ANALYSIS AND DEVELOPMENT OF PROCEDURES TO UPDATE THE KANSAS INDEX OF LEADING ECONOMIC INDICATORS by RUSLAN VOLODYMYROVYCH LUKATCH B.S., Donetsk State University, Ukraine, 1997 A REPORT submitted in partial fulfillment of the requirements for the degree MASTER OF ARTS Department of Economics College of Arts and Sciences KANSAS STATE UNIVERSITY Manhattan, Kansas 1999 Approved by: Major professor Steven Cassou
ABSTRACT The purpose of this report is to analyze the Kansas Index of Leading Economic Indicators and to consider different ways for improvement of its structure in order to obtain increase in its performance. Initially the Index was constructed by Department of Economics at Kansas State University in 1988. New Index of Leading Indicators consists of eight economic series: real wheat prices paid to Kansas farmers, real cattle prices paid to Kansas farmers, an average stock prices for one hundred Kansas-based and Kansas-related firms, new housing units authorized for construction in Kansas, average weekly hours in manufacturing in Kansas, initial claims for unemployment insurance in Kansas, the real M2 money supply in the US, and the interest rate spread (the difference between the rate paid on ten-year Treasury bond and federal fund rate). The eighth component (interest rate spread) has been added to the index in order to reflect changes in the economy, which take place because of different monetary regulating policies. Another change, proposed for Index involved reconsideration of its weight structure. Each component has weights reevaluated and reassigned. New Kansas Index of Leading Economic Indicators has been recompiled and recalculated on the basis of historical data covering the period from January of 1970 to December of 1997. After the Index was updated its performance was reevaluated. New Index has shown an increase in its ability to predict recession stages of business cycles comparing to the previous version. An additional aspect of the research was the choice of a criterion to be used as a "signal generator" for the index of leading indicators. Three alternatives have been considered. The first rule was the if an index of leading indicators gives three consecutive monthly declines, it signals a fore-coming recession. Secondly, a downward movement in the 2
composite index of leading indicators of 2 percent (annual rate) or more over six months, coupled with declines in the majority of the component series, is needed for a recession warning. Third was that a recession is forecast if the composite index of leading indicators declines in four out of seven consecutive months. After close consideration it was concluded that the last "signal" criterion has shown the most satisfactory performance for forecasting recessions with the Kansas Index of Leading Economic Indicators. The report is concluded by suggestions toward an update of existing Index. Also there have been several considered directions to extend the research in the area of leading indicators. One of these directions implied use of sophisticated econometric techniques to create a new "signal" criteria, based on probability distributions of the index and its components. 3
TABLE OF CONTENTS LIST OF FIGURES LIST OF TABLES ii iii CHAPTER I. INTRODUCTION 1 Justification for the Study 1 The Structure of the Report 3 II. THE LEADING INDICATORS APPROACH 5 A Literature Review 5 III. REVISION OF THE KANSAS INDEX OF LEADING ECONOMIC INDICATORS 9 The Structure of the Current KILEI 9 Comment on the Measure of Economic Performance for the Kansas Economy 10 Components of the KILEI 11 Weight Structure of KILEI Components 13 New Kansas Index of Leading Economics Indicators - KILEI-99 19 Comparison of New and Older Version of KILEI 22 IV. CONCLUDING REMARKS 25 4
LIST OF FIGURES DIAGRAM 1. Kansas Index of Leading Economic Indicators and Real Kansas Per-capita Personal Income. 2. Older version of KILEI. 3. Three Criteria for determining the signals from Index of Leading Indicators. Signals provided by new KILEI. 4. Three Criteria for determining the signals from Index of Leading Indicators. Signals provided by new KILEI. 5. Wheat Price 6. Cattle Price 7. Stock Prices Index 8. New Housing Units 9. Claims for Unemployment Insurance 10. Average Weekly Hours 11. M2 12. Interest Rate Spread 5
LIST OF TABLES TABLE 1. Weights for components of the KILEI. 2. Calculation of weights of KILEI components 3. Leads, provided by two versions of the KILEI 4. False signals provided by two versions of the KILEI. 5. Raw Data for compiling the Kansas Index of Leading Economic Indicators 6. New KILEI and corresponding changes in the components. 6
Chapter One Introduction Leading economic indicators are a group of statistical time series that have proven to be useful in predicting expansion and contraction during the business cycle. They are widely used to predict the economic performance of the economy. Leading indicators reflect anticipation and early links in the sequences of business decisions, early stages of investment and production processes, and measure the changes in the level of economic activity. Indices of leading economic indicators which pool the information provided by several economic series, have been constructed for the US economy on the national level as well as for several regional and state economies. The ability of leading indicator indices to predict peaks and troughs of the business cycle makes such indices good tools for predicting future changes in economic activity. Each component of the index of leading indicators covers one particular sector of the economy. Because changes in the business cycles can occur for different reasons, the index of leading indicators uses a number of components, each of which is chosen to identify economic performance in a different way. This increases the chances of obtaining correct market signals. The composite index aggregates the predictive abilities of the separate indicators, and thus provides signals regarding developments in an economy as a whole. The composite index has been shown to be more capable of predicting changes in the economic activity than are the individual components of the index. 7
