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Applied Intermediate Macroeconomics Draft 2, 24 March 2005 Chapter 5 Trends and Cycles Word Count: 6210 2004 Kevin D. Hoover, All Rights Reserved AWL Page Equivalent 11
1
5 Trends and Cycles
The last three chapters focused on the measurement of key national accounting variables:
GDP and prices. While these are the centerpiece of macroeconomic analysis, there are
thousands of other measures of the economy most related in one way or another to
GDP and its components. In this chapter, we begin a wider examination of the economy,
shifting our focus to the question, how do GDP and large variety of other economic
variables behave over time? We begin by dividing their movements into longer run
trends and shorter run cycles. We then ask, are the cycles in different variables are
closely related in an economy-wide business cycle? And, finally, what are the properties
of the business cycle?
5.1 Decomposing Time Series
Look back at Figure 2.10, 2.12, or 2.14. Each shows the path of U.S. real GDP over a
period of about fifty years. Two characteristics of these graphs stands out. First, the
dominant movement of U.S. GDP is upward. But, second, the dominant movement is
unsteady: there are frequent and, at best, roughly regular ups and downs. A large
proportion of the thousands of economic time series that describe the economy behave
similarly. Take three examples: Figure 5.1 shows the time series for personal disposable
income (less transfers), industrial production, and employment. Each one resembles
GDP; each displays a pattern of fluctuations around a dominant upward path.
The economist often finds it useful to distinguish the dominant path, known as the
TREND, from the fluctuations, known as the CYCLE, because distinct factors explain each.
-
Source: Personal income, Bureau of Economic Analysis; industrial production, Federal Reserve; employment, Bureau of Labor Statistics.
Figure 5.1 Trends and Cycles in Selected Times Series
0
50
100
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1959
1961
1963
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1969
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Employment
Industrial Production
Personal Income (less transfers)
Like real GDP many economic time series show a pattern of fluctuations (a cycle) around an underlying growth path (a trend).
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Applied Intermediate Macroeconomics Draft 2, 24 March 2005 Chapter 5 Trends and Cycles Word Count: 6210 2004 Kevin D. Hoover, All Rights Reserved AWL Page Equivalent 11
2
Most of the later chapters of this book aim to explain the trend (especially Chapters 6 and
7) or the cycle (especially Chapters 9 and 12-16).
The upper panel of Figure 5.2 shows a stylized version of an economic time
series, which cycles regularly about a smooth exponential trend. The time series may be
decomposed in two steps: first, estimate the trend and, second, express the fluctuations
as deviations from the trend. The lower panel shows the cycle, now measured as the
difference between the time series and its trend expressed as a percentage of the trend.
Displaying the cycle as percentage of the trend makes sense: although the fluctuations of
an economic variable are likely to be absolutely smaller when its average value is small,
there is no reason to believe that they will be relatively smaller than when its absolute
value is large.
As we saw in Chapter 2, it is sometimes convenient to display economic time
series on logarithmic graphs. Figure 5.3 displays the same information as Figure 5.2
using a logarithmic scale. The exponential trend becomes a linear trend. The lower
panel shows the difference log(time series) log(trend). Since the difference in
logarithms is a ratio, just like a percentage difference, the lower panel is qualitatively
identical to the lower panel in Figure 5.2. And, if we multiply by 100, it too can be read
in percentage points. (See Box 2.3 and the Guide, section G.11, on logarithms and
logarithmic graphs.) The key to decomposing any time series into its trend and cycle is
the identification of the trend. Box 5.1 discusses some useful methods for estimating
trends.
In either the original or the logarithmic representation, a local high point is a
CYCLICAL PEAK and a local valley is a CYCLICAL TROUGH (rhymes with off). A
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Figure 5.2The Trend and Cycle of Stylized Economic Time Series
Time
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Trough
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Detrended Series(right axis)
Original Series(left axis)
Peak
Peak
Trough
Trough
The detrended series is the difference between the trend and the original series expressed as a percentage of the trend.
Peaks and troughs of the original series are also the peaks and troughs of the detrended series.
Deviation from trend
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Figure 5.3The Trend and Cycle of a Stylized Economic Time Series:
A Logarithmic Version
Time
V
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e Peak
0
Detrended Series
Original Series
log scale
The detrended series is the difference between the trend and the original series . Since the difference of logarithms is a ratio, the detrended series can be interpreted as a percentage of the original trend series.
Peaks and troughs of the original series are also the peaks and troughs of the detrended series.
Peak
Peak
Trough
Trough
Trough
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Applied Intermediate Macroeconomics Draft 2, 2 April 2005 Chapter 5 Trends and Cycles, BOX 5.1 Word Count: 961 2004 Kevin D. Hoover, All Rights Reserved
Box 5.1. Working with Economic Data: Detrending Time Series
The distinction between trend and cycle is not given in nature. There is no one right way
to detrend a time series. The question is not one of right or wrong, but of useful or not
useful. Does it help us to see more clearly what is happening in the economy? In this
book, we will use three of the many methods of detrending.
The Constant Trend
If we believe that, despite cyclical fluctuations, the average growth rate of a series does
not change much over a long period, then it is reasonable to assume that the trend has a
constant rate of growth and can be described by an equation
trend = a(1 + b)t
or
trend = aexp(bt),
where t is time, and a and b are constants. Each equation describes exponential growth at
a constant rate, b. The trend line in Figure 5.2 can be described by these equations.
Box 5.1 1
The difference between the time series and the trend is
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Applied Intermediate Macroeconomics Draft 2, 2 April 2005 Chapter 5 Trends and Cycles, BOX 5.1 Word Count: 961 2004 Kevin D. Hoover, All Rights Reserved
deviation from trend = time series trend
= time series a(1 + b)t
or
= time series aexp(bt).
At each period, there is a different deviation from trend (see Figure 5.2).
If we knew the values of the constants a and b, we could calculate the values of
each of the deviations and the variance of those deviations. We can calculate the
variance of these deviations (see the Guide, section G.4.2). Different values for a and b
would give us different sets of deviations and different variances. One rule for choosing
the trend is to pick values for a and b that maximize portion of the change in the time
series attributed to the trend, minimizing the portion attributed to the cycle. This is
equivalent to choosing a and b such that the variance of the deviations is as small as
possible. Fortunately, common spreadsheets (such as Excel) can do this at the click of
mouse (see the Guide, section G.15).
Box 5.1 2
If a time series grows at a steady proportionate rate, then log(time series) will
grow at a steady absolute rate as in Figure 5.3. The trend is then described by a linear
function, not an exponential function:
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Applied Intermediate Macroeconomics Draft 2, 2 April 2005 Chapter 5 Trends and Cycles, BOX 5.1 Word Count: 961 2004 Kevin D. Hoover, All Rights Reserved
trend = a + bt.
