Transcript Chapter # 6 - College of Business Administration @ Kuwait University

503
Applied Macroeconomics
Trends and Cycles
Prof. M. El-Sakka
Dept of Economics
Kuwait University
• This chapter provides a wider examination of the economy, it
focuses on the question, how do GDP and large variety of other
economic variables behave over time?
• We begin by distinguishing between 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?
• Look at the following 3 figures. Each shows the path of U.S.
real GDP over 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.
Decomposing Time Series
• The following figure 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. It is useful to
distinguish the dominant path, known as the TREND, from the
fluctuations, known as the CYCLE, because distinct factors
explain each.
• The upper panel of the following figure 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.
• The following figure displays the same information as the
above figure 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. The key
to decomposing any time series into its trend and cycle is the
identification of the trend.
• In either the original or the logarithmic representation, a local
high point is a CYCLICAL PEAK and a local valley is a
CYCLICAL TROUGH. A
Working with Economic Data: Detrending Time Series
• 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.
• The difference between the time series and the trend is:
deviation from trend = time series – trend
• = time series – a(1 + b)t
• or
• = time series – aexp(bt).
• If a time series grows at a steady proportionate rate, then
log(time series) will grow at a steady absolute rate, the trend is
then described by a linear function, not an exponential
function:
• trend = a + bt.
• 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
• average growth rates may not be 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:
• In 1963, the moving average would drop Y60 and add Y65:
• 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 number of periods in the
average, the more fluctuations the trend will display.
• Differences and growth rates
• 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:
• ΔXt = Xt – Xt-1.
• More commonly, we calculate the proportional first difference,
which is just the growth rate:
• 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. 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.
The Business Cycle
• THE LANGUAGE OF BUSINESS CYCLES
• 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.
• 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.
• 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. 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
• Depression: a particularly severe recession. Originally,
“depression” was a synonym for a recession. Unfortunately, it
became associated with the largest slump in U.S. and world
economic history:
• 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.
(Complete) cycle: the period between a peak and the following
peak or between a trough and the following trough.
• 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. 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.
• The National Bureau of Economic Research (NBER) is widely
regarded in the United States as the arbiter of the beginnings
and ends of recessions. 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.
• In the 1992 presidential campaign, the delay in announcing the
end of the recession allowed Bill Clinton to claim that the
economy was in one of the longest recessions of the postwar 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.
• 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. NBER did not announce that the economy had reached
its cyclical trough in November 2001 until March 2003.
THE TYPICAL BUSINESS CYCLE
• 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 indices. Since1995, the indices have been
compiled by the Conference Board, 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.
• How can we characterize the typical business cycle? The
following figure provides one answer with another view of the
relationship between the coincident indicators and the NBER
cycle dates. 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. 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, 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.
• The following three figures examine the typical cyclical
behavior of personal income, industrial production, and
employment. The pattern of industrial production 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. 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
personal income 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. 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 April 1991 is the longest.
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. 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. 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).
• 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.
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 U.S. Department of Commerce developed, and the
Conference Board now maintains and publishes monthly,
indices of leading and lagging economic indicators. See table
5.2.
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. The
following figure 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. 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.
• The correlation between the leading and coincident indicators
is 0.44,. But we should not really expect a strong correlation
between the leading indicators today and coincident indicators
today. 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 the leading economic
indicators.
• The row labeled 0 is the correlation when both indices are
measured in the same month. 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
• 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.
• 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, 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
themselves, explain the why the business cycle behaves as it
• Kevin D. Hoover ; Applied Intermediate Macroeconomics