attrition rates from circulation
cinclodes
Posts: 66 ✭
Has anyone ever done a mathematical study of the attrition rate of coins from circulation? It may be obvious from this question that I'm a mathematician. A simple (but probably pretty good) model would be that a certain percentage of coins are lost from circulation each year (the attrition rate). The rate probably varies from denomination to denomination and with time and other factors. People would be more likely to safeguard higher denominations, and it's probably harder to lose larger coins. The attrition rate would be expected to vary as the economy gradually evolved from cash transactions to credit. The attrition rate probably changed for certain coins as interest in coin collecting evolved, as the minting of regular gold and then silver coins were terminated, etc. One way to obtain data for such a study would be to find hordes of coins that were saved years ago (with no emphasis on dates) and perhaps even from wishing wells and other places where coins are thrown. It would be interesting to obtain estimates of when certain rarities and old designs began to vanish from circulation. For a simple study one might assume a constant attrition rate, try different values, and search for a value that is consistent with a known date when a certain coin started to become scare (e.g., the buffalo nickel by the mid 1960s).
Comments
That would be an incredibly complex study....and I am not at all sure such information, if indeed there was any way to gather it, could be even reasonably reliable. Having spent many years dealing with studies, analysis and data accumulation, I would be loathe to even approach it. Good luck to anyone who attempts it....Cheers, RickO
Too many variables at play to come up with a rational answer.
I think it would be rather easy to obtain some meaningful results. When dealing with large populations, simple statistical approaches are often very effective at revealing patterns. I will take a shot at it.
You better first define attrition.
Zincoln cents will corrode away to nothing, but most other U.S. coins will continue to exist indefinitely even if temporarily "lost" or virtually unidentifiable.
You also need a non-linear model. Precious metal coins were rapidly disappeared from circulation in 1965 even though they circulated for a century before that. Wheat cents disappeared from circulation fairly rapidly in 1959 with the design change, though not as rapidly as the silver coins in '65.
I'm also not sure what meaningful result you would obtain. So 0.03% of coins attrit per year... Great. I've just learned that virtually every coin ever minted still exists somewhere in the environment.
US Mint’s...
Reports: https://www.usmint.gov/about/reports
FOIA Reading room: https://www.usmint.gov/foia
Then there’s the Federal Reserve...
https://www.federalreserve.gov/paymentsystems/coin_about.htm
Reports: https://www.federalreserve.gov/apps/reportforms/default.aspx
FOIA Reading room: https://www.federalreserve.gov/foia/about_foia.htm
Some mintages contain large numbers of coins that never make it into circulation.
This is all pretty straight forward math for moderns since the FED has rotated their coin stocks since 1972. Indeed, even meaningful numbers for wear can be calculated since each date has a narrow range in grade caused by said rotation. However, in the last fifteen years the value of quarters has eroded so much that their velocity has decreased substantially. This means that some coins will sit out more often and for longer periods.
Of course numbers for pennies are nearly meaningless since they don't really "circulate" much. Significant numbers are sitting around for years and years before getting back into circulation. Many people just dispose of pennies since they are dirty and have no value at all (negative real value). Nickels circulated well until the LME default in '07 and now they are hoarded by too many people to have meaningful attrition rates. Dimes have long had low velocity and high attrition. This means it's very hard to find the low mintages but when you do they might be very high grade.
Pennies had about a 4% attrition until 1982. Nickels had a 3+% rate until '07. Dimes 3+%. Quarters 3-%. A lot of pennies lost in the woodwork will never come back and this applies especially to the post '82 issues which almost evaporate in air.
The Chicago FED did a rather exhaustive study on circulating quarters back '04 (IMS). I was not able to secure the results but then I'm sure they found essentially the same thing I had been watching since the clads came into circulation 54 years ago this month. Nearly 55% of the early quarters have been lost to time and tide now and most of the survivors are in F condition or less.
It would be interesting seeing the actual numbers rather than my estimates. This is a pretty easy project for a mathematician since the coins in circulation are extremely well mixed by date. Collectors just don't separate these much like in the old days which destroy nice neat equations. Older quarters are even pretty random by mint mark.
With a large sample you might see one thing collectors have been doing in the last 20 years; they have been removing high grades of the better dates. I rarely see any nice pre-1972 quarters any longer other than an XF 1965 once in a blue moon. Even pre-'78 coins are getting a little tough in nice attractive XF. There is a definite skew toward lower grades and culls in the better dates. Somehow about 95% of pre-'80 quarters are culls now because most are just covered with little dings and scratches from vending and counting machines. Quarters used to get enough "normal wear" to remove this damage. Now days they go from bank to store to bank.
