What trade deficits really mean

Harvard's Greg Mankiw explains in this NYT Upshot column what happens when a country runs a trade deficit.  When imports are greater than exports, this results in lower GDP.   But is this something we should really be concerned about?

Mankiw points out that the trade deficit is accompanied by a foreign investment surplus.  When businesses overseas sell more to us than we sell to them, they have to do something with the funds they accumulate.  In practice that means they either end up buying US assets or make physical investments in the US, e.g., Siemens opening facilities here.  And guess what?  The investment foreign companies make in the US is considerably larger than the investments US firms make overseas.  In other words, there are many more cases like Siemens than like Carrier.  

Viewed differently, US consumers are able to have a higher standard of living by being able to import goods from overseas.  Investors overseas are able to invest in a relatively "vibrant and safe" economy.  So why would you want to mess with this?