503Applied Macroeconomics

Trends and Cycles

Prof. M. El-SakkaProf. M. El-SakkaDept of EconomicsDept of Economics

Kuwait UniversityKuwait University

• This chapter provides a This chapter provides a wider examination wider examination of the economy, it of the economy, it focuses on the question, how do GDP and large variety of other focuses on the question, how do GDP and large variety of other economic variables economic variables behave over timebehave over time? ?

• We begin by distinguishing between We begin by distinguishing between longer run trends longer run trends and and shorter run shorter run cyclescycles. We then ask, are the cycles in different . We then ask, are the cycles in different variables are closely related in an variables are closely related in an economy-wide business economy-wide business cyclecycle? And, finally, what are the ? And, finally, what are the properties of the business properties of the business cycle?cycle?

• Look at the following 3 figures. Each shows the path of U.S. Look at the following 3 figures. Each shows the path of U.S. real GDP over about fifty years. Two characteristics of these real GDP over about fifty years. Two characteristics of these graphs stands out. graphs stands out. FirstFirst, the dominant movement of U.S. GDP , the dominant movement of U.S. GDP is is upwardupward. But, . But, secondsecond, the dominant movement is , the dominant movement is unsteadyunsteady: : there are frequent and, at best, roughly there are frequent and, at best, roughly regular ups and downsregular ups and downs. . A large proportion of the thousands of economic time series A large proportion of the thousands of economic time series that describe the economy behave similarly.that describe the economy behave similarly.

Decomposing Time SeriesDecomposing Time Series

• The following figure shows the time series for personal The following figure shows the time series for personal disposable income (less transfers), industrial production, and disposable income (less transfers), industrial production, and employment. Each one resembles GDP; each displays a pattern employment. Each one resembles GDP; each displays a pattern of fluctuations around a dominant upward path. It is useful to of fluctuations around a dominant upward path. It is useful to distinguish the dominant path, known as the TREND, from the distinguish the dominant path, known as the TREND, from the fluctuations, known as the CYCLE, because distinct factors fluctuations, known as the CYCLE, because distinct factors explain each. explain each.

• The upper panel of the following figure shows a The upper panel of the following figure shows a stylized stylized versionversion of an economic time series, which cycles regularly of an economic time series, which cycles regularly about about a smooth exponential trenda smooth exponential trend. The time series may be . The time series may be decomposeddecomposed in two steps: first, in two steps: first, estimate the trend estimate the trend and, second, and, second, express the fluctuations express the fluctuations as deviations from the trendas deviations from the trend. The lower . The lower panel shows the cycle, now measured as the difference between panel shows the cycle, now measured as the difference between the time series and its trend expressed as a percentage of the the time series and its trend expressed as a percentage of the trend. Displaying the cycle as percentage of the trend makes trend. Displaying the cycle as percentage of the trend makes sense: although the fluctuations of an economic variable are sense: although the fluctuations of an economic variable are likely to be absolutely smaller when its average value is small, likely to be absolutely smaller when its average value is small, there is no reason to believe that they will be relatively smaller there is no reason to believe that they will be relatively smaller than when its absolute value is large.than when its absolute value is large.

• The following figure displays the same information as the The following figure displays the same information as the above figure using a logarithmic scale. The exponential trend above figure using a logarithmic scale. The exponential trend becomes a linear trend. The lower panel shows the becomes a linear trend. The lower panel shows the difference difference log(time series) – log(trend). Since the difference in log(time series) – log(trend). Since the difference in logarithms is logarithms is a ratio, just like a percentage difference, the lower panel is a ratio, just like a percentage difference, the lower panel is qualitatively identical to the lower panel in Figure 5.2. The key qualitatively identical to the lower panel in Figure 5.2. The key to decomposing any time series into its trend and cycle is the to decomposing any time series into its trend and cycle is the identification of the trend. identification of the trend.

