In Chaptcr 12 wc represented technological progress as an increase in A, the state ol technology, in the production function:
Y = F/K.AN)
13.1)
Output per worker' (YIN) and 'the state of technology' (A) are in general not the same. Recall from Chapter 12
that an increase in > output per worker may come from an increase in capital per worker, even if the state of technology hasn't changed.They are the same here because, in writing the production function as equadon (13.1). we ignore the role of capital in production.
Technological progress, not capital accumulation is central to the issues we will be discussing in this chapter. So, for simplicity, wc will leave aside capital here, and assume that output is produced according to the following production function:
Y = AN
Under this assumption, output is produced using only labour, and each worker produces A units ol output. Increases in Л represent technological progress.
The variable /1 has two interpretations here. One is indeed as the state of technology. The other, which follows from the lact lhat Y/N = A, is as labour productivity (output per worker). So, when referring to increases in A, we will use technological progress or (labour) productivity growth interchangeably.
( 13.2
Rewrite equation (13.1) as
N = Y/A
Employment is equal to output divided by productivity. Given output the higher the level ol pro¬ductivity, the lower the level ol employment. This naturally leads to the question: When productivity increases, does output increase enough to avoid a decrease in employment—equivalently, an increase in unemployment? In this section, we look at the short-run responses of output, employment and unemployment. In the next, we look at their medium-run responses and in particular, at the relation between the natural rate of unemployment and the rate ol technological progress.
Technological progress, aggregate supply and aggregate demand
The right model to use when thinking about the short-run and medium-run response of output to a change in productivity in the short mn is the aggregate supply and aggregate demand model developed in Chapter 7. Recall its basic structure:
• Output is determined by the intersection of the aggregate supply curve and the aggregate demand curve.
• The aggregate supply relation captures the effects ol output on the price level. The aggregate supply curve is upward sloping: an increase in the level of output leads to an increase in the price level. Behind the scenes, the mechanism is that an increase in output leads to a decrease in unemployment. The decrease in unemployment leads to an increase in nominal wages, which leads to an increase in prices—an increase in the price level.
• The aggregate demand relation captures the effects ol the price level on output. The aggregate demand curve is downward sloping: an increase in the price level leads to a decrease in the demand lor output. The mechanism behind the scenes: an increase in the price level leads to an increase in the gap between it and the central banks price level target. This leads it to increase the interest rate, which decreases the demand for goods, and then output.
The aggregate supply curve is drawn as /IS in Figure 13.1. The aggregate demand curve is drawn as AD. The intersection of the aggregate supply curve and the aggregate demand curve gives the level ol output, V consistent with equilibrium in labour, goods and financial markets. Given the equilibrium level of output V. the level of employment is determined by N = YM. For a given level ol output, the higher the level ol productivity, the smaller the number of workers needed to produce it.
Suppose productivity increases from level A to level A'. What happens to output, and to employ¬ment and unemployment in the short mn? The answer depends on how the increase in productivity shilts the aggregate supply curve and the aggregate demand curve.
Aggregate supply curve: Given P5. Yt => ul =j
4 Aggregate demanc curve: Pf =» it => Yl
4 A and A' refer to levels cf productivity here, not points on the graph. (To avoid confusion, points in the graph are denoted by 8 and 8 .)
TFCHNOLOGICAL PROGRESS. WAGES AND UNFMPi OYMFNT
chapter 13
Take the aggregate supply curve lirst. "1 he ellect of an increase in productivity is to decrease the amount ol labour needed to produce a unit of output, reducing cost lor firms. This leads lirms to reduce
Figure 13.1
\ AS Aggregate supply
\ for a given level of A and aggregate
\ / demand for a
\ / given level of
\ / productivity
0. \ /
"5 /
jj \ /
v
X P — \B
0.
ad
for a given level of A
l
Y Output, y ▼
Employment N = yia
The aggregate supply curve is upward sloping: an increase in output leads to an increase in the price level. The aggregate demand curve is downward sloping: an increase in the price level leads to a higher interest rate and thus lower output
the price llicy charge at any level ol output. The aggregate supply curve shifts down, Irom AS to AS' in Figure 13.2.
Now take the aggregate demand curve. Docs an increase in productivity increase or decrease the demand lor goods at a given pricc level: There is no general answer because productivity increases don't appear in a vacuum, what happens to aggregate demand depends on what triggered the increase in productivity in the first place:
• Fake the case where productivity increases come Irom the widespread implementation of a major technological breakthrough. It is easy to see how this change may be associated with an increase in demand at a given price level. The prospect ol higher growth in the future leads consumers to feel more optimistic about the future, and so to increase their consumption given their current income. The prospect of higher prolits in the future, as well as the need to put the new technology in place, may also lead to a boom in investment. In this case, the demand lor goods increases at a given price level,- the aggregate demand curve shifts to the right.
• Now lake the case where productivity growth comes not from the introduction of new technologies hut Irom the more efficient use of existing technologies. One ot the implications ol increased international trade has been an increase in foreign competition. This competition has forced many firms to cut costs by reorganising production and eliminating jobs • this is often called downsizing ). When such reorganisations are the source ot productivity growth, there is no presumption that aggregate demand will increase: reorganisation ol production may require little or no new invest¬ment. Increased uncertainty and worries about job security may well lead workers to want lo save more, and so to reduce consumption spending given their current income. In this case, aggregate demand may shili lo the lelt rather than lo the right.
I.els assume the most lavourable case unost lavourablc from the point ol view ol output and employment)—namely, thc case where the aggregate demand curve shifts to thc right. In this case, the increase in productivity shifts the aggregate supply curve down. Irom AS ю Л5', and shilts the aggregate demand curve lo the right, from AD to AD'. These shifts are drawn in Figure 13.2. Both shilts contribute to an increase in equilibrium output, from У lo У. In this case, the increase in productivity unambiguously leads to an increase in output. In words: Lower costs and high demand combine lo create
Figure 13.2 AS
The effects of ? , 7 \
an increase in у ^ /
productivity on ж
output in the as'
short run Price level, p ь BV.
1 Чв' 4 ^^AD' AD
У У'
Output, У
An increase in productivity shifts the aggregate supply curve down. It has an ambiguous effect on the aggregate demand curve, which may shift to the left or to the right In this figure, we assume a shift to the right
an economic boom. Il this reminds you of what has happened in Australia since 1995, you are right. See ihe focus box Technological progress, unemployment and the Australian expansion since 1996' ai the end of the next section, i
Without more information, however, we cannot toll what happens to employment. To sec why, note that equation 113.2' implies the following relation:
% change in employment % change in output - % change in productivity
Thus, what happens to employment depends on whether output increases proportionately more or less than productivity. Il productivity increases by 2 per cent it takes an increase in output of at least 2 per cent to avoid a decrease in employment—that is an increase in unemployment. And without a lot more information about the slopes and the size ol the shilts ot the Л5 and AD curves, we cannot tell whether this condition is satisfied in Figure 13.2. In the short run increases in productivity may or may not lead to an increase in unemployment. Theory alone cannot settle the issue.
The empirical evidence
Can empirical evidence help us to reach a conclusion? At tirst glance, it would seem to. Look at Figure 13.3, which plots the behaviour ol labour productivity and output lor the Australian market sector from 1966 to 2(107.
I he figure shows a strong positive relation between year-to-year movements in output growth and productivity growth. Furthemiore the movements in output are typically larger than the movements in productivity. This would seem to imply that, when productivity growth is high, output increases by more than enough to avoid any adverse effect on employment. But this conclusion would be wrong. The reason is that, in the short rim. the causal relation mns mostly the other way, from output growth to productivity growth. That is, in the short am output growth leads to productivity growth, not the other way around.
Start from the production function У = AN. From proposition 7 in Appendix 2 at the end of the book, this relation ^ implies that gr = & + gn- Or equivalent^
gN = gГ ~
The discussion has assumed that fiscal policy was given and monetary policy was directed at ^ achieving a medium-run price target. But. by shifting the aggregate demand curve, fiscal policy could dearly affect the outcome. Suppose you were in charge of fiscal policy in this economy. What level of output would you try to achieve?
Correlation versus causality: If we see a 4 positive correlation between output growth and productivity growth, should we conclude that high productivity growth leads to high output growth, or that high output growth leads to high productivity growth?
TEG INOLOGICAL PROGRESS. WAGES AND UNEMPLOYMENT
chapter 13
We saw why when we discussed Okun's law in Chapter 9: in bad times, firms hoard labour—they keep more workers than is necessary for current production. When the demand tor goods increases for any reason, firms respond partly by increasing employment and partly by having currently employed workers work harder. This is why increases in output lead to increases in productivity. And this is what we see in Figure 13.3—high output growth leads to higher productivity growth. This isn't the relation we arc alter. Rather, we want lo know what happens to output and unemployment when there is an exogenous change in productivity—a change in productivity that comes trom a change in technology,
Figure 13.3 Australian labour productivity and output growth, 1966-2007
12
10
4 -
OJ -J -
■U L
Output growth
Productivity growth
1970
I I I I I I
1975
■ I I I Г "1 I I I I I I I
1980 1985 1990
1995
т I I I I Г"
2000
2005
8
С <
-Л
1965
There is a strong positive relation between output growth and productivity growth. But the causality runs from output growth to productivity growth, not the other way around.
SOURCE: Australian Bureau of Statistics, cat. no. 5204. table 22. Productivity growth is the rate of increase of real GDP per hour worked.
(13.3)
Price setting:
A
W WN
T = T%
sometimes called 'unit labour costs', the labour cost per unit of output produced.
Think of workers and firms setting the wage to divide (expected) output between workers and firms according to their relative bargaining power. If both sides expect higher productivity, and so higher output, this will be reflected in the bargained wage. How productivity affects wage setting is one of the ► questions examined in the book by Edmund Phelps. Stwctural Slumps (Cambridge. MA: Harvard University Press. 1994). already mentioned in Chapter 6.
Wage setting:
13.4)
not trom the response of firms to movements in output. Figure 1 3.3 doesn't help us much here. And the conclusion from the research that has looked at thc effects of exogenous movements in productivity growth on output is that the data give an answer just as ambiguous as thc answer given by the theory:
• Sometimes increases in productivity lead to increases in output sufficient to maintain or even increase employment in the short run.
• Sometimes they don't, and unemployment increases in the short run.
13.2 PRODUCTIVITY AND THE NATURAL RATE OF UNEMPLOYMENT
TECHNOLOGICAL PROGKl SS. WAGES AND UNbMPLOTMfcM
chapter 13
The price-setting equation determines the real wage paid by firms. Reorganising equation (13.3), we can write
JV P
1 +
(13.5)
The real wage paid by firms, IV/P. increases one for one with productivity, Л: the higher the level ol productivity, the lower ihe price set by firms given the nominal wage, and therefore the higher the real wage paid by firms.
This equation is represented in Figure 13.4. Ihe real wage is measured on the vertical axis. The unemployment rate is measured on the horizontal axis. Equation 13.5' is represented by the solid horizontal line at W/P AJ{ I + ft): the real wage implied by price setting is independent ol the unemployment rate.
Turn to the wage-setting equation. Under the condition that expectations arc correct—so both P' = P and A' - A—the wage-setting equation 1 I3.4i becomes
W
(13.6)
The reason for using 8 rather than A to denote ' the equilibrium is that we are already using the letter A to denote the level of productivity.
у = AF(u,z)
The real wage, W/P, implied by wage bargaining depends on both the level ot productivity and the unemployment rate. The higher the level ol productivity, the higher the real wage. The higher the unemployment rate, the lower the real wage. For a given level ol productivity, equation (13.6) is represented by the solid downward-sloping curve in Figure 13.4: the real wage implied by wage setting is a decreasing function ol the unemployment rate.
Equilibrium in the labour market is given by point И, and the natural rate of unemployment is it,,. Let's now ask what happens to the natural rate ol unemployment in response to an increase in productivity. Suppose that A increases by 5 per cent, so the new level ol productivity A' equals 1.05 times A.
Figure 13.4 The effects of an increase in productivity on the natural rate of unemployment
AF(u.z)
A'
a. 1 + *
v
M rt
i A
1+M
re V QC
Price setting
Wage setting
Unemployment rate, u
An increase in productivity shifts both the wage-setting and the price-setting curves in the same proportion and thus has no effect on the natural rate of unemployment
• From equation (13.5) we see that the real wage implied by pricc setting is now higher hy 5 per cent—the price-setting curve shilts up.
• From equation 13.6) wc see that, at a given unemployment rate, the real wage implied by wage setting is also higher bv 5 per cent—the wage-setting curve shilts up.
• Note that at the initial unemployment rate ;/,,. both curves shift up by the same amount—namely, 5 per cent ol the initial real wage. That is why thc new equilibrium is at H' directly above В—the real wage is higher by 5 per cent, and the natural rate ot unemployment remains the same.
The intuition lor this result is straightlorward. A 5 per cent increase in productivity leads lirms to reduce prices by 5 per cent given wages, leading to a 5 per cent increase in real wages. This increase exactly matches the increase in real wages Irom wage bargaining at the initial unemployment rate. Real wages increase by 5 per cent, and the natural unemployment rate remains the same.
There is also substantial evidence that the slowdown in
since thc 1970s.
We have looked at a one-time increase in productivity, but thc argument we have developed also applies to productivity growth. Suppose that productivity steadily increases so that each year A increases by 5 percent. Then, each year real wages will increase by 5 percent, and the natural rate ot unemployment will remain unchanged.
The empirical evidence
Wc have derived two strong results. The natural rate of unemployment should depend neither on the level of productivity nor on the rate of productivity growth. How do these two results tit the tacts?
An obvious problem in answering this question is dial we don't observe the natural rale of unemployment. But we can work around this problem hy looking at the relation between average productivity growth and the average unemployment rate over decades. Because the actual unemployment rate moves around the natural rate, looking at the average unemployment rate over a decade should give us a good estimate of the natural rate ol unemployment lor that decade. Looking at average productivity growth over a decade also takes care of another problem we discussed earlier. While changes in labour hoarding can have a large effect on yearly changes in labour productivity, these changes in labour hoarding are unlikely to make much difference when we look at average productivity growth over a decade.
Figure I 3.5 plots average Australian labour productivity growth and the average unemployment rate during each decade since 1901. There seems to be a negative relation between the two. The decade ol World War I 1910—19) is very different Irom the rest. Both employment and unemployment were fairy steady, but output tell dramatically during the war. mainly due to tailing exports and then consumption and real investment. 11 we ignore that decade, thc negative relation between productivity growth and the unemployment rate becomes much stronger. A one-percentage point increase in productivity growth over a decade leads to a tail of more than tour percentage points in unemployment. But this is thc opposite of the relation predicted by those who believe in technological unemployment.
Periods of high productivity growth such as the 1950s and 1960s, have been associated with a lower unemployment rate. Periods ol low productivity growth, such as Australia saw in the 1900s, 1930s and 1980s, have been associated with a higher unemployment rate. Thc 1990s saw an increase in productivity over the 1980s not matched by the expected decrease in unemployment, but the increase productivity growcti has * was sma" and dominalcd ЬУ lhc тл3()г recession in 1901-92.
played an important role Can the theory we have developed be extended to explain this inverse relation in the medium a n in the rise of US and between productivity growth and unemployment? The answer is yes'. To see why, wc must look more European unemployment closely at the formation ot expectations ol productivity in wage setting.
Lip to this point we have looked at the rale ot unemployment that prevails when both price expectations and expectations of productivity are correct. However one of the lessons or the 1970s and 1980s is that it takes a very long time for expectations ol productivity lo adjust to the reality ol lower productivity growth. When productivity growth slows down lor any reason, il lakes a long time for society in general, and workers in particular, to adjust their expectations. In the meantime, workers keep asking tor wage increases lhat are no longer consistent with the new lower rate ot productivity growth.
TECHNOLOGICAl PROGRESS. WAGES AND UNEMPLOYMENT
chapter 13
3.0-
I 1951-60
2.5-
s?
Figure 13.5 Productivity growth and unemployment in Australia, 1901-2008
i
1960-69
1990-99
2 2.0-
1.5-
■a
о
I 1970 79
12000-08 11901-09
1940—49
1 1.0- JS
n
э с
5 0.5-
1920-29 I
11980-89
1930-391
4
0.0-
1910-19
-0.5-
T
10
T 12
i
14
Average unemployment rate (%)
There is a negative relation between the ten-year averages of producbvity growth and the ten-yeor overages of die unemployment rote.
