Inflation, Activity, and Nominal Money Growth

Inflation, Activity, and Nominal Money Growth

The Volcker Disinflation
In October 1979, the Fed, under Paul Volcker, decided to reduce nominal money growth and decrease inflation, then close to 14% per year. Five years later, after a deep recession, inflation was down to 4% per year.

The Volcker Disinflation
How did the Fed reduce inflation? It did it by changing the relationship between inflation and unemployment It caused a recession to prove it was serious about inflation. This changed expectations of inflation.

Output, Unemployment, and Inflation
9-1 This chapter builds on three relations: Okun’s Law, which relates the change in unemployment to output growth. The Phillips curve, which relates the changes in inflation to unemployment. The aggregate demand relation, which relates output growth to both nominal money growth and inflation.

Output Growth, Unemployment, Inflation, and Nominal Money Growth

We are used to thinking in terms of AS-AD AS, which shows the effect of output on prices, is split in this chapter into two parts: Output affects unemployment through Okun’s Law. A higher growth rate of output reduces unemployment. Previously, we assumed Y = N = L(1-u), but life is richer and more complicated. Unemployment affects inflation through the Phillips Curve. A lower unemployment rate causes inflation to rise.

We are still using AD. Higher prices lower output demanded. Suppose the Central Bank increases the nominal money supply at a constant, positive rate = 5%. Inflation = 3%, so the rate of growth of real money supply is 2% = 5% – 3%. Suppose inflation rises unexpectedly to 4%. Then the real money supply will rise more slowly, at 1% per year. Higher inflation reduces the rate of growth of real money, which reduces the output growth rate.

Okun’s Law: From Output Growth to Unemployment

If output grows, unemployment should fall, right? Assume Y = N Y = L – U. Yt – Yt-1 = (Lt – Lt-1) – (Ut – Ut-1) Assume the labor force doesn’t grow (Lt – Lt-1=0). Then Yt – Yt-1 = – (Ut – Ut-1)

Yt – Yt-1 = – (Ut – Ut-1) This also implies that the unemployment rate (u) is negatively related to the output growth rate (g): We’ve made a lot of assumptions: no inputs besides labor, no diminishing returns Particularly, we assumed no changes in labor productivity, constant labor force, etc.

The change in the unemployment rate could be equal to the negative of the growth rate of output. For example, if output growth is 4%, then the unemployment rate should decline by 4%. Now, let’s be more realistic.

The actual relation between output growth and the change in the unemployment rate is known as Okun’s law. This relation allows for more realistic production functions, labor market behavior, etc. Particularly, it allows for changes in labor productivity, and a growing labor force, etc, so the economy can be expected to be growing constantly.

Changes in the Unemployment Rate Versus Output Growth in the United States, High output growth is associated with a reduction in the unemployment rate; low output growth is associated with an increase in the unemployment rate. Using thirty years of data, the line that best fits the data is given by:

Okun’s Law Across Countries
The coefficient β in Okun’s law gives the effect on the unemployment rate of deviations of output growth from normal. A value of β of 0.4 tells us that output growth 1% above the normal growth rate for 1 year decreases the unemployment rate by 0.4%. Table 1 Okun’s Law Coefficients Across Countries and Time Country β β United States 0.39 United Kingdom 0.15 0.54 Germany 0.20 0.32 Japan 0.02 0.12

According to the equation above,

To maintain the unemployment rate constant, output growth must be 3% per year. This growth rate of output is called the normal growth rate. Output growth 1% above normal leads only to a b%<1 reduction in unemployment.

Output growth 1% above normal leads only to a b%<1 reduction in unemployment, for two reasons: Labor hoarding: firms prefer to keep workers rather than lay them off when output decreases. When employment increases, not all new jobs are filled by the unemployed. Because some workers are hired away from other jobs rather from the unemployed, the number of the unemployed decreases slowly.

Output growth above normal leads to a decrease in the unemployment rate. If output grows below normal, the unemployment rate. Increases. This is Okun’s law:

Assume ut-1 = 6% gyt 4% 5% 6% ut gyt 2% 1% 0% ut gyt 3% ut

The Phillips’s Curve: From Unemployment to Inflation

The Phillips Curve: From Unemployment to Inflation
Inflation depends on expected inflation and on the deviation of unemployment from the natural rate of unemployment. Suppose et is well approximated by t-1. Then: The Phillips curve implies that

The Aggregate Demand Relation From Nominal Money Growth and Inflation To Output Growth

The Aggregate Demand Relation: From Nominal Money Growth and Inflation to Output Growth
If the IS curve is And the LM curve is Then the AD curve is Aggregate Expenditure depends on all sorts of parameters (the c’s, the b’s, the d’s, t, and G), positively on M and negatively on P.

