Pesky Trade Deficit

Let's use national income accounts to prove that the trade deficit is equal to capital inflows. If Y, income, equals consumption, C, plus Investment, Ig, plus Government spending, G, plus Net Exports, Nx, the Y - C - G -I equals Nx. The terms on the left represent savings, S. So our equation becomes S - I = Nx. Because the balance of payments uses double entry accounting Nx = KI. Rearranging this equation becomes 0 = KI - Nx. If Nx is less than 1, then KI + Nx = 0.
Wow, is this esoteric or what? Why have I taken the time to do this rigorous algebra. Because a trade deficit means that we are selling off part of the United States. According to my textbook, 4.3 trillion of US assets are owned by foreign countries. This is 37% of US GDP.
What does high government borrowing mean? Higher interest rates that might crowd out investment. Foreign countries might doubt our ability to repay our debt. Lastly, there's the threat of inflation through government borrowing.