The method of finding the trend by choosing a and b to minimize the variance of the
deviations remains the same. Linear trends arise naturally when we consider the
logarithms of steadily growing data, but may also be appropriate even for natural data
that do not grow exponentially.
The Moving-Average Trend
In Chapter 2 (especially Figures 2.11 and 2.12) we saw that average growth rates were
not constant decade by decade. In such cases, a constant trend may not be appropriate.
We could perhaps use the average growth rate each decade to approximate the trend. But
that would imply, wrongly, that decades were somehow natural breaks. Instead, we can
calculate a centered moving average. Suppose that we have annual data on real GDP
from 1960 to 2006. A five-year centered moving average would start in 1962 would
average the value for 1962 with the values for two years before and two years after:
trend1962 = 56463626160 YYYYY ++++ .
In 1963, the moving average would drop Y60 and add Y65:
Box 5.1 3
trend1963 = 56564636261 YYYYY ++++ ,
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Applied Intermediate Macroeconomics Draft 2, 2 April 2005 Chapter 5 Trends and Cycles, BOX 5.1 Word Count: 961 2004 Kevin D. Hoover, All Rights Reserved
and so on until 2004.
One disadvantage, of course, is that the centered moving average cannot start
right at the beginning of the sample and must end before the end of the sample in order to
accommodate the leading and lagging terms. Centered moving averages should have an
odd number of terms, to preserve symmetry. The narrower the window (i.e., the number
of periods in the average), the more fluctuations the trend will display. There is no one
right choice of window, but for detrending economic time series, a fairly long window is
appropriate. The 25-quarter window used in Figure 5.4 approximates the average length
of the U.S. business cycle, ensuring that the trend averages both upswings and
downswings at every point.
Differences and Growth Rates
The previous two methods truly decompose the trend and the cycle into separate parts.
Sometimes we may not really care about the trend but just want to focus on fluctuations.
This is easily done by taking the first difference of the data:
Xt = Xt Xt-1.
More commonly, we calculate the proportional first difference, which is just the growth
rate:
Box 5.1 4
1
1
1
==t
tt
t
tt X
XXX
XX .
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Applied Intermediate Macroeconomics Draft 2, 2 April 2005 Chapter 5 Trends and Cycles, BOX 5.1 Word Count: 961 2004 Kevin D. Hoover, All Rights Reserved
Figure B5.1 shows a time series that has been detrended by calculating growth
rates. Notice that differencing a time series (or calculating a growth rate) causes a phase
shift: When the original time series is falling, its growth rate is negative; when the level
time series is rising, the growth rate is positive. The growth rate reaches its peak one-
quarter cycle ahead of the original series. This makes sense. When the level is exactly at
its peak or exactly at its trough it is neither rising nor falling, so its growth rate must be
zero. After one of these extreme points, it changes faster for a while and then slows
down to no change just at the next extreme point. Its growth rate must, therefore, reach
its fastest absolute value between the peak and the trough of the level series. What this
means economically is that we cannot judge the peak or trough of economic activity from
the peak or trough of the growth rate of GDP, but instead from noting when that growth
switched from positive or negative or back to positive. Growth rates should be fastest
somewhere in the middle of economic expansions and slow to nothing at the cyclical
peaks and troughs, and should reach their most extreme negative rates somewhere in the
middle of recessions.
Box 5.1 5
See the Guide, section G.12, for more on detrending time series.
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Figure B5.1A Stylized Time Series and in Levels and Percentage Changes
Time
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Times Series in Levels(left axis)
Time Series in Percentage Changes(right axis)
Peak
Peak
Peak
Trough
Trough
Trough
Plotting the growth rate of a time series shifts its phase .: The peaks and troughs of the original series occur when the growth rates are zero, while the fastest positive and negative growth rates (the peaks and troughs of the growth -rate series) occur one quarter cycle later in mid-expansion and mid-recession.
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3
complete CYCLE can be measured from peak to peak or from trough to trough.
Sometimes the trend growth is referred to as secular change (or growth) to distinguish it
from cyclical fluctuations.
Of course, Figures 5.2 and 5.3 are only stylizations. Compare Figure 5.2 to
Figure 5.4, which shows actual real GDP and its trend in the upper part and the
percentage deviations from trend below for the 1970s. The graphs of actual data are not
so regular as the stylized graphs, but the overall similarity is clear.
5.2 The Business Cycle
5.2.1 THE LANGUAGE OF BUSINESS CYCLES
A careful look at Figure 5.1 shows that the ups and downs of the four series are closely
related. When the data are detrended (Figure 5.5), the pattern is even more clear. This is
not mere chance. The cyclical patterns of a large number of economic time series are
closely related. The tendency of many measures of economic activity to move in concert
suggests that there are common driving forces and that we can think, not just about the
trends and cycles of the individual measures, but of a business cycle. A reasonable
definition runs:
The BUSINESS CYCLE is the alternation in the state of the economy of a roughly
consistent periodicity and with rough coherence between different measures of the
economy.1
1 Occasionally, one still hears a older name of the business cycle: the trade cycle.
-
Source: Bureau of Economic Analysis
Figure 5.4Real GDP: Trend and Cycle, 1970-1980
2500
3000
3500
4000
4500
5000
1970:1 1972:1 1974:1 1976:1 1978:1 1980:1
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Real GDP(left axis)
Trend
Detrended real GDP(right axis)
Trend is a 25-quarter centered moving average.
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Source: Personal income, Bureau of Economic Analysis; industrial production, Federal Reserve; employment, Bureau of Labor Statistics.
Figure 5.5Selected Detrended Time Series
-20
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1959 1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001
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Industrial Production(left axis)
Personal Income less transfers (right axis) Employment (right axis)
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Applied Intermediate Macroeconomics Draft 2, 24 March 2005 Chapter 5 Trends and Cycles Word Count: 6210 2004 Kevin D. Hoover, All Rights Reserved AWL Page Equivalent 11
4
Rough coherence in this definition reflects the tendency of different economic
time series to move up or down in closely related patterns. Saying that the economywide
ups and downs are roughly consistent acknowledges the fact that, even though they are
not evenly spaced, the pattern of ups and downs does not appear to be completely
random: over the past 150 years, the average business cycle lasted four to five years; the
shortest, less than two years; the longest, ten years.
As with cycles in particular times series, business cycles are identified by their
peaks and troughs (see Figure 5.6). A specialized language has developed to describe
business cycles. Key terms include:
RECESSION (synonyms: slump, contraction): the period between the cyclical
peak and the cyclical trough, when economic activity is falling.