More simply, we can say that Even more simply, suppose that changes in output are caused only changes in the real money stock, then:

Let’s put this in terms of growth rates: gyt = (Yt-Yt-1)/Yt-1 gmt = (Mt-Mt-1)/Mt-1 p = (Pt-Pt-1)/Pt-1 And since g is a parameter (gt-gt-1)/gt-1=0. From this we can derive

How do we go from to ? The easiest way is to use logarithms and calculus: Log Y = log (gM/P) Log Y = log g + log M - log P Taking a total derivative

In terms of the growth rates of output, money, and the price level: According to the aggregate demand relation: Given inflation, expansionary monetary policy leads to high output growth.

Assume pt = 3% gmt 7% 5% 3% 1% gyt Assume gmt = 6% pt 6% 4% 2% gyt

The Three Relations Okun’s Law Phillips Curve AD Relation

9-2 The Medium Run

The Medium Run In chapter 6 we defined the medium run as the time when Pe=Pt-1=Pt. This meant that there was no reason for Pe to change. No changes in Pe meant that the WS would stay put, yielding a “steady-state”, medium-run level of unemployment, the natural rate of unemployment.

The Medium Run The medium run: Pe=Pt-1=Pt.
In growth rates rather than levels, t = e. Then, by the Phillips curve, u = un. So inflation is constant. Because un is constant, so is unemployment.

The Medium Run Inflation is constant.
Because nominal money growth is a policy variable, it changes exogenously and it is more natural to imagine that its constant. Then, by the aggregate demand curve, output growth must be constant.

The Medium Run Is this constant equal to which is normal output growth? It has to be. If it weren’t, u would have to be changing, which is inconsistent with u = un.

The Medium Run t = t-1. ut = ut-1. For any level of gm. t = e.
ut = un . For any level of gm.

The Medium Run Alternatively, Start by assuming that
This makes sense as a definition of the medium run because we want the MR to be a time of rest, stability, constancy.

The Medium Run So Okun’s Law implies that output grows at its normal rate.

The Medium Run Assume nominal money growth is
We know output growth is equal to its normal rate Then the aggregate demand relation ( ) implies that inflation is constant:

The Medium Run According to the equation above, in the medium run, inflation equals the difference between nominal money growth and normal output growth. Call adjusted nominal money growth.

The Medium Run If inflation is constant, then t = t-1,
if this is true, the Phillips curve implies that ut = un. Therefore, in the medium run, the unemployment rate must equal the natural rate of unemployment.

The Medium Run Changes in nominal money growth have no effect on output or unemployment in the medium run, because in the medium run ut = un and , and neither un nor normal output growth depend on the money supply. So changes in nominal money growth must be reflected one for one in changes in the rate of inflation.

The Medium Run Inflation and Unemployment in the Medium Run In the medium run, unemployment is equal to the natural rate of unemployment, at any level of inflation.

The Medium Run Inflation and Unemployment in the Medium Run In the medium run, inflation is equal to adjusted nominal money growth.

The Medium Run Inflation and Unemployment in the Medium Run In the medium run, a decrease in adjusted nominal money growth reduces inflation at the same level of unemployment.

The Medium Run Suppose In the medium run, gyt = ut = pt =
Adjusted money growth =

From the Short Run to the Medium Run

Above we defined Okun’s Law as “Unemployment falls if output grows above the normal growth rate of output.” But other authors define it as “Cyclical unemployment arises if if output grows below the normal growth rate of output.”

If we use this definition of Okun’s Law And we remember that the Phillips curve is Then we can write an “Inflation Adjustment” curve. It will say that inflation rises when output is above normal.

An “Inflation Adjustment” curve. It says that inflation rises when output is above normal. Okun’s Law Phillips’ Curve Inflation-Adjustment curve

An “Inflation Adjustment” curve
Higher output growth reduces unemployment and increases inflation. IA ab If gyt = gy, pt=pe pe - abgy

The Aggregate Demand curve. (For a given rate of nominal money growth), The AD curve says that if inflation rises, the real money supply grows more slowly. This raises interest rates, lowers the growth rate of spending, and lowers the growth rate of actual real output.

