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An evaluation of the composite index of leading indicators for signaling turning points in business and growth cycles.

This study of cyclical indicators found: (1) the composite indexes contain more reliable turning point information than most of the individual indicators; (2) the Commerce Department's composite index would benefit by some component substitutions; (3) the ratio of the coincident to lagging indicators is more reliable in calling business cycle turning points than the composite of leading indicators, but that ratio has a poor track record in calling growth cycles; and (4) most of the individual components of the composite index of leading indicators signal growth cycle turning points better than business cycles turning points.

THE U.S. COMMERCE Department's composite index of leading economic indicators (LEI) was devised to anticipate business cycle turning points in the economy. The components were selected based on their breadth and reliability in forecasting cyclical turning points. In this paper, we examine each component of the composite and apply a new evaluation criterion, which we will call the "Neftci criterion." The Neftci methodology is an application of sequential analysis, which uses a statistical nonlinear probability model to call turning points. We believe this method could supplement the existing Commerce Department/National Bureau of Economic Research (NBER) composite indicator component selection techniques.

Our study examined cyclical indicators over the post-World War II business and growth cycles. We graded the individual LEI components and an extended list of financial indicators based on how well each called a turning point in the business or growth cycle. We concluded that several of the existing components of the leading indicator contain little useful cyclical information for real-time forecasting while some measures not included provide more insight into the future direction of the business cycle. Moreover, we established that the Commerce Department's composite indicators are superior to individual indicators for forecasting cyclical turning points in the economy.

THE SEQUENTIAL ANALYSIS APPROACH

Calling cyclical turning points in the economy always has been a difficult task for forecasters. The most popular approach for forecasting business cycle turning points is to look at the Commerce Department's composite index of leading indicators. Various "rules of thumb" have been devised, for example, three months of consecutive declines in the leading indicator composite, to alert one to an upcoming recession. The popular three months of decline rule, unfortunately, had many false signals. Even when rules of thumb appear to work, numerous reversals in direction of the leading indicator composite complicate the interpretation. On average, the composite index of leading indicators was expanding about 25 percent (see column 3 of Table 1) of the time during a down trend. An alternative to using those rules of thumb is a statistical method called "sequential analysis," which can be used to interpret fluctuations in the cyclical indicators.

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USING THE NEFTCI FORMULA

Neftci (1982) proposed a method using sequential analysis to calculate the probability of cyclical turning point. This method is based on a theoretical and empirical claim that the onset of a recession is marked by a pronounced decline in aggregate economic activity. The Neftci methodology allows for a statistically optimal evaluation of monthly movement in a time series by drawing upon three pieces of information. The first piece of information is the likelihood that the latest observation is from the recession sample or the recovery/expansion sample. The second piece of information used is the likelihood of a recession (recovery), given the current length of the expansion (recession) relative to its historical average. Finally, these two components are combined with last month's probability estimate in order to incorporate previous information. (1)

The logic underlying this method is that business activity declines rapidly when a business cycle peak has been reached, and that activity in sensitive (leading) indicators shows sharp declines prior to a recession or shortly thereafter, and sharp increases in sensitive indicators occur prior to a recovery or shortly therafter.

Neftci formulated the problem of forecasting turning points as recognizing when this abrupt switch in probability distributions occurred. This method can be applied to both recessions and expansions as follows:

1. Set up probability distributions. The economic time series is segmented into two distributions -- a downturn and an expansion sample. From these two segments, two probability distributions are fitted to the data.

2. Develop an a priori probability distribution. The user determines a subjective probability distribution that a recession (recovery) will develop so many months after the expansion (recession) began. In our application, we held this probability constant, because the empirical evidence suggests that the probability of a turning point does not increase as calendar time lengthens.

3. Apply the Neftci recursive formula. Neftci derived a probability formula using optimal stopping time theory. This formula predicts when an event will occur and not the level of the economic variable. The formula is:

[Prob.sub.t] = [[Prob.sub.t-1] + (Prior (1 - [Prob.sub.t-1]) Prob1)] / [[Prob.sub.t-1] + (Prior (1 - [Prob.sub.t-].[sup.1]) Prob1) + (1 - [Prob.sub.t-1]) Prob2 (1 - Prior)]

where the Prob is the probability of a recession (recovery) in the nearterm, Prior is the prior probability determined in step 2, Prob1 is the probability a new observation is in the downturn (upturn) distribution, while Prob2 is the probability that the new observation comes from the upturn or expansion case (downturn).

