July 1990
Federal Reserve Bank of Dallas

The Texas Index of Leading Economic Indicators: A Revision and Further Evaluation

Abstract In this article, Keith R. Phillips revises the Texas index of leading economic indicators that he introduced two years ago. He does so in response to recent structural changes in the state economy and the availability of new data. The Federal Reserve Bank of Dallas has produced the Texas leading index monthly since July 1988. Using a newly developed technique for evaluating leading indexes, Phillips finds that the revised Texas leading index has performed well in predicting movements in the Texas economy since 1981. He also finds that monthly revisions in the leading index are generally small and that preliminary estimates are good predictors of final values. Together, these results indicate that the new Texas leading index can be a useful tool in improving forecasts of the state’s dynamic economy.

In the July 1988 Economic Review, I presented a composite index of leading economic indicators for Texas (TLI). The index proved to be a good predictor of turning points in the state economy. Recent structural changes in the Texas economy and the availability of new data have made it possible to construct a new, improved index.

The new leading index incorporates two changes. First, the weight given the two energy variables in the index has been reduced by half. This change reflects recent research, such as Fomby and Hirschberg (1989), showing that the Texas economy has become less dependent on the energy industry.

The second change in the leading index was to incorporate the newly available data on Texas exports by country of destination. With these data, I constructed a new Texas trade-weighted value of the dollar as a substitute for a less directly measured Texas value of the dollar.

The new Texas leading index (NTLI) moves very similarly to the original index. In fact, the turning points in the two indexes match almost exactly. Nevertheless, the NTLI has done a better job of predicting movements in the Texas economy. The index also appears to foreshadow significant changes in the rate of economic growth, not merely contractions or upturns.

Every month, as different agencies revise the components of the NTLI, the NTLI is revised for the preceding seven months. I analyzed the NTLI to see how monthly revisions would have affected its performance. In the short sample period, monthly revisions in the NTLI were small, and the preliminary estimates were unbiased and efficient predictors of the final index values. One conclusion drawn from these results is that the user of the NTLI can be confident that the signals given by the early estimates of the NTLI will not change significantly as the index is revised.

Developing a new Texas leading index
Although the TLI was sensitive to changes in the Texas economy, it is appropriate to improve the index when new indicators become available and when the economy changes. Several changes were considered and implemented. Table 1 shows the components and weights used in both the old and the new Texas leading indexes.

One adjustment was to construct a more directly measured Texas trade-weighted international exchange rate. The Texas dollar index originally used in the TLI was computed by first calculating industry-specific measures of the dollar, based on national trade by industry and country, and then weighting these measures by the importance of the various industries to the Texas economy. One problem with this type of dollar index is its disregard for geographic and cultural ties to Mexico; Texas may trade much more with that country than the state’s industry structure suggests.

Texas exports by country of destination, released by the Foreign Trade Division of the Bureau of the Census, U.S. Department of Commerce, allowed me to calculate a more direct measure of the Texas exchange rate.[1] The index measures movements in real exchange rates for 44 countries, accounting for more than 91 percent of Texas exports.

To judge which Texas exchange-rate index was a better leading indicator, I used criteria that are very similar to those used by the Bureau of Economic Analysis (BEA), U.S. Department of Commerce, in choosing variables for the national BEA composite index of leading economic indicators. The BEA scores variables on the basis of economic significance, statistical adequacy, cyclical timing, business cycle conformity, smoothness, timeliness, and revisions. The procedure I used places particular emphasis on business cycle conformity (see Phillips 1988b). By using these criteria, the new Texas trade-weighted value of the dollar was determined to be a better leading indicator of movements in the Texas coincident index.[2] Consequently, the new Texas dollar index was substituted for the old measure.[3]

Another change in the TLI was to reduce the weight given to the two energy variables. Recent research has shown that the energy sector is less important to the Texas economy than it has been in the past (for example, see Fomby and Hirschberg 1989). To account for this change, I considered dropping one of the two energy variables from the TLI. In evaluating whether the real oil price or the number of drilling permit applications was preferred, no clear answer emerged. Although the number of well permits showed stronger leading abilities, its lead was shorter, and the series was more volatile than the real oil price. Because each series has equal but separate advantages, I chose to weight each series by half its original weight. In effect, this step combines the two series into one energy sector variable.

