Discuss the technique

J.Y. Ping

Have you guys heard the Planet Money podcast about hunting for the hundred dollar bills? Apparently, 80% of cash is in the form of $100 dollar bills but when's the last time you saw a Benjamin Franklin? The fact is we don't know where most of the $100s are.

Why is that? And just how many $100s are floating around out in the world? Well, that's exactly what the Federal Reserve wanted to know. They begin with a hypothesis that the $100s are "hiding". They guessed that the $100s are used as long term stores of sketchy wealth, stored in vaults and in between pages of books, by international drug dealers and their ilk.

Working off that hypothesis, they concocted a way to "count" how many $100s are out in the world.

They borrowed a clever technique from fish biologists that wanted to count fish in a lake. Like $100s, fish hide too. What you do is you catch say 100 fish, you tag them and you set them back into the lake. Later, you pull up another 100 fish, randomly. You check to see how many of the fish are tagged. If all 100 are tagged, then there's probably only 100 fish in the lake. But, if only 50 are tagged, then there's probably 200 fish in the lake.

The Federal Reserve used the same trick. They tagged $100s and tossed them into the world's lake of $100s. They waited, they resampled, and they got their "answer".

Regardless of the results, my question concerns their technique. What you do think about their technique? Would it yield accurate results? Would it over or under count?

Source:
http://www.npr.org/blogs/money/2014/08/13/339827662/episode-560-hunting-for-the-hundreds
5:48 is where they talk about the fish biologists sampling technique

joegotbored-1

Seems to me that this assumes the hiding $100 bills are released. If they're a store of value in a vault and don't come out to play, then when you resample, you just get your tagged $100 bills back. Based on this, I think it has the potential to undercount the number of $100 bills hiding in the wild.

Hoping I have not just embarrassed myself by raising my hand.
-J

Edit: English.

Judyyyyy

I second joegotbored-1.

If their premise is true that the $100 bills are "hiding," this would be the exact reason why their method is flawed. These bills are being hidden by those with ill-gotten wealth. Thus, they have reason to be kept hidden. Why does the Federal Reserve believe that these hidden bills would come out and participate with their sampling technique when they have reasons for hiding in the first place?

The 180 Bro_OVO

^^^agreed

chase62442

If they resampled and found fewer 100s than they had even thrown out into the world, that would offer some evidence that even those 100s that they themselves had released are now "in hiding" and thus give some evidence that their theory about hiding might be correct.

Alejandro

mmmmmm lets say that they estimate 1 million $100 bills to be out there (including the ones that are hidden) and they tag 50% of them (500,000). I'm guessing that if no $100 bills are hiding, in theory, they should get a total close to 250,000 tagged bills back after pulling up another random sample of 500,000 bills or 50% of the ones in existence. Whatever number less than 250,000 that they get after resampling should indicate the amount of bills that are hiding. So, if t only 50,000 of the bills that they pull back up are tagged that should mean that around 80% of 100$ bills out there are hiding. The smaller the sample (tagged bills) compared to the total amount of bills out there should create a larger expected variance between the test results and real amount of bills that are hiding, and that should be taken into account as well.

By this reasoning, the method they used should be theoretically sound.
Anyone has opinions, questions, concerns, dirty looks?

Will Edwards

The hidden bills don't need to come out and play for this to be accurate. The reason it works is they are measuring what percentage of a certain printing of hundreds goes out of the country or "into hiding." From there you can extrapolate for all the printings in a certain amount of time and come up with a rough figure.

7Sage Admin

@joegotbored-1!

You were the first to respond, and gave an excellent analysis of a potentially huge flaw in the technique.

You get the secret mystery prize...

Keeping with the theme of this thread you get your very own - untagged - C note, in the form of a $100 Amazon gift card

Congratulations!

joegotbored-1

Ha! What an awesome surprise to come home to Thank you 7Sage!! My kindle has been severely neglected since March when I started studying. Will be nice to use this gift to re-populate it with post-LSAT reading that has nothing to do with physics, ancient law, obscure authors, or abstract art! (even if I have secretly started to enjoy RC...)

Thanks again!