4. Interpret the results. When the cumulative probability exceeds a preset level of confidence, say 90 percent, then a signal of a turning point occurs.

5. Look for the next turning point. Once a turning point signal is given, the calculated probability is reset to zero and the search begins for the next turning point. Although this application lends itself to a two-state world, Hamilton (1989) has extended the methodology to n dimensional states (that is, in Neftci's original application he posited two states -- recession and expansion, but Hamilton's elaboration of the methodology allowed for a multidimensional world).

To interpret the monthly probabilities, a 90 percent "threshold" level of statistical confidence was selected for our application, i.e., we allow for a 10 percent chance of an error. When the probability of a recession exceeded 90 percent, this was said to "signal" a recession or recovery.

Several studies have applied this technique to the overall composite index of leading indicators for either the business or growth cycle (Neftci 1982, Palash and Radecki 1985, Niemira and Klein 1988, and Niemira 1991). Our application is an extension of those studies.

THE BEST AND WORST LEADING INDICATORS

We applied the Neftci sequential analysis method to the eleven components of the composite index of leading indicators, four additional financial variables (the treasury yield curve, the interest rate on the ten-year government note, a measure of credit market risk, and the three-month Treasury bill rate), and two composite indicators (the leading indicator composite and the ratio of the coincident to lagging indicators). This approach provided a formal statistical test of the turning point forecasting ability of each of these series, which accounted for the recognition lag necessary to determine whether a turning point signal is real or not.

To compare the performance of the individual series and the composites, we calculated an adjusted accuracy ratio, defined as the number of correct turns minus the number of missed turns divided by the total number of turns in the series. All statistics reported were calculated between 1948 and 1982. Based on those statistics, the conincident to lagging indicator ranked superior to the other sixteen indicators examined in its ability to call business cycle turning points. The accuracy rate of that composite was 88.9 percent (see Table 2). The composite index of leading indicators ranked fifth in our list behind the coincident to lagging index, the Treasury yield curve, consumer expectations and the ten-year government bond yield.

Figure 1 shows the performance of all seventeen indicators based on accuracy and timing. This figure suggests possible component substitutions for the composite index of leading indicators. For example, the index of stock prices (designated as L6 in the chart) has a lower accuracy rate in calling business cycle turning points than some other financial variables that we tested, such as the ten-year government note (designated as F1 in the chart), the yield curve (designated as F3), or the three-month Treasury bill rate (designated as F4). This would suggest that there could be some improved accuracy in replacing the index of stock prices in the LEI with another component from the "financial group" of indicators. (2) Figure 2 presents the average timing between the Neftci signals for each series compared

Table 2

Cyclical Indicators Ranked by Neftci Criterion

Based on Business Cycle Turning Point Signals

(1948-1982)
Rank Cyclical Measure Accuracy Rate (*)
 1 Coincident to Lagging Indicator 88.9%
 2 Treasury Yield Curve 80.0
 3 Consumer Expectations 76.5
 4 10 Year Treasury Note Yield 75.0
 5 Composite Index of Leading Indicators 72.7
 6 Building Permits 71.4
 7 Average Weekly Hours 65.2
 7 Initial Claims 65.2
 7 Mfg. New Orders 65.2
 7 Change in Sensitive Prices 65.2
11 Contracts and Orders 64.7
12 Vendor Performance 57.9
13 Stock Prices 51.7
14 Three-Month Treasury Bill Rate 50.0
15 Change in Unfilled Orders 48.4
16 Real M2 41.2
17 Credit Risk 16.7
 (*) Based on adjusted accuracy rate defined as:
100* (# of correct turns minus the # of missed turns)/(total #
of turns)


[TABLE DATA OMITTED]

with the business cycle turning points. (3) Those summary statistics, as shown in Figure 2, call into question the use of average weekly hours and initial claims for state unemployment insurance in the LEI, because their Neftci signals suggest they are confirming indicators of a turning point and provide no advance information, on average.

We should stress that this test is more than a method to discriminate between recessions and expansions; it is an aid to real-time monitoring. With the benefit of hindsight it is much easier to "see"

[TABLE DATA OMITTED]

a turning point in a series; however, in real-time monitoring it is far less obvious. The Neftci method provides statistical assurance that a turning point is or will be at hand. Therefore, although it can be argued that weekly hours "should" be included in the LEI, the combination of its short "theoretical" lead time and its recognition time made the indicator much less useful for forecasting. It is the turning point recognition lag that often is ignored in the LEI indicator selection process.