A final change considered was the use of the new experimental leading index produced by Stock and Watson at the National Bureau of Economic Research (NBER).[4] Although the NBER leading index moves closely with the BEA leading index, their construction is quite different, and the NBER index could possibly add further information about the U.S. economy to the Texas leading index.

On the basis of the criteria described in Phillips (1988b), the NBER leading index was shown to be inferior to the BEA index in its ability to lead movements in the Texas coincident index. The NBER index also showed no marginal predictive power over the BEA index, so the NBER index was not included in the new Texas leading index.

The NTLI was compared with the TLI, using the procedure described in Phillips (1988b). Although peaks and troughs in the two indexes matched almost exactly, the business cycle conformity criteria showed that the NTLI had a stronger relationship with the coincident index than did the TLI.

As shown in Chart 1, the NTLI moves close to the old TLI.[5] But during several periods, the two series diverge somewhat. In 1985, the original index was much weaker because of the larger weight given to the energy indicators. In late 1985, however, both indexed began to plunge as the large drop in oil prices affected almost every sector of the state economy.

Notice also that the NTLI showed more of an upward trend over the past several years than did the original index. This also is due mostly to the weighting of the energy variables, which were generally more negative than the rest of the indicators during this period.

Turning points in the NTLI have had a strong relationship with turning points in the Texas coincident index. As seen in Chart 2, the NTLI turned down four months before the August 1981 peak in the coincident index, and it rebounded five months before the trough in March 1983.

The leading index then peaked in April 1984, 16 months before the coincident index peaked in August 1985. This lead time may be deceiving, however, because the decline in the leading index was likely signaling the growth recession that began in the coincident index in late 1984. (For more details about growth cycles, see Box A ).

Following a long and rather sharp decline of the leading index from April 1984 until December 1984, the index began a pattern of gains and declines with a gradual upward drift. This seems consistent with the general pattern of weak growth in the coincident index. The steep plunge in oil prices beginning in late 1985, however, caused the leading index to plunge and the Texas economy to decline sharply.

The leading index then rebounded in July 1986, eight months before the beginning of the state’s economic recovery. The index rose fairly steadily until September 1987, when it declined for five consecutive months and then began a period marked by short spans of strength and weakness. The decline in the NTLI late in 1987 may have been signaling a growth slowdown. Since early 1988, the coincident index has fluctuated between strength and weakness, with only a slight upward trend.

Using the NTLI to compute the probabilities of recession and expansion
In determining the success of the leading index in signaling upcoming turning points, using a real-time approach is important. Looking at past data to find peaks and troughs is easy, but one must determine when the user of the index could be aware that a turn had occurred. One common real-time approach is that three consecutive declines in the leading index signal an upcoming recession and three consecutive increases signal an expansion. Although this procedure has some validity, recent research shows that, at least in the case of the BEA leading index, a sequential probability method has a better forecasting record (See Diebold and Rudebusch 1989).

In a sequential probability approach, the probability of an upcoming recession is calculated when the economy is in an expansion. Once a recession begins, the probability of an expansion is calculated. A probability of 90 percent or more is regarded as a strong signal. Expansion and recession can be defined in terms of changes in levels or growth rates.

The sequential probability method as developed by Neftci (1982) uses two principal steps to determine the probability of an upcoming recession or expansion. The first step is determining the likelihood that the current change in the leading index would occur during a business cycle expansion or contraction. This is calculated by looking at past data to see how often similar changes took place in expansions and contractions. For example, if the leading index increases 1 percent, and in the past this occurred 15 times while signaling expansions and only once while signaling contractions, then the probability is high that the current change is signaling an expansion.

The next step is using the previous period’s probability to strengthen or weaken the probability calculated for the current period. For example, if the leading index had been declining for many months and then jumped 1 percent, it may at first be difficult to distinguish if the jump is a temporary blip or a true signal. If the jump is followed by another 1-percent increase, however, then the probability of expansion should increase.[6]

Charts 3 and 4 show the probabilities of recession and expansion for Texas from January 1981 to November 1989. As shown, the probability of recession rose above 90 percent three months before the peak in September 1981.