Probably the best known index of leading economic indicators is the one compiled and published by The Conference Board (TCB: a private research organization) to reflect changes in the U.S. economy. 1 TCB index consists of ten leading indicators summarized from statistical data for the U.S. economy: average weekly hours in manufacturing, average weekly initial claims for unemployment insurance, manufacturers new orders for consumer goods and materials, index of vendor performance, manufacturers new orders of non-defense capital goods, new private housing building permits issued, stock prices of 500 common stocks, the M2 money supply, the interest rate spread (10-year treasury bond less federal funds), and an index of consumer expectations. Because the TCB index averages movements across regional economies, it fails to predict changes in economic activity within particular regions. Regional economies do not always experience the same performance or follow national business cycle trends. Because of this, separate regional indices of leading indicators that account for the special features of particular region may be able to produce more reliable signals for local economies. In 1988, the Department of Economics at Kansas State University constructed such an index for the Kansas economy. This index is known as the Kansas Index of Leading Economic Indicators (KILEI). 2 The KILEI was constructed using methods similar to those used by the U.S. Department of Commerce and more recently The Conference Board. The current version of the KILEI index consists of seven components: real wheat prices paid to Kansas farmers, real cattle prices paid to Kansas farmers, an average of stock prices for 100 1 This index was previously computed and released by the Bureau of Economic Analysis of the U.S. Department of Commerce (The Conference Board, 1997). 2 See Willard (1988). 8
Kansas-based and Kansas-related firms, new housing units authorized for construction in Kansas, average weekly hours in manufacturing in Kansas, initial claims for unemployment insurance in Kansas, and the real M2 money supply in the U.S. These components are seasonally adjusted and adjusted for their variance. Each series is assigned a weight and entered into the KILEI according to The Conference Board's approach. The KILEI is published monthly by the Department of Economics at Kansas State University and has proven to be a useful tool for analyzing the Kansas economy. Since the Index was constructed, it has not undergone serious revisions or updates. However, it has become clear that it is in need of updating to incorporate changes in the regional, national, and state economies that have occurred since the index was initially constructed. This report evaluates the performance of the original version of the KILEI and suggests adjustments to the KILEI that are designed to incorporate changes that have occurred in the regional and national economies during recent years and to utilize improved techniques of index construction. It is shown that such changes can improve the predictive power of the Index. The Structure of This Report This report consists of four chapters. The current chapter provides an introduction and motivation for the research. The second chapter is devoted to a discussion of leading indicators and a review of the literature in this area. Chapter three describes steps taken to update and improve the KILEI, assesses the performance of the current Index, and 9
suggests a set of possible changes and improvements. A new index is then calculated using these suggestions and is evaluated on its ability to predict changes in business conditions. Chapter four provides concluding remarks and a discussion of possible future extensions for the Index. These extensions are not implemented here, but are suggested as directions for future development and improvement of the KILEI. The Appendix contains data used in the weight reevaluation and the index compilation process. Diagrams and tables accompanying the research are also presented. 10
Chapter Two The Leading Indicators Approach. The business indicators approach to economic and business forecasting is based on the view that market-oriented economies experience business cycles indicated by repeating sequences of similar form (Kahiri and Moore, 1991). Mitchell and Burns (1946, p. 3) developed the most widely used and most well known definition for the business cycle: Business cycles are a type of fluctuation found in the aggregate economic activity of nations that organize their work mainly in business enterprises: a cycle consists of expansions occurring at about the same time in many economic activities, followed by similarly general recessions, contractions, and revivals which merge into the expansion phase of the next cycle; this sequence of changes is recurrent but not periodic; in duration business cycles vary from more than one year to ten or twelve years; they are not divisible into shorter cycles of similar character with amplitudes approximating their own. It is necessary to point out that this definition does not place any particular requirement on the duration, amplitude or scope of expansions or contractions. This is because observed business cycles are quite different in their characteristics, exhibiting different duration and amplitudes for the peaks and troughs. 11
The main purpose of leading indicators is to provide signals and indications of future changes in economic activity, rather than providing explicit forecasts for some predetermined time. These signals have great importance to business leaders, policy makers, investors, and other economic agents. Although indices of leading indicators remain popular and widely used as a forecasting tool, they are not without their critics. One of the most famous critiques is presented by Koopmans (1947). He argued that the leading indicators approach relies purely on statistical methods, directed to observe statistical regularities. Thus this approach does not have a substantial theoretical basis to provide reliable inference or consistent forecasts about the effect of stabilization policies. Koopmans further argued that having an adequate theoretical basis would make it possible to select more appropriate data series to describe the most relevant factors predicting shifts in the economy. Furthermore, he stated that the combined effect of several different components may not replace a partial effect of unobserved but relevant factors (for example, wars, weather, etc.) Mitchell and Burns argued that their approach, although not theoretically supported, is based on reasonable rational assumptions. Components of the index are selected on the basis of rational criteria by measuring their economic significance and ability to lead changes in economic activity. These indicators either directly or indirectly are able to predict a business cycle. De Leeuw (1991) made an effort to develop fundamentals of the theory of leading indicators. He argued that production time, ease of adaptation, market expectations, prime movers (major economy-moving forces, such as monetary and fiscal policy), and 12