If the objective is to call turning points in the growth cycle, i.e., the trend-adjusted business cycle, then the accuracy rankings change and sometimes dramatically. The LEI was at the top of our list of seventeen series, which were ranked by their adjusted accuracy rates (see Table 3). The surprising conclusion from this statistical test was that the composite index of leading indicators was a better gauge of the growth cycle than of the business cycle, whereas the coincident to lagging indicator was superior to the LEI for forecasting business cycle turning points. Moreover, for either the business or growth cycle, composite cyclical indicators provided more reliable turning point signals than simply following the individual indicators. This reason is important in using composite indicators, because more information is available in the composite than in the individual series. Additionally, the actual turning point accuracy for both composite indexes was similar to the preselected 90 percent theoretical level of statistical confidence.

The building permits series had the next highest accuracy rate following the LEI for signaling turning points in the growth cycle (see Table 3). Consumer expectations ranked third for both the growth and business cycle. The coincident to lagging indicator

Table 3

Cyclical Indicators Ranked by Neftci Criterion

Based on Growth Cycle Turning Point Signals

(1948-1982)
 Accuracy
Rank Cyclical Measure Rate (*)
 1 Composite Index of Leading Indicators 90.9%
 2 Building Permits 90.5
 3 Consumer Expectations 88.2
 4 Average Weekly Hours 82.6
 5 Credit Risk 80.0
 6 Contracts and Orders 76.5
 7 Change in Sensitive Prices 65.2
 7 Initial Claims 65.2
 9 Real M2 64.7
10 Change in Unfilled Orders 61.3
11 Treasury Yield Curve 60.0
12 Vendor Performance 57.9
13 Mfg. New Orders 56.5
14 Stock Prices 51.7
15 10 Year Treasury Note Yield 50.0
15 Three-Month Treasury Bill Rate 50.0
17 Coincident to Lagging Indicator 44.4
 (*) Based on adjusted accuracy rate defined as:
100* (# of correct turns minus the # of missed turns)/(total #
of turns)


finished last in our list with an accuracy rate of 44.4 percent in calling turning points in growth cycles. This suggested that the coincident to lagging indicator should be used to call business cycle turns alone. As might have been expected, the signals of growth cycle turning points from these indicators, on average, had shorter leads or longer recognition times (see Figures 3 and 4).

AN EXAMINATION OF INDIVIDUAL

LEADING INDICATORS

In this section we examine the individual turning point performance of the eleven components of the LEI and the two composite indexes based on the Neftci sequential signals between 1948 and 1982.

Ratio of the coincident to lagging indicators: Percent changes in the ratio of the Commerce Department's coincident to lagging indicators signaled turning points in the business cycle with an average of 5.8 months at peaks (or, with a median of 3.0 months) and a lag of 1.6 months at troughs (or, with a median of 2.0 months). The ratio of the coincident to lagging indicators had no missed business cycle turning points between 1948 and 1982 but two false signals (11.1 percent of the total turns).

Composite index of leading indicators: While there were no missed turns, there were six extra turning point calls that were not associated with a business cycle decline. Yet, of those six extra turns,

[TABLE DATA OMITTED]

four were associated with growth cycle recessions.

Average Workweek: The workweek had eight too many business cycle turning point signals and required an average of four months after a turning point occurred to get confirmation of that turn. It had an adjusted accuracy rate of 65.2 percent for business cycles and 82.6 percent for growth cycles.

Initial claims for Unemployment Insurance: This series had an accuracy rate of 65.2 percent for both business and growth cycles. Turning point signals based on initial claims lagged the business cycle on average, by three months and slightly longer for growth cycles. Nearly 35 percent of the signals were false for the business cycle.

New Orders for Consumer Goods: This series had an adjusted accuracy rate of 65.2 percent for the business cycle but a slightly lower accuracy rate for signaling growth cycle turning points. On average, its turning point signals lagged actual NBER determined turning points by two months.

Building Permits: As the housing industry goes, so too goes the nation. At least that is the message from the evaluation of turning point signals for the growth cycle. This series had an accuracy rate of 90.5 percent with an average of one month lead for growth cycles. Understandably, its performance was slightly less impressive in calling business cycles turns. The building permits series was an ideal indicator for calling turns in the growth cycle. Yet, 28.6 percent of the turning point signals were false calls for the business cycle, which produced a business cycle accuracy rate of 71.4 percent.