Following the 1981 signal and the start of subsequent recession, the probability of expansion increased to a rate higher than 90 percent in February 1983, two months before the recovery in the coincident index. The probability of recession then rose above 90 percent in September 1984, eleven months before the peak in the coincident index and about the same time or slightly before the apparent growth recession began. The probability of expansion then signaled an upcoming expansion in January 1987, three months before the expansion actually began.

The next signal from the index came in October 1987, when the probability of recession rose above 90 percent. This signal came before the growth recession that began in early 1988. Starting in early 1988, the probability of a growth cycle expansion was calculated.[7] The probability of a growth cycle expansion fluctuated, but in only one month did the probability reach higher than 90 percent. This signal occurred in May 1989, and it is too early to judge whether a growth expansion followed.

Overall, changes in the leading index appear to lead changes in the coincident index. The probability of recession reached 90 percent before every recession and growth cycle recession in this limited time period. The lead time, however, has been relatively short, about three months.

Sensitivity of the NTLI to revisions in component data
The value of NTLI in any given month is revised as the component data are revised. An evaluation of the predictive content of the index that is based on the final revised series, such as the evaluation in the previous section, could be quite different from one based on the first estimate of the index.[8]

From September 1988 until November 1989, the original TLI was produced on a monthly basis, and the data were stored. By using these data, it is possible to construct the NTLI on a real-time basis to evaluate how revisions in the index would have affected its performance.[9]

Every month, the data for the previous seven months of the NTLI are revised to incorporate revisions in component data. For each month from September 1988 through May 1989, I recorded the first to the seventh estimate of the change in the index. Based on this sample, the standard deviation of the revisions from the first to the final estimate was 0.25. This represents a moderate degree of revision. For example, if the preliminary estimate showed a change of 1.32 percent (1.32 was the average absolute value of the percentage changes during this period), then one could be 90-percent confident that the final estimate of the change would be between 0.91 percent and 1.73 percent, assuming normality. This performance compares favorably with that of the BEA national leading index, which generally has had much larger revisions.[10]

While the revisions in the NTLI have been moderate overall, the earlier revisions generally have been larger than later revisions. The average absolute value of the revision in the percentage changes in the NTLI was 0.15 for the first revision, 0.17 for the second, 0.09 for the third, 0.08 for the fourth, 0.06 for the fifth, and 0.02 for the sixth.

Another important aspect of the preliminary estimates, other than how close they are to the final values, is whether they are efficient in a statistical sense. In the limited sample period, the preliminary estimates of the changes in the NTLI were unbiased and efficient estimators of the final values of the NTLI. Box B describes the tests for these properties. If the preliminary estimates were biased or inefficient, then the researcher could use this information to improve the preliminary estimates.

Summary
Although my original composite index of Texas leading economic indicators is sensitive to changes in the Texas economy, I utilized recent information to construct a new Texas leading index (NTLI). The NTLI tracks the old index closely but should predict future turning points in the Texas economy better than the old index would.

In evaluating the NTLI with the sequential probability method, I find that the new index has performed well in predicting growth cycle turning points. Also, during a short experimental period, the revisions in the NTLI were small, and the preliminary estimates were unbiased and efficient.

The results of this study imply that the NTLI is a useful tool in evaluating the changing conditions of the Texas economy. Used along with other tools, such as forecasting models, demographic and industry studies, and judgmental analysis, the NTLI offers the analyst an opportunity to improve his forecasts of the state economy.