The Aggregate Demand curve
gmt Higher inflation reduces the real money supply and reduces real output growth. AD

IA = OL + PC AD IA At point A, output growth is below the natural rate of output growth, and inflation is below expected inflation. A AD

IA AD IA In the short-run, pt<pe. IA In the medium-run, wage-setters will lower their expectations of inflation, which shifts the IA curve down. A This happens until gyt = gy. AD

Imagine the Central Bank shifted the AD curve up repeatedly by raising gmt in order to get short-run reductions in unemployment. IA AD In the medium-run, the IA curve will shift up over and over, keeping gyt = gy. gyt = gy means that u=un, At any level of gmt and pt.

In the medium run, pt=pe The short-run relation between output growth and inflation disappears and the IA equation becomes While AD determines inflation. AD

In the short run, Aggregate demand influences output: output grows faster if inflation is below nominal money supply growth. Inflation adjusts upward if output grows above the normal rate. In the medium run, Expectations of inflation adjust so and u=un. AD only determines inflation.

The Medium Run Inflation and Unemployment in the Medium Run In the medium run, a decrease in adjusted nominal money growth reduces inflation at the same level of unemployment.

The Medium Run Suppose The CB changes In the medium run, gyt = ut =
pt = Adjusted money growth =

The Effects of Money Growth

Okun’s law relates the change in the unemployment rate to the deviation of output growth from normal: The Phillips curve relates the change in inflation to the deviation of the unemployment rate from the natural rate: The aggregate demand relation relates output growth to the difference between nominal money growth and inflation.

Output Growth, Unemployment, Inflation, and Nominal Money Growth

The Medium Run Assume that the central bank maintains a constant growth rate of nominal money, call it In this case, the values of output growth, unemployment, and inflation in the medium run: Output must grow at its normal rate of growth, If we define adjusted nominal money growth as equal to nominal money growth minus normal output growth, then inflation equals adjusted nominal money growth. The unemployment rate must equal to the natural rate of unemployment.

The Short Run Now suppose that the central bank decides to decrease nominal money growth. What will happen in the short run? Given the initial rate of inflation, lower nominal money growth leads to lower real nominal money growth , and thus to a decrease in output growth. Now, look at Okun’s law, output growth below normal leads to an increase in unemployment. Now, look at the Phillips curve relation. Unemployment above the natural rate leads to a decrease in inflation.

The Short Run In words: In the short run, monetary tightening leads to a slowdown in growth and a temporary increase in unemployment. In the medium run, output growth returns to normal, and the unemployment rate returns to the natural rate. Table 9-1 The Effects of Monetary Tightening Year 0 Year 1 Year 2 Year 3 1 Real money growth % (gm-π) 3.0 0.5 5.5 2 Output growth % (gy) 3 Unemployment rate % (u) 6.0 7.0 4 Inflation gate % (π) 5.0 4.0 5 Nominal money growth % (gm) 8.0 4.5 9.5

9-3 Disinflation

Disinflation To achieve lower inflation, the rate of nominal money growth must be reduced. This implies a (possibly long) transition between one “medium-run” equilibrium and another “medium-run” equilibrium. This transition happens in the short run, so the downward sloping (Original) Phillips Curve becomes relevant again. Disinflation moves the economy (in the short run) along the short-run (Original) Phillips Curve. In the medium run, Unemployment above natural causes a shift down of the Phillips curve, until unemployment = un in the medium run.

The Medium Run Inflation and Unemployment in the Medium Run In the medium run, inflation is equal to adjusted nominal money growth.

Disinflation Inflation and Unemployment in the Medium Run
In the short run, inflation is decreased by increasing unemployment. In the medium run, higher unemployment and lower inflation cause a fall in expected inflation and a shift down of the SR Phillips Curve. Decrease in expectations of inflation.

Disinflation To achieve lower inflation, the rate of nominal money growth must be reduced. Here is what happens in the Short Run: In the aggregate demand relation, Then, from Okun’s law, Finally, according to the Phillips curve relation: Notice that now u > un.

Disinflation But over time, in the Medium Run,
According to the Phillips curve relation: As p falls, it falls far enough below gm. In the aggregate demand relation, Eventually gy rises enough that gy > gy. Then, from Okun’s law, After a decrease in nominal money growth, unemployment first increases, but eventually it starts decreasing.

Working Out the Path of Nominal Money Growth
Table Engineering Disinflation 1 2 3 4 5 6 7 8 Inflation (%) 14 12 10 Nominal money growth (%) 17 13 11 9 Output growth (%) 2 Unemployment rate (%) The Central Bank wants to cut inflation from 14% to 4%. To do this, it cuts nominal money growth radically, which reduces output growth and increases unemployment. Inflation gradually falls.

How Much Unemployment? and for How Long?
In the Phillips curve relation above, disinflation—a decrease in inflation—can be obtained only at the cost of higher unemployment.  

