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How to Build a Time Machine

by John Hussman, Hussman Funds

With industrial production, capacity utilization, real disposable income, real personal consumption, real sales retail and food service sales, and real manufacturing and trade sales uniformly declining in their latest reports, coincident economic indicators – having generally peaked in July – are now following through on the weakness that we’ve persistently observed in leading economic measures. We continue to believe that the U.S. economy joined a global economic downturn during the third quarter of this year.

While we use a broad range of signal extraction and noise-reduction methods in our own work, the economic data in recent months has required less and less sophisticated analysis, as many of the most reliable leading economic measures have turned clearly lower (e.g. Philly Fed Index, Chicago Fed National Activity Index, and the new orders and order backlog components of numerous regional and national Federal Reserve and purchasing managers surveys). Still, the leading/coincident/lagging relationships across these indicators remain important. Not surprisingly, analysts have now turned to the last refuge of the economic data, which is to focus on historically lagging measures such as payroll employment.

If you calculate the correlation between various economic measures and recessions in historical data, these leading and lagging relationships can easily be identified (see Leading Indicators and the Risk of a Blindside Recession). Among widely followed economic statistics, it turns out that the Philadelphia Fed Index is among the most reliable single indicators of oncoming recession in the quarter immediately before the downturn. From the start of a recession to about 3 months after it begins, the most reliable early confirmation comes from the 6-month change in industrial production, the new orders components of the Chicago Purchasing Managers Index and the national Purchasing Managers Index for manufacturing (from the Institute of Supply Management), and the percentage change in the 4-week average of new unemployment claims from its 10-month low. Only several months into a recession do employment figures begin to give a reliable confirmation of recession (though initial data is often heavily revised after the fact). In the period 3-6 months after a recession starts, the 6-month change in employment begins to provide a reliable confirmation of recession, and about 7-11 months after a recession starts, the 12-month change in employment reaches its highest cross-correlation with recession. Finally, 12-months after a recession starts, the indicator most strongly correlated with recession turns out to be – no surprise here – the year-over-year change in real GDP.

The chart below plots the standardized values (mean zero, unit variance) of these economic indicators since the 1960’s. Notice that 6-month and 12-month employment growth, as well as year-over-year GDP growth, clearly lag the somewhat more volatile but also more timely signals from production, new orders, and new employment claims.

The chart below provides greater detail of how these indicators have behaved in the past 12 months. Note that the sequence of deterioration has been about what one would expect if a recession indeed began in the third quarter, with weakness in the Philly Fed leading deterioration in other coincident measures.

With the November Philly Fed index surprisingly plunging to -10.7 (from 5.7 in October), the new orders component of the Chicago PMI plunging to 45.3 (from 50.6 in October), and industrial production contracting from its peak in July, neither leading nor coincident indicators are providing much assurance of economic strength. The response has been to focus on historically lagging indicators like payroll employment (see last week’s Bloomberg interview with Lakshman Achuthan of ECRI, where his recession concerns were repeatedly dismissed by citing employment as a counter-argument).

Interestingly, the past several weeks have seen a noticeable spike in new claims for unemployment, with the 4-week average surging to 405,000 from about 360,000 before the storm. Of course, this spike has been quickly dismissed as being a “distortion” due to Hurricane Sandy, with the implication that the spike should be ignored. The problem here is that Sandy very clearly would be expected to affect the week-to-week distribution of new claims, but Sandy does not explain the increase in the average level of claims. Though the expected distortion did emerge (far fewer than normal claims in the week of the storm, and far greater than normal claims in the following week), we’ve also accumulated what amounts to nearly 200,000 more new claims in the past several weeks than the run-rate we saw before the storm. That’s not a “distortion” – those are incremental job losses.

It’s difficult to realistically attribute the rise in the average level of new unemployment claims to Sandy, (and even in that case, it would be a real effect, not a distortion) but Wall Street seems perfectly happy to shrug it off as weather-related. After all, everyone knows that the correct emergency procedure in the event of a hurricane is to immediately fire hundreds of thousands of workers and shut down the Twinkie plant.