Contracts & Orders for Plant and Equipment: This component had an accuracy rate of 64.7 percent in calling business cycle turns. It missed 11.8 percent of the turns and gave false signals 23.5 percent of the time. As a growth cycle indicator, this series had the longest recognition time (nine months) of any of the series tested.

Stock Prices: This component is a prime candidate for replacement in the LEI. It had a very high false signal rate -- 48.3 percent, for business cycles. Its rate of false signals for growth cycles was also high at 41.4 percent. Although it is a sensitive indicator, its turning points often were associated with its own unique behavior.

Real M2: This series missed 23.5 percent of the turning points in the business cycle and had 35.3 percent incorrect calls. Its overall turning point accuracy rate was a very low 41.2 percent for business cycles and 64.7 percent for growth cycles. This series also might be a candidate for replacement in the LEI, in spite of its overall lead time of six months in recognizing turning points in the business cycle.

Vendor Performance: Turning point signals based on this indicator led business cycle turning points by an average of three months. The accuracy rates were 57.9 percent for both the business and growth cycles.

Sensitive Prices: The change in sensitive prices did not miss any business cycle turning points. However, it called an additional eight turns that did not correspond to the business cycle. The adjusted accuracy rates were 65.2 percent for the business and growth cycles.

Unfilled Orders: By far this series had the highest number of false signals of any series that we tested. As a result, its accuracy rate was 48.4 percent for business cycles, although four of those business cycle false signals were associated with growth cycles. The accuracy rate for growth cycles was 61.3 percent.

Consumer Expectations: This series had a relatively high accuracy rate of 76.5 percent for business cycles but required four months of recognition time after a business cycle turn occurred to confirm it. This series performed better for growth cycles, with an accuracy rate of 88.2 percent and a median lag of three months at growth cycle turns.

On balance, our evaluation of the components of the composite index of leading indicators suggested that there is room for improvement. Moreover, while some components were statistically questionable turning point indicators, the blending of those components into the LEI produced a superior turning point indicator compared to any single measure.

AN EXTENDED LIST OF FINANCIAL

LEADING INDICATORS

Because we suggested the replacement of some indicators in the LEI, the logical question to ask is: what should those substitutions be? While an exhaustive study of alternate economic indicators is beyond the scope of this paper, we examined four additional financial indicators. The selection of these additional indicators was motivated by the work of Stock and Watson (1989).

The four indicators using the Neftci criterion were: (1) the yield of the ten-year constant maturity government note, (2) the three month Treasury bill rate; (3) the government yield curve measured as the spread between the one- and ten-year notes, and (4) a credit quality or risk measure determined from the six month commercial paper and Treasury bill rates. For the interest rate "spreads," a ratio calculation was used instead of a difference. Although both methods were evaluated, the ratio removed a trend in interest rates over the past forty years that was preserved by the spread. To remove a trend in the ten-year and three-data transformations, sequential analysis was applied to determine turning point signals. The results are included in Tables 2 and 3.

Our conclusions were in stark contrast to research by Zarnowitz and Braun (1989) that found "favorable evidence" for the risk premium as a cyclical indicator but very weak evidence for the yield curve. We found just the opposite results. The credit risk measure, according to our test, failed to call six business cycle turning points and missed another four. Its adjusted accuracy rate was an extremely poor 16.7 percent, while the Treasury yield curve accuracy rate was 80 percent. Yet, the accuracy was improved for the credit measure if the comparison was the growth cycle (80.0 percent), while the yield

[TABLE DATA OMITTED]

[TABLE DATA OMITTED]

curve accuracy deteriorated to 60.0 percent. Our major concern with the ten-year government note yield as a potential component of the LEI is that had a very large standard deviation -- 29 months, between signals and actual business cycle turning points. Nonetheless, using our performance statistics, we have concluded that the yield on the ten-year government note and the yield curve would be likely candidates for inclusion into the LEI.

KEY OBSERVATIONS AND CONCLUSION

Composite indexes contain more information than most of the specific components of the composite indicator itself. While this has been advocated for a long time by the proponents of the economic indicator approach, little research has been done to establish this hypothesis using modern statistical techniques. We have shown that this hypothesis is correct for the composite index of leading indicators. More generally, we believe that the reason to use composite indicators is based on a "law of diversification," which suggests that the risk of a false signal is reduced with diversification. Our view is an extension of a principle from portfolio risk theory.