EXPANSION (synonyms: boom, recovery): the period between the cyclical
trough and cyclical peak, when economic activity is rising. Recovery is
sometimes used in the more limited sense of the period between the trough and
when the economy regains either (1) the level of activity experienced at the
previous peak or (2) the level it would have experienced had it remained on trend
(see Figure 5.6).
Depression: a particularly severe recession. Originally, depression was a
synonym indeed, a euphemism for a recession. Unfortunately, it became
associated with the largest slump in U.S. and world economic history: the Great
Depression of 1929-33, in which real GDP fell 27 percent and the unemployment
rate rose from just over 3 percent to just under 25 percent from the peak to the
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Figure 5.6A Stylized Economic Time Series
Time
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Peak
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Recovery: Definition 2
Recovery: Definition 1
The period from peak to trough is a recession (also known as a slump or contraction). The period from trough to peak is known as an expansion (also known as a boom or recovery). Recovery is sometimes used to indicate only a portion of the upswing, either: 1. the period from trough to the level of the previous peak; or 2. the period from trough to the level of the trend. A ( complete) cycle is the period between a trough and the subsequent trough or a peak and the subsequent peak.
Complete Cycle
Complete Cycle
Trend
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Applied Intermediate Macroeconomics Draft 2, 24 March 2005 Chapter 5 Trends and Cycles Word Count: 6210 2004 Kevin D. Hoover, All Rights Reserved AWL Page Equivalent 11
5
trough.2 Depression is now largely reserved for a recession that is particularly
severe in both scale and duration. Several of the contractions of the 19th century
are consider depressions, but the Great Depression is the only example of the 20th
century.
Growth recession: a period of slower than trend growth, usually lasting a year
or more. During a growth recession, output continues to rise, but at so slow a rate
that other aspects of the economy particularly, employment may stagnate or
fall. A growth recession, may be a harbinger of a proper recession.
(Complete) cycle: the period between a peak and the following peak or between
a trough and the following trough.
5.2.2 DATING THE BUSINESS CYCLE
The problem of dating business cycles is really just a matter of determining when the
economy reaches its peaks and its troughs. With so ambiguous a notion as the state of
the economy, there is no unique way to identify the business cycle.
A common rule of thumb defines a recession as two consecutive quarters of
negative growth in real GDP. The peak would then be marked at the quarter immediately
before GDP begins to fall, and the trough at the quarter immediately before it begins to
grow again.
2 While technically the trough of the Great Depression was reached in March 1933, many economic
historians regard the entire decade of the 1930s as depressed with recovery not secure until the United
States entered World War II at the end of 1941.
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Applied Intermediate Macroeconomics Draft 2, 24 March 2005 Chapter 5 Trends and Cycles Word Count: 6210 2004 Kevin D. Hoover, All Rights Reserved AWL Page Equivalent 11
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Although it has no official status, the National Bureau of Economic Research
(NBER), a private, non-profit organization, is widely regarded in the United States as the
arbiter of the beginnings and ends of recessions. The NBER explicitly rejects the two-
quarter rule. According to the NBER, a recession is
a recurring period of decline in total output, income, employment, and trade,
usually lasting from six months to a year, and marked by widespread contractions
in many sectors of the economy.3
Declining real GDP is, of course, typical of recessions, but the NBER Business-Cycle
Dating Committee regards it as an inadequate measure, because it is too narrow in its
scope and calculated only quarterly. The NBER casts its net wider and looks closely at
monthly, as well as quarterly, data. There is no formal rule. The NBERs judgment is
based on its overall impressions of the movements of many series. The complete set of
NBER business-cycle dates is given in Table 5.1.
The data that the NBER uses are often published only with a substantial delay,
and the committee usually must wait to see whether a change in direction is reversed or
confirmed by data of the next month or two. As a result, the dates of the peaks and
troughs are not typically announced until six months to a year after they occur. A
recession is usually nearly over before its onset is declared. An expansion is usually well
underway before the end of the recession is known to the public.
3 Quoted from the NBER web site (http://www.nber.org/cycles.html).
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Table 5.1 NBER Business Cycle Dates
Business-cycle Reference Dates Duration in Months Trough Peak Contraction Expansion Cycle
(peak to trough)
(trough to peak)
trough from previous trough
peak from previous peak
December 1854 June 1857 -- 30 -- -- December 1858 October 1860 18 22 48 40 June 1861 April 1865 8 46 30 54 December 1867 June 1869 32 18 78 50 December 1870 October 1873 18 34 36 52 March 1879 March 1882 65 36 99 101 May 1885 March 1887 38 22 74 60 April 1888 July 1890 13 27 35 40 May 1891 January 1893 10 20 37 30 June 1894 December 1895 17 18 37 35 June 1897 June 1899 18 24 36 42 December 1900 September 1902 18 21 42 39 August 1904 May 1907 23 33 44 56 June 1908 January 1910 13 19 46 32 January 1912 January 1913 24 12 43 36 December 1914 August 1918 23 44 35 67 March 1919 January 1920 7 10 51 17 July 1921 May 1923 18 22 28 40 July 1924 October 1926 14 27 36 41 November 1927 August 1929 13 21 40 34 March 1933 May 1937 43 50 64 93 June 1938 February 1945 13 80 63 93 October 1945 November 1948 8 37 88 45 October 1949 July 1953 11 45 48 56 May 1954 August 1957 10 39 55 49 April 1958 April 1960 8 24 47 32 February 1961 December 1969 10 106 34 116 November 1970 November 1973 11 36 117 47 March 1975 January 1980 16 58 52 74 July 1980 July 1981 6 12 64 18 November 1982 July 1990 16 92 28 108 March 1991 March 2001 8 120 100 128 November 2001 8 -- 128 -- Average, all cycles:
1854-2001 (32 cycles) 17 38 55 5611854-1919 (16 cycles) 22 27 48 4921919-1945 (6 cycles) 18 35 53 53 1945-2001 (10 cycles) 10 57 67 67
continued next page
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Average, peacetime cycles: 1854-2001 (27 cycles) 18 33 51 523 1854-1919 (14 cycles) 22 24 46 474 1919-1945 (5 cycles) 20 26 46 45 1945-2001 (7 cycles) 10 52 63 63 Notes: 131 cycles. 215 cycles. 326 cycles. 413 cycles. Figures printed in bold italic are the wartime expansions (Civil War, World Wars I and II, Korean War, and Vietnam War); the postwar contractions, and the full cycles that include the wartime expansions. Source: U.S. Department of Commerce, Survey of Current Business, October 1994, Table C-51.
