This appendix shows how to go from the relation between the price level, the expected price level and the unemployment rate given by equation (8.1)
P = Pc( 1 + д)( 1 - «0 + z)
(8A.I)
to the relation between inflation, expected inflation and the unemployment rate given by equation (8.2):
77 = if + (p. + z) - ttu
First, introduce time subscripts for the price level, the expected price level and the unemployment rate, so Pt, Iх, and u, refer to the price level, the expected price level and the unemployment rate in year t. Equation (8.1) becomes
P, = Pf (1 + M)d - 'Щ + z)
Next, go from an expression in terms of price levels to an expression in terms of inflation rates. Divide both sides by last year's price level, Pt_i:
+ М)<1 ~ «М, + z)
THF NATURAL RAI L OF UNtMPLOYMFNT ANDTHF PHILLIPS CURVE
chapter 8
Rewrite the fraction Pt/P,_i on the left side as
P, P, ~ P,-t + P;-1 . P, ~ PM . 7— = p =1 + —r~— = >+Щ
г,-1 г,_1 г
where the first equality follows from adding and subtracting P,.t in the numerator of the fraction, the second equality follows from the fact that P,_i/P, 1 = 1, and the third follows from the definition of the inflation rate (тт, = (Р,- Pm)/PM).
Do the same for the fraction P°,IP, , on the right side, using the definition of the expected inflation rate
(~,c = (Pc,-P,-,)/P1 1):
Jj_ f", ~ P, i + Рм 1 1 ~ P.-1 ^ Pt-1 pt-i P(1
Replacing P,/P, , and P,'/P, ! in equation (8A.I) by the expressions we have just derived:
(1 + 7Гг) = (1 + 7rf)(1 + M)(1 - + 2)
This gives us a relation between inflation щ, expected inflation тг? and the unemployment rate, u,. The remaining stops make the relation look friendlier. Divide both sides by (1 + ;rf)(1 + д):
(1 = (1 - ац, + z)
(1 + Tf)(1 + M)
As long as inflation, expected inflation and the markup are not too large, a good approximation to this equation is given by
1 + ir, — irf— /t=1- o/u, + z (See Propositions 3 and 6 in Appendix 2 at the end of the book.) Rearranging gives
IT: = IT? + (M + Z) -
CHAPTER ф
Inflation and Economic Activity
I
n 1989, the Reserve Bank of Australia (RBA) decided to raise the overnight interest rate—the cash rate—because it was concerned that inflation, then about 7 per cent per year, was too high. Five years later, after a deep recession, inflation was down to about 2 per cent per year. This disinflation of 5 per cent induced a five-percentage point increase in unemployment over that period.
Why did the RBA decide to reduce inflation?To what value was it aiming? How did it do it? Why was there a recession? More generally, what are the effects of higher interest rates on inflation, on output and on unemployment? Given that the RBA actually set itself an inflation target for its monetary policy in the mid-1990s, how does a change in that target affect the economy? Our treatment of expectations and our assumption that the RBA had a price level target in Chapter 7 were just too simple to allow us to take up these questions. But. with our discussion of expectations and the introduction of the Phillips curve relation in Chapter 8. we now have what we need to answer them. This is what we do in this chapter:
• Section 9.1 looks at the three relations between output, unemployment and inflation—Okun's law, the Phillips curve and the aggregate demand relation in a growth context.
• Section 9.2 shows that, in the medium run, changes in the inflation target are reflected one for one in changes in inflation and in nominal money growth, with no effect on either output growth or unemployment.
• Section 9.3 shows that, in the short run, changes in the inflation target require changes in the interest rate, which affect both output growth and unemployment. A decrease in the inflation target leads to a period of lower output growth and higher unemployment.
• Section 9.4 discusses the role of credibility and the role of expectations in the adjustment of the economy to a decrease in the inflation target.
• Section 9.5 returns to the Australian disinflation of 1989-94. 9.1 OUTPUT, UNEMPLOYMENT AND INFLATION
Okun's law: From output growth to unemployment change
When we wrote the relation between output and unemployment in Chapter 6 we did so under two convenient but restrictive assumptions. We assumed that output moved one lor one with employment, so changes in output led to equal changes in employment. And we assumed that the labour force was constant, so changes in employment were reflected one lor one in opposite changes in unemployment, 4 Wo assumed that • - N
We must now move beyond these assumptions. To understand why, let's see what they imply lor the and " ' lbour : " relation between the rate ol output growth and the unemployment rate. II output and employment move together, a I per cent increase in output leads to a I per cent increase in employment. And it movements in employment arc reflected in opposite movements in unemployment, a I percent increase in employment leads to a decrease ol I per cent in the unemployment rate. Let n, denote the unemploy¬ment rate in year t, u, , the unemployment rate in year f - I, and gyl the growth rate of output from year t - I to year I. Then, under these two assumptions, the lollowing relation should hold:
u, - u,_, - -gyl (9.1)
The change in the unemployment rate should he equal to the negative of the growth rate ol output. II output growth is, say, 4 per cent then the unemployment rate should decline by 4 per cent.
