above the natural rate during one year; or unemployment has to be 1 percentage point above the natural rate during two years 2
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Nominal Rigidities and Contracts Often, even if people change their expectations of inflation, the wage contracts are written so that it’s not possible to change very quickly, so inflation cannot fall very quickly. In particular, wages are renegotiated at different times in the year: they are staggered. It would take a huge amount of unemployment to bring inflation down quickly. To prevent this, one has to wait until wage contracts are changed. Stanley Fischer and John Taylor argued that the path of inflation ought to be more like this: The monetary authority announces its intentions to follow this path at time 1, and over time workers adjust their wage requests to match the announced path. The problem is that people might not believe a monetary authority’s intention to reduce inflation if inflation takes years and years to come down. Empirical Evidence The disinflation of the 1980s created 12 point‐years of excess unemployment, along the lines of the Traditional Approach. 1. Disinflations typically are accompanied by higher unemployment (supports traditional). 2. Faster disinflations have smaller increases in unemployment (supports Lucas‐Sargent). 3. Sacrifice ratios are smaller in countries with shorter wage contracts (Supports Fischer‐
Taylor). Nominal and Real Interest Rates in the Short­Run and in the Long­Run Assume the economy starts at . Then the Central Bank raises the rate of growth of money supply. We know that in the short run, higher money supply growth shifts the AD+OL curve up, leading to lower unemployment and higher inflation. (In terms of our Chapter 7 analysis, it shifts AD to the right, pushing output above the natural level; output growth is faster than the normal rate.) PC AD+OL
B AS‐π A B
AD’‐
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AD‐π u
Inflation rises, but it doesn’t rise by very much because expectations of inflation are fixed. Unemployment falls below the natural rate of unemployment (and output goes above the natural level of output) pushing inflation above expected inflation. In the medium run, when expectations of inflation rise too, inflation will rise by more. Then unemployment rises back to the natural rate and output falls back to the natural level; output growth is equal to the normal rate. PC C
B AS’‐π AD+OL
AS‐π A C
B
AD’‐
A AD‐π u
Sticky Inflation This means that in the short run, inflation is somewhat sticky. Expectations of inflation don’t change very fast, so inflation doesn’t move a whole lot in response to changes in output. In the medium run, inflation is flexible, so inflation adjusts fully. By how much? •
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In the medium run, output doesn’t change. By the AD‐inflation curve, the real money supply must go back to the original level. This only happens if, in the medium run, prices rise by as much as the nominal money supply. o That is, if inflation rises as much as But inflation is slow to adjust. Then, when inflation begins to move, it has to speed up at first above the new rate of growth of money supply, and then come back to the original speed. o
Imagine a car race in which car A starts at 100 miles per hour while car B is slow to start, starting at only 80 mph. The only way car B can catch up with car A is by first speeding up to, say, 120 mph, and then, once it’s level with car A, slowing to 100 mph. % Money Supply growth rate, % Inflation rate, %
B
C
A time Nominal Interest rates If then is constant (points A, B, and C) If then falls (between A and B) If then rises (between B and C) •
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At the beginning, sticky inflation fails to catch up with the new, higher rate of growth of money supply. Nominal interest rates fall. Lower interest rates cause output to be higher than the natural level of output, so inflation rises ), and nominal interest rates stop falling. and rises until it catches up (
However, nominal interest rates have stopped falling but at a low level. Output is still higher than the natural level of output, so inflation keeps rising. and nominal interest rates rise. They keep rising until they get output to fall back Now to the natural level of output. again, now to stay. As output falls, inflation slows down. Eventually Real Interest Rates In the first few months, because inflation changes just a little bit, real interest rates fall a little bit more than nominal interest rates. Remember What happens afterwards? In the long run, output goes back to the natural level of output. What happens to medium‐run real interest rates? In the case of an expansion in spending (e.g., government spending), in the medium run output goes back to the natural level, but medium‐run interest rates change. The reason is that a change in spending at any level of output implies a change in saving. Imagine i
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The government decides to spend more but leave taxes alone. It will borrow more, at any level of private saving Real interest rates (the real cost of borrowing) will rise. •
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LM Curve
IS Curve
So changes in saving and investment change the real interest rate.1 Y
Yn
On the other hand, consider the case of a monetary expansion. Nothing happens in the medium run to the levels of consumption, investment, government spending, or net exports. Therefore, in the case of a monetary expansion, nothing happens to the real interest rate in the long run. There are two possibilities. 1. Money supply rises, but the growth rate of money supply doesn’t rise (it’s a one‐off increase). a. In the medium run prices rise as much as the money supply. b. Expected inflation doesn’t rise (its’s only a one‐off increase in money supply, so prices grow but inflation goes back to the original level). c. The LM curve shifts back to where it started and nominal interest rates go back to the original level. 2. The growth rate of money supply rises. a. In the medium run prices rise as much as the money supply. b. Expected inflation eventually rises, in the medium‐run, to match the growth rate of money supply (to keep nominal interest rates from constantly changing). c. Because nothing happens to the real interest rate in the long run, if expected inflation rises, the change in nominal interest rates must equal the i change in expected inflation. LM Curve
In the case of a monetary expansion, nothing happens to the real interest rate in the long run. •
At the beginning, as sticky inflation fails to catch up with the rate of growth of money supply and nominal interest rates fall, real interest IS Curve
Y
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The quantity of investment and the quantity of saving must equal in equilibrium . If government spending rises, real interest rates will rise, households will want to increase the quantity of saving, and firms will find borrowing more expensive, and will reduce the quantity of investment. Y
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rates fall too, by a little more than the fall in nominal rates. Because inflation keeps rising, real interest rates keep falling even after nominal interest rates have stopped and even begun to rise. As nominal rates rise, real interest rates also begin to rise (but more slowly, because expected inflation rises). In the medium run, real interest rates must go back to the original level and expected inflation must equal the new rate of growth of money supply. So nominal interest rates equal their sum.