consideration regarding the change-versus-level of variables are important rationales for index construction. These rationales (especially the first three) are justified based on costminimizing behavior of firms. Several interesting developments have been provided by studies that use leading indicators in empirical equations suitable for forecasting. Neftci (1982) considers leading economic indicators as time-series data consisting of three major components: a trend, a noise, and a Markov process. The Markov process switches between two states, upturn and downturn, providing numerical reflection of the state of economy in time. This state of the economy is also called a "regime." Usage of this "regime" component makes it possible to estimate probabilities of recession at each particular point in time based on available data, which can include leading indicators as well. Neftci proposes a model based on the introduction of a "regime" into an autoregressive structure for the variable. He shows that the index of leading indicators can be a reasonable instrument for forecasting a "regime" for the economy under several conditions. These conditions state that economic time series (components of the index) are affected by the "regime" of the economy, and these series do not contain serially correlated noise. Under these assumptions Neftci proposes a procedure that allows him to build a posterior probability for a change in the state of the economy (for example, "falling" into recession) using historical data and a leading indicator. The economic "regime" idea was also used by Stock and Watson (1989) in their research estimating an "unobserved component," which contributes to the comovement of different economic variables. Similar research was conducted by Sargent and Sims 13
(1977), where unobserved factors were combined with a set of joint prior distributions in order to develop a posterior distribution for future data conditional on observed data. In general, the literature review has shown that the theory of leading indicators is in the process of continuous development. There are efforts both to improve the theoretical basis for leading indicators and to extend use of leading indicators in complex empirical models. 14
Chapter Three Revision of the Kansas Index of Leading Economic Indicators The Structure of the Current KILEI Since the Kansas Index on Leading Economic Indicators was constructed, the regional and national economies have experienced a number of important changes. For example, there has been observed a shift in employment from traditional manufacturing and agricultural industries toward the service sector. The population of Kansas increased roughly 4 percent from 1988 to 1995, while the employment in agriculture declined over the same period of time. In order to incorporate these and other changes and to maintain the performance of the KILEI, it is necessary to make certain modifications to its structure. For example, the change in the share of agricultural employment in Kansas suggests that the influence of this industry should be decreased in the KILEI. Also there is an opportunity to expand the index structure by including additional indicators of economic activity. Revisions of the current version of the index can be divided into two major groups: structural adjustment (changing the set of indicators included in the index); and benchmark adjustment (changing the weights assigned to index components). In this research, the KILEI had undergone both type of adjustment, as well as changes in the calculation procedure. We now briefly summarize the changes made to the KILEI. These changes are described in more detail later. 15
First, we proposed a major structural adjustment, by expanding the index's structure by one additional component the interest rate spread. Second, weights of the components in the KILEI were reevaluated using the weighting criteria set. Third, we made an additional correction in the weights assigned to wheat and cattle prices in order to decrease their joint effect in the index. Fourth, a set of corrections was applied to the technical procedure of calculating of the index. This includes shifting the basis of the index to January 1970, elimination of the long-term trend factor in the index, and application of a new procedure for adjusting components for their variation. We now turn to a more detailed description of these changes. Comment on the Measure of Economic Performance for the Kansas Economy In order to evaluate the performance of a leading indicator and make suggestions about its improvement, we need an instrument to measure economic performance of the Kansas regional economy. In this research Real Per Capita Personal Income in Kansas is used as an indicator variable of economic activity in Kansas. The rationale for this choice is that, although the data on the Gross State Product is available, it is calculated only on an annual basis and thus cannot be used for the present purpose. The closest measure of economic welfare in the region is personal income, reports of which are available on a quarterly basis. In his research Willard used Real Kansas Personal Income to indicate recessions (Willard, 1988). Thus our measure accounts population growth as another economic factor. 16
This choice has influenced certain aspects of the research, such as the number of regional recessions observed during the January 1970 to December 1997 period covered by our analysis. Judging by real personal per-capita income, the Kansas economy has experienced three recessions during the observed period. Here the recession is defined as two consecutive quarterly decreases in GDP or real per capita personal income in this case (Oyen, 1991). These three recessions have occurred in the time periods between January 1974 and December 1974, between July 1979 and June 1980, between July 1990 and March 1991. For the most part, these periods of regional recessions in Kansas coincide with the corresponding periods of decreased economic activity on the national level. However one difference is that the personal per-capita income in Kansas does not indicate that a recession happened in the period of 1981 to the end of 1982 as in the national economy. This fact serves as an evidence for differences in economic activity in regions and the nation as a whole. In Diagrams 1-12 in the appendix, shaded areas correspond to the periods of recession in Kansas based on the dynamics of real per-capita personal income in Kansas. Components of the KILEI As noted earlier, the current KILEI consists of seven economic series (Willard, 1988, pp. 20-25): 1) Wheat price - average monthly price paid to Kansas farmers for their wheat as reported by Kansas Agricultural Statistics. 17