SOURCES: M. Butlin RBA Discussion Paper. 1977; RBA. various; ABS. various.
To see what this description implies let's look, at what happens to the unemployment rate when price expectations arc correct ' that is. P' - P but expectations of productivity, A' may not be. /V may not be equal to /1.) In this case, the relations implied by price setting and wage setting are:
A
P W
1 + м
- A-F(ti.z)
'rice setting:
Wage setting:
Suppose productivity growth declines. Л increases more slowly than before. II expectations of productivity growth adjust slowly, then A' will increase tor some time by more than A does. What will then happen to unemployment is shown in Figure I ЗА II Л' increases by more than A, the wage-setting relation will shili up by more than the price-setting relation. The equilibrium will move Irom В to B'. and the natural rate ol unemployment will increase from it., to i/'„ The natural rale of unemployment will remain higher until expectations ol productivity have adjusted to the new reality, until A1' and Л arc again equal.
To summarise what we have seen in this and the preceding section: There is noi much support, either in theory or in the data, for the idea that taster productivity growth leads to higher unemployment.
4 The price-setting relation shifts up by the factor A.The wage- setting relation shifts up by the factor. A'. If A5 > A. the wage-setting relation shifts up by more than the price- setting relation.
• In the short run there is no reason lo expect, nor does there appear to be a systematic relation between movements in productivity growth and movements in unemployment.
Unemployment rate, u
If it takes time for workers to adjust their expectations of productivity growth, a slowdown in productivity growth will lead to an increase ir the natural rate of unemployment for some time.
• In the medium run, if there is a relation between productivity growth and unemployment, it appears to be an inverse relation. Lower productivity growth leads to higher unemployment. Higher productivity growth leads to lower unemployment. Indeed, many economists see a connection between the decrease in the natural unemployment rate and the increase in the rate ol technological progress in Australia in the second hall ol the 1990s. We lake up the issue in the focus box Technological progress unemployment and the Australian expansion since 1996'. Given this evidence, where do lears of technological unemployment come from? They probably come Irom the dimension ol technological progress we have neglected so far, structural change ihe change in the structure of the economy induced by technological progress. For some workers, those with skills no longer in demand, stnictural change may indeed mean unemployment, or lower wages, or both.
TECHNOLOGICAL PROGRESS, UNEMPLOYMENT AND THE AUSTRALIAN EXPANSION SINCE 1996
Why did the Australian economy do so well in the second half of the 1990s? Do the 2000s look any different? Table I gives the basic numbers for growth, unemployment, inflation and labour productivity. We first asked these questions in Chapter I. In later chapters we looked at various pieces of the answer. Here, we put these pieces together.
Wage setting
Price setting
Figure 13.6 The effects of a decrease in productivity growth on the unemployment rate when expectations of productivity growth adjust slowly
• The buzz in the second half of the 1990s was of the New Economy and the rise of the high-tech sector. As you saw in Chapter 12. there is indeed some evidence of a pickup in the underlying rate of productivity growth, coming mainly from a high rate of technological progress, in part due to the substantial uptake of information and communications technologies in Australian industries. This improved Australian performance was also a result of the many microeconomic reforms introduced by successive Australian
tLCHNOLOGICAL PROGRESS. WAGtS AND UNEMPLOYMENT
chapter 13
Table 1 Selected Australian macroeconomic variables. 1996-2008
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
GDP growth 4.0 3.9 4.4 5.0 3.9 1.9 3.7 3.1 3.9 2.8 2.9 3.3 3.6
Unemployment rate 8.0 8.2 7.9 6.7 6.2 6.9 6.5 6.1 5.5 5.0 4.8 4.3 4.3
Inflation rate 2.3 1.3 1.2 0.2 2.1 4.6 2.8 2.8 3.7 3.5 4.6 4.3 4.2
Labour productivity
growth 3.1 3.0 2.4 4.6 2.0 0.1 2.4 1.4 2.5 -0.1 1.2 1.0 1.3
1 I
SOURCES: RBA Table G10 and G7 The inflation rate is for thc GDP deflator.
governments in the 1980s and 1990s. In terms of Figure 13.2. there was a downward shift of the aggregate supply curve.
• This development was associated with a strong increase in aggregate demand. Hopes of high profits led to a boom in investment. From 1996 to 1999, real business investment grew on average by almost 8 per cent per year. Anticipations of higher incomes in the future led to a boom in consumption, which grew at almost 4 per cent per year in real terms. In terms of Figure 13.2, there was a large shift of the aggregate demand to the right, resulting in a large increase in output, a large increase in employment, and a steady decrease in unemployment from 8 per cent in 1996 to reach 6.2 per cent by 2000. Unemployment had to fall and employment rise because average output growth (4.3 per cent) outstripped productivity growth (3.3 per cent).
• The decrease in the unemployment rate to historically low levels wasn't associated with an increase in inflation, suggesting a decrease in the natural unemployment rate. In fact, inflation decreased gently until 2001 when the series was temporarily spiked by the introduction of the goods and services tax (GST) of 10 per cent. As you saw in Chapter 8. there were many factors behind the decrease in unemployment. But the main factor was probably the increase in productivity growth.The increase in productivity growth was largely unexpected, thus leading not to real wage increases but. along the lines developed in this section, to a likely decrease in the natural rate of unemployment
• Growth in Australia slowed down in 2001 in tandem with what was happening in the rest of the OECD. The IT bubble had burst and global investment fell. This slowdown was already under way before the terrorist attacks of 11 September 2001. which served to amplify the negative sentiments of investors and consumers. However. Australia managed to grow fastest among the OECD countries for a few years, and to avoid a recession. Output growth averaged 3.6 per cent from 2002 to 2004, but fears remained about the robustness of this growth in the face of a strengthening Australian dollar, a pervasive drought and a struggling world economy.
• From 2005 to 2008. the Australian economy seemed to change down a gear, with productivity growth slowing dramatically to 0.9 per cent, and average output growth slipping a little to 3.1 per cent. What was going on? Why did technological progress average a mere 0.9 per cent from 2005 to 2008, while it averaged 3.3 per cent from 1996 to 1999? One reason was the big hike in relative oil prices—by 43 per cent from 2005 to 2008. and which only began easing in the second half of 2008.This is a negative supply shock, which if permanent will raise the natural rate of unemployment (as you saw in Chapter 7). It also contributed to the rise in inflation from 2005 to 2008. Still, in this period the economy grew steadily and at a much higher rate than productivity growth, which meant that unemployment continued to fall.What was the reason for the healthy output growth? A key factor was the boom in commodity prices, which meant a significant gain in the value of Australia's mining and rural exports.This contributed to a boom in real business investment in those sectors, which grew in aggregate at an average rate of just under 10 per cent from 2005 to 2008. This meant that the growth came from capital accumulation rather than productivity improvements. Can the Australian economy hope to continue to operate at high output growth, low unemployment and
low inflation? It is useful here to emphasise the distinction between the actual rate of unemployment and the
natural rate of unemployment. In the short run. the actual rate of unemployment depends largely on what happens to aggregate demand. What about the natural rate of unemployment? As we argued in this section, the effect of low productivity growth in recent years has not raised the natural rate, because workers have adjusted their expectations and have not pushed for real wage rises. But if there is a real wage breakout in the future, and if oil prices remain high, sooner or later the natural rate of unemployment will increase from its recent low level. When and by how much is difficult to predict.
13.3 TECHNOLOGICAL PROGRESS AND DISTRIBUTION EFFECTS
Technological progress is a process ol structural change. New goods are developed, making old ones obsolete. New techniques ol production arc introduced, requiring new skills and making some old skills less useful. The essence ot this churning process is nicely reflected in the following quote from the president ot the Federal Reserve Bank ol Dallas, in ihe United States, in his introduction to a report, The Chum:
My grandfather was a blacksmith, as was his father. My dad, however, was part ol the evolutionary process of the churn. Alter quitting school in the seventh grade to work for the sawmill, he got the entrepreneurial itch. He rented a shed and opened a tilling station to service the cars that had put his dad out of business. My dad was successlul, so he bought some land on the top of a hill, and built a truck stop. Our tmck stop was extremely successful until a new interstate went through 20 miles to the west. The churn replaced US 41 I with Interstate 75, and my visions of the good lite laded.
Many professions, from those ol blacksmiths to harness makers, have vanished forever. There were more than eleven million larm workers in the United Stales at the beginning ol the twentieth century,- because ol very high productivity growth in agriculture, there are lewer than one million today. There are now more than three million truck, bus and taxi drivers in the United States,- there were none in 1900. There are more than one million computer programmers,- there were practically none in I960. F.ven lor those with the right skills, higher technological change increases uncertainty and the risk of unemployment. The firm in which they work may be replaced by a more efficient lirm, and the product their firm was selling may be replaced by another product.
The increase in wage inequality
For those in growing sectors, or those with the right skills, technological progress leads to new opportunities and higher wages. Hut lor those in declining sectors, or those with skills that are no longer in demand, technological progress can mean the loss ol their job, a period ol unemployment, and possibly much lower wages. In the United States, there is good evidence to suggest that there has been a large increase in wage inequality sincc 1980. Most economists believe that one of the main culprits behind this increase is technological change. Has this phenomenon been seen in Australia? The last twenty years in Australia have seen only small changes in wage inequality.
Figure I 3.7 shows the evolution of relative wages for various groups of male full-time workers, by education level, from 1969 to 2005 in Australia. The ligure is based on inlormation on individual We describe the ABS's ► workers trom ABS surveys, liach ol the lines in the ligure shows the evolution ol the wage of workers LFS survey and some of with a given level of education—incomplete high school completed high school', trade qualilication/ its uses in Chapter 6. diploma , university degree'—relative to the wage ot workers who have just completed high school, which is normalised to 100.
Ti e Churn:The Paradox ► of Progress (Dallas.TX: Federal Reserve Bank of Dallas. 1993).
Starting in the early 1980s, workers with a low level ol education 'that is, incomplete high school) have seen their relative wage steadily decrease over time, while workers with a trade qualification have seen their relative wage decrease and then increase. At the low end ol the education ladder, the relative wage of workers who haven t completed high school has declined by about 8 perccnt. This implies that, in some cases, these workers have seen a decrease not only in their relative wage but in their absolute real wage as well. At the high end ol the education ladder, the relative wage ot those with a university degree has declined substantially since 1969. This is because of the great expansion in the number ot
TEC! iNOLOQCAi. PROGRESS. WAGES AND UNEMPLOYMEN"
chapter 13
Figure 13.7 The evolution of relative wages in Australia by education level, 1969-2005
2.0 ~
1.8 -
University degree
о о
X
в
1/1
X ВО X
1.6 "
1.4
Trade qualification/Diploma
1.2 ~
V
се
1.0 -
Completed high school
Incomplete high school
1 1 1 1 1 1 1 1
1969 1974 1979 1982 1986 1990 2001 2005
Since the mid-1980s, the relative wage of male full-time workers with a low educational level has decreased. The relative wage of workers with a high educational level has decreased since 1969.
SOURCES: For i 969 to 1989: calculatcd from data in Jeff Borland. 'Earnings inequality in Australia: changes, causes and consequences'. Economic Record. June 1999.Table 4. For 2001 and 200S ABS. cat no. 6278.
university places over that period. In the future, the proportion ot university graduates with post¬graduate qualifications will increase signilicantly, and they now generate on average an extra 20 per cent income premium relative to undergraduates. This should increase the relative return Irom university education. The relative benefits from post-secondary technical education in the TAFE sector seem to have been quite stable over the thirty-five years.
In short, increasing wage inequality due to educational outcomes hasn t been an issue in Ausiralia over the last thirty-live years but this could change as the economy matures further. In other rich OECD countries, increasing wage inequality is a serious problem particularly in the United States.
The causes of increased wage inequality
What are the causes of the increase in wage inequality in rich countries like the United States? There is general agreement that the main factor behind thc increase in the wage ol high-skill workers relative to the wage of low-skill workers is a steady increase in the demand for high-skill workers relative to thc demand for low-skill workers.
This trend in relative demand isn't new to thc United States: it was already present to some extent in the 1960s and 1970s. But it was offset then by a steady increase in the relative supply of high-skill workers—a steadily larger proportion ol children finished high school, went to university, finished university, and so on. Since the early 1980s, relative supply has continued to increase, but not fast enough to match the continuing increase in relative demand. The result has been a steady increase in thc relative wage ot high-skill workers versus low-skill workers.
0.8
What explains this steady shift in relative demand? • One line of argument focuses on thc role ol international trade. Those local firms that employ higher proportions ol low-skill workers, the argument goes, are increasingly driven out ol markets by imports from similar lirms in low-wage countries. Alternatively, lo remain competitive, lirms must relocate some of their production to low-wage countries. In both cases, the result is a steady decrease in the relative demand tor low-skill workers locally. There are clear similarities between the effects ot trade and the effects ol technological progress: while both trade and technological
progress are good tor the economy as a whole, they hoth lead to structural change, and leave some workers worse oil.
There is no question that trade is partly responsible lor the increased wage inequality in the United States. For example, textile machine operators are among the ten occupations with the largest job decline in the United States, which is testimony to this lact—the US textile industry has largely moved to low-wage countries. But a closer examination shows that trade accounts lor only part of the shilt in relative demand. The most telling lact against explanations based solely on trade is that the shilt in relative demand towards high-skill workers appears to be present even in those sectors that aren't exposed to loreign competition.
• The other line ol argument focuses on skill-biased technological progress. New machines and new methods of production, the argument goes require high-skill workers, more so today than in the past. The development of computers requires workers to be increasingly computer-literate. The new methods of production require workers to be more flexible, better able to adapt to new tasks. Greater flexibility, in turn, requires more skills and more education.
Unlike explanations based on trade, skill-biased technological progress can explain why the shift in relative demand appears to be present in nearly all sectors of the economy. At this point, most economists believe that it is the dominant factor in explaining the increase in wage dispersion.
Does all this imply that the rich OHCD countries are condemned to steadily increasing wage
inequality? Not ncccssarily. There are at least three reasons to think that the luutre may be dillcrcnt
Irom the recent past:
• The trend in relative demand may simply slow down. For example, il is likely thai computers will become easier and easier to use in the future, even by low-skill workers. Computers may even replace high-skill workers, those workers whose skills involve primarily the ability to calculate or to memorise. Paul Krugman has argued—only partly tongue in check—that accountants, lawyers and doctors may be next on the list ol professions to be replaced by computers.
• Technological progress isn't exogenous. This is a theme explored in Chapter 12. How much firms spend on R&D and in what directions they direct their research depend on expected profits. The low relative wage of low-skill workers may lead lirms to explore new technologies that take advantage ol low-skill workers. In other words, market forces may lead technological progress to become less skill-biased in the future.
Ф
• The relative supply of high-skill versus low-skill workers is also not exogenous. The increase in the relative wage of more educated workers implies that the returns to acquiring more education and training arc higher than they were one or two decades ago. Higher returns to training and education can increase the relative supply of high-skill workers and. as a result, work to stabilise relative wages. Many economists believe that policy has an important role to play here, to make sure that ine¬quality of primary and secondary education lor the children of low-wage workers doesn't further deteriorate, and that those who want to acquire more education can borrow allordablv in order lo pay for it.
13.4 INSTITUTIONS,TECHNOLOGICAL PROGRESS AND GROWTH
To end this chaptcr, we want to return to the issue raised at the end ol the previous chapter, l or poor countries, technological progress is more a process of imitation than a process of innovation. China and other Asian countries make it look easy. So, why arc so many olhcr countries unable ю do the same? As indicated in Chaptcr 10, this question takes us Irom macroeconomics to development economics, and it would take a textbook in development economics to do it justice. But it is too important a question to leave il aside entirely here.
Pursuing the effects of ►
international trade would take us too far afield. For a more thorough discussion of who gains and who loses from trade, look at the textbook by Paul Krugman and Maurice Obstfeld. International Economics. 8th edn (New York: Pearson. 2008).
-IUN
To get a sense of the issues, let's go beyond the set of rich countries wc have focused on and compare Kenya and the United Stales. In 2004, PPP GDP per capita in Kenya was about one-thirtieth of PPP GDI' per capita in the United States. Part ol the difference was due lo a much lower level of capital per worker in Kenya. The other part ol the dillerence was due to a much lower technological level in
Kenya. It is estimated that the variable Л. the slate ol technology in Kenya, is about one-tenth ol the US level. Why is the state ol technology in Kenya so low? Alter all Kenya, like most poor countries, has access to most ol the technological knowledge in the world. What prevents it from simply adopting much ol the advanced countries' technology and quickly closing much of its technological gap with the United States?
