national debt

In the past couple of years, politics seems largely to have given up on the idea that the federal deficit is of any importance; some people go so far as to actively say that it doesn't matter.  There is some truth to the statement that the budget constraint is a bit different for a government than for an individual, but I do believe that it represents some kind of (fuzzy) constraint, with some kind of attendant (hard-to-price) cost associated with incurring more debt.  Right now, though, I want to think about it from a different angle than the idea that, at some point, we would be unable to borrow more money or buy goods with the money we can print.

For a closed economy, total savings equals investment; investment in new capital is one of the important factors in the long-run increase in real wages.  With an open economy, people from other countries can invest in US capital as well, so we get an accounting identity

federal deficit + investment = private savings + trade deficit

If the federal deficit were to come down, investment would go up, or private savings would go down, or the trade deficit would go down.  What I'm wondering is how much of each would be likely to happen?

Presumably it depends on the details -- at the coarsest level, a tax hike would probably have a different effect than a spending cut, and it seems likely to matter which tax you hike or which spending you cut.  It seems like we ought to be able to say something useful about a general tendency, though, perhaps with caveats.  Twentieth century macroeconomics would suppose that this is intermediated through interest rates, and would probably expect all three to absorb some of the change, with the portion depending on how sensitive investment, private consumption/savings decisions, and foreign trade partners (including foreign exchange markets) were to interest rates.  The identity holds regardless of mechanism, though, and interest rates don't seem to have been obviously responsive to government deficits; perhaps more importantly, I don't think the people who deny any meaning to the deficit could be persuaded by this mechanism.  The identity itself, however, is pure arithmetic.  Something must give.

So what happens when the government gives a bunch of money to a group of people, whether in exchange for goods or services or not?  In the latter case, those goods or services and/or the scarce resources that went into their production are no longer available; a Keynesian might believe that some nonscarce resource is being newly employed, in which case that's not a factor.  If you're removing a consumer good from the market and prices aren't changing, it seems that you're forcing private savings or the trade deficit to change; if you're removing more of a capital good, perhaps you expect investment or the trade deficit to change.  If you hand out the cash and it doesn't go anywhere, private savings is what automatically absorbs it at the first instance, but it seems likely that a lot of it would quickly go to investment or trade deficit.

While correlation is, of course, not causation, if I really wanted to pursue this a first thing to do would probably be to look at data on these four variables and see both which linear combinations change the most and what the time behavior looks like over the course of a year or two.  I would think that the federal deficit is the most exogenous of the four, and that interpreting the correlations as exhibiting the causal effect of federal deficits would be a good first pass, but I would hope more generally that some regularity would suggest a next step in the investigation.