When and why does the Confidence Fairy appear? The very sharp-witted Karl Smith has long had a genuinely-different way of looking at the national income identity. I think his approach can shed much light on this question. And it can also shed light on the closely related question of when and whether governments seeking full employment should greatly concern themselves with “confidence”.

Start with the household side of the circular flow of national income: national income Y is received by households, which use it to fund consumption spending C, savings S, and to pay taxes T:

(1) Y = C + S + T

Continue with the expenditure side: Aggregate spending Y–the same as national income–is divided into spending on consumption, investment, government purchases, and net exports:

(2) Y = C + I + G + NX

Substitute the right-hand side of the first for the left-hand side of the second, and subtract taxes T from both sides:

(3) S = I + (G-T) + NX

Now what do investment spending I, the government deficit G-T, and net exports NX have in common? They all require financing. Banks and shareholders must be willing to lend money to and allow firms to retain earnings to fund investment. The government must borrow to cover its deficit. Exporters must find financiers willing to lend their foreign customers dollars in order for them to buy net exports. Add all these three up and call them the amount of lending BL, “BL” for “bank lending”:

(4) BL = I + (G-T) + NX

So we then have:

(5) S = BL(i,π,ρ)

Here i is the nominal cost of funds to the banking sector–the thing the Federal Reserve controls. Here π is the expected inflation rate. And here ρ is an index of the effext of risk on bank lending, and is determined by the balance between the perceived riskiness of the loans made and the risk tolerance of the financial-intermediating banking sector.

Now equation (5) must be true: it is an identity. The level of national product and national income Y will rise to make it true. If something raises BL–either lower i, higher π, or lower ρ–for a given Y, then Y will rise so that S can rise to match BL. If something lowers S for a given BL, then Y will rise so that S can recover and continue to match BL.

This framework hides things that are obvious in the usual presentation, and brings to the forefront things that are usually hidden. As Karl writes:

[If] the government is… a good credit risk… a rise in government borrowing suddenly makes overall lending safer, and so the BL curve moves out.

Thus fiscal policy is indeed expansionary. But in Karl Smith’s framework fiscal policy is expansionary because lenders have more confidence in the government’s debts than in private-sector debts, and so funding government debt does not use up any scarce risk-bearing capacity. And, if we move into an open-economy framework, capital flight–a loss of confidence that diminishes net exports–is expansionary as long as banks have more confidence in the loans to foreigners they are making to fund net exports than in their average loan.

We can then see how fiscal policy might not be expansionary:

Governments which may directly default (rather than inflate) lose traction…. It is not at all clear that Greece can move the BL curve…

because it is not the case that additional debt borrowed by the government of Greece will raise the average quality of liabilities owed to the banking system.

And we can see how capital outflows–a loss of confidence–might not be expansionary: it is not that loans to foreigners will reduce the quality of liabilities owed to the banking system, for the exchange rage will move to make the loans to foreigners high-quality, it is the capital outflow carries with it a reduction in financial-intermediary risk-bearing capacity.

And we can see where the result of Blanchard et al. that capital inflows can be expansionary comes from: when they bring additional risk-bearing capacity into the economy and so raise financial-intermediary risk tolerance, they lower ρ, even with a constant quality of liabilities owed to the banking system.

Karl Smith’s approach requires that all factors affecting national income determination work through their effects on:

• the desired savings rate,
• the nominal opportunity cost of funds to the banking sector,
• expected inflation,
• the risk-tolerance of financial intermediaries, and, last,
• the perceived quality of the liabilities owed to the banking sector.

This is a valid framework. And it is one in which concerns about “confidence” are brought to the forefront and highlighted in ways that they are not in the standard modes of presentation.