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Applied Intermediate Macroeconomics Draft 2, 24 March 2005 Chapter 5 Trends and Cycles Word Count: 6210 2004 Kevin D. Hoover, All Rights Reserved AWL Page Equivalent 11
7
In the 1992 presidential campaign, the delay in announcing the end of the
recession allowed Bill Clinton to claim (with some plausibility) that the economy was in
one of the longest recessions of the postwar period which, of course, he blamed on the
first President Bush. His catch phrase was, Its the economy, stupid! In fact, the
recession of 1990-91 was the second shortest in the postwar period, having lasted only
eight months, and had ended in March 1991 twenty months before the election. In
fairness to Clinton and the voters who agreed with his view of the economy, the
unemployment rate did not begin to fall until June 1992 (three months after the trough)
and did not reach its level at the cyclical peak (6.8 percent) until August 1993 more
than two years after the recovery had begun. This is not unusual; the peak in the
unemployment rate typically lags the cyclical trough. As we saw in Chapter 3, section
3.6.2, the NBER did not announce that the economy had reached its cyclical trough in
November 2001 until March 2003. And the Democrats again (and again with some
plausibility) blamed a President Bush for an economy effectively in recession in the run-
up to the 2004 election.
5.2.3 THE TYPICAL BUSINESS CYCLE
How well do the NBER business-cycle dates capture the cyclical fluctuations in the U.S.
economy? This is largely a question of how well they cohere with the movements of
time series that can be taken to be good reflections of the general state of the economy.
Economists have studied thousands of economic time series and classified their cyclical
behavior. To try to give some feeling for the business cycle as a whole, the U.S.
Department of Commerce created indices of ECONOMIC INDICATORS, similar to price
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Table 5.2 Component Series of the Indices of Business-Cycle Indicators
Index of Leading
Indicators Index of Coincident
Indicators Index of Lagging
Indicators 1. Average weekly hours, manufacturing
1. Employees on nonagricultural payrolls
1. Average duration of unemployment *
2. Average weekly initial claims for unemployment insurance*
2. Personal income less transfer payments
2. Inventories to sales ratio, manufacturing and trade
3. Manufacturers' new orders, consumer goods and materials
3. Industrial production 3. Change in labor cost per unit of output, manufacturing%
4. Vendor performance, slower deliveries diffusion index
4. Manufacturing and trade sales
4. Average bank prime rate%
5. Manufacturers' new orders, nondefense capital goods
5. Commercial and industrial loans
6. Building permits, new private housing units
6. Consumer installment credit to personal income ratio
7. Stock prices, 500 common stocks
7. Change in consumer price index for services%
8. Money supply, M2 9. Interest rate spread, 10-year Treasury bonds rate minus federal funds rate%
10. Index of consumer expectations
Source: Conference Board *inverted series, a negative change in this component makes a positive contribution. % in percent change form, contributions based on arithmetic changes.
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Applied Intermediate Macroeconomics Draft 2, 24 March 2005 Chapter 5 Trends and Cycles Word Count: 6210 2004 Kevin D. Hoover, All Rights Reserved AWL Page Equivalent 11
8
indices. (Since 1995, the indices have been compiled by the Conference Board, a non-
profit business organization.) Each of the three indices (leading, coincident, and lagging
indicators of the business cycle) is a weighted average of several monthly time series and
is expressed as an index number based such that the average value for 1992 equals 100.
Table 5.2 shows the component series for each index. At this stage, we are concerned
only with the index of coincident indicators a group of time series whose peaks and
troughs should correspond to the peaks and troughs of the business cycle. (We will
consider leading and lagging indicators in section 5.3 below.) Figure 5.7 shows that the
peaks and troughs of the (detrended) coincident indicators closely match the NBER cycle
dates.
How can we characterize the typical business cycle? Figure 5.8 provides one
answer with another view of the relationship between the coincident indicators and the
NBER cycle dates. The figure is centered on the business cycle peak, marked 0. The
index of coincident indicators is rescaled to take the value of 100 at the business cycle
peak (see the Guide, section G.8.1). The figure shows twelve months before the peak (1
to 12) and thirty-six months after (+1 to +36). The vertical lines indicate the NBER
peaks and troughs. Heavy lines show average values for the seven business cycles
between 1960 and 2004, while the lighter lines show the values for the 1990-91
recession. (As noted in Chapter 3, the recession of 2001 is somewhat unusual. Students
are asked to examine it in problem 5.13.) The average index peaks exactly at the NBER
peak. At +16 months, its trough is about five months past the average trough for the
seven business cycles (+11). This shows that, when recessions are longer than average,
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Source: Index of coincident indicators, The Conference Board; recession dates, National Bureau of Economic Research.
Figure 5.7Coincident Indicators and the Business Cycle
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1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996
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Shaded areas are NBER recessions.
The index of coincident indicators conforms well, though not perfectly, with the NBER business cycle
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Sources: index of coincident indicators, The Conference Board; business-cycle dates, National Bureau of Economic Research
Figure 5.8Coincident Indicators and the Business Cycle
96
97
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-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36Months from Peak
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Average coincident indicators (last seven business cycles)
Coincident indicators(1990-91 business cycle)
Average trough (last seven business cycles)
Peak
Trough(1990-91
business cycle)
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Applied Intermediate Macroeconomics Draft 2, 24 March 2005 Chapter 5 Trends and Cycles Word Count: 6210 2004 Kevin D. Hoover, All Rights Reserved AWL Page Equivalent 11
9
they are also deeper than average drawing down the average level of the coincident
indicators. In 1990-91 the coincident indicators track the NBER cycle dates exactly.
Figures 5.9 (a) (c) examine the typical cyclical behavior of the three time series
already displayed in Figure 5.1: personal income (less transfers), industrial production,
and employment. These are three of the four components of the index of coincident
economic indicators. The pattern of industrial production most strongly resembles that of
the index of coincident indicators. The average data peaks at the NBER business cycle
peak, but the trough is some five months behind the NBER trough. And the data for
1990-91 are nearly perfectly coincident. The pattern for employment is similar for the
average; but the major losses in employment tend to come early in the recession, so that
employment falls only slowly to its trough. The pattern of employment in the 1990-91
recession is different: it peaks before the NBER peak flattens out near the NBER trough,
and begins a steady recovery only eight to ten months after the NBER trough. It was this
anomalous pattern that supported the Democrats claim that the economy was still in
recession at the time of the 1992 election. The pattern of personal income less transfers
is almost perfectly coincident in 1990-91; yet, on average, it appears to peak before the
NBER peak and to rise very slowly from the NBER trough. One striking feature is that
personal incomes are far less variable over the average recession than are industrial
production or employment.
