But these estimates always seem to hold velocity of money constant; ie, they assume that the velocity of bitcoin in these situations would be the same as dollars or whatever they're comparing to. Is that true?
On the last day of the month, starting about an hour before midnight the parking lot at Walmart begins to fill. That is because when the clock strikes twelve, the customer's funds become available for spending and the cashiers become very busy.
If those funds were to be tracked, they would likely turn over several times over a couple of days and thus have a high velocity for that short period of time.
Then take the example of me sending in a payment. Before writing the check I had to deposit adequate funds. These funds took several days before the amounts I deposited were available to me for spending. I then write the check and mail it to my creditor. Several days will pass before the amount of that check is drawn from my account.
It might seem that there was a low velocity there, because there was maybe 10 days from when I received the money to when it was drawn from my bank account. But while those funds were in the bank, they were loaned out, and with fractional reserve ... maybe 9 times as much as I had on deposit was loaned out.
So the payment network being slow didn't really hurt the velocity -- those funds could still have been responsible for turnover that occurred.
With bitcoin though, we have no fractional reserve yet (that we know of). So every day that a bitcoin isn't "in play" velocity of the money supply is reduced. Countering that is the fact that transactions received are available for spending within minutes. That will cause velocity to be able to increase -- assuming the recipient wants to spend. Consider that Walmart example above. Spending by those without access to credit will often occur as soon as those funds are available. So the faster payments clear, the higher the velocity potential.
I just made the concusion that for those without access to credit there is an advantage to receiving bitcoin funds (wages or trade revenues) over receiving funds through the legacy banking networks. But I'm not an economist. Most economists refuse to believe that bitcoin has any use in this world and thus, I suspect, they won't be considering what effect faster clearing times has on Bitcoin's velocity of money.
Here's a little more from those who, umm ... aren't big fans of bitcoin: http://forum.bitcoin.org/index.php?topic=11627.msg167838#msg167838