Causes of trade deficit: Multiple views
Often a good answer consist the most of shedding light on some aspects of the terms of the question itself. I hope a couple of remarks could be useful.
About causality, the fact is that current deficit implies reserves exit from USA, which only can be supported by reserves entering, otherwise resulting in a diminishing stock of reserves, eventually exhausting it. A capital-account superavit --net inflow of capital-- represents an inflow of reserves, in that sense financing trade deficit (see Economic Report of the President, 2004). Letting aside causality --which can be very complex and call for other matters-- both imbalances are bond to present themselves simultaneously. In other terms, the fact that trade deficit and capital superavit pop up strongly correlated doesn't mean a causality. I suspect --sorry again for the lack of evidence-- that there's no causality there indeed. Instead, those paths suggested in the question about rates of interest or foreign exchange rates could be more promising sources of explanations, probably besides productivity and cost structures (again, see Conclusions in Economic Report of the President, 2004). It would be an example of third -unknown- causal factor.
About repaying the debt with capital inflows, we have to keep in mind that those capital inflows are new debt. For example, see Kirabaeva, Koralai &amp; Razin, Assaf. (2010). Composition of Capital Flows: A Survey, NBER Working Paper Series. Aside with debt-instruments, capital inflows also comprise equity-instruments, i.e. Foreign Direct Investments and equity purchases. Depending on the context, even the last ones could also be considered national 'debt', as it represents foreign ownership of 'local' firms.
Interestingly, the &quot;US's control to decide what to do with the capital we get&quot; reflects the conflation in an unique agent &quot;US&quot; which in practice is a set of --millions of-- firms, consumers, authorities... There is no central control on the employment of all those flows, even though all those agents are acting, and controlling, in the USA, in that sense all them constitute &quot;US's control&quot;.