• In either the original or the logarithmic representation, a local In either the original or the logarithmic representation, a local high point is a CYCLICAL PEAK and a local valley is a high point is a CYCLICAL PEAK and a local valley is a CYCLICAL TROUGH. ACYCLICAL TROUGH. A

Working with Economic Data: Detrending Time SeriesWorking with Economic Data: Detrending Time Series

• The constant trendThe constant trend

• If we believe that, despite cyclical fluctuations, the average If we believe that, despite cyclical fluctuations, the average growth rate of a series does not change much over a long growth rate of a series does not change much over a long periodperiod, then it is reasonable to assume that the trend has a , then it is reasonable to assume that the trend has a constant rate of growth and can be described by an equationconstant rate of growth and can be described by an equation

• trend = a(1 + b)trend = a(1 + b)tt

• oror

• trend = aexp(bt),trend = aexp(bt),

• where t is time, and a and b are constants. where t is time, and a and b are constants.

• The difference between the time series and the trend is: The difference between the time series and the trend is: deviation from trend = time series – trenddeviation from trend = time series – trend

• = time series – a(1 + b)= time series – a(1 + b)tt

• oror

• = = time series – aexp(bt).time series – aexp(bt).

• If a time series grows at a steady proportionate rate, then If a time series grows at a steady proportionate rate, then log(time series) log(time series) will grow at a steady absolute ratewill grow at a steady absolute rate, the trend is , the trend is then described by a linear function, not an exponential then described by a linear function, not an exponential function:function:

• trend = a + btrend = a + btt..

• Linear trends arise naturally when we consider the logarithms Linear trends arise naturally when we consider the logarithms of steadily growing data, but may also be appropriate even for of steadily growing data, but may also be appropriate even for natural data that do not grow exponentially.natural data that do not grow exponentially.

• The moving average trendThe moving average trend

• average growth rates may average growth rates may not be constant decade by decadenot be constant decade by decade. In . In such cases, a constant trend such cases, a constant trend may not be appropriatemay not be appropriate. We could . We could perhaps use the perhaps use the average growth rate each decade average growth rate each decade to to approximate the trend. But that would imply, wrongly, that approximate the trend. But that would imply, wrongly, that decades were somehow decades were somehow natural breaksnatural breaks. Instead, we can . Instead, we can calculate a calculate a centered moving averagecentered moving average. Suppose that we have . Suppose that we have annual data on real GDP from 1960 to 2006. A five-year annual data on real GDP from 1960 to 2006. A five-year centered moving average would start in 1962 would average centered moving average would start in 1962 would average the value for 1962 with the values for two years before and two the value for 1962 with the values for two years before and two years after:years after:

• In 1963, the moving average would drop In 1963, the moving average would drop Y60 and add Y65:Y60 and add Y65:

• and so on until 2004. One disadvantage, of course, is that the and so on until 2004. One disadvantage, of course, is that the centered moving average centered moving average cannot start right at the beginning cannot start right at the beginning of of the sample the sample and must end before the end of the sample and must end before the end of the sample in order in order to accommodate the leading and lagging terms. Centered to accommodate the leading and lagging terms. Centered moving averages should have an odd number of terms, to moving averages should have an odd number of terms, to preserve symmetry. The preserve symmetry. The narrower narrower the number the number of periods of periods in the in the average, the average, the more fluctuations the trend more fluctuations the trend will display. will display.

• Differences and growth ratesDifferences and growth rates

• Sometimes we may not really care about the trend but just Sometimes we may not really care about the trend but just want to focus on fluctuations.want to focus on fluctuations.

• This is easily done by taking the first difference of the data:This is easily done by taking the first difference of the data:

• ΔΔXXtt = X = Xtt – X – Xt-1t-1..

• More commonly, we calculate the More commonly, we calculate the proportional first differenceproportional first difference, , which is just the growth rate:which is just the growth rate:

• Figure B5.1 shows a time series that has been detrended by Figure B5.1 shows a time series that has been detrended by calculating growth rates.calculating growth rates.

