A Helpful Analogy

Let’s suppose that I get out my headphones and IPod and take the dog for a walk.  Let’s further suppose that someone has given me a gadget — a pedometer — and at the return from my walk it says that we have traveled exactly one mile — 5280 feet.  If my stride is even (sometimes a little tough on a dog walk) I might be pretty close to the estimated distance.  Let’s say the walk was actually 5290 feet.  Well getting it within ten feet would be excellent, an error of less than two-tenths of one percent.

Taking this little example another step, let’s suppose that the next day I choose a different route and I plan to stop for a break after walking exactly one mile.  Suppose that I estimated even better than the day before, missing by only one tenth of one percent, stopping after 5275 feet.

Now finally, let’s suppose that a Genie appeared and offered me a prize if I could tell him the actual difference in length between the two walks.  I would win only if my estimate of the difference was accurate to within two feet!

The problem in winning the prize is pretty clear.  While my estimate of each walk is excellent, my estimate of the relative difference in these two large distances is not so good.  An error which is small in percentage terms in the first case, is quite large when viewed as a percentage of the deviations.

The difference of two feet in the dog walks is the equivalent of a 50K change in the estimates for monthly non-farm payrolls.  No wonder it is difficult to win a bet with the market "genie" on this report.  Even if you knew the truth, you could lose because the estimate was wrong!