Multifactor Productivity Explained and the Rule of 8

"Multifactor" quote unquote productivity is the official statistical designation for "We don't know what the hell" -- as in productivity with no obvious driver. "Multifactor Productivity Explained" is a self-consciously grandiose way of announcing some success in our search for the missing half of productivity improvements not accounted for by economic science. "The Rule of 8" as explained below is a very simple relationship between productivity and unemployment.

I must say that when I first saw the trendlines on the Excel chart, I was amazed. So amazed that fifteen minutes later I played a computer game, which I haven't done in a while, and after that went and scrubbed some pots in the kitchen. Having allowed reality to settle in this way, I returned to the chart, but it had not changed. It still seems a bit improbable.

This is from among the first cuts, using the most commonly cited data for the unemployment rate and productivity -- output per hour -- directly out of the Economic Report of the President.

The correlation between a smoothed line of change in productivity and a smoothed line of the unemployment rate is nearly complete. They essentially mirror each other around a central trend of 4.0.


So without further ado, Demand Side presents:
The Rule of Eight

Eight minus the unemployment rate equals the change in productivity. Eight minus the change in productivity equals the unemployment rate.
There is a very close correlation between a smoothed line of unemployment and a smoothed line of productivity. As productivity rises, unemployment falls. As unemployment rises, productivity falls. Whether or not one causes the other, the correlation is nearly complete. Emphasizing that this is for a trendline described by a polynomial equation.

Our postulate here, and the hypothesis we set out to test, is that the rate of unemployment causes a change in productivity because as unemployment falls, workers are shifted to more productive tasks, retrained as necessary, equipped better, or simply used more efficiently. This idea would not be surprising to a worker or a manager, since they would be familiar with the dynamics of the workplace. Not being able to hire appropriate skill levels, currently employed skills are improved. But so far as I am aware it does not appear in the economics literature.

Here we would like simply to publish the fact of our being first to the finding and to sketch the outlines of its implications. The chart displays the irrefutable correlation. In subsequent pieces we will identify the appropriate statistical metrics.

Provisional Explanation

1.  A change in the rate of unemployment influences productivity.
A change in the rate of unemployment influences productivity. In tight employment climates, managers shift current assets -- including labor -- to more productive tasks.
2.  Loose employment markets mean sluggish productivity growth
A corresponding absence of focus occurs when employment markets are looser, as when the unemployment rate rises. From the Demand Side perspective, a rise in unemployment relates to a drop in demand. Lower demand means current assets are not used to previous capacity, which means a fall in productivity.
3.  The short-term correlation is in the opposite direction as the medium term correlation.
A close look at the data will show that officially measured productivity seems to anticipate the change in unemployment. We believe this is due to output being a function of labor inputs over a longer period than the currently measured productivity. That is, the organization of plant and facilities and systems over time contributes to output measured in a specific quarter. Following from this, when demand falls and workers are let go, the surviving smaller workforce may be credited with production that actually involves more people over a longer time frame.

A good illustration of this is in the productivity data for Q2 2009, which showed an historically high reading for productivity, but obviously driven by a complete collapse of hours worked. This simultaneous fall in labor input and rise in productivity as measured by current methodology is frequently observed. This exclusively short-term phenomenon has led to confusion around the relationship between unemployment and productivity, and sometimes to the fatuous attempt to describe higher unemployment as good for productivity. The best workers are more productive and the rest are being carried. In fact, as we see here, the relationship is systemic and opposite.

Simply reflecting on the fact that capacity utilization is lower during times of falling demand and rising unemployment should abort this line of reasoning. In any event, as noted, the long-term correlations are in exactly the opposite direction.
4.  Other considerations as to why short- and medium-term correlations are opposed
One might suggest other causal connections for why the short-term and long-term relationships act in the opposite direction. For example, as one industry prospers, the wages in that industry rise and people train to obtain the skill sets necessary to that industry. Should that industry subsequently decline, the cohort of trained workers is left behind to accept lower level positions. That may have been the situation with the high-tech boom and we may see it soon following the financial sector boom and collapse.
5.  The relationship has decayed over time
The decline in the measured level of unemployment may bring this unemployment-productivity relationship to the "Rule of Seven" from its inception in 1948 as being the Rule of Eight. We believe the methodology for calculating unemployment has deteriorated over time, and so the long-term decay is a result of measurement, not of dynamics.

Alternatively, and still to be investigated, manufacturing may be more amenable to automation and other productivity improvements than services, so a shift to a service-based economy may influence the general trend of productivity downward.

Another explanation could be the shift to overseas suppliers of low-productivity manufacturing, leaving the higher productivity work to be counted domestically.
6.  The finding refutes the Phillips Curve.
Increasing productivity with declining unemployment implies a contradiction to the Phillips Curve, which suggests a lower unemployment rate leads to higher inflation. Since productivity increases ought to subtract from inflation pressure, the rule of eight implies lower inflation with lower unemployment. This should be the finding in all cases where supply is not constrained.
7.  The equation is complex, but the relationship is not.
Polynomials are complex equations. The equation describing the trend in unemployment is

y = 4E-07x5 - 5E-05x4 + 0.0024x3 - 0.0448x2 + 0.3476x + 3.7556

with an R2
of 0.4357

But P = 8 - f(U) where P is productivity and U is the unemployment rate

is not complex.


It turns out that the mirror of a fifth order polynomial curve for the unemployment rate explains changes in productivity. Not a parallel line, a mirror image. When unemployment, or the polynomial trend for unemployment goes up, productivity goes down. And vice versa.

What does this mean?

We have long suspected that tighter labor markets generate more efficient use of labor assets and thus higher productivity. The data for the unemployment rate and productivity in raw form do not exhibit contemporaneous correlations in the same direction, even if massaged.

But the inverse relationship between unemployment and productivity is incontrovertible. Whether this is a causal relationship or a situation in which both are functions of another dynamic is not provable. A frequent error in economics arises from the assumption of cause and effect from simple correlations.

Our hypothesis is that low unemployment causes the natural shift of workers to more productive occupations and to improvement in the industry-specific skill sets of workers.

Has anybody else ever made this comparison?

In responding to our finding, the great economist James K. Galbraith wrote:
Thank you.  I make a very similar argument in the chapter on standards in The Predator State.  It reflects the longstanding Rehn-Meidner (Swedish model) approach to combining wage compression, high employment, and rapid productivity growth.
We'll be putting up our investigation of these two leads soon.

We are looking for feedback on this issue.  Give us your thoughts and links.