• Notice that differencing a time series (or calculating a growth Notice that differencing a time series (or calculating a growth rate) causes a rate) causes a phase shift: When the original time series is phase shift: When the original time series is falling, its growth rate is negative; when the level falling, its growth rate is negative; when the level time series is time series is rising, the growth rate is positive. When the level is exactly at 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, 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 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 points, it changes faster for a while and then slows down to no change just at the next extreme point. Its growth rate must, change just at the next extreme point. Its growth rate must, therefore, reach its fastest absolute value between the peak and therefore, reach its fastest absolute value between the peak and the trough of the level series. What this means economically is the trough of the level series. What this means economically is that we cannot judge the peak or trough of economic activity 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 the peak or trough of the growth rate of GDP, but instead from noting when that growth switched from positive or from noting when that growth switched from positive or negative or back to positive.negative or back to positive.

The Business Cycle

• THE LANGUAGE OF BUSINESS CYCLESTHE LANGUAGE OF BUSINESS CYCLES

• The cyclical patterns of a large number of economic time series The cyclical patterns of a large number of economic time series are are closely relatedclosely related. The tendency of many measures of . The tendency of many measures of economic activity to move in concert suggests that there are economic activity to move in concert suggests that there are common driving forces common driving forces and that we can think, not just about and that we can think, not just about the trends and cycles of the individual measures, but of a the trends and cycles of the individual measures, but of a business cycle. business cycle.

• The BUSINESS CYCLE The BUSINESS CYCLE is is the alternation in the state of the the alternation in the state of the economy of a roughly consistent periodicity and with rough economy of a roughly consistent periodicity and with rough coherence between different measures of the economy.coherence between different measures of the economy.

• Over the past Over the past 150 years150 years, the average business , the average business cycle lasted four cycle lasted four to five yearsto five years; the shortest, ; the shortest, less than two less than two years; the longest, years; the longest, ten ten yearsyears. As with cycles in particular times series, business cycles . As with cycles in particular times series, business cycles are identified by their peaks and troughs. Key terms include:are identified by their peaks and troughs. Key terms include:

RECESSIONRECESSION (synonyms: (synonyms: slump, contractionslump, contraction): ): the period between the period between the cyclical peak and the cyclical trough, when economic activity the cyclical peak and the cyclical trough, when economic activity is falling.is falling.

EXPANSIONEXPANSION (synonyms: (synonyms: boom, recoveryboom, recovery): ): the period between the the period between the cyclical trough and cyclical peak, when economic activity is cyclical trough and cyclical peak, when economic activity is rising. “rising. “RecoveryRecovery” is ” is sometimes used in the more limited sense sometimes used in the more limited sense of the period between the trough and when the economy of the period between the trough and when the economy regains either (1) regains either (1) the level of activity experienced at the the level of activity experienced at the previous peakprevious peak or (2) the level it would have experienced had it or (2) the level it would have experienced had it remained on trendremained on trend

• DepressionDepression: : a a particularly severe recessionparticularly severe recession. Originally, . Originally, “depression” was a “depression” was a synonym for a recession. Unfortunately, it synonym for a recession. Unfortunately, it became associated with became associated with the largest slump the largest slump in U.S. and world in U.S. and world economic history: economic history:

• SeveralSeveral of the contractions of the 19th century are consider of the contractions of the 19th century are consider depressions, but the Great Depression is the depressions, but the Great Depression is the only example only example of of the 20the 20thth century. century.

Growth recessionGrowth recession: : a period of a period of slower than trend growthslower than trend growth, usually , usually lasting a lasting a year or moreyear or more. . During a growth recession, output During a growth recession, output continues to rise, continues to rise, but at so slow a rate but at so slow a rate that other aspects of the that other aspects of the economy – particularly, employment – may stagnate or fall. economy – particularly, employment – may stagnate or fall.

(Complete) cycle(Complete) cycle: the period between a peak and the following : the period between a peak and the following peak or between a trough and peak or between a trough and the following trough.the following trough.

• DATING THE BUSINESS CYCLEDATING THE BUSINESS CYCLE

• The problem of dating business cycles is really just a matter of The problem of dating business cycles is really just a matter of determiningdetermining when the economy reaches its when the economy reaches its peaks and its peaks and its troughstroughs. A common rule of thumb defines a . A common rule of thumb defines a recession as two recession as two consecutive quarters of negative growth in real GDPconsecutive quarters of negative growth in real GDP. The . The peakpeak would then be marked at the quarter immediately before GDP would then be marked at the quarter immediately before GDP begins to fall, and the begins to fall, and the troughtrough at the quarter immediately before at the quarter immediately before it begins to grow again.it begins to grow again.