—Keith R. Phillips

About the Author Phillips is an economist at the Federal Reserve Bank of Dallas. Notes I would like to thank John K. Hill, Thomas B. Fomby, William C. Gruben, and Stephen P. A. Brown for helpful comments. I am also grateful to John J. Sciortino and D’Ann M. Ozment for their research assistance. The new Texas leading index is available monthly, without charge, by writing Keith R. Phillips, Research Department, Federal Reserve Bank of Dallas, Station K, Dallas, Texas 75222. The export data came from a secondary source, Texas Department of Commerce (1989). Although the data are reported by origin of movement and not origin of production, the statistical analysis performed showed the index to be a good leading indicator of growth in the Texas economy. To compute the index, I selected the top 44 countries ranked by exports from Texas. These countries accounted for about 91 percent of Texas’ exports in 1988. As explained in Phillips (1988a), I developed the Texas coincident index as a timely measure of changes in the Texas economy. The construction of the index is similar to that of the U.S. coincident index produced by the BEA. The Teas coincident index, however, is limited to two variables, while the national coincident index contains four variables. The two components of the Texas coincident index, nonagricultural employment and industrial production, have national counterparts in the U.S. coincident index. Like the original dollar measure, the new measure is not available on a timely basis because of the lagged availability of international consumer price index (CDI) data. This was not a significant problem because the lead time of the dollar index was much greater than the lead time for the other components in the leading index. The original dollar index was lagged six months so that its lead time would be more consistent with the other components and to avoid problems with data availability. To accomplish the same objective with the new dollar measure, I established a lag of four months. The NBER releases the new leading index monthly. For information on its construction, see Stock and Watson (1989). The new Texas leading index is amplitude-adjusted. This procedure sets the amplitude of the leading index equal to that of the coincident index. This procedure makes the comparison with the coincident index more visually appealing, although it does not affect its predictive ability. In Chart 1, the original leading index is amplitude-adjusted to facilitate comparison with the new index. In constructing the probability-of-recession index for Texas, I utilize some adjustments to the Neftci method from Diebold and Rudebusch (1989). The first adjustment is due to their earlier findings that the probability of recession is not a function of the length of the current recovery. The second adjustment is to adopt their use of the normal density function, instead of deriving the probability distributions directly from historical data. The third adjustment addresses the issue that if the probability of recession or expansion reaches 1, then all following probabilities will also equal 1. To allow more flexibility in the equation and still enable the prior probability to affect the current probability significantly, I set an upper bound of 0.95 on the prior probability that feeds into the recursive formula. A drawback of a leading index that signals growth recessions is that, once a growth recession has begun, the leading index may be of little use in determining whether a classical business cycle recession will follow. In applying the probability-of-recession formula to growth cycles in the United States and other nations, Niemira (1990) concentrates solely on the growth cycle and does not address the question of shifting from slow growth to decline. The prediction of such a shift may be above the bounds of the leading indicator approach, although it deserves some research. Certainly, in Texas the number of past observations is so small that little can be learned about this aspect of business cycles. Diebold and Rudebusch (1988) addressed this issue. In evaluating the performance of the BEA index of leading economic indicators, the authors found substantially weaker performance when using the real-time index values. The index calculated this way differs slightly from the NTLI. The calculation used the original Texas value of the dollar because of the difficulty involved in reconstructing past values of the new Texas value of the dollar on a real-time basis. Past CPI data for the 44 countries in the new Texas value of the dollar were not available at a reasonable cost on a real-time basis during the sample period. I used the original Texas value of the dollar because it had already been calculated on a real-time basis and stored. Both indexes contain many of the same countries, however, and revisions in the original dollar indicator should serve as a good indicator of revisions in the new dollar indicator. Results from Diebold and Rudebusch (1988) show that, for December 1968 to January 1987, one could be 90-percent confident that if the preliminary estimate of the BEA leading index increased 1.32 percent, then the final series would change between –0.09 percent and 2.73 percent. References Diebold, Francis X. and Glenn D. Rudebusch (1988), “Ex Ante Turning Point Forecasting with the Composite Leading Index,” Finance and Economics Discussion Series, no. 40 (Washington, D.C.: Board of Governors of the Federal Reserve System, Division of Research and Statistics, October). _____, and _____ (1989), “Scoring the Leading Indicators,” Journal of Business 62 (July): 369–91. Fomby, Thomas B., and Joseph G. Hirschberg (1989), “Texas in Transition: Dependence on Oil and the National Economy,” Federal Reserve Bank of Dallas Economic Review, January, 