Do we have any idea of the amount of unemployment we must inflict on an economy to reduce the inflation rate? Are there measures of this sacrifice? What are the determinants? How should we design disinflation programs?

For example, let’s assume that  =1/2 Then reducing inflation by 10 percentage points requires increasing unemployment above the natural rate by 20 percentage points over a number of years: Notice that while the left-hand side is a year-per-year change, the right-hand side is just the difference between two variables, one of which doesn’t change with time.

If  =1/2, reducing inflation by 10 percentage points requires 20 percentage points of excess unemployment over a number of years: Suppose we want to achieve the disinflation over 5 years: then we need 5 years of unemployment at 4 percentage points above the natural rate. Achieving the disinflation over 10 years means 10 years of unemployment at 2 percentage points above the natural rate.

If  =0.8, reducing inflation by 10 percentage points requires 12.5 percentage points of excess unemployment over a number of years: Achieving the disinflation over 2 years means 2 years of unemployment at 6.5 percentage points above the natural rate. Achieving the disinflation over 25 years means 25 years of unemployment at 0.5 percentage points above the natural rate.

A point-year of excess unemployment is a difference between the actual and the natural unemployment rate of one percentage point for one year. So if  =1/2, reducing inflation by 10 percentage points requires 20 points-years of excess unemployment. If  =0.8, reducing inflation by 10 percentage points requires 12.5 points-years of excess unemployment :

The sacrifice ratio (=1/a) is the number of point-years of excess unemployment needed to achieve a decrease in inflation of 1%. For example, if the sacrifice ratio is 1.32, then a 10% disinflation requires 13.2 point-years of excess unemployment.

If inflation is a bad thing and the number of point-years of excess unemployment is unchangeable (because a is fixed), why not “get it over with” in one year? At the very temporary cost of high unemployment. This policy would have the great benefit of full credibility: there’s no need to wonder if the disinflation program will continue. This works if the announcement of the policy immediately changes pe.

But if pe = pt-1, then seeing is believing, and you need at least two years. Moreover, the output loss could be huge, by Okun’s Law. Many of the effects of the recession would be permanent: discouraged workers, bankruptcies, political instability, etc.

Suppose the Central Bank wishes to reduce inflation by 9%. If a = 1.15, what is the number of point-years of excess unemployment? Given the goal of reducing inflation by 9%, can the Central Bank affect the number of point-years of excess unemployment calculated above? a 1.5 1.3 1.15 1 0.9 Sacrifice ratio

An important question for policy makers is what is the optimal path of money growth to achieve a disinflation. This is worked out in this way: The path of inflation shows the values of inflation before achieving a desired 4%. The path of unemployment shows the unemployment required to achieve the decrease in inflation.

The path of output shows the output growth required to achieve the required path of unemployment. The path of nominal money growth shows the growth required to achieve the required path of output.

Table Engineering Disinflation 1 2 3 4 5 6 7 8 Inflation (%) 14 12 10 Nominal money growth (%) 17 13 11 9 Output growth (%) 2 Unemployment rate (%) This table shows the path of nominal money growth needed to achieve 10% disinflation over five years, which we assume requires 10 point-years of excess unemployment. That is, u > un by 2 points every year for 5 years.

Table Engineering Disinflation 1 2 3 4 5 6 7 8 Desired path of Inflation (%) 14 12 10 Unemployment rate (%) Output growth (%) Nominal money growth (%) 17 a=1

Table Engineering Disinflation 1 2 3 4 5 6 7 8 Inflation (%) 14 12 10 Nominal money growth (%) 17 13 11 9 Output growth (%) 2 Unemployment rate (%) If (Okun’s Law) , then gy must fall by 5 points the first year (2 / (-0.4)) = -5 below normal growth, from 3 to -2 percent. Raising unemployment by 2 points means lowering inflation by 2 points. Because , -5 = Dgm – (– 2), then Dgm = – 7. 1

Table Engineering Disinflation 1 2 3 4 5 6 7 8 Inflation (%) 14 12 10 Nominal money growth (%) 17 13 11 9 Output growth (%) 2 Unemployment rate (%) The second year, ut=ut-1. By Okun’s Law, gy must go back to normal growth, 3%. Because still u – un = 2 points, inflation falls by by 2 points, to 10%. From the AD relation , = Dgm – (-2), then Dgm = 3. 2

Notice that although money growth rises in year 7, inflation does not : the reason is that unemployment goes back to its natural level.

