I have seen a lot of ways to arrive at the sectoral balances identity, which states that the sum of the change in net financial assets of the private, the public and the external sector sums up to zero. I prefer to show my students six equations – hence five steps – to make them understand the nature of the identity. We start with two definitions (in bold), which are those of GDP (Y) and private saving (Sp). From there, we arrive at the sectoral balances through rearranging the private saving equation, then subtracting the GDP identity from it and rearranging again:
(1) Y = C + I + G + EX – IM
(2) Sp= Y – C – T
(3) Y = Sp+ C + T
(4) 0 = Sp+ T – I – G – EX + IM [eq. (3) – eq. (1)]
(5) Sp – I + T – G + IM – EX = 0
(6) (Sp – I) + (T – G) + (IM – EX) = 0
This is not rocket science, but in terms of macro state-of-the-art. As I am currently building a textbook around this identity, keep on coming back to my blog to see some more stuff related to this way of theorizing macroeconomics that was pioneered by Wynne Godley and others before him.