Contrast this with the actual relation between output growth and the change in the unemployment rate, the relation known as Okun's law. Figure 9.1 plots the change in the unemployment rate against the rate ol output growth tor each year since 1982. It also plots the regression line that best fits the scatter ol points. The relation corresponding to the line is given by
и, - u,., = - 0.5{gyi - 3.3%) (9.2)
is constant.
Like equation (9.1 i, equation >9.2 gives a negative relation between the change in unemployment and output growth. But it dilfers from equation (9.1) in two ways:
~i 1 1 1 1 1 1 1
0 I 2 3 4 S 6 7
Output growth (%)
• Annual output growth has to be at least 3.2 per cent to prevent the unemployment rate from rising. This is because ol two factors we have neglccted so far—both the size of the labour force and the productivity of labour are growing over time. Why do these matter?
Figure 9.1 Changes in the unemployment rate versus output growth in Australia, 1982-2007
High output growth is associated with a reduction in the unemployment rate: low output growth is associated with an increase in the unemployment rate.
because the employment rate plus the unemployment rate и must add up to 1.
Looking at the above identity, we can work out why labour productivity growth and labour lorce growth are important. To maintain a constant unemployment rate, employment must grow at the same rate as the labour lorce. Suppose the labour lorce grows at I.9 per cent per year then employment must grow at 1.9 per cent per year. II, in addition, labour productivity—output per worker—grows at i .3 per cent per year, this implies that output must grow at 1.9% + 1.3% = 3.2% per year. In other words, to maintain a constant unemployment rate, output growth must be equal to 3,2 per cent per year.
In Australia, the sum of the rate of labour-force growth and the rale ol labour-productivity growth has been approximately equal to 3.2 per cent per year on average since 1982. and this is essentially why the number 3.2 percent appears on the right side ol equation '9.2). In what follows, we will call the rate ol output growth needed to maintain a constant unemployment rate the normal growth rate.
The coefficient on the right side ol equation 9,2) is -0.5, compared with -1.0 in equation (9.1). Put another way, output growth I per cent above normal leads it) only a 0.5 per cent reduction in the unemployment rate in equation 9.2 • rather than to a I per cent reduction in the unemployment rate in equation (9.1).
The above identity also tells us that il either labour productivity Y/N or the labour lorce L also responds in the short run to the Okun's law relation between gy and и will be moderated. And it turns out that they both do increase when output growth rises—in macroeconomic jargon, they are procyclical. Therefore, there are two ways of understanding why the coefficient in 9.2) is less than I:
1. firms adjust employment less than one for one in response lo deviations ol output growth from normal. More specifically, output growth I per cent above normal lor one year leads to only a 0.5 per cent increase in the employment rale.
One reason is that some workers are needed no matter what thc level ol output is. The accounting department of a firm, lor example, needs roughly the same number ot employees whether the lirm is selling more or less than normal.
Another reason is that training new employees is costly,- for this reason, firms prefer to keep current workers around rather than lay them off when output is lower than normal, and ask them to work overtime rather than hire new employees when output is higher than normal In had limes, lirms in effect hoard labour,- this behaviour is called labour hoarding.
for these two reasons labour productivity, Y/J\ rises when the economy booms and falls during downturns.
By definition, output niusi equal thc product ol labour productivity Y/\. the employment rate N/l and the labour lorce, L
2. An increase in lhe number ol employed doesn't necessarily lead to a one-lor-one decrease in the number ol unemployed. The reason is that labour lorce participation may increase. When employment increases, not all the new iobs are tilled by ihe unemployed. Some ol the jobs go lo people who were classified as out ol the labour force meaning they weren't actively looking lor a job. And as labour-market prospects improve tor the unemployed, some discouraged workers who were previously classilied as out ot the labour lorce—decide to start actively looking lor a job. and become classilied as unemployed . Therefore, when the economy booms, participation rises, which increases the labour lorce. In a slump, the labour force declines.
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