2) Cattle price - average monthly price per hundredweight paid to Kansas farmers for all beef cattle marketed. This series also comes from the Kansas Agricultural Statistics. 3) Stock prices index - stock prices for Kansas owned and Kansas Related companies. For a given month, the index is calculated by averaging the stock prices listed for the last Monday of the month in the newspaper, Wichita Eagle. 4) New housing units - monthly number of new housing units authorized in Kansas. 5) Initial claims for unemployment - number of initial claims for unemployment insurance filed by Kansans in a given month. 6) Average weekly hours - hours in manufacturing in Kansas. 7) M2 - Money supply variable. The rationale for six out of the seven components was given by Willard (1988) when the KILEI was initially constructed. In the early stages of development of the KILEI, one variable, the average weekly hours in manufacturing, was added into the Index. The rationale for this variable is that the manufacturing sector in Kansas has become more important part of Kansas economy. TCB national index also uses a similar average weekly hours variable. In this work, we explore the possibility of including another additional component: the interest rate spread (the difference between the rate paid on the ten-year Treasury bond and the federal funds rate). The spread was introduced into the TCB index in December 1996 based on the rationale that it has become widely accepted as a forecasting variable that is closely related to the stance of monetary policy. Looking at Diagram 12, it is clearly visible that it consistently turns in advance of the business cycle (TCB, 1996). Following this rationale and using Diagram 12 to verify the leading 18
performance of the interest rate spread, we decided to include it into KILEI as well. Thus, the new version of the index will have eight structural components instead of seven. Weight Structure of KILEI Components This section discusses the procedure used to assign weights to particular components of the KILEI. The procedure used for assigning weights was developed by the Commerce Department, and is used in its formulation of the U.S. Index (later TCB Index). Each indicator was evaluated according to several major criteria (Oyen, 1991): 1) Economic significance is the extent to which the series makes sense as an indicator. The better the theoretical justification for an indicator, the higher the score. 2) Statistical adequacy evaluates the statistical reporting system for the series. The better the reporting system, the higher the score. 3) Timing, in the case of a leading indicator, refers to the length and consistency of a series lead time. The longer and the more consistent the lead time, the higher the score. 4) Conformity to the business cycle refers to such questions as does the series give off false signals? The fewer false signals, the higher the score on conformity. 5) Smoothness is concerned with the extent to which the series is erratic. The less erratic the series, the higher the score for the smoothness criterion. 6) Currency is the speed with which the data for the series are available for use. The faster the data are available, the higher the score on the currency criterion. The initial weights used in publishing the KILEI are listed in Table 1 in the Appendix. One objective of this study is to investigate the possibility of recalculating 19
these weights, taking into account the changes that occurred in the Kansas economy since the initial construction of the index. The process of assigning weights using the stated criteria is subjective. The total criteria scores are uniform both in the TCB index and the KILEI. Thus the principal technology for weighting leading indicators in the TCB index and the KILEI is the same, although there will be differences in final weights obtained in similar situations. Because of the subjectiveness of the procedure, the revised weights should be considered as outcomes of the author's judgment made in the process of modifying the existing weights. An in-depth description of the procedure of scoring time series against these criteria is provided in Willard 1988, so we will limit ourselves to providing more or less final results of weighting. The Economic significance criterion carries a total weight of 0.167 (Willard, 1988 and Oyen, 1991). In the existing structure of KILEI all seven components receive a full score on this criterion. Each of the indices provides important information about a particular component of economic activity, and this information plays an important role in the decision making process on the state and national level. This part of the weighting procedure remains unchanged. Another important issue is the sign attached to the weight. All components except unemployment insurance received a positive sign since they are positively correlated with the business cycle. Unemployment insurance claims received a negative sign because of its negative correlation. Statistical adequacy also has a weight of 0.167. It is obtained from the result of the summation of eight elementary scores, listed in italics over the next two pages. First, quality of reporting service, assigns 0.025 from overall statistical adequacy score. In the older version of the index a full score was given to 6 components, but not the stock price 20