Well...
Certainly large numbers of pennies or states quarters or bicentennial quarters were set aside but for the main part this is a small fraction of mintage. Bicentennial quarters didn't circulate much until the end of the last decade but most of these were pulled out of circulation in '76/ '77 rather than saved as Uncs. Now most of them are back in pocket change and have very light wear. I bet not even 2% are still BU. A lot of the recent quarters are higher though.
I did some calculations for nickels for the case of a 4% per year attrition rate. I included the mintages of all nickels from 1866 until 1964. I stopped the calculation after 1964, which was a year when public interest in coin collecting increased (and thus the rate of setting aside obsolete designs may have increased). The above plot shows the percentage of all nickels that are buffalo nickels under this model. The prediction that this design started to become rare in the early to mid 1960s is consistent with my experiences as a budding coin collector back in that period.
I did a study like this for a high school statistics class many years ago. I forget the exact numbers that I came up with, but they were in line with what @cladking posted (small single-digit yearly attrition).
I remember being surprised how close my numbers were to a standard exponential decay once you take variable yearly mintages into account.
This is way cool.
The model didn't work quite as well starting in 1941 because people had money from war jobs and started setting aside much larger numbers of coins including higher denominations like nickels. One cent coins were already picked over by 1941. The Numismatist reported that about 90% of the '09-S VDB's were pulled out or gone by 1944 IMS. Buffalo nickels circulated pretty well in the late-'50's and had a lower attrition rate in those days (probably a little over 3%. The introduction of clad seemed to drive them out pretty fast. By 1965 there were few nice post-1929 nickels (the ones with dates) and most remaining were dateless and/ or culls. These were almost gone by 1970. By early '71 the silver was gone as well.
The attrition on nickels now is likely near 5% because people are hoarding them for their metal. They are big, heavy, and such little value that they are tossed in the trash a lot too.
The actions of collectors and the general public has a large influence on the incidence of a design once a "tipping point" is reached. As soon as the perception a coin is getting rare occurs the coins are pulled pretty fast. Right now only 32% of circulating quarters are the old eagle reverse design. But there should be no rush to save them for years yet but people are starting to notice the earlier dates are getting elusive in higher grades. Whitman (et al) are making a lot of folders for the coins and this has a big impact on higher grades as people select nicer examples for their folders and albums. This process started in 1999 and is accelerating at a high rate right now.
Generally almost everything follows this same model but coins have higher attrition because they are continually changing hands while being dropped and otherwise becoming lost or damaged. Nowadays people won't even bend over to pick up most coins. Then they have little value which leads to more being in the home before redemption so more are destroyed in fires and floods. Cars are like magnets and hidey holes for errant coins and are like piggy banks when they get recycled. The mint was actually accepting truckloads of Chinese counterfeit half dollars purportedly recovered from recycled American cars!!! City incinerators generate very large volumes of burnt coins for redemption every day.
I believe mintages are staying so high not to supply a growing economy so much as to replace the nearly worthless coins that suffer such high attrition. Quarters are a little harder to figure since they do have some value and their mintages are high as well. It's probably not caused by hoarding or there would be less premium on the numismatic coins and BU rolls.
I am a coin hoarder and have jars of coins all over the house. Conservative estimate would be around $1700 face across the spectrum of cents to half dollars (don't save the dollar coins, give them away as tips when we go out to eat). So, that's not a huge amount of change to take out of circulation but my family has no interest in it except as face value so upon my demise they will take all the jars and loose change laying around and cash it in either through the change counter at my bank or through coin star, depending on which one is open as I'm still cooling. So, even though that amount was taken out of circulation over the course of 5 to 10 years, all at once it will return to circulation. Multiply that amount by the number of potential coin hoarders and it comes to a pretty penny (oh, and this includes people overseas, When stationed in England and visiting with English neighbors they brought out their treasure trove of coins left there during World War II and passed down through the family from American service men. These coins will probably never return to circulation and it was a hodge podge of nickles, dimes, quarters and half dollars, oddly no cents).