One can think ol a number of potential answers, ranging from Kenya's geography and climate to its culture. Most economists believe, however, that the main source o' the problem, for poor countries in general and for Kenya in particular, lies in their poor institutions.
What institutions do economists have in mind? At a broad level, the protection ol property rights may well be the most important. Few individuals are going to create firms, introduce new technologies and invest il they expect that prolits will he either appropriated by thc state, extracted in bribes by corrupt bureaucrats or stolen by other people in the economy. Figure 1.3.8 plots PPP GDP per capita in 1995 (using a logarithmic scale) lor ninety countries, against an index measuring the degree of pro¬tection from expropriation, constructed for each of these countries by an international business organisation. The positive correlation between the two is striking (.the ligure also plots the regression line . Low protection is associated with a low GDP per capita (at the extreme left ot the figure are Zaire and Haiti),- high protection is associated with a high GDP per capita fat the top right are the Llnited Slates, Luxembourg, Norway, Switzerland, the Neiherlands and Australia .
Kenya's index is 6. Kenya is below the regression line, which means that Kenya has a lower GDP per person than would be predicted based just < on the index.
i The importance of property rights for growth was also painfully obvious dunng the transition of Eastern European countries from central planning to a market economy in the early 1990s. In many of these countries, poorly defined property rights, poorly enforced laws and corrupt public officials severely constrained the growth of new firms and led to a decline in output.
! ECHNOLOGICAL PROGRESS.WAGFS AND UNFKPLOYMENT
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There is a strong positive relation between the degree of protection from expropriation and the level of CDP per capita. SOURCE DaronAcemoglu. Understanding Institutions', Lionel Robbins Lectures. 2001.
Figure 13.8 Protection from expropriation and GDP per capita
What does protection of property rights mean in practice? It means a good political system, in which those in charge cannot expropriate or seize thc property ol the citizens. It means a good judicial system, where disagreements can be resolved efficiently and rapidly. Looking at an even liner degree ol detail, it means laws against insider trading in the slock market, so people are willing to buy stocks and so provide financing to firms.- it means clearly written and well-enforced patent laws, so lirms have an incentive to do research and develop new products. It means good anti-trust laws, so competitive markets do not turn into monopolies with few incentives to introduce new methods ot production and
new products. And the list obviously goes on. (A particularly clear example of the role ot institutions is given in the focus box The importance ol institutions: North and South Korea'.)
For example, political instability and ethnic conflicts are at the source of output stagnation in a number of African countries. And, in turn.
output stagnation contributes to political instability and exacerbates ethnic conflicts. ►
This still leaves one essential question.- Why don't poor countries adopt these good institutions? The answer is that it is hard: C.ood institutions are complex and dillicult lor poor countries to put in place. Surely, causality runs both ways in Figure I 3.8. Low protection against expropriation leads to low GDP per capita. But it is also the case that low GDP per capita leads to worse protection against expropria¬tion. Poor countries arc often too poor to afford a good judicial system—to maintain a good police force, lor example. Thus, improving institutions, and starting a virtuous cycle ol higher GDP per capita and better institutions, is often very difficult. The fast growing countries of Asia have succeeded. The focus box 'What is behind Chinese growth?' explores the case ot China in more detail i So far. much of Alrica has been unable, however, to start such a virtuous cycle.
THE IMPORTANCE OF INSTITUTIONS: NORTH AND SOUTH KOREA
Following the surrender of Japan in 1945. Korea formally acquired its independence, but became divided at the 38th parallel into two zones of occupation, with Soviet armed forces occupying the north and US armed forces occupying the south. Attempts by both sides to claim jurisdiction over all of Korea triggered the Korean War, which lasted from 1950 to 1953. At the armistice in 1953, Korea became formally divided into two countries, the 'Democratic People's Republic of North Korea' in the north and the 'Republic of Korea' in the south.
An interesting feature of Korea before separation was its ethnic and linguistic homogeneity. The north and the south were inhabited by essentially the same people, with the same culture and the same religion. Economically, the two regions were also highly similar at the time of separation. PPP GDP per capita, in 1996 dollars, was roughly the same, about $700 in both north and south. If anything. North Korea had much better infrastructure, natural resources and even schools, which meant it had much greater potential for future growth.
Yet, fifty years later, as shown in Figure 1, GDP per capita was ten times higher in South Korea than in North Korea—$ 12,000 versus $ 1. 100! On the one hand. South Korea had joined the OECD. the club of rich countries. On the other. North Korea had seen its GDP per capita decrease by nearly two-thirds from its peak of $3,000 in the mid-1970s. and was facing famine on a large scale.
What happened? Institutions and the organisation of the economy were dramatically different during that period in the two countries. South Korea relied on a capitalist organisation of the economy, with strong state
Figure I
GDP per capita in North and South Korea. 1950-2000
14,000 12,000 ■ 10,000 -
1
a
| 8,000 - (Л
D
2 6.000 о
4,000 2,000 -
South Korea
I960
1970
1980
1990
1950
1998
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intervention but also private ownership and legal protection of private producers. North Korea relied on central planning. Industries were quickly nationalised. Small firms and farms were forced to join large cooperatives, so they could be supervised by the state. There were no private property rights for individuals. The result was the decline of the industrial sector and the collapse of agriculture. The lesson is sad, but transparent: institutions matter very much for growth. SOURCE: Daron Acemoglu.'Understanding institutions'. Lionel Robbins Lectures. 2004.
WHAT IS BEHIND CHINESE GROWTH?
What lies behind China's remarkable growth in the last decade? From 1949 -the year in which the People's Republic of China was established—to the late 1970s, China's economic system was based on central planning. Two major politico-economic reforms, the 'Great Leap Forward' in 1958 and the 'Cultural Revolution' in 1966. ended up as human and economic catastrophes. Output decreased by 20 per cent from 1959 to 1962. and it is estimated that 25 million people died of starvation during the same period. Output again decreased by more than 10 per cent from 1966 to 1968. After Chairman Mao's death in 1976, the new leaders decided to progressively introduce market mechanisms in the economy. In 1978,an agricultural reform was put in place, allowing farmers, after satisfying a quota due to the state, to sell their production on rural markets.
Over time, farmers obtained increasing rights to the land, and today state farms produce less than I per cent of agricultural output. Outside of agriculture, also starting in the late 1970s. state firms were given increasing autonomy over their production decisions, and market mechanisms and prices were introduced for an increasing number of goods. Private entrepreneurship was encouraged, often taking the form of'Town and Village Enterprises', collective ventures guided by a profit motive.Tax advantages and special agreements were used to attract foreign investors.
The economic effects of these cumulative reforms have been dramatic. Average growth of output per worker increased from 2.5 per cent between 1952 and 1977 to more than 8 per cent since then.
Is such high growth surprising? One could argue that it is not. Looking at the ten-fold difference in productivity between North and South Korea that we saw in the previous focus box. it is clear that central planning is a poor economic system. Thus, it would seem that, by moving from central planning to a market economy, countries could easily experience large increases in productivity. The answer is not so obvious, however, when one looks at the experience of the many countries that, since the late 1980s. have indeed moved away from central planning.
In most Central European countries, this transition was typically associated initially with a 10-20 per cent drop in GDP. and it took five years or more for output to exceed its pre-transition level. In Russia and the new countries carved out of the former Soviet Union, the drop was even larger and longer lasting. (Most transition countries now have strong growth, although their growth rates are far below China's.) In Central and Eastern Europe, the initial effect of transition was a collapse of the state sector, only partially compensated by slow growth of the new private sector. In China, the state sector has declined more slowly, and its decline has been more than compensated by strong private-sector growth.This gives a proximate explanation for the difference between China and the other transition countries. But it doesn't explain how China was able to achieve this smoother transition.
Some observers offer a cultural explanation.They point to the Confucian tradition, based on the teachings of Confucius, which still dominates Chinese values and which emphasises hard work, respect for one's commitments, and trustworthiness among friends. All these traits, they argue, are the foundations of institutions that allow a market economy to perform well.
FOCUS
, ж
' BOX
Some observers offer an historical explanation.They point to the fact that, in contrast to Russia, central planning in China lasted for only a few decades. Thus, when the shift back to a market economy took place, people still knew how such an economy functioned and adapted easily to the new economic environment.
Most observers point to the strong rule of the Communist party in the process. They point out that, in contrast to Central and Eastern Europe, the political system did not change, and the government was able to control the pace of transition. It was able to experiment along the way. to allow state firms to continue production while the private sector grew, and to guarantee property rights to foreign investors. (Look at Figure 13.8, where we see that China has an index of property rights of 7.7, not far from the value in rich countries.) Foreign investors have brought with them technology from rich countries, and, in time, this knowledge has been transferred to domestic firms. For political reasons, such a strategy was simply not open to governments in Central and Eastern Europe.
The limits of the Chinese strategy are clear. Property rights are still not well established, and the banking system is still inefficient. So far, however, these problems have not stood in the way of growth. Note: For more on China's economy, read Gregory Chow. China's Economic Transformation /New York: RlackweH Publishers. 2002). For a comparison of the transition in Eastern Europe and that in China, read jcn Svejnar. China in Light of the Performance of Central and East European Economies, IZA Discussion Paper 279/, May 2007.
SUMMARY
• People often lear that technological progress destroys jobs and leads to higher unemployment. Theory and evidence suggest that these fears are largely unfounded. There is not much support, either in theory or in thc data, lor the idea that laster technological progress leads to higher unemployment.
• In the short run there is no reason to expect, nor does there appear to be a systematic relation between changes in productivity and movements in unemployment.
• If there is a relation between changes in productivity and movements in unemployment in the medium run, it appears to be an inverse relation: lower productivity growth appears to lead to higher unemployment,- higher productivity growth appears to lead to lower unemployment. One plausible explanation is that it takes high unemployment to reconcile workers wage demands with lower productivity growth.
• Technological progress isn't a smooth process in which all workers are winners. Rather, it is a process ol structural change. liven il most people benelit from the increase in the average standard ol living, there are losers as well. As new goods and new techniques ol production are developed, old goods and old techniques of production become obsolete. Some workers find their skills in higher demand, and they benefit Irom technological progress. Some find their skills in lower demand and stiller unemployment or reductions in relative wages.
• Wage inequality has increased in the past twenty years in most rich countries. The real wage ol low- skill workers has declined, not only relative to the real wage ol high-skill workers. The two main causes are international trade and skill-biased technological progress.
• Sustained technological progress requires thc right institutions. In particular, it requires well- established and well-protected property rights. Without good property rights, a country is likely to remain poor. But. in turn a poor country may lind it difficult to put in place good property rights.
KEYTERMS
• technological unemployment, 299 • churning, 31()
• creative destruction, 300 • skill-biased technological progress, 3I2
• structural change, 308 • property rights, 313
QUESTIONS AND PROBLEMS
Quick check
I. Using the information in this chaptcr, label each of the following statements 'true', 'false' or 'uncertain'. Explain brie flu.
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a. The change in employment and output per capita in Australia since 1900 lends support to the argument that technological progress leads to a steady increase in employment.
b. Workers benefit equally Irom ihe process ol creative destruction.
c. In ihe last two decades, the real wages ol low-skill Australian workers have declined in both a relative and an absolute sense.
d. Technological progress leads to a decrease in employment il, and only if, the increase in output is smaller than the increase in productivity.
c. Studies have found that exogenous increases in productivity sometimes lead to unemployment in the short run.
I. The apparent decrease in ihe natural rate ol unemployment in Australia in the second hall of the 1990s can be explained by the lact that productivity growth was unexpectedly high during that period
g. II we could stop technological progress, this would lead to a decrease in the natural rate ol unemployment.
2. Suppose ач economy is characterised by ihe following equations:
Price setting: P - (I + /x)( W/A) Wage setting: VV = /VP'i I - it)
a. Solve for the unemployment rate if P' - P but .-V doesn't necessarily equal A. Lxplain the effects of A''J A on the unemployment rate.
Sow suppose that expectations of both prices and productivity are accurate.
b. Solve lor the natural rate ol unemployment if the markup is equal to 5 per cent.
c. Does the natural rate of unemployment depend on productivity? Hxplain.
3. 'Higher labour productivity allows firms to produce more goods with the same number of workers, and thus sell the goods at the same or even lower prices. That's why increases in labour productivity can permanently decrease the rate of unemployment without causing inflation.' Discuss.
4. How might each of the following affect the wage gap between low-skill and high-skill -workers in Australia?
a. Increased spending on computers in government schools.
b. Limits on the numbers ol loreign backpackers allowed to enter and work in Australia.
c. Increasing the number of places at universities
d. Increasing the minimum wage.
Dig deeper
5. Technological progress, agriculture and employment
'Those who argue that technological progress does not decrease employment should look at agriculture. At the start of the last century, farm employment in Australia was 9 per cent of the total population. In 2007, it teas down to 1.2 per cent of the total population. If all sectors start having the productivity growth that took place in agriculture during the twentieth century, nobody will be employed a century from now.' Discitss.
6. Productivity and the aggregate supply curve
Consider an economy where production is given by Y = AN. Assume that price setting and wage setting are given by
Price setting: P = (1 + fi)(W/A) Wage setting: W = Л' РЧ \ —и)
Recall that the relation between employment /N/, the labour force I LI and the unemployment rate lul ii given by
N = (1 - u)L
a. Derive the aggregate supply curve (that is, the relation between the price level and the level ol output given the markup, the actual and the expected level ol productivity, the labour force, and the expected price level'. Explain the role ol each variable.
b. Show the ellect ol an increase in both actual productivity, A, and expected productivity, Л
so A'/A remains equal to 11 on the position ol the aggregate supply curve. Explain.
c. Suppose instead that actual productivity, A increases but expected productivity, AL\ doesn't change. Compare with the conclusions in (b). Explain the difference.
7. Technology and the labour market
In the appendix to Chapter 6, we learned how the wage-setting and price-setting equations could be expressed in terms of labour demand and labour supply.
Consider the wage-setting equation
W/P - Flu, z)
as the equation corresponding to labour supply. Recall that for a given labour force, I., and where N is employment, the unemployment rate, u, can be written as
N = (\ —u)L
a. Substitute the expression lor и into the wage-setting equation.
b. Using the relation you derived in part (a), graph the labour supply curve in a diagram with \ on the horizontal axis and W/P, the real wage, on the vertical axis.
We write the price-setting equation as follows:
P = (I + fi)MC
where MC is the marginal cost o f production. To generalise our discussion in the text, we will write MC.= W/MPL, where W is the wage and MPI. is the marginal product of labour.
c. Substitute the expression lor Alt' into the price-setting equation and solve lor the real wage, W/P The result is the labour demand relation, with W/P as a function ol the MPL and the markup, p..
In the text, we assumed for simplicity that the MPL was constant, for a given leve! of technology. Here, we assume that the MPL falls with employment (again for a given level of technology), a more realistic assumption.
d. Assuming lhat the MPL lalls with employment, graph the labour demand relation you derived in part (c). Use the diagram you drew for part (b).
e. What happens lo the labour demand curve if the level of technology improves? (Hint: What happens to MPL when technology improves?) Explain. How is the real wage affected hy an increase in the level of technology?
Explore further
8. Skill-biased technological change in Australia and Europe
This problem uses the labour demand/labour supply framework developed in problem 7 to explore the labour market histories o f Australia and Europe.
Australia: Imagine that there are two labour markets, one for high-skill labour and one for low- skill labour.
a. Suppose there is an increase in demand tor high-skill labour and a decrease in demand for low- skill labour. For a given labour force, what happens to the real wage in each sector?
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Europe: Imagine that there are also two labour markets in Europe, but the low-skill labour market has a binding minimum (real) wage. A binding minimum wage means that the equilibrium wage would be lower than the required minimum wage. /4s a result, employment is determined by the intersection of the minimum wage and the labour demand curve. The difference between labour supply and labour demand at the minimum wage represents unemployment.
b. Consider a decrease in labour demand for low-skill labour in Europe. What will be the effect on the real wage lor low-skill workers? What will be the effect on unemployment? Compare these results with those you obtained lor the low-skill labour market in part (a> for Australia.