index. The argument against stock prices was that this index was compiled by a constructor of the index and not released by official reporting service. Previously the stock price index obtained two thirds of the maximum quality of reporting score. Here we advocate that the stock price index deserves a full score, because the calculation of the stock price index does not include any unnecessary manipulation with data, which could change the quality of reporting. This index is obtained by a simple averaging of published stock prices, which are actually provided by an official reporting service. New KILEI has stock prices index carrying full score for quality of reporting service. Coverage of the process carries a weight of 0.025. Level of coverage of the process depends on whether the component represents a full enumeration or a statistical sample. Initially, by this criterion the stock prices index, new housing units and M2 received two thirds of the score and all other components received a full score. This research addresses this weight from a different angle by putting a stricter requirement on the coverage of the process. We agree that the stock index, new housing units, and M2 represent a certain sample of the whole population, but instead of two thirds, half of the weight is assigned. Also one half of the coverage weight was assigned to average weekly hours and to unemployment insurance claims. A maximum score 0.017 is given to the component by the criterion of coverage of time period. If the data covers the full time period, it is assigned a full weight. If the data represents a particular date or week, it will have a lower score according to this criterion. Thus the stock prices and M2 will obtain one third of the coverage of time period score. 21
These two components represent the data, given for one particular moment in time, but not the whole period. There is one component of the statistical significance criterion on which no judgments can be made. It is the availability of estimates of sampling or/and reporting errors. This criterion carries a 0.08 score. All series in both the older and newer versions of the Index do not provide such information and thus all of them receive a zero score. The length of the series determines whether the series will receive a full score of 0.025. In the older version of the index (Willard, 1988 p. 28) it was taken as a rule, that if the series extends back to 1948 or farther, it receives full weight. According to the data, initial claims for unemployment reporting started in 1960; thus it received half of the available score. This decision rule is used also in new revision. According to it, average weekly hours and interest rate spread received a full score. An additional consideration is given to the frequency of revisions. More frequent revisions mean that the data reported is changed toward a closer reflection of reality. Thus the more frequent data revisions, the higher score is given to the corresponding indicator. It is known from the reporting service, that M2 and average weekly hours are subject to regular revisions, thus they received full score. All other series are reported on the final basis at the moment of publication. These series obtain half of the revision score. Timing is one of the important criteria in the set. It brings a maximum score of 0.267 score and is assigned to the series based on a special calculation procedure. This procedure is described by Willard. New estimates obviously differ from the initial, due to the extended length of the series and the one additional recession in the 90s. The procedure of weighting the series towards the timing criteria includes checking for two 22
components of timing. One is the statistical probability that the lead, coincidence, or lag signaled by the series is attributable to chance. An assumption was made that the probabilities of rise, fall, or keeping the same level in the business cycle are one third in each case. The probability that the lead is attributable to chance is calculated according to following formula: P x = 0. 33, where P is the probability that the lead is attributable to chance, x is the average lead, displayed by the series. Each series receives its weight depending on the value of P, divided by the smallest P among all component series. Another 20 percent of the timing score is awarded depending on the standard deviation of leads and lags of the series around the corresponding means for leads and lags, calculated earlier. Conformity to the business cycle is assigned a score of 0.167. The degree to which the series conforms to the business cycle is measured by comparing the number of business cycles, which were signaled by corresponding movements of the series with the total number of business cycles observed (Willard, 1988, p. 30). Each component of the original KILEI received half of the conformity score based on the percentage of business cycles that were matched by the series since 1970. In the new weighting process, all components went through the procedure of matching leads and cycles. As a result of this, average weekly hours received one third of the score (having given only one signal out of three) and the other indicators received this part of the score in full. 23
Thirty percent of the conformity criterion is obtained from the number of extra turns given by the series. Extra turns provide false signals in the business cycle. Thus the lower the number of extra turns, the higher is the score. The formula used in this calculation is (Willard, 1988): Weight 1 = 1 + x 0. 05 where x is the number of extra turns shown by series. Each of the components except the cattle prices provided at least one extra turn and had its weight assigned correspondingly (see Table 2 in Appendix). The amplitude of the series determines twenty percent of the conformity criterion. The amplitude of changes for each series was divided by the highest amplitude among all of them. New housing units had the largest amplitude and thus obtained the full weight (this fact is the same for the old and new versions of the Index). Now consider the smoothness criteria. Its weight is 0.133 and it is based on the relationship between the irregular and cyclical components of the series. The computational procedure uses the decomposition from the X11 seasonal adjustment algorithm, which provides a parameter for the trend cycle. The currency of the data provided by an indicator is assigned a maximum weight of 0.1. How promptly the data become available determines the score given to the series. All indicators except wheat and cattle prices become available promptly in the first week after the end of the period. Agricultural prices come out with a two-week lag and thus obtain half the weight for currency. Other components got full weight. 24
