Am I splitting hairs or is this materially misstated?

For the past decade I have thought that something was dreadfully wrong with two figures released by the US Department of Labor and their Bureau of Labor Statistics:  Specifically Unemployment and Productivity. Today I only have time to comment on one so let’s look at unemployment.

Unemployment is defined by the BLS as: 

"Persons aged 16 years and older who had no employment during the reference week, were available for work, except for temporary illness, and had made specific efforts to find employment sometime during the 4-week period ending with the reference week. Persons who were waiting to be recalled to a job from which they had been laid off need not have been looking for work to be classified as unemployed."

The unemployment rate is the unemployed as a percentage of the labor force. 

What bothers me most about this definition is that it does not take into consideration the Free Agent Nation we live in i.e. the independent contractors, business owners and temporary workers.  This exclusion leads me to believe that the unemployment rate is actually higher than the stated rate at times.

Some may argue that the exclusion is immaterial as these people are not included in the numerator nor are the included in the denominator. 

If we agree the number of non-counted persons is material which I believe it to be the question then becomes one of flow.  During any given 4 week measurement period are more people joining the ranks of Free Agent Nation or rejoining the traditional Labor Force? 

First let's consider the size of those not counted in the unemployment rate.  I haven't found a great data point on the number of independent contractors in America but there are some solid data points estimating some 14 million small businesses are owned by Americans and the temp industry appears to be sized at about 2 million people. My gut tells me 6+ million people are contractors. So I will guess about 22 million people are not counted.  So if I take 300 million Americans as the population less those under 16 years old (~65 million) and less retirees of 36 million (ok, I'm taking people over 65 years old some may not be retired) you get about 200 million potential people in the potential labor force. I cross check that estimation with the BLS and they report a labor force of ~152 million. So, my 22 million person estimation may be low and I probably have missed a few categories of people in the population that are not in the labor force (military, government (?), disabled persons etc). Either way let's use 22 million as the figure for those not included in the unemployment rate calculation that 'could' be.

If during times of prosperity more people decide to try their hand as a Free Agents and during times of uncertainty some Free Agents seek the security of permanent employment... the question becomes does the flow in and out of Free Agent Nation skew the rate calculation? I think it does by up to about a percentage point each way. So while the calculation isn't 'dreadfully' wrong it may be a bit misleading.