*Advisor Perspectives welcomes guest contributions. The views presented here do not necessarily represent those of Advisor Perspectives.*

In this previous June 2012 article we questioned whether the ECRI Weekly Leading Index (WLI) was still a relevant predictor of the U.S. economy and concluded then that it was not. We have now analyzed 10 years of representative component data of the index from which we constructed the Shadow WLI (ShWLI). After an investigation into the discrepancies between the WLI and our ShWLI we came to the conclusion that ECRI still uses M2 as a component in the WLI, whereas leading economists, more than ten years ago, had already downgraded and excluded M2 as a leading indicator from their models (Appendix A).

(Economists use M2 when looking to quantify the amount of money in circulation and trying to explain different economic monetary conditions. M2 was traditionally recognized as a reliable indicator of economic conditions. Recently, however, M2 had ceased to perform well as a leading indicator due to structural changes that have occurred in the U.S. economy in the last several decades.) |

Furthermore, we found that for the period August 2008 to September 2011 the average error between the ShWLI and the WLI was statistically double that of the average error for the remaining time, i.e. before and after the mentioned period. This implies that the WLI reacted very differently than the ShWLI to their respective underlying components during the 2008/9 recession and the recovery years thereafter.

ECRI has not disclosed the current components of the WLI, nor how the index or its growth is calculated. However, in 1999 for a short time on the ECRI website, they did publish the underlying components of the WLI as:

- Initial claims for unemployment insurance,
- Money supply (M2 plus),
- Industrial materials price index,
- Mortgage loan applications,
- 10 year treasury bond yield / BAA corporate bond yield
- BAA corporate bond yield; and
- Stock price index.

According to ECRI, the WLI is designed to anticipate turns in the business cycle, while the growth of the index should anticipate turns in the growth rate cycle. It is supposed to provide leads to cycle peaks and troughs of about 10 months and 3 months, respectively. ECRI publishes this widely followed index together with its growth figure every Friday morning.

We have no idea why ECRI is still keeping the components of the WLI and their weightings in the index a secret, similarly it is absurd that they did not disclose how the growth of the index was calculated. The formula for the growth rate was found and it is given in Appendix B.

We have been able to successfully replicate the WLI thanks to Franz Lischka's pioneering work, and we have since June 2012 produced the ShWLI one day ahead of the ECRI's Friday publication.

We set out to improve the ShWLI algorithm with the aim to better the tracking accuracy of our model with the ECRI's published values. We began by plotting the error over the last 10 years using the formula ShWLI/WLI-1, and noticed the higher error values in the period August 2008 to September 2011. (See Figure 1) We then proceeded to optimize the "old" ShWLI excluding this period for best fit with the WLI to obtain the "new" ShWLI.

We calculated the standard deviation (sigma) of the error to evaluate the performance of the new model against the old and found that 99.7% of all samples are below the three-sigma level, meaning that they are within 3 standard deviations away from the mean. Table 1, further down, shows the standard deviation of the error of our ShWLI models and the improvements obtained, which can be seen in the fourth column of the table.

When studying Figure 1 it is apparent that before August 2008 the old and new ShWLI was tracking the WLI within normal statistical limits. The first major deviation of minus 1.5% was for the WLI record date week ending Sep-26-2008. This deviation is a 7 sigma event (7 standard deviations away from the mean); statistically a seven sigma event has a probability 0.000000000256% of occurring (that's nine zeros after the decimal – to put this into perspective, the fraction represents 13 days in the existence of the universe).

As both our old and new ShWLI exclude M2 in the algorithm, and wanting to explain this unexpected error, we introduced the 'M2 seasonally adjusted' into a "trial" ShWLI model and we were astounded to see this 1.5% error reduced to 0.6%, which is within normal statistical expectations.

The next logical step was to calculate the correlation between the weekly changes in M2 and the error of the ShWLI for both the "new" (excluding M2) and the "trial" (including M2) models. The result of this calculation is highlighted in Table 1, columns 5 and 8. The correlation between the error of the new ShWLI (excluding M2) and changes in M2 are also observable in Figure 2; a positive change in M2 in most cases corresponds with a negative error of the new ShWLI, hence a minus value in the correlation coefficient.

The correlation between the tracking error and the weekly change of M2 is given by the correlation coefficients -0.33 and -0.43 (column 5 of Table 1). The values of the coefficients is indicative that M2 is a component of the WLI. All doubt of this being coincidental is removed by the fact that these correlation coefficients are reduced to near zero (column 8), merely by changing the ShWLI algorithm with an algorithm that included M2. This is irrefutable evidence that M2 is a component of ECRI's WLI.

The second remarkable observation from Figure 1 is the periodic occurrence of statistically unexpected high errors in the three years after the 2008 stock market collapse; the trial model that included M2 only slightly reduced these high errors. This period was, of course, when the Fed expanded the money supply by unprecedented levels; the WLI with M2 as a component reacted accordingly and probably distorted the signals that it was supposedly designed to provide. M2 increasing during a recession due to monetary policy can hardly be construed as a positive indication of economic growth, but would have been reflected as such by the contribution of the M2 component to the index.

