503 Applied Macroeconomics Chapter 5. Trends and Cycles 2004 Kevin D. Hoover Applied Intermediate Macroeconomics

1. 503 Applied Macroeconomics Chapter 5. Trends and Cycles 2004 Kevin D. Hoover Applied Intermediate Macroeconomics Prof. M. El-Sakka Dept of Economics Kuwait University

2. 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.

6. 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.

8. 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.

10. 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

12. 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

13. 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.

14. 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:

15. 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.

16. 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.

19. 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.

20. 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.

22. 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

24. 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.

25. 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.

27. 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.

28. 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 laggingindicators 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.

31. 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.

33. 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.

37. 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.

38. The Business Cycle and the Economy WHAT CAUSES THE BUSINESS CYCLE? Economists have found it useful to distinguish two aspects of the cycle: IMPULSE and PROPAGATION MECHANISMS. 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 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.

39. 2. A second class of theories holds that the cycles in the economy are the result primarily of cycles in the impulse mechanisms. Exogenous cycles in technology cause the business cycle. Others believe that recurring recessions are induced by the actionsof policymakers. If the fed would just leave the economy to its own devices, and not raise interest rates from time to time, the economy would suffer few recessions. 3. 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.)

40. The following figure shows a random walk with a drift. The apparent cyclical patterns in the figure are purely accidental and do not describe a genuine phenomenon in need of a theoretical explanation. But which type of account of business cycles describes the actual economy: Are its ups and downs governed by laws. 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. 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.”

42. 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.

43. 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).

44. 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.

46. 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.

48. 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.

49. 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 indicators and the coincident indicators.