Comparing the effccts
c. Putting everything together, alter an increase in demand for high-skill labour and a tall in demand lor low-ski I labour, in which economy will the increase in wage inequality be higher? In which economy will the increase in unemployment be higher? ( Assume that neither economy has a binding minimum wage in the high-skill labour market.)
d. Although the distinction between Australia and Europe drawn in this problem is crudc, how does your analysis relate to the labour-market histories ol these economies over the past two decades?
9. The churn in the United States
The Bureau of Labor Statistics in the United States presents a forecast of occupations with the largest job decline and the largest job growth. Examine the tables at
a. Which occupations in decline can be linked to technological change? Which can be linked to foreign competition?
b. Which occupations that are forecast to grow can he linked to technological change? Which can be linked to demographic change—in particular, the aging of the LIS population?
c. Compare the educational requirements (the last column of the tables) for the occupations in decline and on the rise. Can you see evidence ol the effects ol technological change?
d. Another development in the LIS labour market is the increased use ol temporary workers. How does this phenomenon fit with the educational requirements ot occupations in decline and on the rise?
We invite you to visit the Blanchard-Sheen page on the Pearson Australia website at
www.pearson.com.au/highered/blanchardsheen3e
for many World Wide Web exercises relating to issues similar to those in this chapter.
FURTHER READINGS
Extensions
Expectations
The next four chapters represent the first major extension of The Core. They look at the role of expectations in output fluctuations.
CHAPTER 14
Chapter 14 introduces two important concepts. The first is the distinction between the real interest rate and the nominal interest rate. The second is the concept of expected present discounted value. The chapter ends by discussing the Fisher hypothesis proposition that, in the medium run, nominal interest rates fully reflect inflation and money growth.
CHAPTER 15
Chapter 15 focuses on the role of expectations in financial markets. It first looks at the determination of bond prices and bond yields. It shows how we can learn about the course of expected future interest rates by looking at the yield curve. It then turns to stock prices, and shows how they depend on expected future dividends and interest rates. Finally, it discusses whether stock prices always reflect fundamentals, or may instead reflect bubbles or fads.
CHAPTER 16
Chapter 16 focuses on the role of expectations in consumption and investment decisions. The chapter shows how consumption depends partly on current income, partly on human wealth and partly on financial wealth. It shows how investment depends partly on current cash flow and partly on the expected present value of future profits.
CHAPTER 17
Chapter 17 looks at the role of expectations in output fluctuations. Starting from the IS-LM model, it modifies the description of goods market equilibrium (the IS relation) to reflect the effect of expectations on spending. It revisits the effects of monetary and fiscal policy on output. It shows, for example, that in contrast to the results derived in The Core, a fiscal contraction may sometimes increase output, even in the short run.
CHAPTER ф
Expectations: The Basic Tools
T
he consumer who considers buying a new car must ask: Can I safely take out a new car loan? How much of a wage raise can I expect over the next few years? Is a recession coming? How safe is my job?
The manager who observes an increase in current sales must ask: Is this a temporary boom that I should meet with the existing production capacity? Or is it likely to last, in which case should I order new machines? The pension fund manager who observes a boom in the stock market must ask: Are stock prices going to increase further, or is the boom likely to fizzle? Does the increase in stock prices reflect expectations of firms' higher profits in the future? Do I share those expectations? Should I move some of my funds in or out of the stock market?
These examples make clear that many economic decisions depend not only on what is happening today but also on expectations of what will happen in the future. Indeed, some decisions should depend very little on what is happening today. For example, why should an increase in sales today, if it is not accompanied by expectations of continued higher sales in the future, lead a firm to alter its investment plans? The new machines may not be in operation before sales have returned to normal. By then, they might sit idle, gathering dust.
We haven't paid systematic attention until now to the role of expectations in goods and financial markets. We ignored expectations in our construction of both the IS-LM model and the aggregate demand component of the AS-AD model that builds on the IS-LM. When looking at the goods market, we assumed that consumption depended on current income and that investment depended on current sales. When looking at financial markets, we lumped assets together and called them 'bonds': we then focused on the choice between bonds and money, and ignored the choice between bonds and stocks, the choice between short-term bonds and long-term bonds, and so on. We introduced these simplifications to build the intuition for the basic mechanisms at work. It is now time to think about the role and the determination of expectations in economic fluctuations, which we do in this and the next three chapters.
This chapter lays the groundwork.The first two sections introduce two key concepts:
• Section 14.1 introduces the distinction between the real interest rate and the nominal interest rate.
• Section 14.2 introduces the concept of expected present discounted value.
• Sections 14.3 and 14.4 build on the distinction between real and nominal interest rates to revisit the effects of monetary policy on interest rates. They derive a surprising but important result: an easier monetary policy in the form of a higher inflation target leads to lower nominal interest rates in the short run but to higher nominal interest rates in the medium run.
14.1 NOMINAL VERSUS REAL INTEREST RATES
In December 1978 the rate on the five-year Commonwealth Treasury bond (orT-bond)—the annualised interest rate on government bonds maturing in five years time—was 8.8 per cent. In September 2008 the five-year T-bond rate was only
5.2 per cent. Although most ol us cannot borrow ai ihe same interest rale as the government, the interest rates we face as consumers were also substantially lower in 2008 than in 1978. It was much cheaper to borrow in 2008 than it was in 1978.
Or was it? In 1978, actual inflation was around 10 percent. In 2008. actual inflation was around 5 per cent. This would seem relevant. The interest rale lells us how many dollars we will have to pay in the future in exchange for having one more dollar today. But we don't consume dollars. We consume goods.
When we borrow what we really want to know is how many goods wc have to give up in the future in exchange for ihe goods we gel today. Likewise, when we lend, we want to know how many goods— not how many dollars—we will gel in the future lor the goods we give up today. The presence ot inflation makes the distinction important. What is the point ol receiving high interest payments in the future il inflation between now and then is so high that we are able to buy few goods with the proceeds? This is where the distinction between nominal interest rates and real interest rates comes into play:
• Interest rates expressed in terms of dollars (or, more generally in units of the national currency) arc called nominal interest rates. The interest rales printed in the financial pages of newspapers arc nominal interest rates. Whether they are one-year, two-year, tive-year or even ten-year bonds, the interest rate given is the annualised return—ihe return per year. We will discuss the relationships between these different maturities in the next chapter. For now, consider a one-year bond. When we say that the one-year T-bond rate is 5 per ccnt, wc mean that, for every dollar the government borrows by issuing one-year T-bonds, it promises to pay 1.05 dollars a year from now. More generally, il the one-year nominal interest rate lor year t is /',. borrowing one dollar this year requires you to pay I + i, dollars next year. Wc will use interchangeably this year for today', and next year' tor 'one year from today'.)
• Interest rates expressed in terms of a basket of goods arc called real interest rates. It we denote the real interest rate lor year / by r, then, by definition borrowing the equivalent of one basket of goods this year requires you lo pay the equivalent ol I + r. baskets of goods next year.
What is the relation between nominal and real interest rates? How do wc go from nominal interest rates—that we observe—to real interest rates—that we typically don't observe? The answer: We must adjust the nominal interest rate to take into account expected inflation. Let's go through the step-by-step derivation.
Assume there is only one good in the economy, bread wc shall add jam and other goods later). Denote the one-year nominal interest rate, in terms ol dollars hv /,: il you borrow one dollar this year, you will have to repay I + i, dollars next year. Bui you aren i interested in dollars. What you want to know is how much you will have to rcpav next year, in terms ot loaves ot bread, if you borrow enough to eat one more loat of bread this year.
Figure 14.1 helps us to derive the answer. The lop part repeats the definition of the one-year real interest rate. The bottom part shows how we can derive the one-year real interest rate from information about ihe one-year nominal interest rate and the price of bread.
• Start with the arrow pointing down in the lower left ol Figure 14 I. You want to eat one more loal ot bread this year. Il ihe price ol a loaf of bread this year is P, dollars, to eat one more loaf ot bread you must borrow P, dollars.
• If /, is the one-year nominal interest rate—the interest rate in terms ot dollars—and if you borrow P, dollars, you will have ю repay (I + i,)P, dollars next year. This is represented by the arrow from left to right at the bottom of Figure 14.1.
Nominal interest rate: interest rate in terms of
4 dollars. In Australia, the government doesn't issue one-year bonds. It has issued two-year, five-
4 year and ten-year bonds. As you will see later in the chapter, it makes no difference whether you hold a one-year bend for one year, or a two- year bond for one year, etc.
4 Real interest rate: interest rate in terms of a basket of goods.
If you have to pay $10 next year, and you expect the price of bread next year to be $2 a loaf, you expect to have to repay the equivalent of 10/2 = 5 loaves of bread next year. This is why we divide the dollar amount (1 + у P, by the expected price of bread < next year. Pf,,.
• What you care about isn't dollars, but loaves ol bread. Thus, the last step involves converting dollars to loaves of bread next year. Let P',., be the price ot bread you expect lor next year. (The superscript с indicates this is an expectation—you don't know yet what the price ol bread will be next year.) How much you expect to repay next year, in terms ot loaves ol bread, is therefore equal lo (1 t i,)P, • the amount ol dollars you have to repay next yeari divided bv P)., i the price of bread in terms of dollars you expect lor next year1, so (1 + i,)Pt/Pj+l, This is represented by the arrow pointing up in the lower right ol Figure 14.1.
Figure 14.1 Definition and derivation of the real interest rate
This year
Next year
Goods
Definition of the real rate:
(1 + r,) goods
С + Kt+i
~<1+i,)Pt~ goods
L J
Goods
Derivation of the real rate:
(1 +IJP, dollars
Putting together what you see in the top part and what you see in the bottom part ol Figure 14.1 it follows that the one-year real interest rate, r,f is given hy
P,
14.1
Add 1 to both sides ► in (I4.2): 1 + wf =
1 ♦(Fh-W
Reorgan se: 1+Trf=Pf*,/P, Take the inverse of both sides: 1/(1 + jtI) = P, №f»,
See proposition 6. Appendix 2 at the end of the book. Suppose i = 10 per cent and v' = 5 per cent The exact relation (14.3) gives r = 4.8 per cent. The approximation given by equation (14.4) gives 5 per cent—close enough.
The approximation can be quite bad when i and r* are high. If i = 100 per cent and = 80 per cenc. the exact relation gives r = 11 per cent: the approximation gives r = 20 per cent—a big difference. ►
rt (I + h)-j— ' i.t
This relation looks intimidating. Two simple manipulations make it look friendlier Denote expected inflation by тт\. C.iven there is only one good—bread—thc expected rate of inflation equals the expected change in the dollar price of bread between this year and next year, divided by thc dollar pricc ol bread this year:
тг;
(14.3)
- P,
(14.2
P,
Using equation 114.2), rewrite P./P'j. , as I I . Replace in : 14.1 > to get
P, dollars
(I + i,)
' + Г' = (I + T7f)
One plus the real interest rate equals the ratio of one pln> the nominal interest rate, divided by one plus the expected rate of inflation.
(14.4)
Equation 14.3 gives us the exact relation of the real interest rate to the nominal interest rate and expected inflation. However when thc nominal interest rate and expected inflation aren't too large say, less than 20 per cent per year—a close approximation to this equation is given by the simpler relation
i, - Ki;
Equation i I4.4i is simple. Remember it. It says that the real interest rate is IapproximatelyI equal to the nominal interest rate minus expected inflation. (In the rest ol the book, we will often treat the relation 14.4 as if it were an equality. Remember however, that it is only an approximation.
Note some ol the implications ol equation < I 1.4):
• When expectcd inflation equals zero the nominal and the real interest rates are equal.
• Because expected inflation is typically positive, the real interest rate is typically lower than the nominal interest rate.
• For a given nominal interest rate, the higher the expected rate ol inflation, the lower the real interest rate.
The case where expected inflation happens to he equal to the nominal interest rate is worth looking at more closely. Suppose the nominal interest rate and expected inllation both equal 10 per cent, and you arc a borrower. For every dollar you borrow this year, you will have to repay 1.10 dollars next year. But dollars will be w orth 10 per ccnt less in terms of bread next year. So i! you borrow the equivalent of one loaf of bread you will have to repay the equivalent ol one loal ol bread next year: the real cost of borrowing—the real interest rate—is equal to zero. Now suppose you are a lender. For every dollar you lend this year, you will receive 1.10 dollars next year. This looks attractive but dollars next year will be worth It) per cent less in terms of bread. If you lend the equivalent of one loal ol bread this year, you will get the equivalent ot ore loaf ol bread next year. Despite the 10 per cent nominal interest rate, the real interest rate is equal to zero.
Though this particular bond matures in five years, the interest rate yield is always expressed in annualised terms We explain this in more detail in the next < chapter.
We have assumed so tar that there was only one good—bread. But what we have done generalises easily. All we need lo do is to substitute the price level the price ol a basket ol goods—(or the price of bread in equation 114.1 i or equation 14.3). If we use the Consumer Price Index (the CP1) to measure the price level, the real interest rate tells us how much consumption wc must give up next year to consume more today.
Nominal and real interest rates in Australia since 1975
l.ct us return to the question at the start ol this section. Wc can now restate it as follows: Was the real interest rate lower in 2008 than it was in 1978? More generally, what has happened to the real interest rate in Australia since the early 1980s?
"I he answer is given in Figure 14.2, which plots both nominal and real interest rates since 1975. For each year, the nominal interest rate shown is the five-year T-bond rate at the beginning ol the year. To construct the real interest rate we need a measure tor expected inflation—more precisely, the rate of
Nominal interest rate
' \>/ \
Real interest rate
1975
I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I
1980 1985 1990 1995 2000 2005
/ к'/О/'^ъ
5.2%
Figure 14.2 The nominal and real interest rate on a five-year Australian Commonwealth Treasury Bond since 1975
While the nominal interest rate has declined considerably since the late 1970s, the real interest rate was actually higher in 2008. The real interest rate is the annualised yield on a five-year nominal T-bond less the one-year ahead expected inflation produced by the Melbourne Institute. The dashed line is what the real interest rate would be if the actual inflation rate in the coming year is subtracted from the nominal rate in the current year. SOURCE: RBA Bulletin. Tables F02. G03 aid G04.
inflation expected as of the beginning of each year. Expected inflation measures are produced from a variety of sources, and are based on either surveys of individuals or forecasts from macrocconomctric models by organisations such as the central bank, the Old) or the IMF. As an example we use thc forecast of inflation for a year published at the end of the previous year by the Melbourne Institute (which is available on the RBA website). This forecast is based on surveying consumers to find out what they think will happen to the CPI. For example, the forecast ot inflation used in constructing thc real interest rate for 2008 is the forecast of inflation published bv the Melbourne Institute in September 2008—4.4 percent.
Figure 14.2 shows the importance ol adjusting lor inllation. While the nominal interest rate was much lower in 2008 than it was in 1978, the real interest rate was actually higher in 2008 than il was in 1978—0.8 per cent in 2008 versus ().() per cent in 1978. Put another way, despite the large decline in interest rates, borrowing was actually a little more expensive in 2008 than it was in 1978. This comes from the tact lhat inflation 'and. with it, expected inflation) has steadily declined since the early 1980s.
Another important fact is apparent from Figure 14.2. Though the nominal interest rate can never be negative, the real interest rate certainly can. In the late 1970s the real rate ot interest on five-year T-bonds was negative. Naturally, borrowers love negative real interest rates, but they cannot remain negative lor too long because lenders will refuse to lend.
The real interest rate ► (i - тт-') is based on expected inflation. If actual inflation turns out to be different from expected inflation, the realised real interest rate (i - тг) will be different from the real interest rate. For this reason, the real interest rate is sometimes called the ex-cnte real interest rate (ex-onle means 'before the fact'—here, before inflation is known).
The realised real interest rate is called the ex-post real interest rate (ex-post means 'after the fact'—here, after inflation is known).
14.2 EXPECTED PRESENT DISCOUNTED VALUES
Figure 14.3
Calculating
present
2 years from now
This year
$1
Next year
► $(1 4) $1
1
$
(1 -4) $1 1
+ $(1 + i() (1 $1
$
(1 H)< 1
discounted values
ГХРГСТАТЮГ chapter 14
nominal interest rate this year. /,, is known today, so it does not need a superscript e.l Thc expected present discounted value ol this expected sequence ol payments is given hy
i-i
$Vf
(14.5)
•i+1
Expected present discounted value is a heavy expression to carry,- instead, we will often use tor short, just present discounted value or even present value. Also, it will be convenient to have a shorthand way of writing expressions like equation 14.5 To denote the present value of an expected sequence for $2, we will write V($z,or just V($;l.