• The National Bureau of Economic Research (NBER) is widely The National Bureau of Economic Research (NBER) is widely regarded in the United States as the arbiter of the beginnings regarded in the United States as the arbiter of the beginnings and ends of recessions. According to the NBER, a and ends of recessions. According to the NBER, a recession is a recession is a recurring period of recurring period of declinedecline in total output, income, employment, in total output, income, employment, and trade, usually lasting from and trade, usually lasting from six months to a yearsix months to a year, and marked , and marked by widespread contractions in many sectors of the economy.by widespread contractions in many sectors of the economy.

• In the In the 19921992 presidential campaign, the delay in announcing the presidential campaign, the delay in announcing the end of the recession allowed Bill Clinton to claim that the end of the recession allowed Bill Clinton to claim that the economy was in one of the longest recessions of the postwar In economy was in one of the longest recessions of the postwar In fact, the recession of 1990-91 was the second shortest in the fact, the recession of 1990-91 was the second shortest in the postwar period, having lasted only eight months, and had postwar period, having lasted only eight months, and had ended in March 1991 – twenty months before the election. ended in March 1991 – twenty months before the election.

• The unemployment rate did not begin to fall until June 1992 The unemployment rate did not begin to fall until June 1992 (three months after the trough) and did not reach its level at (three months after the trough) and did not reach its level at the cyclical peak (6.8 percent) until August 1993 – more than the cyclical peak (6.8 percent) until August 1993 – more than two years after the recovery had begun. This is not unusual; two years after the recovery had begun. This is not unusual; the peak in the unemployment rate typically lags the cyclical the peak in the unemployment rate typically lags the cyclical trough. NBER did not announce that the economy had reached trough. NBER did not announce that the economy had reached its cyclical trough in November 2001 until March 2003. its cyclical trough in November 2001 until March 2003.

THE TYPICAL BUSINESS CYCLETHE TYPICAL BUSINESS CYCLE

• Economists have studied thousands of economic time series Economists have studied thousands of economic time series and classified their cyclical behavior. To try to give some feeling and classified their cyclical behavior. To try to give some feeling for the business cycle as a whole, the U.S. Department of for the business cycle as a whole, the U.S. Department of Commerce created indices of Commerce created indices of ECONOMIC INDICATORSECONOMIC INDICATORS, , similar to price indices. Since1995, the indices have been similar to price indices. Since1995, the indices have been compiled by the compiled by the Conference BoardConference Board,, each of the three indices each of the three indices ((leading, coincidentleading, coincident,, andand lagging lagging indicators indicators of the business of the business cycle) is a weighted average of several monthly time series and cycle) is a weighted average of several monthly time series and is expressed as an index number based such that the average is expressed as an index number based such that the average value for 1992 equals 100.value for 1992 equals 100.

• How can we characterize the How can we characterize the typical business cycle? typical business cycle? The The following figure provides one answer with another view of the following figure provides one answer with another view of the relationship between the coincident indicators and the NBER relationship between the coincident indicators and the NBER cycle dates. cycle dates. The figure shows twelve months before the peak (–1 The figure shows twelve months before the peak (–1 to –12) and thirty-six months after (+1 to +36). The vertical to –12) and thirty-six months after (+1 to +36). The vertical lines indicate the NBER peaks and troughs. Heavy lines show lines indicate the NBER peaks and troughs. Heavy lines show average values for the seven business cycles between 1960 and average values for the seven business cycles between 1960 and 2004, while the lighter lines show the values for the 1990-91 2004, while the lighter lines show the values for the 1990-91 recession. The average index peaks exactly at the NBER peak. recession. The average index peaks exactly at the NBER peak. At +16 months, its trough is about five months past the average At +16 months, its trough is about five months past the average trough for the seven business cycles (+11). This shows that, trough for the seven business cycles (+11). This shows that, when recessions are longer than average, they are also deeper when recessions are longer than average, they are also deeper than average drawing down the average level of the coincident than average drawing down the average level of the coincident indicators. In 1990-91 the coincident indicators track the indicators. In 1990-91 the coincident indicators track the NBER cycle dates exactly. NBER cycle dates exactly.