The erratic behavior of the WLI over the above mentioned period is also observable in its growth rate, WLIg, shown in Figure 3. The extreme high and low values and oscillations of WLIg from June 2009 to March 2012, when compared to the more steady characteristics of the growth rate of the Conference Board Leading Economic Index® (CBg) are noteworthy. Both, WLIg and CBg, were raised by 2.63 and 2.35, respectively, to provide for best recession capturing using our recession indicator evaluation system.

In September 2011 ECRI did a major revision of the WLI that affected it back to Jan-2011. This revision stabilized the index as the excessive swings of the errors disappeared from that point onwards and the growth rate also appears to have normal characteristics from that time onwards.

The WLI has been a poor predictor of oncoming recessions in the past. The fact that M2 is included impairs the quality of this index. This should have been corrected, especially since it has been generally accepted for many years that M2 does not help in predicting recessions. Since ECRI has kept the components of the index in a "black box", it was incumbent on them to fix this problem. The WLI enjoyed prime status and guided many analysts including ourselves; we use it is also as a major parameter in one of our market timing models. It is therefore distressing to be confronted with the fact that the ECRI WLI may be impaired by the inclusion of M2.

In September 2011 ECRI made a recession call without providing any hard evidence in support of it, partly relying on the WLI according to their statement. (For the actual recession call and TV interview transcript see Appendix B in this article.) The vertical black lines in Figure 3 show the dates of their calls. It is of interest that CBg was not in recession territory in September 2011, unlike at the previous ECRI recession calls of 2001 and 2008.

It is not surprising then that ECRI's dire 2011 recession predictions turned out to be incorrect, given the impaired WLI model which supported their forecast. Their other models may be equally compromised as none of them can be checked by outsiders. This state of affairs is unacceptable; it is high time for ECRI to disclose how their models are constructed.

ECRI has for the past 17 months continued to maintain that their September 2011 forecast cannot yet be discounted. It is evident from Figure 3 that the WLIg has steadily risen from the September 2011 nadir to a level which is now well out of recession indicating territory. It is astounding for ECRI to maintain that the U.S. economy is in recession when their own indicator does not support this position.

Since their initial recession call the S&P 500 has gained a lot, 37.5% with dividends reinvested is the performance of SPY (which tracks the S&P) over this period. This shows how bad recession calls can hurt investors if they heed the call and act as advocated in Beating the Business Cycle, by Lakshman Achuthan and Anirvan Banerji, co-directors of ECRI - *"historically, the prospect of an economic downturn has been bad for stock prices" and "you should move most of your money into cash"*.

On our website imarketsignals.com we publish every Thursday morning the Shadow WLI for underlying component data to Friday of the prior week. Furthermore, on Monday and Wednesday we publish the development of the Shadow WLI as the components become available. To help estimating the trend we also publish a graphic representation of the weekly change of the Shadow WLI and WLIg.

**Appendix A**

Anderson and Vahid, Macroeconomic Dynamics September 2001 concluded in their research paper that M2 does not help in predicting recessions; the fact that M2 was a negligible leading indicator was observed already from the late nineteen-eighties onwards. Quoting Anderson and Vahid:

M2 has traditionally been recognized as a particularly reliable indicator of economic conditions. Recently, however, with the introduction of new financial instruments and the increasing importance of credit markets, the value of M2 as a leading indicator has been questioned.
For example, Stock and Watson (1989) decided against including M2 in their index of leading indicators. In 1993, the Federal Reserve Chairman, Alan Greenspan, informed Congress that M2 had been "downgraded as a reliable indicator of financial conditions in the economy" and that "the historical relationships between money and income had broken down". |

Also, after an extensive reevaluation, the 2011 Comprehensive Benchmark Revisions for the Conference Board Leading Economic Index® removed M2 from the index back to 1990, and replaced it with a newly developed Leading Credit Index. According to their research M2 had ceased to perform well as a leading indicator due to structural changes that have occurred in the U.S. economy in the last several decades.

**Appendix B**

WLIg is the compound annualized growth rate of the WLI for a 26.5 week period.

WLIg = [100*(MA1/MA2)^( 52/26.5)] – 100

MA1 is the 4 week moving average of the WLI.

MA2 is the moving average of MA1 over the preceding 52 weeks.

The ratio MA1/MA2 yields the change over a 26.5-week period, i.e. over six months, because the 52-week average in the denominator is centered 26.5 weeks before the current middle of the week.

Anton Vrba & Georg Vrba

*Anton Vrba is an electrical engineer. He pursued a career in R&D, manufacturing and construction project management. His interests are mathematics and physics. He is a lateral thinker and has ideas that challenge the established explanations to the workings of the universe, which he is in the process of publishing on his website.*

*Georg Vrba is a professional engineer who has been a consulting engineer for many years. In his opinion, mathematical models provide better guidance to market direction than financial "experts." He has developed financial models for the stock market, the bond market, yield curve, gold, silver and recession prediction, all published in Advisor Perspectives. The models are updated weekly at http://imarketsignals.com/.*