Table 5.1 and Figures 5.7-5.9 give us a good picture of the history of recent U.S.
business cycles. At least two characteristics are worth noting. First, the average
recession in the post-World War II period lasted eleven months, while the average
expansion lasted fifty months. Far from acting like the simple, symmetrical sine waves in
-
Sources: employment, Bureau of Labor Statistics; business-cycle dates, National Bureau of Economic Research
Figure 5.9 (a)Industrial Production and the Business Cycle
95
96
97
98
99
100
101
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104
105
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36Months from Peak
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Average industrial production (last seven business cycles)
Industrial production (1990-91 business cycle)
Average trough (last seven business cycles)
Peak
Trough(1990-91
business cycle)
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Sources: employment, Bureau of Labor Statistics; business-cycle dates, National Bureau of Economic Research
Figure 5.9 (b)Employment and the Business Cycle
97
98
99
100
101
102
103
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36Months from Peak
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Average employment (last seven business cycles)
Employment(1990-91 business cycle)
Average trough (last seven business cycles)
Peak
Trough(1990-91
business cycle)
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Sources: employment, Bureau of Labor Statistics; business-cycle dates, National Bureau of Economic Research
Figure 5.9 (c)Personal Income (less transfers) and the Business Cycle
96
98
100
102
104
106
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36Months from Peak
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Average personal income (last seven business cycles)
Personal income (1990-91 business cycle)
Average trough (last seven business cycles)
Peak
Trough(1990-91
business cycle)
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the stylized graphs of Figures 5.2, 5.3, and 5.4, business cycles are asymmetrical. The
process of economic growth over the last fifty years can be characterized as a pattern of
five steps forward and one step back.
Second, the expansion that began in December 1982 is the third longest on record,
the expansion that began in April 1991 is the longest, and the recession that separated
them is tied with the 2001 recession as the second shortest. Consequently, the typical
college student in 2005 has lived through the longest sustained period of growth in U.S.
economy history and has virtually no personal experience with highly unfavorable
economic conditions.
5.3 The Business Cycle and the Economy
5.3.1 WHAT CAUSES THE BUSINESS CYCLE?
The causes and proper analysis of the business cycle have been hotly debated by
economists since it was first identified as a regular phenomenon in the 19th century.
Economists have found it useful to distinguish two aspects of the cycle: IMPULSE and
PROPAGATION MECHANISMS. A child on a swing follows a cyclical pattern. A mother
who gives the child an occasional push provides the impulse. In this case, the cycle is
caused by the propagation mechanism that is, by gravity and the construction of the
swing that limits its motion, guaranteeing that an outward motion reaches a peak, is
reversed and reaches a trough on the backswing. Theories of the business cycle differ in
whether they place the main emphasis on the impulse or the propagation mechanism.
One class of theories argues that the propagation mechanisms in the economy are
like the swing intrinsically cyclical. Many of the cycles in nature, such as the tides or
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the paths of the moon and the planets, are intrinsic. Even a complex cycle, such as the
vibrations of a guitar string, which needs impulses from time-to-time to continuing
sounding, is mainly governed by its propagation mechanism. If the economy has an
intrinsic cycle it is necessarily a highly complex one more complex than the guitar
string or the tides.
A second class of theories holds that the cycles in the economy are the result
primarily of cycles in the impulse mechanisms themselves. In the 19th century, William
Stanley Jevons (1835-1882) argued that variations in solar activity, correlated with
sunspots, caused variations in agricultural harvests and, ultimately, caused the business
cycle. Although Jevons theory was never widely accepted, some economists today argue
that exogenous cycles in technology cause the business cycle. Others believe that
recurring recessions are induced by the actions of policymakers. If the Federal Reserve
would just leave the economy to its own devices, and not raise interest rates from time to
time, advocates of this view believe that the economy would suffer few recessions.
A third class of theories argues that business cycles are ultimately irregular. Yes,
there are ups and downs, but the patterns that we see in these ups and downs are illusory.
Imagine that GDP tends to grow on average 2 percent per year, but that each year
completely random good or bad events events with no cycle occur. Statisticians
describe such a pattern as a random walk with a drift. (The drift is the 2 percent trend
growth.) The pattern is called a random walk because it resembles the path that a
drunken man might take after leaving the tavern: since each step is just as likely to go in
one direction as another, the best average prediction of where the man will be after his
next step is where he is now standing. Figure 5.10 shows a random walk with a drift that
-
Figure 5.10 A Random Walk with a Drift
3000
4000
5000
6000
7000
8000
9000
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61
Years
G
D
P
With random walk with a drift, today's value is yesterday's value plus a percentage growth term (the drift) plus a random term as equally likely to move up as down (the random walk). Such a series may appear to have a cycle (this one looks remarkably like the graph of real GDP), but there is no genuine regularity behind its fluctuations.
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looks strikingly similar to graphs of real GDP (e.g., Figure 2.10). The apparent cyclical
patterns in the figure are purely accidental and do not describe a genuine phenomenon in
need of a theoretical explanation.
The jury is still out on which type of account of business cycles describes the
actual economy: Are its ups and downs governed by laws as regular as (if more complex
than) those of physics and biology? Or are the ups and downs really just a reflection of
the way in which the economy processes random influences? Or is there room for some
combination of these mechanisms (for example, random influences superimposed on
underlying regular patterns)? We cannot hope to give definitive answers in an
intermediate textbook. They are the agenda for cutting-edge economic research.
If the random-walk explanation is correct, then the cyclical behavior of the
economic is an illusion. Economists who do not want to imply the strong notion of
regularity that often attends the word cycle sometimes use economic fluctuations as a
more neutral description than business cycle. But there is something lifeless about this
term; so, we shall continue to use business cycle throughout this book.
5.3.2 THE CLASSIFICATION OF ECONOMIC INDICATORS
Our definition of the business cycle had two parts: (1) alternation in the state of the
economy; and (2) coherence among different measures of the economy. While
economists continue to debate the ultimate sources of alternation, and even whether the
patterns are truly recurring ones, they understand much better the nature of the coherence
among different measures. Sometimes the connections are obvious. It takes workers to
produce goods; therefore, it is not surprising that employment and industrial production
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follow similar patterns over time. It takes income to support expenditure; therefore, it is
not surprising that consumption follows a similar pattern to income. Other connections
are less obvious, and much of economic theory (and much of this textbook) aim to make
them more clear. As a starting place, it is useful to have a good vocabulary to describe
the relationships among different time series.