• The following three figures examine the typical cyclical The following three figures examine the typical cyclical behavior behavior of personal incomeof personal income, , industrial productionindustrial production, and , and employmentemployment. The pattern of industrial production resembles . The pattern of industrial production resembles that of the index of coincident indicators. The average data that of the index of coincident indicators. The average data peaks at the NBER business cycle peak, but the trough is some peaks at the NBER business cycle peak, but the trough is some five months behind the NBER trough. The pattern for five months behind the NBER trough. The pattern for employment is similar for the average; but the major losses in employment is similar for the average; but the major losses in employment tend to come early in the recession, so that employment tend to come early in the recession, so that employment falls only slowly to its trough. The pattern of employment falls only slowly to its trough. The pattern of personal income is almost perfectly coincident in 1990-91; yet, personal income is almost perfectly coincident in 1990-91; yet, on average, it appears to peak before the NBER peak and to on average, it appears to peak before the NBER peak and to rise very slowly from the NBER trough. One striking feature is rise very slowly from the NBER trough. One striking feature is that personal incomes are far less variable over the average that personal incomes are far less variable over the average recession than are industrial production or employment.recession than are industrial production or employment.

• Table 5.1 and Figures 5.7-5.9 give us a good picture of the 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 history of recent U.S. business cycles. At least two characteristics are worth noting. First, the average recession in characteristics are worth noting. First, the average recession in the post-World War the post-World War II period lasted eleven monthsII period lasted eleven months, while the , while the average expansion lasted fifty monthsaverage expansion lasted fifty months. The . The process of economic process of economic growth over the last fifty years can be characterized as a growth over the last fifty years can be characterized as a pattern of five steps forward and one step back.pattern of five steps forward and one step back.

• Second, the expansion that began in April 1991 is the longest.Second, the expansion that began in April 1991 is the longest.

THE CLASSIFICATION OF ECONOMIC INDICATORSTHE CLASSIFICATION OF ECONOMIC INDICATORS

• Our definition of the business cycle had two parts: (1) Our definition of the business cycle had two parts: (1) alternationalternation in the state of the economy; and (2) in the state of the economy; and (2) coherencecoherence among different measures of the economy. As a starting place, among different measures of the economy. As a starting place, it is useful to have a good vocabulary to describe the it is useful to have a good vocabulary to describe the relationships among different time series.relationships among different time series.

• Economic indicators can be classified according to how they Economic indicators can be classified according to how they behave compared to the business cycle. An indicator is said to behave compared to the business cycle. An indicator is said to be be coincidentcoincident if it reaches its peak at or near the peak if it reaches its peak at or near the peak of the of the business cycle and reaches its trough at our near the trough of business cycle and reaches its trough at our near the trough of the business cycle. Economic indicators are classified by the business cycle. Economic indicators are classified by whether or not they generally move in the same direction as the whether or not they generally move in the same direction as the main positive measures of the business cycle, such as GDP, main positive measures of the business cycle, such as GDP, industrial production, or employment. industrial production, or employment.

• Indicators can beIndicators can be

procyclicalprocyclical: they move in roughly the same direction as the : they move in roughly the same direction as the business cycle (for example, retail sales are procyclical);business cycle (for example, retail sales are procyclical);

countercyclicalcountercyclical: they move in roughly the opposite direction as : they move in roughly the opposite direction as the business cycle (for example, the unemployment rate is the business cycle (for example, the unemployment rate is countercyclical); orcountercyclical); or

acyclicalacyclical: they have no regular relationship to the cycle (for : they have no regular relationship to the cycle (for example, agricultural production and population are acyclical).example, agricultural production and population are acyclical).