In any event, the data over the next few months should clarify the actual course of the economy. Generally, new claims for unemployment reach their peak correlation with recession a few months after the recession starts. A typical recessionary pattern would emerge if the new orders components of various purchasing managers surveys were to remain weak, and if new claims were to persist above 400,000 on the 4-week average (though not necessarily in every weekly reading) and gradually crawl toward 450,000 or higher.

How to Build a Time Machine

A couple of weeks ago, Lance Roberts of StreetTalkLive presented a nice chart of the ratio of coincident to lagging indicators from the Conference Board, noting that each time the ratio has fallen to current levels, the economy has either been in or close to a recession.

We can identify numerous other points of concern regarding the economy, but this indicator is interesting in itself for purely intellectual reasons. The coincident/lagging ratio has been followed by analysts for a long time, but it only makes sense to pay attention to an indicator if you fully understand it. Even Geoffrey Moore and Victor Zarnowitz – who pioneered the use of this ratio – didn’t really give it a mathematical backbone. So the question is, why would the relationship between a coincident indicator and a lagging indicator be useful as a leading indicator? How do two indicators – neither which looks ahead – possibly see into the future?

After scribbling down some math, it became clear how this “time machine” is created – the answer has to do with what’s called a “phase shift.” It’s easiest to explain this using a graph. Suppose we have two waves, one that moves first (blue) and one that lags slightly (red). The ones below are just cosine waves. It turns out that the difference between those two waves reaches its extreme when the two waves are roughly in mid-cycle, and that difference actually leads the two waves themselves. The blue coincident line peaks before the lagging red one, but the green line peaks even before the blue, during the same cycle – it is legitimately leading.

[Geeks Note: The mathematics work like this - The blue line is just cos(x) and red lagging line is cos(x+w), where the “phase” w is negative (which makes the red peaks occur after the blue peaks). Mathematically, if L is the number of months that the red line lags, where L is negative, and N is the number of periods in the full cycle, w = L * 2pi / N where -pi < w < 0. For example, a 3-month lag in a 4 year cycle would be w = -pi/8. The green line is just cos(x) – cos(x+w), and the first order condition for the maximum is satisfied when x = (3pi - w)/2, which is before cos(x) reaches its maximum at 2pi, so the difference has positive phase of (pi+w)/2: it is a leading indicator. In our example of a 3-month lag and a 4-year cycle for the red line, the green line would lead by 10.5 months. Our resident math guru, Russell Jackson, was quick to chip in that cos(x) and cos(x+w) intersect at –w/2 + n*pi for all integer n, so the difference reaches its extreme value half-way between adjacent intersections. We're a fun bunch some days.]

Note that this analysis is based on the difference between the two waves, because they fluctuate around zero, and the ratio would produce divide-by-zero problems. The coincident/lagging indicator using Conference Board data takes the ratio, but this doesn’t change analysis since the difference and the ratio rise and fall in lockstep.

To confirm this in other data, the chart below uses the coincident and lagging measures noted earlier. The “coincident” line below is the average standardized value (mean zero, unit variance) of the Philadelphia Fed Index, the new orders component of the Chicago PMI, the 6-month change in industrial production, and the change in the 4-week average of new unemployment claims from its 10-month low (times -1). The “lagging” line is the average standardized value of the 3-month change in payroll employment, the 6-month change in payroll employment, and the year-over-year change in real GDP. For this set of data at least, the green difference does indeed lead the coincident data (which you can see by the order in which peaks and troughs occur). Before recessions, it sometimes leads only slightly and primarily due to deterioration in the coincident data. That may reflect the fact that the coincident measures I chose are generally very timely in identifying recessions in the first place. In any event, what’s most striking is the tendency for the “coincident-lagging” index using this particular set of indicators to surge very quickly as new economic recoveries take hold. That will certainly be something to monitor, so we’ll plan to return to this data if we see any significant change as the economic picture unfolds.

In addition to recessions, shaded in grey, I’ve also placed light blue shading over the periods where all three of these indices were below -0.2, which is presently the case. For now, it’s evident that the economic evidence is moving dramatically in the wrong direction if one is looking for fresh economic strength.

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