Economic indicators can be classified according to how they behave compared to
the business cycle. We have already used the index of coincident indicators as a measure
of the cycle. An indicator is said to be coincident if it reaches its peak at or near the peak
of the business cycle and reaches its trough at our near the trough of the business cycle.
Economic indicators are classified by whether or not they generally move in the same
direction as the main positive measures of the business cycle, such as GDP, industrial
production, or employment. Indicators can be
procyclical: they move in roughly the same direction as the business cycle (for
example, retail sales are procyclical);
countercyclical: they move in roughly the opposite direction as the business
cycle (for example, the unemployment rate is countercyclical); or
acyclical: they have no regular relationship to the cycle (for example, agricultural
production and population are acyclical).4
4 Even though it has its own ups and downs, agricultural production follows the seasons and year-to-year
fluctuations in the weather, rather than fluctuations in the economy as a whole. Agriculture now constitutes
only 2.5 percent of the economy by total employment. In the past, when its share in the economy was
larger, it would have been more closely related to the business cycle.
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Indicators are also classified by their phase relationship to the business cycle
that is, according to whether their extreme points occur before, after, or at the same time
as the extreme points of the business cycle. Some possibilities for procyclical time series
are illustrated in Figure 5.11:
A leading indicator reaches its peak and trough before the corresponding peak or
trough of the business cycle;
A lagging indicator reaches its peak and trough after the corresponding peak or
trough of the business cycle;
A mixed indicator follows a regular pattern different from either the leading or
lagging indicator. The third series in Figure 5.11 shows a mixed indicator that
leads the business-cycle peak at the peak, but is coincident at the business-cycle
trough. There are many possible mixed patterns.
Countercyclical indicators can also be leading, lagging, or mixed indicators. The average
duration of unemployment, for example, is a countercyclical, lagging indicator of the
business cycle.
The U.S. Department of Commerce developed, and the Conference Board now
maintains and publishes monthly, indices of leading and lagging economic indicators.
Table 5.2 shows the component series of these indices, as well as those of the index of
leading economic indicators.
5.3.3 IS THE BUSINESS CYCLE PREDICTABLE?
The fact that a number of time series are consistent leading economic indicators suggests
that it may be possible, to some degree, to predict the course of the business cycle.
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Figure 5.11Classification of Economic Indicators
Time
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Leading Indicators
Lagging Indicators
Mixed Indicators: leading at peak; coincident at trough
Acyclic Indicators
Shaded areas indicate recessions.
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Figure 5.12 shows the three indices of economic indicators (detrended). Notice first, the
broad similarity of the fluctuations. All three series are procyclical, and they show the
rough coherence that characterizes the business cycle.5 Looking more closely, we see the
expected pattern (especially clear at the peaks and troughs): the leading indicators move
ahead of the coincident indicators, which, in their turn, move ahead of the lagging
indicators.
How well can the relationships among the indicators be exploited to forecast the
path of the business cycle? There are two questions: First, how long on average is the
lead between the leading and coincident indicators? Second, how strongly related are the
two indices? The second question can be answered by calculating the coefficient of
correlation between the two indices. (Box 5.2 describes the measurement of correlation.)
The correlation between the leading and coincident indicators is 0.44, which is a
moderate, positive correlation. But we should not really expect a strong correlation
between the leading indicators today and coincident indicators today. We know that the
leading indicators move ahead of the coincident indicators. We can instead calculate the
correlation between the coincident indicators in each period and the leading indicators
one or more months earlier. The correlation between the index of coincident indicators
and the index of leading indicators one month earlier is 0.54 a little bit stronger.
Table 5.3 presents the results of such calculations for leads and lags of twelve
months. The first column shows the correlations between the coincident indicators and
5 One of the component series of the index of leading indicators and one of the lagging indicators are
actually countercyclical, but they are multiplied by 1 before being entered into the indices, so that all
components tend to move in the same direction relative to the business cycle.
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Box 5.2. Working with Economic Data: Correlation
Data that move together systematically are said to be correlated. The left-hand side of
Figure B5.2, panel A, shows two perfectly positively correlated series plotted against
time. They have different means and different amplitudes, but a 20 percent rise in X is
matched by a 20 percent rise in Y and a 3 percent fall by a 3 percent fall and so on. The
correlation coefficient (r) measures degree of conformity between the series (see the
Guide, section G.13, on the details of its calculation). A correlation coefficient of r = +1
indicates perfect correlation. Look at the data another way. The right-hand side of panel
A, which shows the same two series plotted against each other rather than against time,
illustrates the hallmark of perfect correlation: the points lie on a straight line.
See the Guide, section G.12, for more on detrending time series.
The correlation coefficient takes the value r = 1, when series are perfectly
negatively correlated. Then each movement of X would be matched by a proportional
movement of Y in the opposite direction. It takes the value r = 0, when there is no
relationship between the series. Besides these extreme points, values in the interval
0 < r < 1, indicate different degrees of conformity between fluctuations between series.
Panel B shows two highly, but imperfectly, correlated series (r = 0.9). For the most part
the series fluctuate together. Once in a while they move in opposite directions, and, when
they move together, it is not always with a constant proportion. The right-hand side of
Panel B shows that the scatterplot forms a cloud of points. The more oblong this cloud,
the closer it comes to a straight line, the higher the correlation.
Panel C illustrates a case of zero correlation (r = 0). Here there is no common
pattern to the movements of the time series. The cloud of points are scattered in a diffuse
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oval rather than tightly grouped along a line. Panel D shows a moderate negative
correlation (r = 0.5). The points in the scatterplot form an obviously downward tilting
cloud neither as diffuse as panel C nor as tight as panel B.
Although the illustrations are all time series, the correlation coefficient can also
measure the conformity among cross-sectional data. We can equally calculate the
correlation between GDP growth rates and inflation rates for the United States since the
1970s or for the G-7 countries in 2004.
Like other summary statistics, the coefficient of correlation is interpretable only
for stationary data. The Guide, section G.14.1, discusses nonsense correlation, which
arise when data do not have constant means. Two trending series will generally have a
high correlation coefficient. Yet, there may or may not be a genuine relationship between
them. It is important to detrend nonstationary time series before calculating the
coefficient of correlation (see Box 5.1 and the Guide, section G.13).