• Indicators are also classified by their Indicators are also classified by their phase relationship phase relationship to the to the business cycle –that is, according to whether their extreme business cycle –that is, according to whether their extreme points occur before, after, or at the same time as the extreme points occur before, after, or at the same time as the extreme points of the business cycle. points of the business cycle.

A leading indicatorA leading indicator reaches its peak and trough before the reaches its peak and trough before the corresponding peak or trough of the business cycle;corresponding peak or trough of the business cycle;

A lagging indicatorA lagging indicator reaches its peak and trough after the reaches its peak and trough after the corresponding peak or trough of the business cycle;corresponding peak or trough of the business cycle;

A mixed indicator follows A mixed indicator follows a regular pattern different from either a regular pattern different from either the leading or lagging indicator. the leading or lagging indicator.

• The U.S. Department of Commerce developed, and the The U.S. Department of Commerce developed, and the Conference Board now maintains and publishes monthly, Conference Board now maintains and publishes monthly, indices of leading and lagging economic indicators. See table indices of leading and lagging economic indicators. See table 5.2.5.2.

IS THE BUSINESS CYCLE PREDICTABLEIS THE BUSINESS CYCLE PREDICTABLE?

• The fact that a number of time series are consistent leading The fact that a number of time series are consistent leading economic indicators suggests that it may be possible, to some economic indicators suggests that it may be possible, to some degree, degree, to predict the course of the business cycleto predict the course of the business cycle. The . The following figure shows the three indices of economic indicators following figure shows the three indices of economic indicators (detrended). Notice first, the broad similarity of the (detrended). Notice first, the broad similarity of the fluctuations. All three series are procyclical, and they show the fluctuations. All three series are procyclical, and they show the rough coherence that characterizes the business cycle. Looking rough coherence that characterizes the business cycle. Looking more closely, we see the expected pattern (especially clear at more closely, we see the expected pattern (especially clear at the peaks and troughs): the leading indicators move ahead of the peaks and troughs): the leading indicators move ahead of the coincident indicators, which, in their turn, move ahead of the coincident indicators, which, in their turn, move ahead of the lagging indicators.the lagging indicators.

• How well can the relationships among the indicators be How well can the relationships among the indicators be exploited to forecast the path of the business cycle? There are exploited to forecast the path of the business cycle? There are two questions: First, two questions: First, how long on average is the lead how long on average is the lead between between the leading and coincident indicators? Second, how strongly the leading and coincident indicators? Second, how strongly related are the two indices? The second question can be related are the two indices? The second question can be answered by calculating the coefficient of correlation between answered by calculating the coefficient of correlation between the two indices. the two indices.

• The correlation between the leading and coincident indicators The correlation between the leading and coincident indicators is 0.44,. But we should not really expect a strong correlation is 0.44,. But we should not really expect a strong correlation between the leading indicators today and coincident indicators between the leading indicators today and coincident indicators today. We can instead calculate the correlation between the today. We can instead calculate the correlation between the coincident indicators in each period and the leading indicators coincident indicators in each period and the leading indicators one or more months earlier. The correlation between the index one or more months earlier. The correlation between the index of coincident indicators and the index of leading indicators one of coincident indicators and the index of leading indicators one month earlier is 0.54 – a little bit stronger.month earlier is 0.54 – a little bit stronger.

• Table 5.3 presents the results of such calculations for leads and Table 5.3 presents the results of such calculations for leads and lags of twelve months. The first column shows the correlations lags of twelve months. The first column shows the correlations between the coincident indicators and the leading economic between the coincident indicators and the leading economic indicators. indicators.