If I can find it and dust it off, my son did a statistics problem in high school (he is 25 now), and he got $1000 IIRC, 50 cent pieces, and mapped out what was in the boxes versus what the mintage was. I had to help figure out some of the outliers (No coins prior to 1970, IIRC or only a couple), 2 silvers (1 walker 1 Franklin), a couple proofs, and nothing from the latest 7 or so years, but a few proofs (Mint Set only or bag sales, etc.)
The short version was that the older halves were OVER REPRESNTED slightly (except for the anything with silver or proofs). The Bicentennial was the highest % found relative to its mintage. Possible for the aberration was that people had hoarded the earlier coins, got them over the "loss" hump, and now they were being returned. This was also during the recession, so maybe it had jarred loose some micro hoards.
It is probably not representative as people don't circulate 50 centers' and tend not to lose or just toss them.
I would think 5 cents would be the best test as they do not have the wheat cent or composition change, or possibly the dime, albeit have to ignore mintage before 1965.
On a related note, I get all my mom's mail as she is "a bit out of it" now, and get 5 - 10 charitable requests per day. I get to keep any coins that come to try and guilt me into making a donation, and last week, there was a 1940 glued to the paper.
I would be interested in the article where this was reported and how the estimate was obtained. For an attrition rate of 4%, the population would be reduced by only 76% over that time period. So the number would be consistent with a considerable amount of selectively pulling that coin from circulation.
I should have it around here someplace. I'll look when I get a chance.
Here is a plot for the Indian Head penny for an attrition rate of 4%. My grandmother got me interested in coins in the early 1960s. She mentioned finding Indian Head pennies in circulation. I wish that I had asked her how often she would find them in the 1930s and 1940s.
Something similar used to happen with endangered birds. Once a species was perceived to be nearing extinction, there would be a push to collect specimens for museums. In the case of the Ivory-billed Woodpecker, for example, the last known populations were wiped out along several river basins in the southeastern U.S., and this helped push the species to the brink of extinction.
For coins, I would guess that the "tipping point" would be around ten percent. If that is the case, I would guess that the Indian Head penny was essentially gone from circulation by the late 1940s. I know from my own experience that the Buffalo nickel was essentially gone by the late 1960s.
Another memory that I have from collecting coins in the 1960s is that pennies from before 1940 had become very hard to find. There was a sharp cutoff. Dates from 1940 and later were still easy to find. In particular, 1944 was still very common. I would enjoy hearing recollections from others regarding the apparent rarity of coins during that period and, especially, earlier.
These both sound about right. In 1957 when I started there were still indians but all were heavily worn or culls. Buffalos abounded but the better dates had been removed by collectors. There were still some higher grade common dates but pre-'26 issues tended to be worn AND common date. You could find a F 1920 but an '18-D would be very elusive because of collectors filling folders.
It's surprising how well copper memorials are "surviving". But to understand this I think you have to consider how pennies "circulate" now days. People hold them for many years and then they dump them back to the bank. Meanwhile the new zinc coins just don't hold up and are being continually destroyed by oxidation leaving the copper behind. This allows the copper to remain fairly steady at 15 or 20%. That the zincs are disappearing so rapidly isn't readily apparent but they have a huge attrition rate and it's even higher for some dates that have plating issues like the '83 and '84.
A similar thing is occuring with the wheaties which have had a small and fairly steady representation in change for a long time now. As fast as they get snapped up more return to "circulation". There are billions of these made from the '30's to '50's and a small percentage are in circulation at any given time meaning average grade is not decreasing (significantly).
Any attrition study would have been more interesting before people started collecting from circulation in 1999 and the FED amended their FIFO accounting (processes) the same year. But it's fairly easy to factors out these changes to see the attrition rates and nature on dimes and quarters.
Every year that goes by reduces the velocity of coins because they become more and more "worthless". As the velocity decreases the rates of wear decreases and the percentage of coins that are preserved for longer periods increases. ie- the odds that a specific coin will experience very little wear even over a ten year period soars.
Circulation of coins has fascinated me from a very young age and is one of the chief reasons I collect at all. I was surprised when I was told that it didn't matter which quarter you tended at the grocery or filling station! The implications of this just seemed staggering and trying to understand how each moves about seemed rather complex. So I just keep watching them and trying to understand the story they each tell, and trying to understand what the movement says about the economy and its facets.
It was the introduction of clad that destroyed collecting from pocket change to most people in the '60's. All of a sudden there were no old coins except some pennies and nickels and people started pulling them fast. By about 1967 there were no buffalos except slicks and culls. There were lots of wheats but people pulled them based on decade. The steels that had previously been shunned disappeared first and then most issues before 1940.
