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Is There A Half-life For Coins In Circulation?

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Valued Member
Canada
89 Posts
 Posted 03/24/2020  08:12 am Show Profile   Bookmark this topic Add Silver101 to your friends list Get a Link to this Message
Weird question.

Does anyone know if there's ever been an attempt to estimate/calculate the rate at which coins in regular circulation are lost over time? For many coins we know the starting mintage and we may know about specific times when large numbers of coins were melted down to be replaced or for various war efforts etc...

But, it seems to me that it should be possible to determine a sort of "half life" for a coin of whatever size and composition that would allow you to estimate how many are still on earth X years later.

Any thoughts on that Numismaticians?
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United States
19172 Posts
 Posted 03/24/2020  08:54 am  Show Profile   Bookmark this reply Add just carl to your friends list Get a Link to this Reply
No idea but I'm still trying to spend coins made hundreds of years ago.
just carl
Pillar of the Community
United States
1543 Posts
 Posted 03/24/2020  09:18 am  Show Profile   Bookmark this reply Add hfjacinto to your friends list Get a Link to this Reply
I asked this question before and the answer is no one really knows. For example if you look at ASE, there are probably 99.999% of all ever minted still around, but looking at small cents (Canadian/USA) probably 50% from every year are tossed or mutilated (based on what people post as errors). So I guess the answer is the half life is proportional to its worth and its appeal, coins that have little appeal are tossed/chucked/mutilated fairly often, coins that have high worth and appeal tend to last longer.
Valued Member
Canada
89 Posts
 Posted 03/24/2020  10:07 am  Show Profile   Bookmark this reply Add Silver101 to your friends list Get a Link to this Reply
That makes a lot of sense - also, lower value coins are used more routinely for everyday purchases. I'm particularly interested in the silver 5 cent coins. They seem to me (at least the Newfoundland and Canada versions) to be more scarce than their original mintage numbers would suggest.
Valued Member
United States
160 Posts
 Posted 03/24/2020  10:18 am  Show Profile   Bookmark this reply Add river4449 to your friends list Get a Link to this Reply
That may be the case in terms of 5 cent silvers, but for collecting sake, they are still available in all kinds of conditions and at all sorts of price points. I've purchased an 1858 small date in what I observe to be VF/XF for 25 dollars. No, not the most valuable date but certainly it can be a more expensive find, I just so happened to get lucky. In the case of the 1875H, (compared to the rest of the series) it had a respectable mintage year, but remains one of the most expensive if not the key coin in the series. But several factors probably went into that...

Jasper
regards, Jasper- "river4449"
Canada 5 cent silver collector.
PMs are open, whether you have a question or simply wish to talk.
Edited by river4449
03/24/2020 10:19 am
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United States
3162 Posts
 Posted 03/24/2020  10:18 am  Show Profile   Bookmark this reply Add tdziemia to your friends list Get a Link to this Reply
I would guess that there have been attempts to model it mathematically. It's not too hard to imagine what that (the model) might look like for a series like Lincolns or Jeffersons which presumably had no "major" discontinuity...

More difficult for silver coins, where there would have been a large discontinuity in the decay curve in the mid-1960s

The real problem is in checking it against reality, because I doubt anyone is counting the current incidence of any coin in circulation.

But I don't get around much ... maybe there is a Journal of Statistical Numismatics that I am not even aware of .
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United States
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 Posted 03/24/2020  10:25 am  Show Profile   Bookmark this reply Add tdziemia to your friends list Get a Link to this Reply

Quote:
Does anyone know if there's ever been an attempt to estimate/calculate the rate at which coins in regular circulation are lost over time?


Of course the answer turns out to be yes:
https://www.researchgate.net/public...oins_Carried
Edited by tdziemia
03/24/2020 10:27 am
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United States
1543 Posts
 Posted 03/24/2020  10:33 am  Show Profile   Bookmark this reply Add hfjacinto to your friends list Get a Link to this Reply
Well I was off on Lincoln Cents, according to the article around 76% are tossed/lost every year. Or maybe they are all in glass bottles saved for eternity.
Valued Member
Canada
89 Posts
 Posted 03/24/2020  1:55 pm  Show Profile   Bookmark this reply Add Silver101 to your friends list Get a Link to this Reply
So, first of all, thanks for that link @tdziemia - incredible! I guess the answer to all questions is now yes right? I mean, are there any thoughts left that haven't been thought? Also, Journal of Statistical Numismatics...do you have any idea how many of my nerd buttons that pushed? Thanks for making my day!

Stay safe coin weenies: please wash your hands!
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United States
3162 Posts
 Posted 03/24/2020  3:05 pm  Show Profile   Bookmark this reply Add tdziemia to your friends list Get a Link to this Reply

Quote:
The circulation rate for one cent coins in the US was 0.34 in 1995 (Gadsby 1996)


Maybe more like 66%?