Using present values: Examples
Equation 14 .5 has two important implications:
• The present value depends positively on current and expected future payments. An increase in any luturc $;' leads to an increase in the present value.
• Thc present value depends negatively on current and expected future interest rates. An increase in either currcnt t or any future tv leads to a decrease in the present value.
Equation (14.5 isn t simple, however, and intuition lor these eflects is best built by going through some examples.
Constant interest rates
iz or future ►
$z'T=»VT.
i or future i'T => Vl. ►
To locts on the eflects ol the sequence of payments on the present value, assume that interest rates are expected to be constant over time, so that i, ~ , — and denote their common value by i. The present value formula—equation ; I4.5i—becomes
i
$V, =
14.6)
$zU2
I + i, (1 + if)1
The weights correspond» In this case, thc present value is a weighted sum of expected luture payments—the weights decline
geometrically through time. The weight on a payment in the lirst year is 1/(1 + i), and the weight on thc payment и years Irom now is I I + ii". With a positive interest rate, the weights gel closer and closer to zero as we look further and further into thc future, l or example, with an interest rate equal to 10 per cent, the weight on a payment ten years from today is equal to I 1 + 0.10110 - 0.386, so that a payment of $1,000 in ten years is worth $.386 today. The weight on a payment in thirty years is I < I + 0.10)3" - 0.057. so that a payment ot $1,000 in thirty years is worth only $57 today!
Constant interest rates and payments
to the terms of a geometric series. See geometric series in Appendix 2 at the end of the book.
In some cases, thc sequence ot payments tor which wc want to calculate the present value is simple. For example, a lixed-raie thirty-year mortgage requires constant dollar payments over thirty years. Consider a sequence of equal payments—call them $; without a time index—over n years. In this case, thc present value formula in equation (14.6 simpli:ies to
%V,
1 + i
I -
$r
(I +0"
I + i 1 - I.
'< 1 + i)
Because the terms in the expression in brackets represent a geometric series, we can calculate the By now.geometric ► sum of thc series, and get series shouldn't hold any secrets, and you should $; / |
I
I •
1 + i
have no problem deriving this relation. But if you do. see Appendix 2 at the end of the book.
where the lirst line follows by factoring out l/( I + /). The reason lor factoring out I/(I + /) should be clear from looking at the term in brackets in the first line: it is a geometric sum, so we can use the property of geometric sums to get the second line of the equation.
Suppose you have just won $1 million trom Lotto and have been presented with a two-metre-long cheque lor $1 million on TV. Afterwards, you are told that, to protect you Irom your worst spending instincts as well as from your many new friends', the Lotto organisation will pay you the million dollars in equal yearly instalments of $50,000 over the next twenty years. What is the present value of your prize? Taking for example, an interest rate ol 6 per ccnt per year, the preceding equation gives V= ($50,000/1.06 0.6881 (0.0571 or about $573,500. Not bad, but winning the prize didn't make you a millionaire-
Constant interest rates and payments, going on forever
$z
$V, =
$V,=
Lets go one step further and assume that payments are not only constant but go on forever. Real-world examples are harder to come by for this case, but one example comes from nineteenth-century England, when the government issued consols, bonds paying a tixed yearly amount forever. Let be the constant payment I rom the equation above lor a sequence ol equal payments over n years, we have
I
(I + f)"
1 + /' 1-1,
< I + i)
Our consol has equal payments indefinitely, and so we can see what happens to V as n becomes infinite The top right-hand term in the above equation becomes 1. and so wc get
$2
1 + i I
I + i)
The present value ot a constant sequence of payments $; is equal to the ratio of $; to the interest rate I. II, lor example, the interest rate is cxpectcd to be 5 per ccnt per year forever, the present value of a consol that promises $10 per year lorever equals $10/0.05 = $200. II the interest rate increases and is now expected to be 10 per cent per year forever, the present value ot the consol decreases to $10/0.10 = $100.
Zero interest rates
Because of discounting, calculating present discounted values typically requires the use ol a calculator. There is however, a case where calculations simplify. This is the ease where the interest rate is equal lo zero: il i = 0 then l/( 1 + ; > equals one and so does I •'( 1 + /)" lor any power n. l or that reason, the present discounted value ot a sequence of cxpectcd payments is just the sum of those expected payments.
Because the interest rale is in lacl typically positive, assuming the interest rate is zero is only an approximation Hut it is a very useful one tor back-of-the-envelopc calculations.
Nominal versus real interest rates, and present values
So tar, we have calculated the present value ol a sequence of dollar payments by using interest rates in terms of dollars—nominal interest rates. Specifically, we have written equation (14.5) as
$V, = + ^ + .
i What is the present value if i equals 4 per cent? 8 per cent? (Answers: $679,500. $490,900)
i Most consols were bought back by the British government during the end of the nineteenth century and the early part of the twentieth century. A few are still around.
i + i, (i + ;t)o+/?.,)
where :',, ij'+i ... is the sequence ot current and expected (uture nominal interest rates, and Sr'(',,, .. is the sequence ot current and expected tuiure dollar payments.
Suppose we want instead to calculate the present value ol a sequence of real payments—that is, payments in terms of a basket of goods rather than in terms of dollars Following the same logic as before, what we need to do is to use the right interest rates lor this case: namely, interest rates in terms of thc basket of goods—real interest rates. Specifically, we can write the present value of a sequence ot real payments as
V, =
14.7)
t+r, (I + r,)(l + r ut)
The proof is given in the ► appendix to this chapter. Go through it to test your understanding of the two tools introduced in the chapter: real interest race versus nominal interest rate, and expected present values.
where r,, r*M ... is thc sequence of current and expected future real interest rates, z'j+t. zj'.i ••■ is the sequence ot current and expected future real payments, and V, is the real present value ot future payments.
These two ways ol writing the present value turn out to be equivalent. That is, the real value obtained by constructing $V, using equation (14.5) and dividing by P. the price level, is equal to the real value V, obtained from equation (14.7), so
$V,/P, = V,
In words: We can calculate the present value of a sequence of payments in two ways. One way is lo calculate it as the present value of the sequence of payments expressed in dollars, discounted using nominal interest rates, and then dividing by the price level today. I'he other way is to calculate it as the present value of the sequence of payments expressed in real terms, discounted using real interest rates. The two ways give the same answer.
Do we need both formulas? Yes. Deciding which one is more helpful depends on the context.
lake bonds, tor example. Bonds typically are claims to a sequence ol nominal payments over a period of years. For example, a ten-year bond may promise $50 each year lor ten years, plus a final payment ol $ 1,000 in the last year. So, when we look at thc pricing ol bonds in Chapter 15, wc will rely on equation (14.5) (which is expressed in terms ot dollar payments; rather than on equation 1 14.7' (which is expressed in real terms
But sometimes we have a belter sense ol future expected real values than ol future expected dollar values. You may have little idea ol what your dollar income will be in twenty years its value depends very much on what happens to inllation between now and then. But you may be confident that your nominal income will increase at least as much as inflation—equivalently, that your real income won't decrease. In this case, using equation (14.5;. which requires you to form expectations ot future dollar income, may be difficult; using equation <14.71, which requires you to form expectations ol luture real income, will be easier. For that reason, when we discuss consumption and investment decisions in Chaptcr 16, we will rely on equation 14.7) rather than equation (14.5).
4 We will ignore time subscripts here: the/ aren't needed for the rest of the chapter.
14.8)
14.3 NOMINAL AND REAL INTEREST RATES, AND THE IS-LM MODEL goods. So, what belongs in the IS relation is the real interest rate. Let r denote the real interest rate. The IS relation must therefore be modilied to read
У = C(Y - T) + l(Y, r) + С
4 For the time being, we will focus only on the effect of the interest rate on investment In Chapters 16 and 17 you will see how the real interest rate affects both investment and consumption decisions.
Recall that the money supply. Л1, is endogenous, so that whenever the central bank chooses an interest rate it is obliged to conduct immediate open-market operations to adjust M so that the money market is in equilibrium. So. the LM curve adjusts erdogenously.We con't really need it for short- run analysis, but we keep it there for
4 completeness.
Interest rate in the LM relation: nominal interest
4 rate,i.
4 Interest rate in the IS relation: real interest rate. r.
Investment spending, and thus the demand for goods, depends on the real interest rate not the nominal interest rate, as we assumed until now).
Now turn to the LAI relation. In deriving the LAI relation, we argued that the demand lor money depends on the interest rate. Were wc referring to the nominal interest rate or the real interest rate?
The answer is the nominal interest rate. Remember why the interest rate affects the demand lor money. When thinking about whether to hold money or bonds, people take into account the opportunity cost ol holding money rather than bonds the opportunity cost is what they give up by holding money rather than bonds. Money pays a zero nominal interest rate. Bonds pay a nominal interest rale ol /. Hence, the opportunity cost ol holding money is equal to the dillcrcncc between the interest rate Irom holding bonds minus the interest Irom holding money so j — 0 = i. which is just the nominal interest rate. Therefore, the LM relation is siill given by
M
T = YL(i)
IS: LM:
Real interest rate: Monetary policy rule:
Collecting this equation, equation (14.8i, the relation between the real interest rate and the nominal interest rate, and ihe realistic assumption thai the central bank sets the nominal interest rate using an inflation targeting rule a variation of what we saw in [9.10] in Chapter 9; here r„ is the real interest rate in medium-run equilibrium and rrf is ihe central bank's inflation target), ihe extended 1S—LM model is given by
Y = C(Y - T) + I(Y, r) + C,
M/P = Y L(i)
Г « / — IIе
i - (r„ + 7r) + (?< 77 - 7ТГ)
Note the immediate implications of these four equations:
The interest rate directly affected by monetary policy and the interest rate that enters the LM equation is ihe nominal interest rale.
The interest rate that affects spending and output (the rate that enters the IS relation) is the real interest rate.
So. the effects of monetary policy on output depend on how movements in ihe nominal interest rate translate into movements in the real interest rate. To further explore this question, the next section looks at the eflccts of expansionary monetary policy lor a higher inflation target) on the nominal interest rate and the real interest rale, in both ihe short ain and the medium mn.
14.4 MONETARY POLICY, INFLATION, AND NOMINAL AND REAL INTEREST RATES
the real and the nominal interest rate, and (2) the distinction we developed in The Core between the short run and the medium run. As you will see, thc full answer is:
• An expansionary monetary policy in the form of a higher inflation target leads to lower nominal interest rates m thc short ran, but to higher nominal interest rates iv\ the medium run.
• An expansionary monetary policy leads to lower real interest rates in the short run, hut has no effect on real interest rates in the medium run.
The purpose ot this section is to develop this answer, and draw its implications.
Revisiting the IS-LM model
Y = C(Y - M/P - YL(i) i = {r„ +
Wc have derived four equations—the IS relation, thc LM relation the relation between the real and the nominal interest rate, and the monetary policy rule. It will be more convenient to reduce them to three equations. To do so, replace the real interest rale in thc IS relation by the nominal interest rate minus expected inflation. This gives
IS: LM:
If you want to know ► more about monetary policy rules like this, have a look at Chapter 26.
77-
If r = i - if, then Ar = Ai - Д-'. If is constant, Л if = 0. * so Ar = Ai.
Figure 14.4 Short-run equilibrium output and interest rates
The equilibrium level of output ot the central bank's chosen nominal interest rate is read off the IS curve. In equilibrium, the LM curve must also go through that point and this occurs through the endogenous money supply. The real interest rate equals the nominal interest rate minus Igiven) expected inflation.
Monetary policy rule:
T) 4- l(Y, i - ire) + G
(1( 7Г - 7Г1)
These three equations are the same as in Chapter 5, but with just two differences: investment spending in thc IS relation depends on the real interest rate, which is equal to thc nominal interest rate minus expected inflation,- and the monetary policy rule now explicitly depends on thc inflation target, 77'.
The associated IS and I.M curves are drawn in f igure 14.4, for given values of P, тт, тт', r,„ G and T, and (or a given expected rate ol inllation, тг''.
• for a given expected rale ol inllation (тте), the nominal interest rate and the real interest rale move together Hence, if the central bank chose to reduce the nominal interest rate, this implies an equal
\
decrease in the real interesi rate, leading to an increase in spending and in output. The /5 curve ts downward sloping.
• The LM curve is upward sloping: for a particular value ot the money stock, a higher nominal interest rate, which leads to a decrease in the demand for money, requires an increase in output. In practice given that output won't adjust immediately, a higher nominal interest rate chosen by the central bank requires a reduction in the supply of money through open-market operations which implies that the LM curve shilts up.
• The equilibrium is at the intersection of the IS curve and the LM curve, at point A, with output level Уц and nominal interest rate / .], Given the nominal interest rate, iA, the real interest rate, rA, is given by rA = iA - 7Г'.
Nominal and real interest rates in the short run
Assume that the economy :s initially at the natural rate of output, so YA = Y„. Now suppose that the central bank raises its inllation target. ~T to 77 '. What happens to output, to the nominal interest rate and to the real interest rate in the short run?
One ol the lessons from our analysis ol monetary policy in The Core is that, in the short mn, the actual rate ol inflation, 7r, won't respond much in the short run—so we will assume no response in the short run. Therefore, looking at the monetary policy rule, the nominal interest rate will fall by the amount а !тт'' - тг'). What happens to output and to both nominal and real interest rates in the short run is shown in Figure 14.5
By choosing a lower nominal interest rate, the central bank must undertake immediate open-market operations to increase M, which shilts the LM curvc down. For a given level of output, the decrease in the nominal interest rate requires an immediate increase in the real money stock. II we assume—as seems reasonable—that people and firms don't revise their expectations ol inflation immediately, the IS curve doesn't shift. Given expected inllation, a given nominal interest rate corresponds to the same real interest rate and to the same level ol spending and output. With the nominal interest rale lowered
7Ге
E
о Z
Figure 14.5 The short-run effects of expansionary monetary policy
I L
Ул
+
Output, V
An increase in the inflation target at a given expected inflation rate and an actual rate in the short run leads the central bank to reduce the norrinal interest rate. This leads to an equal decrease in the real interest rate, and so output rises.
Irom /1 to in, thc economy moves down the IS curve,- the equilibrium moves from A to B. Output is higher. The LM curve shilts endogenously Irom LAI to LAI'. With the nominal interest rate lower, and In the short run.» given expected inflation, the real interest rate tails the same amount to r);.
To summarise: In the short run. the expansionary monetary policy leads to a decrease in the nominal interest rate and a higher money supply.
This leads to an identical decrease in the real interest rale and to an increase in output.
exoansionary monetary policy leads to a decrease in both i and r. and so У increases.
Go back lo our lirst imaginary quote: The goal ol the RBA in early 2002 was precisely to achieve this outcome. Worried that the global recession might get worse, the RBA, like most other central banks, chose to decrease the real interest rate to increase output.
Nominal and real interest rates in the medium run
Turn now lo thc medium run. Suppose thai the central bank increases the inllation largei (and. by implication, the rate ol money growth 1 permanently. Whai will happen to output and nominal and real interest rates in the medium run?
To answer that question, wc rely on two of the central propositions we derived in Thc Core:
• In the medium run, output returns lo the natural level ol output.
As you saw in Chapter o, output returns it) the natural level ol output because in the medium run lhe unemployment rate must return to lhe natural rate ol unemployment. I he natural level of output is simply the level ol output associated with the natural rate of unemployment.
Although we spent Chapters 10 to IS looking at growth of output over time, we will, lor simplicity, ignore output growth here. So we will assume that Y„, the natural level of output, is constant over time.
• In the medium run. the rale ol inflation is equal to the central hanks inllation target, which also equals the rate ol money growth minus the rate ol growth ol output.
We derived the last part ol this conclusion in Chapter 9. The intuition lor it is simple: a growing level
The implications ol these two propositions lor the behaviour ol the real interest rate and the nominal interest rate in the medium run are then straightforward:
• Take the real interest rate lirst. l or convenience, let us rewrite thc IS equation:
у - C(Y - T) + l(Y,r + G
One way ol thinking about the IS relation is that it tells us, for given values of G and T, what real interest rate, r, is needed to sustain a given level ol spending, and so a given level ot output, V. Il, lor example, output is equal to the natural level ol output, Yn, then, lor given values ol G and T, the real interest rate must be such that
Y„ C(Y„ - T) + HY„,r) + G
In the medium run. ►
In the medium run ►
(ifgr=0W=7r'" = gw
By analogy with our use of the word natural to denote the level of output in thc medium run, let us call this value of the real interest rate the natural real interest rate, and denote it by r„. Then, our earlier proposition that, in the medium mn, output returns to its natural level Y„, has a direct implication: lor given G and T. in the medium run. the real interest rate returns to the natural interest rate, r,,. Only real shocks can allect the value ol r„—tor example, a higher level ol G requires an equivalent reduction in I, which implies a higher value ot r„. In other words, in the medium run. both
output and the real interest rate are unaffected by changes in the inllation target and the implied rate of money growth.