11–28. Neftci, Calih N. (1982), “Optimal Prediction of Cyclical Downturns,” Journal of Economic Dynamics and Control 4 (November): 225–41. Niemira, Michael P. (1990), “An International Application of Neftci’s Probability Approach for Signalling Growth Recessions and Recoveries Using Turning Point Indicators,” in Leading Economic Indicators: New Approaches and Forecasting Records, ed. Kajal Lahiri and Geoffrey H. Moore (Cambridge: Cambridge University Press, forthcoming). Phillips, Keith R. (1988a), “New Tools for Analyzing the Texas Economy: Indexes of Coincident and Leading Economic Indicators, ” Federal Reserve Bank of Dallas Economic Review, July, 1–13. _____(1988b), “The Development and Uses of Regional Indexes of Leading Economic Indicators,” Federal Reserve Bank of Dallas Research Paper no. 8808 (Dallas, November). Stock, James H. and Mark W. Watson (1989), “Indexes of Coincident and Leading Economic Indicators,” in NBER Macroeconomics Annual 1989, ed. Olivier Jean Blanchard and Stanley Fischer (Cambridge: MIT Press): 351–94. Texas Department of Commerce, Research and Planning Division (1989), Highlights of 1987 and 1988 Texas Exports (Austin, October). Box A Growth Cycles Analysts measuring the business cycle in Japan and many European countries use growth cycles more often than the classical business cycle. A classical business cycle is marked by periods of growth and decline in the levels of overall economic activity. In a growth cycle context, however, a recession (expansion) occurs when growth in the economy declines below (increases above) its long-run trend rate. The Center for International Business Cycle Research (CIBCR) at Columbia University studies U.S. growth cycles. The CIBCR analyzes changes in many series it classifies as coincident to the business cycle. In each series, a growth cycle turning point occurs when growth in the series goes below or above its long-run trend rate. The process of establishing the long-run trends is not straightforward. In computing these trends, the CIBCR attempts to measure long-run rates of growth that are allowed to move over time but are independent of shorter cyclical movements. Using a computer program to aid in the selection of these turning points but still allowing subjective decision making, the CIBCR has established a growth cycle chronology for the United States. To define growth cycles in the Texas economy during the 1980s, I took a different approach than that of the CIBCR. Because the Texas economy generally experienced strong growth during the 1970s and weak growth during the 1980s, it was difficult to estimate an underlying long-run rate of growth over this period. Instead, in the case of growth recessions, I looked for periods in which growth in the Texas economy slowed significantly and was close to or less than zero. In the case of growth cycle expansions, I looked for periods in which growth increased significantly after a growth recession. I first examined movements in the Texas coincident index. A plot of this index revealed two distinct periods in which growth in the economy slowed but remained positive. The first period began around the fourth quarter of 1984 and ended with the start of the classical business cycle recession in August 1985. The second period began in early 1988 and continued until the end of the data in November 1989. The plot revealed no growth cycle expansions other than the normal classical business cycle expansions. Statistical tests provided further evidence that growth cycle recessions occurred in the two periods of weak growth. In each period, the average growth rate in the coincident index was not statistically different from zero at the 5-percent level of significance. The average growth rates were also statistically different from growth in the earlier stages of the expansions. Box B Statistical Properties of the NTLI Preliminary Estimates The tests I used to evaluate the statistical properties of the preliminary estimates involved the following ordinary least squares regression: Finalt = A + B Prelimt + et, Where Finalt is the final estimate of the percentage change in the NTLI for period t, A is an intercept parameter, B is the slope parameter, Prelimt is the preliminary value of the change in the NTLI at time t, and et is the error term. Six regressions were run, one for each of the six preliminary estimates. Autocorrelation functions derived for the residuals of each regression dampened quickly, implying stationarity in the errors. This was not surprising because the variables were measured as percentage changes. Box Q statistics of the residuals also indicated that the residuals were white noise. Because the error terms appear to be stationary, white noise processes, it is appropriate to use the standard errors on the intercept and slope coefficients to make inferences about the value of these coefficients. Likewise, the use of conventional F statistics is appropriate for joint hypothesis tests. In all six regressions, the joint hypothesis that A was equal to 0 and B was equal to 1 could not be rejected at the 20-percent level of significance. This result, along with the error term results, implies that the preliminary estimates were unbiased, efficient estimators of the final value. About Economic Review Economic Review is published by the Federal Reserve Bank of Dallas. The views expressed are those of the authors and should not be attributed to the Federal Reserve Bank of Dallas or the Federal Reserve System. Articles may be reprinted on the condition that the source is credited and a copy is provided to the Research Department of the Federal Reserve Bank of Dallas. Economic Review is available free of charge by writing the Public Affairs Department, Federal Reserve Bank of Dallas, P.O. Box 655906, Dallas, TX 75265-5906, or by telephoning (214) 922-5254.