I've read various stuff recently on the role of savings behaviour in the causes and effects of current account imbalances, some of which I'd say is rather confused.
It has to be said that this is quite a tricky topic, because it has a number of moving parts, various complicating factors and the common problem of lack of clarity over what is being assumed unchanged when we invoke the ceteris paribus assumption.
Here's one way I think about this question.
We start from the sectoral balances identity that says that private sector net acquisition of financial assets (NAFA) is equal to the public sector borrowing requirement (PSBR) plus the current account surplus (CAS). The PSBR we will assume is a negative function of GDP (Y) and the current account surplus we will assume is a negative function of GDP, a positive function of the GDP of the rest of the world (Y*) and a negative function of the real exchange rate (e). Thus we have for each national economy:
NAFA = PSBR ( Y ) + CAS ( Y, Y*, e )
So, the first question is what happens if the private sector in country A decides to increase its net saving, i.e. if NAFA rises? Well, the answer is that it depends. And what it depends on is a portfolio decision. The portfolio decision here is whether the private sector wants to accumulate domestic public sector assets or foreign assets.
In the first instance, assume that the private sector wants to accumulate domestic government bonds, so that PSBR increases to match the rise in NAFA and the CAS stays unchanged. In order for the PSBR to rise (within our limited framework here), GDP has to fall. And for the CAS to stay constant with falling GDP (and constant GDP in other countries), the real exchange rate has to rise.
In the alternative case, the private sector wants to accumulate foreign assets, so the CAS must rise to match the increase in NAFA whilst the PSBR remains unchanged. As the PSBR is unchanged, GDP is unaffected and the real exchange rate falls to facilitate the rise in the current account balance.
At this point, we need to turn to the implications of this for other national economies. To do this, let's assume there are only two countries, so for the other country - country B - the current account surplus is simply the negative of country A's, and the real exchange rate is the inverse of country A's. Country B has the same sectoral balances equation and we will further assume that country B's NAFA does not change. Y* for country B is Y for country A and visa versa.
In the first instance, where country A's private sector accumulates only domestic public sector debt, country B's CAS is unchanged, because country A's CAS is unchanged. Therefore country B's PSBR is also unchanged and so its GDP is unaffected. Country B experiences a fall in its own exchange rate, but any impact on exports and imports is offset by the change in Country A's GDP.
In the second scenario, country A's GDP stays the same but country B sees a rise in its own exchange rate and a fall (i.e. becoming more negative) in its own current account surplus. As its own NAFA is assumed unchanged, the fall in the CAS implies a rise in the PSBR which implies that country B's GDP must fall. This fall in GDP feeds back into the function for the CAS, but given our assumptions about country A, this only impacts on the exchange rate not the actual level of the CAS.
So, the overall effects are as follows.
1. If country A's private sector wants to save more, the impact depends on whether it wants to accumulate domestic or foreign assets.
2. If it wants to accumulate domestic assets, this will hit domestic GDP and not foreign GDP.
3. If it wants to accumulate foreign assets, this will hit foreign GDP and not domestic GDP.
4. Only in the latter case does a current account imbalances arise.
Obviously, I've had to make many simplifications here. Two of particular importance are worth noting.
First, I have assumed that the portfolio decisions do not depend on the exchange rate. In practice, capital movements are sufficiently fluid in response to exchange rate deviations that they can dominate the real exchange rate in the short term.
Secondly, I have ignored any kind of inflation mechanism in the relationship between the real exchange rate and the level of GDP. If, in fact, certain levels of real exchange rate create unmanageable inflation pressures, then domestic policy is likely to respond by influencing the NAFA or the PSBR and this will have knock-on effects for the analysis.
Notwithstanding these points, I think the general conclusions still apply. This would mean, for example, that the ability of the US to run a persistent current account deficit is not so much about absolute savings behaviour in the rest of the world as the attraction of the dollar as a vehicle for saving.
 The real exchange rate here is expressed as the number of foreign currency units that can be purchased for one unit of the domestic currency.
 In my opinion, the role of portfolio decisions is one of the most important themes of post-Keynesian economics. It underlies liquidity preference and it goes to the heart of why the role of banks matters to macro-economic outcomes.