• Turn to the nominal interest rate. Recall the relation between the nominal interest rate and the real interest rate:
i = r + 77
You have iust seen that in the medium run the real interest rate equals the natural interest rate.
r„. So,
i = r„ + 7Г'
In the medium run, expcctcd inllation is equal to actual inflation. I People cannot have incorrect expectations of inflation forever. I So,
I = r„ -r 77
In the medium run, inflation is equal to the ccntral bank's inflation target, тг', and thus money growth 'recall that wc arc assuming that the rate ol growth of output equals zero), so,
I - r„ + 7T; = r„ + g„
In words: In the medium run, the nominal interest rate is equal to the natural real interest rate plus the target inflation rate. So, an increase in the inflation target leads to an equal increase in the nominal interest rate.
These medium-run results ol an increase in the inflation target can be shown in our IS-L/V1 diagram. In Figure 14.6. the initial medium-run equilibrium is at point A. The final medium-run equilibrium is at point A'. Output is the same in both equilibria. Y„. The nominal interest rate at A' is higher than at Л by the amount ol the increase in the inllation target. The IS curve has shiltcd up to IS' Irom IS. This is because it is drawn for a given value of cxpectcd inflation, which is higher in
Figure 14.6
The medium-run effects of expansionary monetary policy
©
Output, У
An increase in the inflation target In the medium run leads lo a one-for-one increase in the nominal interest rate and the some value for output
the final medium-run equilibrium. (The LM curve has to go through A' because its position is determined endogenously. I
To summarise: In the medium run, a change in thc stance of monetary policy (that is, a change in thc inflation target) doesn't affect the real interest rate, but it alfects actual inflation and the nominal interest rate one-for-one.
A permanent increase in the inllation target ol, say, 10 per cent is eventually reflected in a 10 per cent increase in the actual inflation rate, and a 10 percent increase in the nominal interest rate—leaving the real interest rate unchanged. The result that, in the medium run, the nominal interest rate increases one-for-one with inflation is known as the Fisher effect, or the Fisher hypothesis, after Irving Fisher, an Irving Fisher. The Rote> economist at Yale Llniversity who lirst stated it and its logic at the beginning of the twentieth century.
of hite ел (New YOI K. This result underlies the second imaginary quote at the beginning ol the section. II financial Macmillan. 1906). . . , , . , in»* it i
investors were worried that the appointment ot a new governor at the KnA in 2006 might lead to a
higher inflation target, they were right to expect higher nominal interest rates in the future.
From the short run to the medium run
We have now seen how to reconcile thc two quotes at thc beginning ot the section: an easier or expansionary monetary policy (a higher inflation target) is likely to lead to a decrease in nominal interest rates in the short ain, but to an increase in nominal interest rates in the medium run.
What happens between the short ran and the medium run? A full characterisation of the movements ol the real interest rate and the nominal interest rate over time would take us beyond what wc can do here. But the basic features of the adjustment process are easy to describe.
In the short run, the real interest rale and the nominal interest rate both go down. Why don't they stay down forever? Because there arc many steps, let us first state the answer in short: because low interest rates lead to high output, which eventually leads to high inllation- high inllation leads in turn to the central bank increasing interest rates. Now the answer step by step:
• As long as the real interest rate is below the natural real interest rate—that is, the value correspond¬ing to thc natural level of output—output is higher than the natural level. Equivalently, unemploy¬ment is below the natural rate. From the Phillips curve relation, we know that as long as unemployment is below the natural rate, inflation increases.
• As inflation increases, it begins to approach the raised inflation target, and so the central bank responds by increasing the nominal interest rate (by the (actor I + a from the monetary policy rule). And, expected inflation starts to rise but at a slower rate than the nominal interest rate, and so the real interest rate rises by a little, which means output begins to return back to the natural rate.
• In the medium ran, the real interest rate increases back to its initial natural value. Output is then back to the natural level of output, unemployment is back to the natural rate of unemployment, and inflation is no longer changing. As thc real interest rate converges back to its initial value, the nominal interest rate converges to a new higher value, equal to the real interest rate plus the new, higher, rate of inflation (equal to thc inflation target and the rate of money growth).
Figure 14.7 summarises these results by showing the adjustment over time ol the real interest rate and thc nominal interest rate to an increase in thc inflation target from, say, 0 per cent lo 10 per cent, starting at time I. Before time I, both interest rales are constant and equal to each other. The real interest rate is equal to r„. Thc nominal interest rate is also equal to r„ (as inflation and expected inflation arc- equal to zero).
At time t, thc inflation target increases from 0 percent to 10 percent. The central bank immediately lowers the nominal interest rate. The real interest rate falls as well. If expected inflation increases a little initially, the decrease in thc real interest rate is larger than the decrease of the nominal interest rate.
In the short run: ►
ii,ri;r < r„ Y>Y„
=)||<и.э тгТ.
Over time: Gradually ►
77 -> тг7 => it
more than r! or
n«T =» rt => Yl.
In the medium run: ► r=r„\Y = Y„;u=u„: тт= = gW
/ = Г, + 7ГТ = Г. +
F.ventually, the nominal interest rate and the real interest rate start increasing. In the medium ran. thc real interest rate returns to its initial value. Inllation and expected inflation converge to the new rate ol money growth, thus 10 per cent. Thc nominal interest rate converges to a value equal to the real interest rate plus 10 per cent.
t
Time
fin increase in the inflation target 'say, by 10 per cent) leads initially to an immediate decrease in both the real and the nominal interest rate. Over time, the real interest rate returns to its initial value. The nominal interest rate converges to a new higher value, equal to the initial value plus the increase in the inflation target
Evidence on the Fisher hypothesis
There is plenty of evidence that a monetary expansion decreases nominal interest rates in the short run (see, tor example, Section 5.5'. But how much evidence is there lor the Fisher hypothesis, the propo¬sition that, in the medium run, increases in inllation lead to one-for-one increases in nominal interest rates?
r„ +
Real interest rate
(j u en
Figure 14.7 The adjustment of the real and nominal interest rates to expansionary monetary policy
Economists have tried to answer this question by looking at two types ol evidence. One is the relation between nominal interest rates and inflation across countries. Because the relation holds only in the medium run, wc shouldn't expect inllation and nominal interest rates to be close to each other in any one country at any one time, but the relation should hold on average. I his approach is explored further in the focus box Nominal interest rates and inllation across Latin America in the early 1990s', which finds substantial support for the Fisher hypothesis.
®
The other type of evidence is the relation between the nominal interest rate and inflation over time for one country. Again, the Fisher hypothesis doesn't imply that the two should move together from year to year But it does suggest that the long swings in inflation should eventually be reflected in similar swings in the nominal interest rate. To see evidence ot these long swings, we need to look at as long a period ot time as we can. Figure 14.8 looks at the nominal interest rate and inllation in Australia since 1930. I he nominal interest rate is the two-year Treasury bond rate, and inflation is the rate ot change of the CPI.
NOMINAL INTEREST RATES AND INFLATION ACROSS LATIN ERICA IN THE EARLY 1990s
Figure I plots nominal interest rate—inflation pairs for eight Latin American countries (Argentina, Bolivia, Chile, Ecuador. Mexico, Peru, Uruguay and Venezuela) for 1992 and 1993. Because the Brazilian numbers would dwarf those from other countries, they are not included in the figure. (In 1992. Brazil's inflation rate was 1.008 per cent and its nominal interest rate was 1,560 per cent. In 1993, inflation was 2,140 per cent and the
Figure I
175 i
■ A93
50
100
ISO
0
0
Nominal interest rates and inflation: Latin America, 1992-93
Inflation rate (%)
Brazil is not shown, as its four-digit nominal interest rate and inflation rate would be way off the scale.
nominal interest rate was 3,240 per cent.) The numbers for inflacion refer to the rate of change of the CPI. The numbers for nominal interest rates refer to the 'lending rate'.The exact definition of this term varies with each country, but you can think of it as corresponding to the prime interest rate—the rate charged to borrowers with the best credit rating.
Note the wide range of inflation rates, from 10 per cent to about 100 per cent. This is precisely why we have chosen to present numbers from Latin America in the early 1990s. With this much variation in inflation, we can learn a lot about the relation between nominal interest rates and inflation. And the figure indeed shows a clear relation between inflation and nominal interest rates.The line drawn in the figure plots what the nominal interest rate should be under the Fisher hypothesis, assuming an underlying real interest rate of S per cent, so that i = 5% + —.The slope of the line is I. Under the Fisher hypothesis, a I per cent increase in inflation should be reflected in a I per cent increase in the nominal interest rate.
As you can see, the line fits well; roughly half of the points are above the line, the other half below.The Fisher hypothesis appears roughly consistent with the cross-country evidence from Latin America in the early
1990s.
Figure 14.7 has at least three interesting features:
• The steady increase in inflation 1 rom the earlv 1960s to the earlv 1980s was associated with a roughly parallel increase in the nominal interest rate. The decrease in inflation since the mid-1980s has been associated with a decrease in the nominal interest rate. These long-run evolutions support the Fisher hypothesis.
• Evidence ol the short-run effects that were discussed earlier is also easy to see. The nominal interest rate lagged behind the increase in inflation in the 1970s (implying negative real interest rates!. Then the disinflation of the late 1980s was associated with an initial increase in the nominal interest rate, followed by a much slower decline in the nominal interest rate than in inflation implying high real interest rates for some time).
• The other episode ol inflation, during and alter World War II. underlines the importance ol the 'medium-run qualifier in the Fisher hypothesis. During that period inflation was high but short-
24 -i
я
с
с
T-bond rate
т 1 1 1 1 1 1 1 1 1 1 1 1 1 1—
1930 1935 1940 1945 1950 1955 I960 1965 1970 1975 1980 1985 1990 1995 2000 2005
О
л
f4
-12
Figure 14.8 The Australian five-year Treasury bond yield and inflation. 1930-2008
The increase in inflation from the early 1960s to the early 1980s was associated with an increase in the nominal interest rate. The decrease in inflation since the late 1980s has been associated with a decrease in the nominal interest rate. The temporary spike in 2000 was just the GST.
4 Maintaining low nominal interest rates was also a deliberate policy to reduce the interest payments on the large government debt created during World War II.
SOURCE:RBA.Table G0I. F02: M. Budir. RBA Discussion Paper. 1977.
lived. And it was gone before it had time to be reflected in a higher nominal interest rate. The nominal interest rate remained very low throughout the 1940s and early 1950s, and the real interest rate was negative, which was a big factor in stimulating investment in those difficult times. More careltil studies confirm our basic conclusion. The Fisher hypothesis < that in the medium run. increases in inflation are reflected in a higher nominal interest rate) appears to lit the data quite well. Hut the adjustment takes a long time. The data confirm the conclusion reached by Milton Friedman, which was quoted in a locus box in Chapter 8. lhat it typically takes a couple of decades' tor nominal interest rates to reflect the higher inflation rale.
The nominal interest rate tells you how many dollars you need it) repay in the future in exchange lor one dollar today.
The real interest rate tells you how many goods you need to repay in the future in exchange for one good today.
The real interest raie is approximately equal to the nominal interest rate minus expected inflation. Thc expected present discounted value ol a sequence ol payments equals the value today ol the expected sequence of payments. It depends positively on current and future expected payments. It depends negatively on current and future expected interest rates.
In discounting a sequence of current and expected future nominal payments, one should use current and expected luture nominal interest rates. In discounting a sequence ot current and expected luture real payments, one should use current and expected luture real interest rates.
Investment decisions depend on the real interest rate. The choice between money and bonds depends on the nominal interest rate. Thus the real interest rate enters the IS relation, while the nominal interest rate enters the LM relation.
In the short run, an expansionary monetary policy typically leads to a decrease of both ihe nominal interest rate and the real interest rate
• In the medium run, an expansionary monetary policy has no ellect on the real interest rate, and increases the nominal interest rate one-lor-one with the higher inllation target.
• The proposition that, in the medium run, changes in inflation are reflected one-lor-one in changes in the nominal interest rate is known as the Fisher effect or the Pisher hypothesis. The empirical evidence suggests that, although it takes a long time, changes in inflation are eventually rellected in changes in the nominal interest rate.
KEYTERMS
• nominal interest rates, 323
• real interest rates, 323
• expected present discounted value. 326
• discount lactor, 326
• discount rate, 326
• present discounted value, present value, 328
• Fisher effect, Fisher hypothesis, 336
QUESTIONS AND PROBLEMS
Quick check
1. Using the information in this chapter, label each of the following statements 'true', 'false' or 'uncertain'. Explain briefly.
a. As long as inflation remains roughly constant, the movements in the real interest rate arc roughly
equal to the movements in the nominal interest rate, h. Il inllation turns out to he higher than expected, then the realised real cost ol borrowing turns out to be lower than the real interest rate.
c. Looking across countries, the real interest rate is likely to vary much less than the nominal interest rate.
d. The real interest rate is equal to the nominal interest rale divided by the price level.
e. In the medium run, the real interest rate isn't allccled by inllation.
f. The Fisher cllcct states that in the medium ran the nominal interest rate isn't affected by inflation.
g. The experience ol Latin American countries in ihe early 1990s supports the Fisher hypothesis.
h. The value today of a nominal payment in the future cannot be greater than the nominal payment itself.
i. The real value today ol a real payment in the future cannot be greater than the real payment itself.
2. For which of the following problems would you want to use real payments and real interest rates, or nominal payments and nominal interest rales, to calculate the expected present discounted value? In each case, explain why.
a. Estimating the present discounted value of the profits from an investment in a new machine.
b. Estimating the present value ol a ten-year Commonwealth government bond.
c. Deciding whether to lease or buy a car.
3. Compute the real interest rate using the exact formula and the approximation formula for each set of assumptions listed in (ai to (c).
a. i - 4%; 7Г' - 2%
b. I - 15%; 77' = 11%
c. i - 54%; 77'' = 46%
d. t= 0; it'' 5%
4. Nominal and real interest rales around the world
a. Can thc nominal interest rate ever be negative? Explain.
b. Can the real interest rate ever be negative? Under what circumstances? II so. why not iust hold cash instead?
c. What are the ellects ol a negative real interest rate on borrowing and lending?
d. Find a recent issue ol The Economist and look at the tables in the back ('Economic Indicators' and 'Financial Indicators ). Use the three-month money market rate as the nominal interest rate and the most recent three-month rate ol change in consumer prices as the expected rate ol inllation (both are in annual terms 1. Which countries have the lowest nominal interest rates? Which countries have thc lowest real interest rates? Are these real interest rates close to being negative?
5. Saving for retirement
You want to save $2,000 today for retirement in forty years. You have to choose between two plans:
i. Pay no taxes today, put the money in a superannuation account, and pay laxes equal to 47 per cent of the total amount withdrawn at retirement.
ii. Pay taxes equivalent to 47 per cent of the investment amount today, put the remainder in an interest-yielding account, and pay 47 per cent in tax each year on interest earned but none when you withdraw your funds at retirement.
a. What is the expected present discounted value of each of these plans il the interest rate on the superannuation account is 5 per cent, and thc interest rate on thc investment account is 2.65 per cent? Which plan would you pick?
b. II the tax on the linal withdrawal from the superannuation account was reduced to 25 percent, what would be the net gain from the lirst plan?
c. With all tax rates being 47 percent, which plan would you pick il the interest rate on both plans was 5 per cent?
6. Approximating the pricc of long-tern: bonds
The present value of an infinite stream of dollar payments of Sz I that starts next year) is Sz/i when the nominal interest rate, i, is constant. This formula gives the price of a consol—a bond paying a fixed nominal payment each year, forever. It is also a good approximation for the present discounted value of a stream of constant payments over long but not infinite periods, as long as i is constant. Let's examine how close the approximation is. Suppose that i = 10 per cent.
a. Let $z = 100. What is the present value of the consol?
b. What is the expected present discounted value for a bond that pays over the next ten years? Twenty years? Thirty years? Sixty years?
c. Repeat the exercise for i - 2 per cent and /' - 5 per cent.