• The row labeled 0 is the correlation when both indices are The row labeled 0 is the correlation when both indices are measured in the same month. The row labeled +1 indicates the measured in the same month. The row labeled +1 indicates the leading indicators in one month and the coincident indicators one leading indicators in one month and the coincident indicators one month later. It measures how well the leading indicators predict month later. It measures how well the leading indicators predict the later coincident indicators and, therefore, the business cycle. the later coincident indicators and, therefore, the business cycle. Again, we already have seen that the value is 0.54. Subsequent Again, we already have seen that the value is 0.54. Subsequent rows (labeled +2 to +12) show the correlation between the leading rows (labeled +2 to +12) show the correlation between the leading indicators and the coincident indicators two, three, and up to indicators and the coincident indicators two, three, and up to twelve months ahead, as well as one to twelve months behind (–1 twelve months ahead, as well as one to twelve months behind (–1 to –12). on. The second column shows a similar set of correlations to –12). on. The second column shows a similar set of correlations between the lagging indicators and the coincident indicators.between the lagging indicators and the coincident indicators.

• The highest correlation between the coincident and leading The highest correlation between the coincident and leading indicators is 0.89 at +9 and +10 months lead (that is, roughly indicators is 0.89 at +9 and +10 months lead (that is, roughly three quarters ahead). Such a strong correlation suggests that three quarters ahead). Such a strong correlation suggests that the leading indicators are a good, though imperfect, predictor the leading indicators are a good, though imperfect, predictor of the future behavior of the business cycle. The point is of the future behavior of the business cycle. The point is reinforced visually in Figure 5.13, which is similar to Figure reinforced visually in Figure 5.13, which is similar to Figure 5.12, except that the index of leading indicators has been 5.12, except that the index of leading indicators has been shifted forward by nine months (that is, the value for January shifted forward by nine months (that is, the value for January is plotted at the following September and so forth). Once is plotted at the following September and so forth). Once shifted, the leading and coincident indicators line up extremely shifted, the leading and coincident indicators line up extremely well.well.

• There is, nevertheless, good reason to believe that the index of There is, nevertheless, good reason to believe that the index of leading indicators does have some predictive power for the leading indicators does have some predictive power for the business cycle. Notice that in Table 5.2 the correlation between business cycle. Notice that in Table 5.2 the correlation between the leading and coincident indicators is above 0.8 for each of the leading and coincident indicators is above 0.8 for each of the months between +6 and +12. This supports the idea that the the months between +6 and +12. This supports the idea that the leading indicators help to forecast recessions. A popular rule of leading indicators help to forecast recessions. A popular rule of thumb states that two months of consecutive declines in the thumb states that two months of consecutive declines in the leading indicators signals an imminent recession. This rule leading indicators signals an imminent recession. This rule often works, but it also works too often: most recessions are often works, but it also works too often: most recessions are predicted accurately, but sometimes a recession is predicted predicted accurately, but sometimes a recession is predicted and none occurs. Others have suggested three months of and none occurs. Others have suggested three months of decline, rather than two, to give more accurate predictions. In decline, rather than two, to give more accurate predictions. In that case, however, there is necessarily less lead time between that case, however, there is necessarily less lead time between the signal and the onset of the recession.the signal and the onset of the recession.

• One reason that the leading economic indicators are important is One reason that the leading economic indicators are important is that, there is often considerable delay in getting relevant that, there is often considerable delay in getting relevant information about coincident indicators. One of the roles of the information about coincident indicators. One of the roles of the index of lagging economic indicators is to buttress the evidence index of lagging economic indicators is to buttress the evidence that the economy actually entered or left a recession and to help to that the economy actually entered or left a recession and to help to resolve the uncertainty that clouds all judgments about the state resolve the uncertainty that clouds all judgments about the state of the economy. Table 5.3 shows that the correlation between the 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 lagging and the coincident indicators is highest at 0.82 with a lag of 8 to 9 months (roughly three quarters behind).of 8 to 9 months (roughly three quarters behind).

• The consistent patterns of the leading, lagging, and coincident The consistent patterns of the leading, lagging, and coincident indicators demonstrate that there are facts about the business indicators demonstrate that there are facts about the business cycle that economists need to explain. They give some clues about cycle that economists need to explain. They give some clues about the course of the business cycle. But they do not, in themselves, the course of the business cycle. But they do not, in themselves, explain the why the business cycle behaves as it does. explain the why the business cycle behaves as it does.

• Kevin D. Hoover ; Kevin D. Hoover ; Applied Intermediate MacroeconomicsApplied Intermediate Macroeconomics