There were millions of baby boomers collecting coins in those days and lots of older people saving out silver. When the FED started pulling silver in mid-'68 it was the death knell for circulation finds for a decade. Most people never noticed how interesting circulating coins had become and still haven't.
Also because fewer and fewer transactions are in cash. The "chip" credit cards make it convenient to make even small purchases with CC, avoiding the time and hassle of fumbling around with change. "Cash back" credit cards add another incentive to switch to cards.
My Adolph A. Weinman signature
I wonder what the attrition ("melt") rate is for silver coins, and how many are left. I've seen estimates of up to 90% of common date silver dimes, quarters and halves being melted, and possibly higher for war nickels. This might turn some of the lower mintages into semi-keys without anyone realizing it.
My Adolph A. Weinman signature
This has been a fascinating discussion of a topic that has always interested me. Thanks to all for the inputs. I did a final calculation. Assuming an attrition rate of 3%, the quarters remaining in circulation in 1964 would have been about 4% pre-1940 and would have totaled about $12 billion. For this calculation, I didn't take into account the fact that some of the 1964 dated quarters were actually minted after 1964. I didn't attempt to go beyond 1964 when silver hoarding commenced.
Correction: There was a typo in the code -- make that $750 million.
I don't have time now to comment much but the attrition rate on quarters was far lower back in the '40's and '50's. It was probably about 1.75% in 1939 and 2% in 1964. Even by 1970 (clad) it was up to only about 2.25%.
Most of the silver 1963 quarters still exist because the attrition rate dropped to under 1% when they were pulled out. Of course melting in 1979 and 2008 took many away and the FED recovered nearly 30% from circulation in '68 which were all destroyed. Probably about 55% of 1963 quarters survive but only 45% of 1966. The silver still has a low attrition rate and the '66 has almost 3.25%. '66 quarters have little value and they are all slick, have low rotational inertia, and are thin which contribute to them being destroyed. The FED removes some damaged and worn coin from time to time which will also spike attrition rates. A significant proportion of '66 quarters (25%) have damage or corrosion which also can lead to them being culled out.
I think private melting destroyed much more of the 1963 and other silver mintage than your post would suggest. The melts in 1979-80 were huge, and they weren't the only ones. The premiums on bags of 90% silver often went negative during the 1970's through the early 2010's, sending many of these coins to the smelters. Ditto for war nickels, which were being melted in quantity even before silver coinage was discontinued in 1966.
My Adolph A. Weinman signature
I remember in the mid 60s, getting Standing Liberty Quarters and Buffalo Nickels from time to time. All of them had the dates worn off. I don't believe I ever found one with the date on it in circulation.
I also remember during that period, that it was rare to find a Walking Liberty Half Dollar or a Washington Quarter dated before 1940.
Velocity is much more dependent on how long a recipient retains them than how many people are using them. It used to be that a coin was in near constant motion from consumer to store and back to the consumer. Now they go from the store to a change jar and sit before being returned to the bank. If everyone were still using cash it would have little effect on this equation.
I find credit card transactions tend to take a lot longer than cash. There should be a charge for using credit instead of a discount.
I don't really know but I've spoken with some of the refiners and the stories they tell just don't add up to very much. They were melting them by the 55 gal drum but would have needed truckloads to amount to very much. I've seen some of their production reports.
I wonder about the poor war nickels as well. Almost nobody seems to like them and they contain a lot of silver. I believe large numbers are used to make electrical contacts but don't know.
These disappeared from circulation a little faster than the silver coins. I don't believe the FED even tried to recover them.
In 1957 there were lots and lots of standing liberties. Many of them were heavily worn post-1924 coins with readable dates. These disappeared by about '63 along with decent buffalos and better date silver.
Nice coins were being selectively removed even before clads came around. Some people couldn't save all their silver so they saved anything interesting. Even as late as 1962 there were still a few Columbian half dollars in circulation. All the coins were already picked clean for key dates and high grades but there were still varieties and recent date Gems.
I was around in 1979-80 when across the nation there were lines around the block to sell 90% silver coins to dealers, often at 25% to 30% back of silver bid. Dealers were shipping the coins to refiners as fast as they came in. Many refiners were going full tilt with backlogs of several weeks or more. I understand that bags of uncirculated Morgan and Peace dollars went to the melting pots during this time.