7. The Fisher hypothesis
a. What is the Fisher hypothesis?
b. Docs thc experience of Latin American countries in the 1990s support or refute the Fisher hypothesis? Explain.
c. Look at the figure in the focus box on Latin America. Note that the line drawn through the scatter ol points doesn't go through the origin. Does the Fisher effect' suggest that it should go through the origin? Explain.
d Consider this statement: II the Fisher hypothesis is true, then changes in the inflation target and thus the medium-run growth rate ol the money stock translate one-for-one into changes in i, and the real interest rate is left unchanged. Thus, there is no room lor monetary policy to allect real economic activity.' Discuss.
Dig deeper
8. When looking at the short ran in Section 14.4. we saw how an expansionary monetary policy led to a lower nominal interest rate, a lower real interest rate and higher output.
The analysis in the text (as summarised in Figure 14.5) assumed that inflation, it. and expected inflation, тг1'. didn't change in the short run. Let's now relax this assumption, and assume that actual and expected inflation increase by Л— and J—1'.
a. Show die ellecl on the IS curve. Explain in words.
b. Is there an effect on the LM curve? Explain in words.
c. Show the ellect on output Could the nominal interest rale end up higher—noi lower—than before ihe change in monetary policy? Why?
d. Fvcn if whai happens to the nominal interest rate is ambiguous, can you tell what happens to the real interest rate? Hint: Whai happens to output relative to Figure 14.5? What does this imply lor what happens to the real interest rate?)
e. II actual and expected inflation immediately jumped to the new inllation target value, what would happen to output and interest rates?
Explore further
9. Some bonds issued by the Commonwealth of Australia make payments indexed to inflation. These inflation-indexed bonds compensate investors (or inflation. Therefore, the current interest rales on these bonds are real interest rate—interest rates in terms of goods. These interest rates can be used, together with nominal interest rates, to provide a measure of expected inflation. Let's see how.
Co to the website of the RBA (www.rba.gov.au/Statistics/iudicative.litmll and get the most recent statistical release for index bonds rates and the current nominal interest rate on a Treasury bonds with the SAME date to maturity. What do you think participants in the financial markets think the average inflation rate will be over the lime to maturity that you have selected?
We invite you to visit the Blanchard-Sheen page on the Pearson Australia website at
www.pearson.com.au/highered/blanchardsheen3e
for many World Wide Web exercises relating to issues similar to those in this chapter.
APPENDIX: DERIVING THE EXPECTED PRESENT DISCOUNTED VALUE USING REAL OR NOMINAL INTEREST RATES
This appendix shows that the two ways of expressing present discounted values, equations (14.5) and (14.7). are equivalent.
Equation (14.5) gives the present value as the sum of current and future expected nominal payments, discounted using current and future expected nominal interest rates:
$zf+i $Zt+2
$v' = T+X + 0 + 00 (,4-5)
Equation (14.7) gives the present value as the sum of current and future expected real payments, discounted using current and future expected real interest rates:
zUl zt+2 ,,, _
'= + (1 + rt)(i + bi) •••
Divide both sides of equation (14.5) by the current price level, P,. So:
$V,__l_$z|ll 1_
P, = 1 + /t Pt + (1 + ,')(1 + J?.,) P,
Let's look at each term on the right side of equation (14A. I), and show that it is equal to the corresponding term in equation (14.7):
• Take the first term:
1
1 + it Pt
Multiply the numerator and the denominator by the price level expected for next year, to get
t+1
1 Pt* 1 $2t+1
1 + it P,
Note that the fraction on the right. is equal to the expected real payment at time t + 1. Note
that the fraction in the middle. P^+i/P,. can be rewritten as 1 + [(P^ - P,)/Pt], thus using the definition of expected inflation, as (1 + nct).
Using these two results, rewrite the first term as
1 + r, 4+1
Recall the relation between the real interest rate, the nominal interest rate and expected inflation, in equation (I4.3) [(1 + rt) = (1 + /,)/(1 + IT*)]. Using this relation in the previous equation gives
1
This term is the same as the first term on the right side of equation (14.7). • The same method can be used to rewrite the next and all subsequent terms: make sure that you can derive the next one.
We have shown that the right side of equations (14.7) and (14A. I) are equal to each other. It follows that the terms on the left side are equal, so.
' Pt
This says:
The present value of current and future expected real payments, discounted using current and future expected real interest rates (the term on the left side), is equal to:
(I4A.I)
The present value of current and future expected nominal payments, discounted using current and future expected nominal interest rates, divided by the current price level (the term on the right side).
CHAPTER ф
Financial Markets and Expectations
n our first pass at financial markets in The Core (Chapter 4), we assumed there were only two assets: money and one type of bond—a one-year bond. We now look at an economy with a richer and more realistic menu of non-money assets: short-term bonds, long-term bonds and stocks.
Our focus throughout this chapter is on the role of expectations in the determination of bond and stock prices.
Section 15.1 looks at the determination of bond prices and bond yields. It shows how bond prices and yields depend on current and expected future short-term interest rates, it then shows how we can use the yield curve to learn about the expected course of future short-term interest rates. Section 15.2 looks at the determination of stock prices. It shows how stock prices depend on current and expected future profits, as well as on current and expected future interest rates. It then discusses the effects of movements in economic activity on stock prices.
Don't worry: we are just introducing the terms here. They will be defined and explained
in this section. ► interest rates. Yields on bonds with a longer maturity are called long-term interest rates.
Section I 5.3 discusses fads and bubbles in the stock market—episodes when stock prices appear to move for reasons unrelated to either profits or interest rates. It introduces house prices and then discusses how central banks might respond to bubbles.
15.1 BOND PRICES AND BOND YIELDS
On any given day, we observe the yields on bonds of different maturities, and so wc can trace graphically how the yield depends on the maturity of a bond. This relation between maturity and yield is called the yield curve, or the term structure of interest rates. (The word term is synonymous with 'maturity'.) Figure 15.1 gives, for example, the term stmclure on Australian Commonwealth government bonds on 6 December 2001 and I September 2008. The choice of the two dates isn't accidental,- why we chose them will become clear shortly.
Note how on 6 December 2001 the yield curve was sharply upward sloping after the six-month rate, increasing from an overnight interest rale of 4.25 per cent to a ten-year interest rate of 5.76 per cent. In other words, long-term interest rates were higher than short-term interest rates. Then on 1 September 2008 the overnight rate of 7.25 per cent was higher than all other maturities, reaching clown to the ten-year rate ol 5.73 per cent.
Why was the yield curve upward sloping in December 2001 but downward sloping in September 2008? Put another way, why were long-term interest rates higher than short-term interest rates in December 2001, but lower lhan short-term interest rates in September 2008? What were financial market participants thinking at each date? To answer these questions, and more generally to think about ihe determination of the yield curve and ihe relation between short-term interest rates and long-term interest rates, we proceed in two steps:
• We derive bond prices lor bonds of different maturities.
4 Note that both bonds are discount bonds (see the focus box 'The vocabulary of bond markets'l.
• We then go from bond prices to bond yields, and examine the determinants of the yield curvc, and ol the relation between long-term interest rates and short-term interest rates.
Bond prices as present values
In much of the section wc will look at just two types of bonds, a bond that promises one payment of $100 in one year—a one-year bond and a bond that promises one payment of $100 in two years—a two-year bond. Once you understand how their prices and their yields arc determined, it will be easy to generalise our results to bonds of any maturity. We will do this later on.
Term structure <: > Yield
4 curve.
< To find out what the term structure of interest rates is at the t me you read this chapter, go to
FINANCIAL MARIO-TS AND EXPECTATIONS chapter 15
Lei's start by deriving the prices of the two bonds. • Given that the one-year bond is a promise lo pay $100 nexl year, it follows from Section 14.2 in Chapter 14 thai its price, call it $PU, must be equal to the present value ol a payment of $100 next
Figure 15.1 Australian yield curves. 6 December 2001 and I September 2008
7.5 "
7.0 -
6.5 -
с 6.0 " 01 и
£ 5 5.0 " 4.5- 4.0 '
I September 2008
6 December 2001
i I I Г
Cash rate I month 3 month 6 month
2 year
5 year 10 year
The yield curve was downward sloping on I September 2008 and upward sloping on 6 December 2001.
SOURCE; RBA. updated OP-10. For ons-month, three-month and six-month yields, we used indexed swaps, which closely approximate Treasury
notes in terms of risk. For two-year, five-year and ten-year yields, vve used Treasury bonds.
F В S
Understanding the basic vocabulary of financial markets will help to make them less mysterious. Here is a
basic vocabulary review.
• Bonds are issued by governments or by firms. If issued by the government or government agencies, the bonds are called government bonds. If bonds are issued by firms, they are called corporate bonds. Although all Australian government bonds and many corporate bonds are quoted on the Australian Stock Exchange (www.asx.com.au), most trading takes place in over-the-counter, wholesale markets.
• In Australia, as in the United States, bonds are rated for their default risk (the risk that they won't be repaid) by two private firms, the Standard & Poor's Corporation (S&P) and Moody's Investors Service. Moody's bond ratings range from Aaa for bonds with nearly no risk of default, such as Australian or US government bonds, to С for bonds where the default risk is high. A lower rating typically implies that the bond has to pay a higher interest rate, or else investors won't buy it.The difference between the interest rate paid on a given bond and the interest rate paid on the bond with the highest (best) rating is called the risk premium associated with the bond. Bonds with high default risk are sometimes called junk bonds.
• Bonds that promise a single payment at maturity are called discount bonds.The single payment is called the face value of the bond.
• Bonds that promise multiple payments before maturity and one payment at maturity are called coupon bonds.The payments before maturity are called coupon payments.The final payment is called the'face value' of the bond. The ratio of coupon payments to the face value is called the coupon rate. The current yield is the ratio of the coupon payment to the price of the bond.
For example, a bond with coupon payments of $5 each year, a face value of $ 100 and a price of $80 has a coupon rate of 5 per cent and a current yield of 5/80 = 0.0625 = 6.25 per cent. From an economic viewpoint, both the coupon rate and the current yield are not interesting measures.The correct measure of the interest rate on a bond is its yield to maturity, or simply yield; you can think of it as roughly the average interest rate paid by the bond over its life. (The life of a bond is the amount of time left until the bond matures.) We will define the yield to maturity more precisely later in the chapter.
• Australian government bonds can range in maturity from a few days to thirty years. Bonds with a maturity of up to a year when they are issued are called Treasury notes. They are discount bonds, making only one payment at maturity. Bonds with a maturity of one to ten years or more when they are issued are called Treasury bonds. Treasury bonds are coupon bonds. (Note: In the United States the definitions are a little different: bonds with a maturity up to one year are called 'Treasury bills', those with a maturity from one to ten years are 'Treasury notes', and those greater than ten years are Treasury bonds'.)
• Bonds are typically nominal bonds. They promise a sequence of fixed nominal payments—payments in terms of domestic currency. However, there are other types of bonds. Among them are indexed bonds, bonds that promise payments adjusted for inflation rather than fixed nominal payments. Instead of promising to pay, say, $ 100 in a year, a one-year indexed bond promises to pay 100 (1 + p) dollars, where fj is the rate of inflation that will take place over the coming year. Because they protect bondholders against the risk of inflation, indexed bonds are popular in many countries. They play a particularly important role in the United Kingdom, where, over the last twenty years, people have increasingly used them to save for retirement. Though they exist in Australia, they haven't been very popular. By holding long-term indexed bonds, people can make sure that the payments they receive when they retire will be protected from inflation. Should inflation become high and therefore more unpredictable in the future, index bonds will surely play a more prominent role.
QCUS BOX
EVOC
Yields of any macurity ► are always expressed in annualised form so that they can be easily compared.
We will discuss securitised bonds again in Chapter 22 when examining the causes of the global financial crisis in 2008. ►
• Some bonds are constructed by packaging the cash flows from a portfolio or pool of other assets.These are called securitised bonds. Securitisation allows a financial institution to transfer risky assets from its own balance sheet to capital markets through the sale of these bonds. A good example is where a bank uses the cash inflows from many of its mortgages to issue bonds.The funds raised from the sale of the bonds would then be used to issue new mortgages.
FINANCIAL MARKETS AND EXPECTATIONS chapter 15
year. Let the current one-year nominal interest rate be /,,. Note lhat we now denote thc one-year interest rate in year I by iu rather than simply by i. as we did in earlier chapters. This is to make it easier lor you to remember that it is the one-year interest rate. So.
$100
$P„ = " (15.1)
I + I,,
The price of the one-year bond varies inversely with the current one-year nominal interest rale. Given lhat the two-year bond is a promise to pay $100 in two years, its price, call it P2( must be equal to the present value ol $100 two years Irom now:
100
$P-f = ■ ,, (15.2)
(I + !,,)( 1 + I?f+I)
where /,, denotes the one-year interest rate this year and denotes the one-year rate expected by financial markets for next year. The price ol the two-year bond depends inversely on both the currcnt one-year rate and thc one-year rale expected lor next year.
Arbitrage and bond prices
Before exploring further the implications of equations (15.11 and (15.21. let us look at an alternative derivation ol equation 1 15.21. This alternative derivation will introduce you to the important concept of arbitrage.
Suppose you have the choice between holding one-year bonds or two-year bonds. What you care about is how much you will have one year from now. Which bonds should you hold?
• Suppose you hold one-vear bonds, for every dollar you put in one-year bonds, you will get1 1 + iu) dollars next year. This relation is represented in the lirst line of figure 15.2.
• Suppose you hold two-year bonds. Because the price ol a two-year bond is $P2(, every dollar you put in two-year bonds buys you $ I $P2t bonds today.
When next year comes, the bond will have only one more year before maturity, and thus one year from today the two-year bond will be a one-year bond. Therefore the price at which you can expect to sell it next year is $P',, which is thc expected price of a one-year bond next year.
So for every dollar you put in two-year bonds, you can expect to receive $l/$P2( times $P"I(+|, or equivalently $Pl'1(4.,/$P?. dollars next year. This is represented in the second line of Figure 15.2.
Which bonds should you hold? Suppose you. and other linanciai investors, care only about expected return. This assumption is known as the expectations hypothesis. Il is a strong simplification: you and other financial investors arc likely lo care not only about the expected return but also about the risk associated with holding each bond. If you hold a one-year bond, you know with certainty what you will get next year. Il you hold a two-year bond, the price at which you will sell it next year is uncertain,- holding the two-year bond is risky. We leave this consideration aside here, but we briefly discuss it in the appendix to ibis chaptcr. i
Under thc assumption that investors only care about expected return, it follows lhat the two bonds must offer the same expected one-year return. Suppose this condition wasn't satisfied. Suppose that, lor example, the one-year return on one-year bonds was lower than the expected one-year return on two- year bonds. Nobody would warn lo hold ihe existing supply ol one-year bonds, and the market for
One-year bonds Year t $1 Year t + 1
$1(1 +i,t)
Two-year bonds $1 $1
$P2I
Figure 15.2
Returns from holding one-year and two-year bonds for one year
one-year bonds couldn't be in equilibrium. Only il the expected one-year return is the same on both bonds will financial investors be willing to bold both one-year bonds and two-year bonds. If the two bonds offer the same expected one-year return it follows from Figure 15.2 that
1
$P,
(15.31
The lelt side gives the return per dollar from holding a one-year bond lor one year,- the right side gives the expected return per dollar Irom holding a two-year bond for one year. We will call equations such as (15.3)—equations which state that the expected returns on two assets have to be equal— arbitrage relations. Rewrite equation (15.3 as
(15.4)
i +1,
Arbitrage implies that the price ol a two-year bond today is the present value of the expected price ol the bond next year. This raises the next question: What does the expected price of one-year bonds next year, $P'j,depend on?
The answer is straightforward, lust as the price ol a one-year bond this year depends on this year's one-year interest rate the price ol a one-year bond next year will depend on the one-year rate next year. Writing equation (15.1) lor next year (year I + I ) and denoting expectations in the usual way:
iioo
SK
' u. I
The price ol the bond next year is expected to equal the final payment, $100, discounted by the one-year interest rate expected lor next year.
Replacing $Р*|,., by $!00/( I + i'lt., i in equation 15.4) gives
$r2,
We use arbitrage to ► denote the proposition that expected returns on two assets must be equal. Some economists reserve arbitrage for the narrower proposition that riskless profit opportunities don't go unexploited.
