IS-LM Watch: Three Ways of Looking at a (Closed-Economy) IS Curve: Karl Smith Raises My intelligence Department

1) The way I was taught: the national income identity:

Y = C(Y-T) + I(r) + G

Spending (the right hand side) must equal production (the left-hand side, which is also income). If spending is greater than production, inventories fall and businesses hire more workers, raising production and income.

2) The way I found in Hicks's (1937), "Mr. Keynes and the Classics": the Wicksellian flow-of-funds through financial markets:

S(Y - T) = I(r) + [G - T]

Planned borrowing (the right-hand side) to finance investment by businesses I plus borrowing to finance the government deficit G-T must equal saving (the left-hand side). If planned borrowing is greater than saving, firms must cut the prices of the bonds they are issuing and so the interest rate r rises.

3) Now Karl Smith comes along with a third way: bank lending: the BL curve:

S(Y - T) = BL(i; π, ρ)

Planned savings (the left-hand side) must be equal to bank lending (the right-hand side). Bank lending is a function of the short-term safe nominal interest rate i (that is the cost of funds to well-capitalized banks, the expected inflation rate π, and a risk premium ρ that depends on (a) the average quality of the loans that banks are making and (b) on banks' risk tolerance. If planned savings are greater than bank lending, businesses find that they cannot go forward with investment projects and so spending falls below planned levels, pushing income and savings below planned levels as well.

As Karl writes, this third approach brings to the foreground things that are hidden in (1) and (2). In (1) and (2) of course an increase in government spending holding taxes constant shifts the IS curve: it raises the right-hand side while doing nothing to the left-hand side. But in (3), the reason that an increase in government spending holding taxes constant increases bank lending is that it raises the quality of the average borrower and so reduces the required risk premium ρ:

Government borrowing changes the game... because the government is... always a good credit risk. Indeed, in a world where reserves are swapped for government bonds [because the government can always print reserves] the government can’t not be a good credit risk.  Thus a rise in government borrowing suddenly makes overall lending safer and the BL curve moves out. Governments which may directly default (rather than inflate) lose traction.... It is not at all clear that Greece can move the BL curve...

This is, I think, a genuine insight. It is not something that I had ever thought of before, and I am a smarter person this afternoon than I was this morning.