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Figure B5.2 Correlations between Time Series
0
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1 3 5 7 9 11 13 15 17 19Time
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Box 5.2
Panel B. r = 0.9 3.5
4 37 19
0
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0 0.5 1 1
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.5
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Panel C. r = 0.0 Continued next page
3
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Figure B5.2 Correlations between Time Series
0
0.5
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4.5
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1 3 5 7 9 11 13 15 17 19Time
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3 3.5 4 4.5 5
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Box 5.2 4
Panel D. r = 0.5
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Source: The Conference Board
Figure 5.12Indices of Business Cycle Indicators
-8
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1962:01 1967:01 1972:01 1977:01 1982:01 1987:01 1992:01
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Index of Leading IndicatorsIndex of Lagging Indicators
Index of Coincident IndicatorsDetrended using a 25-quarter centered moving average.
T he three indices show closely related movements. As seen most easily at the peaks and troughs ,the leading economic indicators anticipate the movements of the coincident indicators, which in turn anticpate the movements of the lagging indicators.
-
Table 5.3 Correlations Among Business-Cycle
Indicators
Number of months lead
Leading indicator
Lagging indicator
-12 -0.41 0.77 -11 -0.37 0.79 -10 -0.32 0.81 -9 -0.27 0.82 -8 -0.20 0.82 -7 -0.14 0.80 -6 -0.06 0.78 -5 0.01 0.75 -4 0.09 0.72 -3 0.17 0.66 -2 0.26 0.60 -1 0.35 0.52 0 0.44 0.44 +1 0.53 0.33 +2 0.61 0.23 +3 0.69 0.13 +4 0.75 0.03 +5 0.80 -0.06 +6 0.84 -0.14 +7 0.86 -0.22 +8 0.88 -0.30 +9 0.89 -0.37 +10 0.89 -0.44 +11 0.88 -0.50 +12 0.86 -0.56
Source: Conference Board and authors calculations Entries represent the correlation coefficient between the current value of the indices of leading and lagging indicators and value of the index of coincident indicators 1 to 12 months earlier and 1 to 12 months later.
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the leading economic indicators. The row labeled 0 is the correlation when both indices
are measured in the same month. It is, as we already observed, 0.44. The row labeled +1
indicates the leading indicators in one month and the coincident indicators one month
later. It measures how well the leading indicators predict the later coincident indicators
and, therefore, the business cycle. Again, we already have seen that the value is 0.54.
Subsequent rows (labeled +2 to +12) show the correlation between the leading indicators
and the coincident indicators two, three, and up to twelve months ahead, as well as one to
twelve months behind (1 to 12). on. The second column shows a similar set of
correlations between the lagging indicators and the coincident indicators.
The highest correlation between the coincident and leading indicators is 0.89 at
+9 and +10 months lead (that is, roughly three quarters ahead). Such a strong correlation
suggests that the leading indicators are a good, though imperfect, predictor of the future
behavior of the business cycle. The point is reinforced visually in Figure 5.13, which is
similar to Figure 5.12, except that the index of leading indicators has been shifted
forward by nine months (that is, the value for January is plotted at the following
September and so forth). Once shifted, the leading and coincident indicators line up
extremely well.
News reports frequently say that the index of leading economic indicators is the
governments main forecasting tool and that the index signals downturns in the
economy six to nine months ahead. The first claim is hyperbole. Most government
forecasts are, in fact, generated from macroeconomic computer-models of the economy
in which tens, or even hundreds, of equations represent different aspects of the economy,
and the index of leading economic indicators plays no part whatsoever. Also, as we
-
Source: The Conference Board
Figure 5.13How well do the leading indicators predict the business cycle?
-8
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-4
-2
0
2
4
6
1962:10 1967:10 1972:10 1977:10 1982:10 1987:10 1992:10
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Index of Leading Indicators
Index of Coincident Indicators
Index of Leading Indicators shifted forward 9 months
Shifting the leading economic indicators forward by nine months aligns them closely with the coincident indicators, giving some evidence of their ability to signal business cycle fluctuations roughly three quarters ahead.
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noted earlier, the government has given over the maintenance of the business cycle
indicators to the private sector.
There is, nevertheless, good reason to believe that the index of leading indicators
does have some predictive power for the business cycle. Notice that in Table 5.2 the
correlation between the leading and coincident indicators is above 0.8 for each of the
months between +6 and +12. This supports the idea that the leading indicators help to
forecast recessions. A popular rule of thumb states that two months of consecutive
declines in the leading indicators signals an imminent recession. This rule often works,
but it also works too often: most recessions are predicted accurately, but sometimes a
recession is predicted and none occurs. Others have suggested three months of decline,
rather than two, to give more accurate predictions. In that case, however, there is
necessarily less lead time between the signal and the onset of the recession.
One reason that the leading economic indicators are important is that, as we
discussed in section 5.2.2, as well as in Chapter 3, section 3.6.2, there is often
considerable delay in getting relevant information about coincident indicators. One of
the roles of the index of lagging economic indicators is to buttress the evidence that the
economy actually entered or left a recession and to help to resolve the uncertainty that
clouds all judgments about the state of the economy. Table 5.3 shows that the correlation
between the lagging and the coincident indicators is highest at 0.82 with a lag of 8 to 9
months (roughly three quarters behind).
The consistent patterns of the leading, lagging, and coincident indicators
demonstrate that there are facts about the business cycle that economists need to explain.
They give some clues about the course of the business cycle. But they do not, in
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themselves, explain the why the business cycle behaves as it does. In later chapters, we
will try to understand the mechanisms that account for these patterns.
Summary
1. Many economic time series are dominated by fluctuations around a dominant tendency
to grow. These may be decomposed into a trend, reflecting growth and a cycle
reflecting the fluctuations.
2. The high point of a cycle relative to trend is known as the peak; and the low point, the
trough. A complete cycle is measured peak to peak or trough to trough.
3. The business cycle is the tendency of the state of the economy (measured by a wide
variety of time series) to fluctuate in a roughly regular manner.
4. A complete business cycle includes a recession (the period from peak to trough) and an
expansion (the period from trough to peak).
5. Business cycles are dated according to their peaks and troughs. The relevant
information often arrives with a substantial delay.
6. The expansion phase of the typical post-World War II business cycle in the U.S. is
about five times as long as the recession phase (11 versus 50 months).
7. Economists remain divided over the causes of business cycles. Some point to cycles in
the extrinsic impulses to the economy. Others point to intrinsic economic behavior
that propagate cycles. Still others believe that the fluctuations are not true cycles, but
random movements that merely suggest a cycle.
8. Whether cycles are genuine or not in the sense of possessing a deep regularity,
economic behavior does explain common movements among economic time series.
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Series can be classified as moving with the business cycle (procylical), against the
cycle (countercyclical), or unrelated to the cycle (acyclical). They may also
systematically lead, lag, or coincide with the business cycle, or have some more
complex relationship to it.
9. The existence of patterns in which some time series are leading indicators for the
business cycle implies that the cycle may itself be predicted. The index of leading
economic indicators tends to lead the business cycle by about nine months.