Significant private melting also took place earlier in the mid through late 1960's.
My Adolph A. Weinman signature
A bit OT, but although there may be convenience for the person using it, cards sure can be less than convenient for the people waiting in line behind to pay while the cardholder beep-beep-beeps on the touchpad for cashback (Yes/No), receipt (Yes/No), loyalty card (Yes/No), etc.
I pay for my morning cola refill with cash and generally, the cardholder ahead of me isn't out the door (and ends up holding it for me) as I leave.
A couple factors that also need to be considered. The value of the coin relative to the what people made had a big impact. Quarters and up were REAL MONEY (see my notes starting with quarters).
I started collecting around 1964,
Lincolns: Everything except the BIG's were drawn out of circulation. No 09-s, 09-s VDB, 14-D, 22 plain or 31-S. Everything else came from change. My mom would go to the bank and get me $10 or so in cents, and I would paw through them. Several kids my age would trade coins back and forth. Probably once a coin dated 1950 or later was in the album, you stopped looking because they were so common.
Indians: We would find a few worn ones in the lot, but the coin store had a lot of them for 25 cents or less.
Nickles were boring, and all the Jeff's, including silvers, came from circulation, except the 50-D. Buffalos with partial dates were like dirt, but the early ones were no where to be found, and no way to pay the $$ for the early ones.
Dimes: Roosevelts were easy, except for the 46's, 49's and the 55-S. But I got them all eventually. Merc's: Everyone searched for the 16-D, etc. , no one ever found one. Post 1926 or so, it was not hard to find them all.
Quarters: Most all the coins came from circulation, even a 32-D in VG. Never got a 32-S. Filled the book, but it was a lot of work, as 25 cents was just too much to be "spending" to fill a book. Standing quarters, had about 10 - 20 from change, all worn.
Half Dollar: Basically, no can do. Too much money to be tied up, so kids (a huge source for book fillers) could not touch them. No one cared about Franklin's, too much money and too common. Walkers, except for about 8 or so, could be found in change, but only the rich kids could save them.
I probably got less than 10 Barbers of any type ever in change, roll searches, etc.
Silver Dollars: I got 1 a year from my Uncle, and saw them at the bank, but they were too much
$5 Gold: I got one for $5, around 1969 or so. Waiting at the store to buy a record, and the kid in front of me was trying to pay for his record with the $5 gold. The cashier had not seen one, and would not take it. I saw it, offered up a $5 for it, and everyone was happy.
No one I knew even bothered with $1 coins, gold, currency, etc. Too rich for our blood.
As far as silver stripping, I lived near New York City, and in the Sunday Paper, there was the BUY for silver coins, for example, 4.6 x face, etc. I scoured coins from paper route, bank roll searching, even the church offering plate (the treasurer would let me swap them out). I gave them to my dad, who rode the train to NYC Grand Central, and he sold them at a coin shop in Grand Central Station. By 1969, maybe 1970, if was effectively over for change.
This weekend, I went back to check over the codes and input data. Slightly modified curves for the Buffalo Nickel and Indian Head Cent and a curve for the 1914-D Lincoln Cent are posted at http://fishcrow.com (scroll down to the section on Buffalo Nickel Population Model).
It would only be an academic exercise and not really useful to hardly any collector, most of the time.
It's only usually meaningful to those who collect it when the coin is at least somewhat scarce, whether in a quality (range) or in total. This can also include die varieties or some other specialization.
Most coins are so common (even in "high" quality) that it takes outsized proportional attrition where it will ever make any difference to either the price or anyone's ability to buy it.
There is an article on Coin Week now about this topic. The article profiles a book which I think I stall have; bought it around 1985. The one I had purported to identify silver US classics subject to (very) high proportional melting which supposedly had predictive value on the future price.
Problem is the coins were and still are so incredibly common, there won't be enough collectors to absorb the supply at meaningful higher prices, even in UNC or the TPG equivalent grades in use at the time. One coin profiled in my book and the article is the 38-D mercury. Except in higher MS grades, it's been dead money the entire time. The TPG population counts make it evident that this coin is still very common, and so are practically all others which are the subject of this book.
Melting of earlier US coinage was a noticeable factor for some coins. Same applies to some foreign, such as South Africa Union silver but the difference with both is that there were few collectors to save many at the time. Definitely not true of more recent US classics.
I have done a calculation for the Liberty Head Nickel. When I get a chance, I will enter the data for dimes, quarters, and halves and do some additional calculations. Below are corrected curves for the Buffalo Nickel and Indian Head Penny and few other curves.