Table 2 presents weights assigned to the components of the new KILEI corresponding to each criteria listed above. There was also a special correction in the weights of two components. The sum of these criteria weights gives the final weight for each component. Wheat and cattle prices both carry considerable weights in the index, although they cover one sector of the regional economy agricultural production. Thus it is reasonable to consider them as two structural components of one leading indicator. In order to prevent a situation where the agricultural sector is overrepresented in the overall index structure, we average their weights. Table 1 provides final total weights for both original and the new version of KILEI. The table shows that the weight structure of the KILEI has been changed to a considerable extent, since new data and new considerations were employed. Given these changes, we should expect changes in its performance as well. New Kansas Index of Leading Economics Indicators - KILEI-99 Certain changes also appeared in compiling the new KILEI. These changes occurred on primarily in the last stages of calculation. The Index is compiled according to the following procedure: 1) The data for all components are collected. 2) Some of the components undergo seasonal adjustment. 3) Symmetric month-to-month percentage changes of each component are calculated. 4) These changes are adjusted for their variance. 25
5) Changes are multiplied by their weights and summed, giving the month-to-month change in the Index. 6) The level of the Index is calculated. The raw data for calculation of the new Index are presented in Table 5. Once the data for a given month are collected, some of series should be corrected using the consumer and producer price indices. The cattle and wheat price are divided by the producer price index, while the stock price index and M2 are divided by the consumer prices index. Next the series go through the procedure of seasonal adjustment. All series are adjusted except M2, which is already in seasonally adjusted form. The procedure of seasonal adjustment is performed using the X11 algorithm programmed into SAS. Period-to-period changes of each series are represented in the form of symmetric percentage changes: x t x = 200 x t t x + x t 1 t 1 In the older version of KILEI, the month to month changes in the component series are divided by the average of their absolute values. This was done in order to correct for the difference in volatility. In the new version we use a more complicated procedure. This procedure was established in 1997 for the TCB Index. Thus, this change makes the KILEI and the TCB Index more alike in their computation. According to this new procedure, the standard deviation for changes in the component is calculated (v x,t ). After that the standard deviations are inverted (1/v x,t ) and their sum is calculated: k = x 1 v x, t 26
This operation ensures that after the calculation so-called standardization factors, r x, t = 1 k v x, t, they will sum to 1. Thus the final volatility-adjusted changes are given in the form m x,t =r x,t *x t and obtained changes are multiplied by their corresponding weights and summed. In the new KILEI we do not add a long-run trend. This was made in the initial version of KILEI in order to facilitate forecasting of month-to-month movements in the business cycle (Willard, 1988). Because our primary goal was to rebuild the index in such a way that it will give more reliable signals of the recession, it was suggested that the long-run trend of series not to be accounted in the new composite index. Another argument for such decision is that adding any positive constant to the index will "offset" some small falls, which are important components for the analysis of leads. Finally the KILEI is brought to the base year, which was taken to be January 1970, and it is given an initial value 100. The standardized Index is then recalculated using the formula: I t I 200 + i i = t 1 200 t t where i t is month-to-month percentage change in index at time period t. 27
Comparison of New and Older Version of KILEI Diagram 1 in the Appendix and Table 6 show values for the new Kansas Index of Leading Economic Indicators. The diagram shows the Index together with corresponding values of real Kansas per-capita personal income and shaded periods indicating recessions. These can be compared with the existing version of the KILEI shown in Diagram 2. Diagrams 1 and 2 show that the new version provides greater leads for all three observed recessions in the region. It also shows that these leads are more "visible" by amplitude. However it is also important to note several agreements about interpreting visible dynamics of new index. More attention should be paid to the actual time when the particular "signal" has occurred. There are several known criteria for concluding that and Index of Leading Indicators has produced the signal for a coming recession. We consider three rules. The first, which is the oldest and most long-standing rule used by economists, is that if an index of leading indicators gives three consecutive monthly declines, it signals a forthcoming recession (TCB, 1997). The second rule currently used by The Conference Board (TCB, 1997) with the TCB Index is a complex criterion stating that a downward movement in the composite index of leading indicators of 2 percent (annual rate) or more over six months, coupled with declines in the majority of the component series, is needed before a recession warning can be considered reliable. The third criterion is a rule that a recession is forecasted if the composite index of leading indicators declines in four out of seven consecutive months. This criterion was suggested by Andersen and Erceg (1989). 28
Diagram 3 shows the new KILEI together with the recession periods and accompanied by the several sets of points each indicating a signal occurred at a particular date according to a certain signal rule. Diagram 4 contains the same plot, corresponding to the previous version of the KILEI. It can be seen from the Diagram 4, that the older version of the KILEI does not provide adequate leads for all recessions. Considering the signals generated by the three different criteria, it can be seen, that the older KILEI is not good at leading a recession using the "4 declines in 7 months" rule. Furthermore it fails to predict two of the three recessions using the "three months" and the "2 percent and majority of components decline" rules. Generally the older version of the KILEI provided lagged signals for observed recessions. According to the first two signal criteria, the performance of the new KILEI does not differ much from the performance of its predecessor. Even worse, the new index predicted none of the recessions when the "three months" rule was used, and predicted only one recession using the second rule. The main difference in the index's performance appears using the third criteria, which is "4 declines in 7 months" rule. By this rule the new KILEI has successfully predicted all three recessions that have occurred in Kansas. The average lead according to this criterion was 10 months, comparing to an average lead of zero provided by the older version. Average leads allow a more formal comparison of the performance of both indices. These averages are given in the Table 3 in the Appendix. Looking at this table we conclude that the new version of the KILEI indeed has shown improvement in the performance, although this improvement depends on some conditions. One of the most 29
