There is no gold/specie transfers under a floating exchange rate regime because neither is a monetary instrument now.
There can be a trade deficit (X>M) in equilibrium under a floating exchange rate but it is not the same thing as a trade deficit under a fixed exchange. Under the former the excess supply of dollars causes the exchange rate to fall until a new equilibrium is reached. Under the latter the outflow of gold/specie reduces the money supply within the country causing income to fall, prices to fall and imports to follow. Exports will increase because the domestic price level deflates.
I don't see any necessary reduction in the money supply due to the deficit in the first case as there is in the second.
You describe the BoP deficit occurring if the authorities intervene to prevent the dollar from devaluing. How is that any different from saying that there is no deficit under a true floating exchange? Never mind, I meant to say BoP deficit earlier and said Trade deficit.
Heller defines "the balance of payments as the difference between the quantity of dollars demanded and supplied in international currency markets."
Yey! You've got it straight now! That's a nice, succinct description. Could not have said it better myself. :)
I don't see any necessary reduction in the money supply due to the deficit in the first case as there is in the second.
You're correct.
You describe the BoP deficit occurring if the authorities intervene to prevent the dollar from devaluing. How is that any different from saying that there is no deficit under a true floating exchange? Never mind, I meant to say BoP deficit earlier and said Trade deficit.
Exactly right. Didn't I tell you earlier that you had the BoP and trade deficits mixed up? I'm glad to see we're not the same page now! :)
Heller defines "the balance of payments as the difference between the quantity of dollars demanded and supplied in international currency markets."
Yes, that's a good definition and it is equivalent to the one I gave you earlier, though described in different terms. If the capital account and current account don't balance (my definition), then you must have either excess supply or excess demand for dollars.
Under floating exchange rates, you by definition can't have excess supply or demand for dollars, since the exchange rate will so that demand=supply. The same mechanism ensures that the capital and current accounts balance.