Key Concepts cycle cyclical peak cyclical trough business cycle expansion
recession economic indicators impulse mechanism propagation mechanism
Suggestions for Further Reading National Bureau of Economic Research, Business Cycle Dating Committee Web Site
(http://nber.org/cycles/main.html) contains useful articles about its procedures and announcements of particular peaks and troughs.
Norman Frumkin. Guide to Economic Indicators. Armonk, N.Y.: M.E. Sharpe, 1990. F.M. OHara, Jr. and F.M. OHara, III. Handbook of United States Economic Indicators, revised edition. Westport, CT: Greenwood Press, 2000.
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Problems Data for this exercise are available on the course website under the link for Chapter 5 (insert web link here). Before starting these exercises, the student should review the relevant portions of the Guide to Working with Economic Data: sections G.4, G.7, and G.13. Problem 5.1. In Problem 2.12 you were supposed to have identified the peaks and
troughs of the business cycle using the two-quarter rule. If you have not done this exercise already, do it now. Table 5.1 gives the NBER monthly dates in which peaks and troughs occurred. Convert these to the equivalent quarters and then construct a table that compares your results from Problem 2.12 to the NBER dates. Go the NBERs Business Cycle Dating Committees website (http://nber.org/cycles/main.html). Read the Frequently Asked Questions and other documents relating to their dating procedures. In light of the information provided by the NBER and your own understanding of the business cycle, explain how and why your dates differ from the official NBER dates.
Problem 5.2. (a) Using Table 5.1, construct your own table identifying by date and
duration in months the shortest and longest booms, slumps, and complete cycles (peak to peak and trough to trough) for the period from 1945 to the present. Also identify by date and duration the median boom, slump, and complete cycle. (b) Repeat the exercise in part (a) for the period before 1942. (c) Does the business cycle have noticeably different characteristics before and after the Second World War?
Problems 5.3 and 5.4 generate data to be used in Problems 5.5 and 5.6. Problem 5.3. Using quarterly real GDP data for the period since 1947, calculate the
percentage change in GDP for each recession (peak to trough), expansion (trough to peak), and complete cycles (peak to peak and trough to trough) and enter them as separate time series on a spreadsheet. For each series calculate the mean and median values.
Problem 5.4. Using monthly employment data for the period since 1947, calculate the
percentage change in employment for each recession (peak to trough), expansion (trough to peak), and complete cycles (peak to peak and trough to trough) and enter them as separate time series on a spreadsheet. For each series calculate the mean and median values.
Problem 5.5. Using the calculated in Problems 4.2, 4.4 and 4.5, describe the quantitative
and temporal characteristics of the typical post-World War II business cycle.
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Problem 5.6. There are a number of competing theories of the business cycle. One suggests that the seeds of the slump are sown in the boom, so that the higher the peak, the lower subsequent trough. Another suggests that the economy is like a guitar string, the further it is plucked (the lower the trough), the more it rebounds (the higher the subsequent peak). Another holds that mild recessions are followed by strong recoveries. Yet another holds that adjacent recessions and expansions are essentially independent of each other. There are other possibilities. How could you state these three views in terms of correlations between the changes in real GDP and adjacent recessions and expansions? (Hint: it is easier to think clearly if the fall in GDP during a recession is measured by its absolute value.) Using the data you generated in Problem 5.3, test your hypotheses by calculating two correlations: 1. between expansions and the subsequent recession; and 2. between recessions and the subsequent expansion. Which of the four hypotheses (or which other pattern) do your calculations favor?
Problem 5.7. Instead of focusing on the size of changes as measured by GDP as in
Problem 5.6 consider the same set of hypotheses using the duration of the recessions and expansions. Using the data in Table 5.1 for post-World War II recessions, repeat the calculations of Problem 5.6. Which of the four hypotheses (or which other pattern) do your calculations favor? Compare these results for those using GDP.
Problem 5.8. Use data on real GDP to establish the dates of the peaks and troughs of the
Canadian business cycle. Explain your procedure. What is the typical Canadian business like measured by the size and durations of its recessions, expansions, and complete cycles? Do Canadian business cycles seem to be closely related to U.S. business cycles?
Problem 5.9. Use data on real GDP to establish the dates of the peaks and troughs of the
Japanese business cycle. Explain your procedure. What is the typical Japanese business like measured by the size and durations of its recessions, expansions, and complete cycles? Should we characterize Japan as having experienced a depression in the 1990s?
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Problem 5.10. How good are the leading indicators as predictors of recessions? One rule (see section 5.3.3) states that if index of leading economic indicators turns down two months in succession, then a recession should be expected. Statisticians recognize two types of error. Type I error (false negative) occurs when a recession is not signaled, but one in fact follows. Type II error (false positive) occurs when a recession is signaled and none in fact follows. Using Table 5.1 and the time series for the index of leading economic indicators, identify all the times in which the 2-quarter rule signals a recession, then check to see whether the business cycle reaches a peak (i.e, a recession begins) within the subsequent year. Similarly, identify all the times in which a recession occurs, then check to see whether the leading indicators signaled a recession within the preceding year. Fill in the number of each case in the following table:
Recession Does Not Occur Occurs
Do NotSignal
Recession
Leave this cell blank.
Any case that does not fall into one of the other cells automatically belongs here.
Type I Error: enter the number of times a recession occurred without having been signaled
Leading Indicators
Signal
Recesssion
Type II Error: enter the number of times a recession was signaled but failed to occur
Success: enter the number of times a recession was signaled and occured
Repeat this exercise using a 3-quarter rule. How do the errors change? Which rule is
best? Why? Is the best rule useful as a predictor of recessions? Explain the reasons for your assessement.
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Problem 5.11. Using whatever calculations and graphical analysis that you find helpful, examine the unemployment rate and identify its cyclicality; i.e., is it: procyclical, countercyclical, or acyclical? Is it a leading, lagging, or mixed indicator? (If mixed, give an accurate description of its properties.)
Problem 5.12. Calculate the time series for the annualized quarterly rate of real GDP
growth. Plot this series against the NBER business cycle dates. Compare your graph to Figure B5.1. Do these two graphs conform roughly to the stylized relationship between fluctuations in a level series and the rate of change series as shown in that figure and discussed in Box 5.1?
Problem 5.13. As observed in Chapter 3, section 3.6.2 (especially Figure 3.6), the 2001
recession appears not to have been a recession at all when judged by the revised data for real GDP. Using whatever data, calculations, and graphical analysis that you find helpful, do a wider range of data support the NBERs identification of a recession in that year?