important conditions is that the best performance has been shown by the new KILEI in the case when the signal was derived using one out of three criteria. There is a second important issue that must be considered in evaluating the performance of an index. This issue is the number of false signals generated by the series. It is said that the false signal has occurred when according to some criteria the signal of recession has been generated, but no actual recession is observed within a reasonable period of time. Table 4 shows the number of false signals generated by two versions of the KILEI using the different signal criteria. It is clearly visible that the newer version of the KILEI also implies a higher number of false signals, especially when the "4 declines in 7 months" criteria is used, which was considered to be the best performer in forecasting recessions. These results raise a question about the trade-offs of a leading indicator. We have seen that improved forecasting performance also implies a higher probability of a false signal. This is a problem for both index structure and signal criteria which are used by researchers. It serves as another argument for continuing search for more robust indices and better theoretically based signal criteria. Later we will discuss several possible directions which pursue improvement of an ability to forecast changes in the economy using the index of leading economic indicators. 30
Chapter Four Concluding Remarks This report has described a number of steps taken toward updating and improving the Kansas Index of Leading Economic Indicators. The main goal was to increase the predictive ability of the Index in order to obtain a better instrument for forecasting changes in the business cycle. The update procedure consisted of bringing structural, benchmark and calculation adjustments into the KILEI. If these adjustments are accepted, KILEI will receive an additional (eighth) component and new weight structure. Several changes were proposed in the calculation procedure to use more effective ways to adjust for variability of the index components. Calculation of the new Index has led to several improvements in its performance. In particular, the new index now shows clear and considerable leads to all three of the most recent recessions, while the older version did not. In order to finalize use of the KILEI as a forecasting tool, close attention was paid to selection of the criteria for forecasting recessions using the index of leading indicators. This research investigated three different criteria for deriving a lead signal for the recession. One criterion has shown to be better at forecasting recessions than others. Signals produced by the Index on the basis of the "4 declines in 7 months" criterion have shown stronger ability to predict recessions. But the same criterion also caused more concern because of the greater number of false signals provided. Results of this work have shown relative improvements in the new KILEI, but have also introduced several questions which require further research. Several topics can 31
be considered as possible directions for future research. In the second chapter, we discussed the development of signal criteria, which are based more on econometric theory, rather than on statistical observations. We already discussed one approach in this area proposed by Neftci (1982). The posterior distributions calculated using his technique are used to estimate the probabilities of change in the economic "regime" which can play a role in defining other kinds of "signal" criteria based on this probabilistic approach. Otrok and Whiteman (1996) proposed another econometric technique in which leading indicators have been used. They employed estimation of posterior distributions of parameters in the model built on the basis of economic variables representing the economy of Iowa. The posterior distributions were used to provide forecasts for the Iowa economy on the basis of an index of leading indicators. These two approaches are part of numerous attempts to employ econometric techniques in research on leading indicators. Given the payoff for improving our ability to forecast recessions using better econometric techniques, we believe this area of study is of economic and political benefit and ideal for future inquiry. 32
References Anderson, Gerald, H. and John J. Erceg, "Forecasting Turning Points with Leading Indicators," Economic Commentary of the Federal Reserve Bank of Cleveland, October 1, 1989 De Leeuw, Frank, "Toward a Theory of Leading Indicators," Leading Economic Indicators. New Approaches and Forecasting Records, Cambridge University Press, 1991 Hidelbrand, George, "Alternative Cycle Indicators and Measures: a Complete Guide to Interpreting Key Economic Indicators," Chicago, Ill, Probus Pub. Co., 1992 Johnson, Christopher, "Measuring the Economy," London, Penguin, 1988 Koopmans, Tjalling C., "Measurement Without Theory," The Review of Economics and Statistics, Aug. 1947 Lahiri, K., and G.H. Moore, Introduction to "Leading Economic Indicators. New Approaches and Forecasting Records," Cambridge University Press, 1991 Mitchell, Wesley C. and Arthur F. Burns, "Measuring Business Cycles," National Bureau of Economic Research, New York, NY., 1946 Neftci, S.N., "Optimal Prediction of Cyclical Downturns," Journal of Economic Dynamics and Control, 1982 Otrok, C., and C.H. Whiteman, "Bayesian Leading Indicators: Measuring and Predicting Economic Conditions in Iowa," The University of Iowa, 1996-97 Oyen, Duane B., "Business Fluctuations and Forecasting," Deaborn Financial Publishing Inc., 1991 33