But remember, we are part of that loss rate every time we pull a wheatie out, or save our change in a jar. It doesn't necessarily mean the coins are lost.
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United States
3162 Posts
 Posted 03/24/2020  3:07 pm  Show Profile   Bookmark this reply Add tdziemia to your friends list Get a Link to this Reply

Quote:
Journal of Statistical Numismatics...do you have any idea how many of my nerd buttons that pushed?


If I could get more interested in statistics (rather than in the actual coins they represent), maybe my bank account would be healtheir.
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United States
1543 Posts
 Posted 03/24/2020  3:08 pm  Show Profile   Bookmark this reply Add hfjacinto to your friends list Get a Link to this Reply

Quote:
Maybe more like 66%?


Ooops typo. (I'm sticking with the typo, NOT that I can't subtract 34 from 100)
Valued Member
New Zealand
326 Posts
 Posted 03/25/2020  7:13 pm  Show Profile   Bookmark this reply Add Princetane to your friends list Get a Link to this Reply
I think a lot of people hoard coins.

It mentioned in a book about NZ Predecimal coins when they were recalled, some denominations had less than half of all the coins turned in and souveniring was rampant.

I would say at least 10% of all coins minted each year are lost at sea, in the ground, accidentally or deliberately destroyed.

As you all know, banknotes is usually recalled when tatty and destroyed. When I visited the Reserve Bank of New Zealand in 2013, one souvenir you could buy was 4 by 6 inch bag about 2 inches (10 x 15 x 5cm) full of minute particles of shredded banknotes, mostly $20s.
Loving Halfcrowns. British and Commonwealth coins 1750 - 1950 and anything Kiwi.
If it's round, shiny and silvery I will love it.
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United States
1208 Posts
 Posted 03/25/2020  9:49 pm  Show Profile   Bookmark this reply Add fortcollins to your friends list Get a Link to this Reply
Several factors influence circulation of particular coins or denominations.
Intrinsic devaluation quickly drives out coins with higher intrinsic value (Gresham's Law). This can be seen with CNC replacement of 90% silver coinage in the U.S. and with nickel and plated steel replacement of 80% silver coinage in Canada.
Convenience can drive out coins that are less convenient. Small cent replacement of large cents and nickel five cent replacement of silver five cent coins are examples. The large cents were awkward compared to the small cents, and the tiny fish scales were too easily lost.
Design changes can make earlier designs disappear prematurely. Advent of the Jefferson nickel in 1938 hastened the exit of the Buffalo nickel from circulation. Conversely, popularity of the Kennedy half dollar in 1964 caused their withdrawal from circulation, leaving later date Franklin half dollars still circulating until replacement of the 90% silver coinage made all of them disappear.
Awkward denominations disappear because of the disdain for the denomination. As an example, twenty cent coins proved far less popular in commerce than twenty-five cent coins, leading to premature withdrawal of twenty cent coins.
Functionally useless denominations disappear because they are not worth circulating. The one cent piece in Canada became that way long before withdrawal of the denomination. They are not functionally circulating in the US either.

A better study would be the lifespan of popular longer-term denominations that have not experienced recent design or metallic changes. In the U.S., that would include Jefferson nickels and CNC Roosevelt dimes.

Just my two cents' worth. Oh wait, they don't circulate either.
Valued Member
Canada
89 Posts
 Posted 03/26/2020  07:33 am  Show Profile   Bookmark this reply Add Silver101 to your friends list Get a Link to this Reply
Yes for sure. I think when I started thinking about this I was imagining a sort of idealized scenario that eliminates things like what you describe @fortcollins. I think you could only describe a meaningful half life under fairly strict conditions.

So, if Queen Victoria had lived for another century and Canada had continued to mint exactly the same coins as in 1876 straight through to 2000 - no errors, none of the obsessive 1903H large H, small H sort of business. Indeed, none of the H/ no H business either. Everything would have to have been produced at the same Heaton mint by the same guys using the same apparatus. And I guess also prices would have to have stayed the same so that the relative values of 1c, 5c, 10c, 25c and 50c would be fixed.

Still, there's definitely something to the idea: even if all other things *aren't* equal, smaller denominations disappear quicker than larger denominations and high grade 5c tend to be more scare than high grade 50c; even though the numbers minted might be identical. Different theoretical half lives.

I may put this on my next mid-term.....throw my students into a complete death spiral!
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United States
3162 Posts
 Posted 03/26/2020  08:03 am  Show Profile   Bookmark this reply Add tdziemia to your friends list Get a Link to this Reply

Quote:
Intrinsic devaluation quickly drives out coins with higher intrinsic value (Gresham's Law).


I understand your point on this, and it rings well with common sense when there are abrupt changes (like from, silver to CuNi), but multiple studies have shown that in normal circumstances, the "loss rate" of low denomination coins is highest.


Quote:
I may put this on my next mid-term.....

@Silver, What do you teach?
Edited by tdziemia
03/26/2020 08:07 am
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