$100
$P2t
(15.5-
(I - i,>)( i +
This expression is the same as equation ( 15.2 <. What we have shown is that arbitrage between one- and two-year bonds implies that the price of a two-year bond is the present value of the payment in two years—namely, $100—discounted using current and next year's cxpcctcd one-year interest rates.
From bond prices to bond yields
The relation between ► arbitrage and present values: arbitrage between bonds of different maturities implies that bond prices are equal to the expected present values of payments on these bonds.
Bond yields for any ► maturity are always expressed in annualised form, which makes comparison easy.
$90 = $100/(1+1а)2=> (1+/j,)2 = $100;$90=J 1+ia = V (100/90) ► =>b= 5.4%.
Having looked at bond prices, we now go on to bond yields. To begin, we need a definition of the yield to maturity. The yield to maturity on an и-ycar bond, or, equivalcntly. the л-year interest rate, is defined as that constant annual interest rate that makes the bond price today equal to the present value of future payments on the bond.
$Pv =
This definition is simpler than it sounds. Take, lor example, the two-year bond introduced earlier. Denote its yield by iv, where the subscript 2 is there to remind us that this is the yield to maturity on a two-year bond, or equivalcntly, the two-year interest rate. Following the definition of the yield to maturity, this yield is the constant annual interest rate that would make the present value of $100 in two years equal to the price of the bond today. So, it satislies the lollowing relation:
ilOO
• 15.6)
(I * i2lP
Suppose the bond sells lor $90 today. Then, the two-year interest rate i2, is given by \ 100/90 - I, or 5.4 per cent. In other words, holding the bond for two years—until maturity—yields an interest rate ot 5.4 per cent per year.
What is the relation of the two-year interest rate to the current one-year interest rate and to the expected one-year interest rate? To answer this look at equations (15.6) and (15.5). Eliminating $P;;f between the two gives
$100
(1+Ь,)2 (1 + /,,)(! + t'S'(t|)
Rearranging:
(I + 12,)2 = (I + !lf)(l + /V.)
This gives us the exact relation between the two-year interest rate iI(, the current one-year interest rate /',,, and next year's expected one-year interest rate iYVm- A useful approximation to this relation is given by
I
ht"J ('if + I'u.i)
Equation (15.7) simply says that the two-year interest rate is (approximately) the average of the current one-year interest rate and next year's expected one-year interest rate.
We have focused so lar on the relation between the prices and yields ol one-year and two-year bonds. But our results generalise to bonds of any maturity.
• We could have looked at bonds with maturities shorter than a year. For example, the yield on a bond with a maturity of six months is (approximately) equal to the average of the current three-month interest rate and next quarter's expected three-month interest rate.
• Or, we could have looked instead at bonds with maturities longer than two years. For example, the yield on a ten-year bond is (approximately ) equal to the average of the current one-year interest rate and the one-year interest rates expected for the next nine years. The approximation for an «-year bond compared with a one-year bond becomes:
"II + 'II-I + 'I I, I + • • - + «ТЫ_.)
Put simply, long-term interest rates rellect current and luture expected short-term interest rates.
Interpreting the yield curve
The relations just derived give us the keys we need to interpret thc slope ol the yield curve. By looking at yields lor bonds ol different maturities, we can inter what linanciai markets expect that short-term interest rates will be in the future. Or to put it another way: the current and future expected short-term interest rates in the formula can be the overnight cash rate, which wc know to be the interest rate set by the central bank. This means that the tormula can be used to understand what determines all other interest rales in terms of current and future monetary policy.
Lets think about one-year and two-year interest rates. Suppose we want to find out what financial markets expect the one-year interest rate to be one year from now. All we need to do is to look at the yield on a two-year bond, ь,, and thc yield on a one-year bond, /,,. From equation (15.7), multiplying both sides by 2 and reorganising, we get
/V, « 2iv - iu (15.8)
Thc one-vear interest rate expected for next year is equal to twice the yield on a two-year bond minus the current one-year interest rate. Suppose, lor example, that the yield curve for 1 September 2008 shows:
• The one-year interest rate, iu, was 6.0 per cent.
$100
4 We used a similar approximation when we looked at the relation between the nomhal interest rate and the real interest rate in Chapter 14. See proposition 3 in Appendix 2.
(15.7)
FINANCIAL MARKETS AND EXPECTATIONS chapter I S
• The two-year interest rale, ь(, was 5.5 per cent.
• From equation 115.8), it follows that, on thai day, linancial markets expected the one-vcar interest rate one year later—that is, the one-year interest rate on I September 2009—to equal 2 x 5.5% - 6% - 5%—that is. 1 percent lower than the one-year interest rate on 1 September 2008. In words: On I September 2008. financial markets expected the one-year interest rate to be substantially lower one year later.
Note that the yield curve on 6 December 2001 was nearly flat for maturities up to six months.What does this tell you about when financial markets expected the economy to turn around, and short-term interest rates to start rising! (The answer: Not right away Make sure you can explain why.) ►
More generally, when the yield curve is downward sloping—that is, when long-term interest rates are lower than short-term interest rales—this tells us thai financial markets expect short-term rates to be lower in the future. When the yield curve is upward sloping—that is, when long-term interest rales are higher than short-term interest rates—this tells us that financial markets expect short-term interest rates to be higher in the future. When the yield curvc is a hump shape, this tells us that financial markets cxpcct short-term interest rales to rise lor a period of time in the future (that is, to where the curve peaks), and then to lall alter that.
The yield curve and economic activity
We can now return to the question as to why the yield curve went from being upward sloping in December 2001 to being downward sloping in September 2008. F.quivalently, why did long-term interest rates go from being higher than short-term interest rates on 6 December 2001 lo being much lower than short-term interest rates on I September 2008? The answers:
• An unexpected slowdown in economic activity in 2001 after many years ol high growth was followed by the temporary sapping ol consumer confidence after the terrorist bombings in September 2001. This had led the RBA lo lower the short-term cash rate by 0.75 percentage points over three months, the lasi cut having been on 5 December 2001. It was widely believed that there would be a soil landing, perhaps with a bounce lor the economy. So, even as the slowdown was taking place, financial markets expected output growth to recover very soon and short-term interest rates to return to higher levels in the future, leading long-term interest rales to lall by much less than short-term interest rates. This is why there was an upward-sloping yield curve on 6 December 2001.
• The Australian economy had recovered by 2004 and the Reserve Bank progressively lifted the cash rate in 0.25 per cent increments to reach 7.25 per ccnt in March 2008. From 2003 to 2007, the world economy boomed and the extra global demand for energy (particularly from China and India) was pushing up the price of oil. as well as other resources. This major supply shock had in turn forced up prices in Australia and by June 2008 CPI inllation was still 4.5 per cent, well in excess of the Reserve Bank's inflation target range of 2-3 per cent. Yet on 1 September 2008, one- day before the central bank's monthly meeting, the yield curvc was downward sloping, with the cash rale at 7.25 per cent and the ten-year bond yield at 5.73 per cent. How can we explain this? Financial markets were expecting economic activity to slow down in 2008-09 because ol ihe negative fallout Irom the global financial crisis—the credit crunch— emanating Irom the LIS housing finance markets, which was increasing in intensity in September 2008. Thus markets expected short-term interest rales to lall in the future. And indeed this began lo happen the very next day, when the RBA cut the cash rate to 7 per ccnt, on 2 September 2008, which flattened the yield curve a little.
To go through the answer step by step, let's use the IS-LM model developed in The Core (Chapter 5) and then extended in Chaptcr 14. Think of the interest rate measured on the vertical axis as a short-term nominal interest rale, and that it is under the control of the central bank. Note: To keep the diagram simple, we will draw in the initial LM curve only in the next three ligures,- this isn't a problem because the LM curve isn't crucial to our analysis—the money supply adjusts endogenously to maintain financial market equilibrium.
The situation in December 2001 is shown in Figure 15.3 as equilibrium at point A. During 2001. the RBA had reduced the cash rate from 6.25 per cent to 4.25 per cent, represented as i, and the mild slowdown in output that led to it is represented by Y being less than Y„. In financial markets, it was believed that recovery would happen very soon, alter six months, shifting the IS curve to IS'. This
(INANCiAL MARKETS AND EXPECTATIONS chapter 15
IS' (forecast)
IS
У У„ Y' Output, Y
о
X
l/l
Figure 15.3 The Australian economy in December 2001
In December 2001 the economy was operating below the natural level of output, reducing inflationary pressures. The RBA eased monetary policy. Forecasts were for a quick bounce-back, a rise of output to perhaps above the natural level of output resulting in inflationary pressures requiring an increase in future short-term interest rates.
was expected to encourage the RBA to raise the cash rate in the luturc to i", which meant thai long-term interest rates were higher than short-term rates.
By 2008 the previously booming world economy had pushed up all commodity prices (which bcnclits incomc in Australia , including oil, which added to the cost ol production in Australia and elsewhere (until later in 2008. when oil priccs more than halved!). Further, the growing global credit crunch threatened reduced lending to lirms and thus real investment demand, and so (ears set in ol a lurther slowdown in economic activity. On I September 2008, financial markets believed that the danger ol economic stagnation were tar greater than the danger ol inflation, which implies that they believed that the economy in the future would lall from point A to A' in Figure 15.4, with lower
z
IS (forecast)
LM (forecast)
Figure 15.4 The Australian economy in September 2008
J_L
У г у
n
Output, Y
In September 2008 the Australian economy was probably just below the natural level of output The global credit crisis led financial markets to expect lower spending and output, perhaps even a recession, leading to easier monetary policy and thus lower short-term interest rates in the future.
aggregate demand and easier monetary policy. This is the likely explanation tor the downward slope ot the yield curve in September 2008.
Remember, there nay
be other possible ► explanations. Who can know the 'mind' of che financial market, which is made up of so many different players!
15.2 THE STOCK MARKET AND MOVEMENTS IN STOCK PRICES
5300 -
4300-
3510
1300-
1980
1984
1988
1992
1996
2000
2004
2008
Figure 15.5 Standard & Poor's ASX 200 stock price index, in nominal and real terms, 1980-2008
Australian nominal stock prices have been multiplied by about 7 since 1980. Real stock prices have only multiplied by almost 2. After the October /987 stock-market crash, real stock prices went through a slump until 1993. The upward trend ended in Australia in September 2007, and the nominal index fell by 37 per cent in the next year, while the real index fell by 31 per cent
after September 2008 when the global financial crisis intensified. The average annual growth rate ol ihe nominal stock price index from 1990 to 2008 was [/n(35IO) - liH 1536)J/19 4.35 per cent.
I his index, however, is nominal—that is, it gives the evolution ol stock prices in terms ol dollars. Of more interest lo us is ihe evolution of the price index in real terms (that is, adjusted for inllation). The evolution ol the real price index, constructed by dividing ihe nominal price index by the price deflator tor GDI' for each year is also shown in Figure 15.5. The price deflator is chosen lo equal 1.0 in January 1980. so the nominal price index and the real price index arc equal by construction in January 1980.
The plot ol the real price index shows a somewhat different picture. It shows how the stock market's perlormance was even more dismal in real terms in the early 1980s which wasn't very different Irom the 1970s and how il continued lo slump lor six years alter the 1987 crash. Roughly constant nominal stock prices and a steadily increasing price level implied steadily decreasing real stock prices. Only since 1992 have real stock prices pertormed well. Stock markets all over the world boomed (probably excessively until the end of the 1990s. This was characterised by Alan Greenspan of the US Fed as irrational exuberance', and was exemplified by the dot.com bubble on the Nasdaq. While all other major stock markets collapsed in 2001 the Australian stock market began a much milder lall more than a year later. This reflects the lact that Australia produces relatively little IT product but is a big user. The real index peaked in September 2007 at 1933. In the next fourteen months it fell to 974. iis value almost twelve years earlier. This fall was seen in stock markets in most other countries in 2007 and 2008 and was largely a result ol the unwinding ol ihe credit crisis brought on by the sub-prime mortgage problems in the United States. While slock prices have always been volatile they have delivered substantial real gains to their owners over the longer term. The annual average growth rate of the real stock price since 1990 was 1.7 percent, hut that gain excludes dividends.
Why did the stock market do so badly tor so long? Why did it rebound in the mid-1980s, and then crash? Why did it increase so much in the mid- to late-1990s? Why did it lall so much in one year in 2007-08? When will this come to an end? More generally, how do stock prices respond lo changes in the economic environment and in macroeconomie policy? This is ihe question we take up in the rest ot this section.
Stock prices as present values
What determines the price ol a stock that promises a sequence ol dividends in the future? Wc are sure that the material in Chaptcr 14 has become second nature lo you by now, and you already know ihe answer: the stock price must equal the present value ol future expected dividends.
Let $Q, be the price of the stock. Let $P, denote the dividend this year $Df4, the expected dividend next year, ihe expected dividend two years from now, and so on.
Suppose we look at the price ol the slock after ihe dividend has been paid this year—this price is known as the 'ex-dividend price—so that the lirst dividend to be paid alter ihe purchase of the stock is next year's dividend. (This is just a matter of convention,- we could alternatively look at ihe price before ibis year's dividend has been paid. What term would we have to add?' The price ol the slock is then given by
$a. J£k ад^
i+t„ (l + i1()(i + jfM)
The price ol the stock is equal to the present value ol the dividend next year discounted using the current one-year interest rate, plus the present value of the dividend two years from now, discounted using both this year's one-year interest rale and next year's expected one-year interest rate, and so on.
As in the case ol long-term bonds, the present value relation in equation ' 15.9) can be derived trom arbitrage, trom the assumption that the expected return per dollar from holding a stock lor one year must be equal to the return Irom holding a one-year bond. The derivation is given in the appendix to this chapter. Going through ihe appendix will improve your understanding ot the relation between arbitrage and present values, but it can be skipped without harm.
liquation 15.9) gives the stock pricc as the present value of nominal dividends, discounted by nominal interest rales. From Chapter It, we know we can rewrite this equation to express the real stock price as the present value of real dividends, discounted by real interest rates. So, we can rewrite the real stock price as
Щ.1
15.10)
(I + r„)(l + rf(,,)
Q, and D, without a dollar sign denote the real price and the real dividend at time t. The real stock price is the present value of future real dividends, discounted hy the sequence of one-year real interest rates. This relation has two important implications:
1. Higher expected future real dividends lead to a higher real stock price.
2. Higher current and expected luture one-year real interest rales lead to a lower real stock price. Let's now see what light ibis relation sheds on movements in the stock market.
The stock market and economic activity
Figure 15.5 showed the large movements in stock prices over the last thirty years. It is not unusual for the price index to go up or down by more than 15 per cent within a year. In thc first month of 1980 it went up by 20 per cent.- between lhe third and fourth quarters ol 1987 it went down by 45 per cent. I rom September to December 2008 it fell by 27 per cent. Daily movements of 2 per cent or more are not unusual. What causes these movements?
The first point to be made is that these movements should be unpredictable, and lor the most part they are. The reason lor this is besi understood by thinking in terms of the choice people have between stocks and bonds. If it were widely believed that, a year Irom now, thc price ol a stock was going to be 20 per cent higher than today s price, holding the stock for a year would be unusually attractive much more attractive than holding short-term bonds. There would be a very large demand lor the slock, lis price would increase today to the point where the expected return from holding the stock was back in line with the expected return on other assets. In other words, the expectation ol a high slock price next year would lead ю a high stock price today. Equally, il the news emerging about the luture of a stock was pessimistic, thc price would have lo lall now to a level so low that a future capital gain could be expected to encourage people to hold the share.
There is indeed a saying in economics that il is a sign ol a well-functioning stock market thai movements in stock prices are unpredictable. The saying is too strong. At any moment a few financial investors may have better information or simply be better at reading the future. II they are only a few, they may not buy enough ol the slock lo bid its price all the way up today. Thus, they may get large expected returns. Hut the basic idea is nevertheless right. The financial market gurus who regularly predict large imminent movements in the stock market over the next few months are quacks. Major movements in stock prices cannot be predicted.
If movements in the stock market cannot be predicted, il they are the result of news, where does this leave us? We can slill do two things:
• We can do what in lhe Llnited Stales is called 'Monday-morning quarterbacking looking back and identifying the news to which thc market has reacted. And anyone can be an expert alter the event:
• We can ask what if questions. For example: What would happen to the slock market il the central hank were going to embark on a more expansionary policy, or it consumers were to become more optimistic and increase spending?
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