As I understand it, if the US government runs a deficit then it (for the most part) "pays" for that deficit by "selling" government bonds. This tends to drive up interest rates somewhat, but also, since the US government is so "trustworthy" as a debtor (and pays fairly attractive rates), it attracts investment from non-US sources.
The net of this is that running a deficit will tend to raise the "value" of the dollar (affect exchange rates) since money coming into the country to buy bonds must ultimately be "bought" with other currencies, and supply/demand dictates that this one-way flow will drive up the dollar and drive down the currencies being exchanged.
The question is, is there some way to (very roughly) calculate HOW MUCH the value of the dollar is affected by the deficit and associated bond sales? This would imply of course having some rough estimate as to what % of bonds are bought by non-US buyers and also some way to estimate how much the money flow implied by these purchases affects exchange rates. (Plus probably two dozen other factors that I haven't thought of.)
Presumably the effect on exchange rates of "exporting" a dollar's worth of government bonds is similar to the effect of exporting an extra dollar's worth of tangible goods in the balance of payments. So if one knows the effect of balance of payments on exchange rates, and can estimate the the % of bonds "exported", one would have my answer.
So, to get me halfway there, what is the best way to estimate the effect of balance of payments on exchange rates (for the US economy)? (I should state that, overall, I'm just looking for an order-of-magnitude answer, not anything precise.)