The composite index of coincident to lagging indicators has a higher statistical degree of accuracy in forecasting business cycle turning points than the composite index of leading indicators. However, the composite index of leading indicators has a better track record in forecasting turning points in the growth cycle than does the coincident to lagging indicators. The importance of this is twofold: (1) to the extent that the coincident to lagging indicators is a proxy for the cost side of the economy (through the inverse of the lagging indicators), it lends support to the Mitchell-Burns view of the cause of the business cycle as amplified by Boehm (1990); and (2) it may be necessary to devise a leading indicator of the growth cycle that is distinct from a leading indicator of the business cycle.

Finally, although another business cycle turning point has occurred since the conclusion of this study, these results still are instructive for compiling composite cyclical indicators.

FOOTNOTES

(1) For a derivation of this recursive formula, refer to Neftci (1982). Our application of the technique differs from Neftci's original formulation in that normal probability distributions were used for the upturn and downturn samples instead of smoothing this histogram of the raw data and that the probability of a turning point given the duration of the cycle is assumed to be constant. Our application follows the work of deLeeuw, et. al. (1986) and Diebold and Rudebusch (1989) and incorporates the McCulloch (1975) finding.

(2) A recompiled version of the LEI was tested, which only substituted the ten-year government note yield for the stock price index. However, the turning point signals (using the Neftci method) were nearly identical between the original and recompiled indexes. This does not necessarily diminish the importance of the evaluation technique but instead suggests that the entire methodology for compiling composite indexes might be re-evaluated. For example, it may be necessary to weight again the individual components instead of the current methodology that equally weights the components.

(3) Although we judged the turning point timing as the time span between when a signal was given and the NBER/Commerce Department turning point date, there is no guarantee that the NBER dates are perfect. Alternatively, this technique could be used to derive a business cycle chronology as implied by Hamilton (1989), Diebold and Rudebusch (1989) and Niemira (1991).

REFERENCES

Boehm, Ernst A. "Understanding Business Cycles Today: A Critical Review of Theory and Facts," in Philip A. Klein, ed. Analyzing Modern Business Cycles, M.E. Sharpe Inc., Armonk, New York, 1990, pp. 25-56.

Coons, James W. "Predicting Turning Points in the Interest Rate Cycle," Huntington National Bank, Columbus, Ohio, mimeo, October 1990.

deLeeuw, Frank, Alma E. Missouri, and Charles S. Robinson. "Predicting Turning Points: A Progress Report on the Neftci Approach," U.S. Department of Commerce, Bureau of Economic Analysis, Discussion Paper 1, March 1986.

Diebold, Francis X. and Glenn D. Rudebusch. "Scoring the Leading Indicators," Journal of Business, Vol. 62, No. 3 (1989), pp. 369-391.

Hamilton, James D. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Vol. 57, No. 2 (March, 1989), pp. 357-384.

McCulloch, J.H. "The Monte-Carlo Cycle in Business Activity," Economic Inquiry, Vol. 13, No. 3 (1975), pp. 303-321.

Neftci, Salih. "Optimal Prediction of Cyclical Downturns," Journal of Economic Dynamics and Control, 1982, pp. 225-241.

Niemira, Michael P. "An International Application of Neftci's Probability Approach for Signaling Growth Recessions and Recoveries Using Turning Point Indicators," in K. Lahiri and G. Moore, eds. Leading Economic Indicators: New Approaches and Forecasting Records, Cambridge University Press, New York, 1991, pp. 91-108.

Niemira, Michael P. and Philip A. Klein. "A New Look at Forecasting the Great Depression," presented at the EURO IX - TIMS XXVIII International Conference, Paris, mineo, July 1988.

Palash, C.J. and L.J. Radecki. "Using Monetary and Financial Variables to Predict Cyclical Downturns," Federal Reserve Bank of the New York Quarterly Review, Summer 1985, pp. 36-45.

Stock, James H. and Mark W. Watson. "New Indexes of Coincident and Leading Economic Indicators," NBER Macroeconomics Annual 1989, The MIT Press, Cambridge, MA, 1989, pp. 351-394.

Zarnowitz, Victor and Phillip Braun. "Comment" on Stock and Watson (1989), NBER Macroeconomics Annual 1989, The MIT Press, Cambridge, MA, 1989, pp. 397-408.
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Author:Niemira, Michael P.; Fredman, Giela T.
Publication:Business Economics
Date:Oct 1, 1991
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