Out of curiosity, what is your interest in this topic?
Is it academic per my prior initial post here?
Is it to project potential future value per my second post here?
I'd consider it common knowledge that the attrition on most coins of any age has been disproportionate, except where the coins were hoarded in large numbers (many later US silver classics) or the survival rate is abnormally high due to known low mintage.
In my area of focus, I am greatly interested in this topic because I'd like to know what exists to be bought so that I can eventually complete my sets. A disproportionate number are either only available damaged, mishandled in some fashion and often, not at all. This is seldom a factor for US coinage, except for specialization such as die varieties. The coins can almost always be bought with only the price adjusting, up or down.
My interest is a mathematician and coin collector since the 1960s with memories of what was in circulation at that time. I am also interested in the history of coins and the proportions of different designs that would have been in circulation at different times.
There are so many variables in a study such as you propose. For instance, the changes in the gold content in 1834 and the changes in the silver content in 1853 devastated the older, heavier coin populations. Ditto the elimination of silver starting in 1965.
At the start of the Civil War you had massive hoarding of gold and silver coins, which returned to circulation in the 1870s. So much silver came back, most of it dated 1853-1861, that the Mint could cut back on production of dimes, quarters and halves for years. The warehousing of silver dollars for decades before release is legendary.
During the Great Depression a lot of people spent family heirloom coins to survive. I wrote an article in COINage Magazine a few years back about how the Mint Reports of that era showed a jump in obsolete coins such as large cents and even a few half cents being returned to the Treasury for redemption. Other older coins circulated for a while until some collector grabbed them up again.
When I started collecting in the very early 1960's it was not unusual to find low-grade Lincoln cents from the teens in rolls. I only ever found a few Indian cents. Buffalo nickels from the 20's and 30's were not rare, but the majority of Buffaloes found in rolls were dateless due to the design. Low-grade Mercury dimes and Walking halves back into the late teens (when production was high due to WWI) were still around, but the Standing Liberty quarters before 1925 were mostly dateless due to the poor design. Dollars were not common in circulation, but the friendly tellers at my parents' bank occasionally saved one for me and it could be anything from 1878 to 1935.
You can start many an argument here by raising the question of how half dollars circulated. I am getting low on coffee, and will leave that for another day.
Tom D.
Except for the Jefferson, all "circulating" coins have had an extinction event. For Cents, change is reverse x 2, and change in composition. For dimes and up, change in composition.
These event artificially drove coins out of circulation. The Jeffersons had a minor event with the silver WW2 issues.
The current dollar coins do not circulate or even be released in large enough numbers to sample.
However, If you went and got say 10,000 Jeffs from the bank, and sorted by date / mint mark and then graphed them against mintage, it might be indicative of losses. * might include geography (west coast versus east coast for mint mark, etc.) and proximity to a coin shop. By that I mean a local coin shop a few years ago took 6 - 7 full milk crates of Jeffs, except for the 50-d, the silvers, and maybe the 38 39 mint marked, literally 10,000 + coins and was heading to the bank to run them through the counter and be turned in. He had broken down countless albums and was tired of them sitting around, so off they went. If you happened to pull your sample from that pile, it would be invalid.
You could get a copy of MIL-STD-105E to determine what sample size you need for an acceptable AQL.
One more plot for nickels. This one is for all four designs since 1866. It was produced by assuming a 4% attrition rate. Note the symmetry of pairs of curves when two designs dominate. The crossing point near 1940 is a little below 50% because the model predicts that some Liberty Head Nickels were still in circulation. I don't know if that was true, but it would make sense since the Buffalo Nickel was produced for a relatively short time.
Those are wonderful graphs that have zero meaning. You've essentially assumed a rate of attrition and then graphed it. Just for fun, double the rate of attrition and graph it again. It will be just as pretty and just as meaningless. The models do not contain the black swan events (composition changes, hoarding of key dates etc.)
A coin that was hoarded because of numismatic value would not follow a random attrition rate like other coins.
https://researchgate.net/publication/227605710_The_attrition_rate_of_United_States_coins_in_circulation_Some_evidence_from_Federal_Reserve_data
https://jstor.org/stable/42678898?seq=1
https://onlinelibrary.wiley.com/doi/pdf/10.1111/1467-8462.12170
https://gao.gov/assets/660/658599.pdf