A Disinflation Path Five years of unemployment above the natural rate of unemployment lead to a permanent decrease in inflation. This figure shows a path of unemployment and inflation similar to the disinflation path in Table 9-1.

Credible Disinflation causes the Phillips curve to shift down. But remember what determines the position of the Phillips curve: expectations of inflation. If expectations change, this works. If they don’t it doesn’t.

Expectations, Credibility, and Nominal Contracts
9-4 This section examines how changes in expectation formation might affect the unemployment cost of disinflation. Two separate groups of macroeconomists challenge the traditional notion that policy can change the timing, but not the number of point-years of excess unemployment.

Expectations and Credibility: The Lucas Critique
The Lucas critique states that it is unrealistic to assume that wage setters would not consider changes in policy when forming their expectations. If wage setters could be convinced that inflation was indeed going to be lower than in the past, they would decrease their expectations of inflation, which would in turn reduce actual inflation, without the need for a change in the unemployment rate.

Thomas Sargent, who worked with Robert Lucas, argued that any in order to achieve disinflation, any increase in unemployment would have to be only small. The essential ingredient of successful disinflation, he argued, was credibility of monetary policy—the belief that the central bank was truly committed to reducing inflation. The central bank should aim for fast disinflation.

Recall that, although we assumed the Phillips curve can be approximated by it is really Our calculations assumed that agents didn’t form expectations based on policy, just on history. What if policy were fully credible, so that if the CB announces a future p =4%, pe becomes 4%, wage-setters set their nominal wage increase at 4%, and price-setters set price increases at 4%. Inflation becomes 4% instantaneously, and u=un.

Which program is more credible, taking into account political pressures, elections, etc.? A disinflation that happens in one year (say, the first year out of a 4-year presidential period), and then you’re done with it? Or a disinflation that is announced to start today and end in 20 years?

If the Central Bank is so credible that its ultimate forecasts of inflation are believed, inflation expectations fall right away to their final level. 1

Normal Rigidities and Contracts
A contrary view was taken by Stanley Fischer and John Taylor. They emphasized the presence of nominal rigidities, or the fact that many wages and prices are not readjusted when there is a change in policy. If wages are set before the change in policy, inflation would already be built into existing wage agreements.

Taylor argued that the staggering of wage decisions imposed strong limits on how fast disinflation could proceed. The way to decrease the unemployment cost of disinflation is to give wage setters time to take the change in policy into account. “Inflation won’t change much over the next year or two (to avoid costs in output). But in two years, inflation will begin to fall drastically.” If the government makes this announcement, how would you negotiate your wages? Slow but credible disinflation might have a lower cost. The central bank should go for slow disinflation. If inflation ain’t changin’, why should we believe it will?

Disinflation Without Unemployment in the Taylor Model With staggering of wage decisions, disinflation must be phased in slowly to avoid an increase in unemployment.

The U.S. Disinflation, 9-5 What did happen in the early eighties? The U.S. disinflation of the early 1980s was associated with a substantial increase in unemployment. The Phillips curve relation proved more robust than many economists anticipated.

The U.S. Disinflation, Table Inflation and Unemployment, Percent 1979 1980 1981 1982 1983 1984 1985 GDP growth 2.5 0.5 1.8 2.2 3.9 6.2 3.2 Unemployment rate 5.8 7.1 7.6 9.7 9.6 7.5 7.2 CPI inflation 13.3 12.5 8.9 3.8 Cumulative unemployment 1.0 2.6 6.3 9.9 11.4 12.6 Cumulative disinflation 0.8 4.4 9.5 9.4 Sacrifice ratio 1.25 0.59 0.66 1.04 1.21 1.32 Cumulative unemployment is the sum of point-years of excess unemployment from 1980 on, assuming a natural rate of unemployment of 6%. Cumulative disinflation is the difference between inflation in a given year and inflation in The sacrifice ratio is the ratio of cumulative unemployment to cumulative disinflation.

The U.S. Disinflation, The Federal Funds Rate and Inflation, A sharp increase in the interest rate from September 1979 to April 1980 was followed by a sharp decline in mid 1980, and then a second and sustained increase from January 1981 on, lasting for most of 1981 and 1982.

The U.S. Disinflation, Laurence Ball, who examined 65 disinflation episodes concluded that: Disinflations typically lead to a period of higher unemployment. This contradicts a radical version of Lucas/Sargent. Faster disinflations are associated with smaller sacrifice ratios. This supports a moderate version of Lucas/Sargent. Sacrifice ratios are smaller in countries that have shorter wage contracts. This supports Fischer/Taylor.

Inflation, Activity, and Nominal Money Growth

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