The dollar wars have raged for years, with various sides battling over what a dollar should look like: Should it be a green piece of paper (cotton, actually) that you can slide in your wallet? Or should it be a metal coin that you put in your pocket?

On one side are the vending machine companies, the miners, and anyone who has traveled enough in Europe to know the convenience of a coin worth one or two euros or pounds. On the other side is Crane, the company that makes the paper for dollar bills, and the banks and retailers that prefer the convenience of paper bills.

A working assumption has been that coins would be cheaper, in the long run, for the government. They cost more to make but last much longer than paper money. The Government Accounting Office estimated the move could save $4.4 billion over the next 30 years. Others have been doubtful that such savings would materialize, as Wonkblog's Brad Plumer details here.

Now, researchers at the Federal Reserve are weighing in, and they, too, find that getting rid of $1 bills entirely wouldn't be the panacea that some analysts have claimed.

The most important points of the new working paper, by Michael Lambert, Shaun Ferrari and Brian Wajert, boil down to this: Coins aren't all they're cracked up to be.

Much of the apparent benefit of moving to coins comes from the fact that people typically store dollar bills in their wallets until they spend them. By contrast, people use coins differently than bills, often dumping them into a jar every day and storing up a horde of coins for years or even decades.

When people hold onto physical money rather than spend it or deposit it into a bank account, they are effectively giving the U.S. government a zero-interest loan. Because people would be likely to store more of their dollar coins, rather than spend them the way they do dollar bills, the government would have to make a lot more of them. The profit the government makes from its ability to print money is known as "seignoraige," and one of the big open questions is what a shift to coins would do to U.S. government seignorage earnings. The answer is less clear-cut than it may seem.

"Although many of the costs to replace $1 notes with $1 coins occur in the near term, seigniorage income from $1 coins that replace $1 notes accumulates over a substantial period of time. Uncertainties such as future discount rates, replacement ratios, and substitution away from cash introduce significant downside risk as it relates to the premise that future seigniorage income will be sufficient to offset the upfront costs from producing sufficient stocks of $1 coins to supply the public. But it also costs more to make coins than it does to make bills." (Separately, the report finds that each coin costs 33 cents to produce, versus about five cents for a $1 bill).

Beyond the government, the costs could be even greater. The Fed researchers found a range of other potential costs, including higher risk of counterfeiting (apparently counterfeit one-pound coins in Britain are a major problem). And for the private sector, banks and other cash-heavy institutions would have to spend a lot of money up front to prepare vaults and coin handling equipment for the change-over (a cost ranging from $10,000 for a medium-sized bank to $28 million for a large bank), plus more each year for worker's compensation, armored-car expenses and equipment.

Add it all up, and this is their conclusion: "We find that, in general, requiring the use of $1 coins instead of $1 notes for transactions is inherently inefficient, as the public would have to replace one $1 note with more than one $1 coin. Replacing $1 notes with $1 coins is also not cost-effective for the government and other payment system participants, primarily because the higher cost to produce coins compared with notes is not offset by the longer life of the coin. Our sensitivity analysis finds, furthermore, that circulating only $1 coins costs more in every scenario (in net present value terms) than continuing to provide $1 notes to the public. Additionally, information from surveys and focus group interviews indicates that increased costs to the private sector could be hundreds of millions of dollars per year and could offset any seigniorage revenue to the government."

So, if the Fed analysis holds, Federal Reserve Notes in one-dollar denomination may have some life in them yet.

Update: Perhaps not shockingly, advocates for the dollar coin do not much care for the Fed working paper. Here is a fact sheet from the Dollar Coin Alliance with their counter-arguments.