Sargent, Thomas J., and Christopher A. Sims, "Business Cycle Modeling Without Pretending to Have Too Much A Priori Economic Theory," New Methods in Business Cycle Research, Minneapolis: Federal Reserve Bank of Minneapolis, 1977 Stock, James H., and Mark W. Watson, "New Indexes of Coincident and Leading Economic Indicators," NBER Macroeconomic Annual 1989, Cambridge: The MIT Press, 1989 The Conference Board, "Business Cycle Indicators," A monthly report from The Conference Board, Volume 1, Number 10, November 1996 The Conference Board, "Business Cycle Indicators," The Conference Board, Inc., 1997 Willard, Mark Allen, "The Kansas Index of Leading Economic Indicators," a Master's thesis, Department of Economics, Kansas State University, Manhattan, KS, 1988 34
Appendix: Tables Table 1. Weights for components of the KILEI. Weight KILEI 1988 KILEI 1999 Wheat Price 0.805 0.379 Cattle Price 0.654 0.395 Stock Prices Index 0.788 0.777 New Housing Units 0.792 0.592 Unemployment Insurance -0.791-0.614 Claims Average Weekly Hours 0.695 0.744 M2 0.912 0.803 Interest Rate Spread 0.820 Note: Weights for KILEI 1999 are given after assigning signs and averaging. Table 2. Calculation of weights of KILEI components Wheat price Cattle price Stocks prices index Housing units Claims for unemp. insurance Average weekly hours M2 Interest rate spread Economic Significance 0.167 0.167 0.167 0.167 0.167 0.167 0.167 0.167 0.167 Statistical Significance - Quality of reporting service 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 - Coverage of process 0.025 0.025 0.025 0.025 0.013 0.013 0.013 0.013 0.025 - Coverage of time period 0.017 0.017 0.017 0.006 0.017 0.017 0.017 0.006 0.017 - Availability of estimates of sampling errors 0.008 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 - Frequency of revisions 0.033 0.017 0.017 0.017 0.017 0.017 0.033 0.033 0.017 - Length of the series 0.025 0.025 0.025 0.025 0.025 0.013 0.025 0.025 0.025 - Other considerations 0.013 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Timing - Probability that lead is attributable to chance 0.214 0.214 0.214 0.214 0.107 0.107 0.200 0.178 0.214 - Dispersion 0.053 0.007 0.027 0.016 0.009 0.016 0.013 0.027 0.010 Conformity - Probability 0.084 0.084 0.084 0.084 0.084 0.084 0.028 0.084 0.084 - Extra turns 0.050 0.017 0.050 0.010 0.006 0.013 0.013 0.013 0.025 - Amplitude 0.033 0.001 0.000 0.000 0.001 0.001 0.001 0.000 0.001 Smoothness 0.133 0.111 0.089 0.089 0.022 0.044 0.111 0.133 0.111 35
Currency 0.100 0.050 0.050 0.100 0.100 0.100 0.100 0.100 0.100 Overall Weight 0.759 0.789 0.777 0.592 0.614 0.744 0.803 0.820 Table 3. Leads, provided by two versions of the KILEI Leads, (month) "Three months decline" "2% and majority of components decline" "4 declines in 7 months" "Three months decline" "2% and majority of components decline" "4 declines in 7 months" Recession Recession Recession Average 1974 1979-80 1990-91 KILEI-99 0 0 0 0.00 0 9 0 3.00 5 12 14 10.33 KILEI-89 0 0 13 4.33 0 0 15 5.00 0 0 0 0.00 Table 4. False signals provided by two versions of the KILEI. Signal criterion The number of false signals KILEI-99 KILEI-89 "Three months decline" 4 2 "2% and majority of components 1 3 decline" "4 declines in 7 months" 5 0 36
Table 5. Raw Data for compiling the Kansas Index of Leading Economic Indicators Date Consumer Price Index Producer Price Index Wheat Price Cattle Price Stock Index 37 New Housing Units Unemployment Insurance Claims Average Weekly Hours M2 Interest Rate Spread Jan-70 39.1 37.8 1.22 26.7 31.03 2266 12784 42.2 591.3 0.87 Feb-70 39.1 38 1.21 28.4 33.13 692 10815 42.2 588.4 0.81 Mar-70 39.2 38.2 1.2 30.1 32.6 1124 7639 41.9 589.3 0.91 Apr-70 39 38.5 1.22 29.1 28.82 1030 8694 42.2 591 0.91 May-70 39.1 38.6 1.17 28.8 25.63 704 6417 42.4 594 1 Jun-70 39.2 38.8 1.13 28.2 23.53 990 7793 40.4 597.2 1.03 Jul-70 39.4 39 1.14 27.8 25.33 825 11162 40.9 600.4 1.03 Aug-70 39.2 39 1.2 26.9 26.71 449 7322 40.9 606.1 1.14 Sep-70 39.4 39.2 1.33 27 28.38 500 7869 41.8 612.4 1.17 Oct-70 39.5 39.4 1.32 27.4 27.53 640 6751 41.1 617.6 1.18 Nov-70 39.7 39.6 1.35 25.9 28.66 807 7553 41.5 622.4 1.22 Dec-70 39.7 39.8 1.32 25.6 30.69 826 11224 41.9 628.2 1.3 Jan-71 40 39.8 1.33 27.2 32.74 735 18860 41.4 634.2 1.51 Feb-71 40.2 39.9 1.31 29.9 33.73 584 8419 40.9 642.5 1.64 Mar-71 40.3 40 1.3 29.5 35 1627 10242 40.9 651.3 1.54 Apr-71 40.3 40.1 1.31 29.4 36.2 1476 7743 41.5 661.2 1.4 May-71 40.5 40.3 1.33 29.5 35 1711 5550 41.8 669.2 1.38 Jun-71 40.6 40.6 1.39 28.8 33.41 984 7370 41.6 674.9 1.33 Jul-71 40.6 40.7 1.29 28.2 38.17 1202 9277 39.9 681.4 1.27 Aug-71 40.7 40.8 1.28 30.2 33.07 1062 6583 41 687.5 1.18 Sep-71 40.6 40.8 1.26 29.6 32.7 928 5226 41.4 694.5 1.11 Oct-71 40.6 40.9 1.29 30.3 31.46 789 5557 41.3 700.4 1.14 Nov-71 40.7 40.9 1.29 31.2 30.41 1423 7295 41.2 706.9 1.18 Dec-71 41 41.1 1.33 31.5 33.22 760 9491 41.3 712.7 1.43 Jan-72 41.2 41.1 1.31 33.5 34.01 969 12447 40.5 719.8 1.7 Feb-72 41.4 41.3 1.3 34.4 34.47 1010 8325 40.5 728 1.85 Mar-72 41.4 41.4 1.31 33.4 34.3 2502 5969 40.6 735.8 1.58 Apr-72 41.3 41.5 1.35 33.5 33.15 1558 4590 41.3 741.8 1.48 May-72 41.5 41.6 1.35 33.9 33.47 1621 4721 41 746.4 1.44 Jun-72 41.7 41.7 1.27 35.3 32.08 898 5137 41.9 752.7 1.37 Jul-72 42 41.9 1.31 35.8 32.03 1073 9913 40.6 762.4 1.34 Aug-72 42 42 1.56 34.8 33.09 1335 6204 40.5 771.8 1.29 Sep-72 42.1 42.1 1.83 36.1 32.47 1328 3660 41.3 780.9 1.34 Oct-72 41.9 42.3 1.92 36.3 32.45 1162 4396 40.9 789.5 1.29 Nov-72 42.2 42.4 1.96 35.2 34.65 1174 5580 42.2 796.7 1.24 Dec-72 42.6 42.5 2.43 37.8 33.78 840 7548 40.9 805.1 1.19 Jan-73 43.1 42.6 2.44 40.1 32.18 406 9988 40.4 813.7 1.09 Feb-73 43.7 42.9 1.86 44.1 30.67 1050 5872 40.3 817.8 1.01 Mar-73 44.4 43.3 1.98 46.7 30.27 1119 5190 40.5 818.7 0.95 Apr-73 44.7 43.6 2.13 44.9 28.88 1165 4668 40.9 823.6 0.94 May-73 45 43.9 2.1 44.9 28.12 1623 4265 41.2 830.6 0.87 Jun-73 45.4 44.2 2.38 45.5 27.69 1488 4307 41.5 837.3 0.81 Jul-73 45.5 44.3 2.4 46.4 29.3 635 9868 41.4 841.2 0.69 Aug-73 47 45.1 4.26 51 28.81 864 5199 41.1 843.6 0.7 Sep-73 46.8 45.2 4.52 47 31.1 881 3867 42 844.6 0.66 Oct-73 46.8 45.6 4.1 43.9 31.91 1329 5467 41.4 848.4 0.68 Nov-73 47 45.9 4.1 42 27.48 1390 5610 41.7 854.5 0.67 Dec-73 47.6 46.2 4.66 39.7 28.13 652 13455 42.1 861 0.68 Jan-74 49 46.6 5.22 44.7 27.77 556 15193 40.4 865.6 0.72 Feb-74 49.9 47.2 5.39 44.1 28.17 472 6825 40.6 870.3 0.78 Mar-74 50.2 47.8 4.57 41.8 26.77 804 5317 40.9 876.5 0.77 Apr-74 50.6 48 3.71 40 25.4 789 5762 40.6 879.2 0.71 May-74 51.2 48.6 3.2 37.1 23.4 713 5469 40.6 881.5 0.67 Jun-74 51.3 49 3.44 31 23.48 581 5003 41.6 884.8 0.63 Jul-74 52.8 49.4 3.96 34.3 21.91 809 8504 41.3 888.3 0.6 Aug-74 53.7 50 3.89 35.1 20.57 1470 5274 40.6 891.1 0.67 Sep-74 54.2 50.6 3.95 30.4 18.49 479 4632 40.5 895.1 0.71