As I told my undergraduates yesterday:

Y = μ[c_o + I_o + NX] + μG – μI_rr

where:

• Y is real GDP
• μ = 1/(1-c_y) is the Keynesian multiplier
• c_o is consumer confidence
• c_y is the marginal propensity to consume
• C = c_o + c_yY is the consumption function–how households’ spending on consumption goods and services varies with consumer confidence, with their income which is equal to real GDP Y, and with the marginal propensity to consume
• I_o is businesses’ and banks’ “animal spirits”–their confidence in enterprise
• r is “the” long-term risky real interest rate r
• I_r is the sensitivity of business investment to r
• NX is foreigners’ net demand for our exports
• And G is government purchases.

And as I am going to tell them next Monday, real GDP Y will be equal to potential output Y* whenever “the” interest rate r is equal to the Wicksellian neutral rate r*, which by simple algebra is:

r* = [c_o + I_o + NX]/I_r + G/I_r – Y*/μI_r

If interest rates are low and inflation is not rising it is not because monetary policy is too easy, but because r* is low–and r* can be low because:

• consumers are terrified (c_o low)
• investors’ animal spirits are depressed (I_o low)
• foreigners’ demand for our exports inadequate (NX low)
• or fiscal policy too contractionary (G low)

for the economy’s productive potential Y*.

The central bank’s task in the long run is to try to do what it can to stabilize psychology and so reduce fluctuations in r. the central bank’s task in the short run is to adjust the short-term safe nominal interest rate it controls i in such a way as to match the market rate of interest r to r. For only then will Say’s Law, false in theory, be true in practice:

Martin Wolf: Negative Rates Not Central Banks’ Fault: “It is hard to understand the obsession with limiting public debt when it is as cheap as it is today…

…Almost nine years after the west’s financial crisis started, interest rates remain ultra-low. Indeed, a quarter of the world economy now suffers negative interest rates. This condition is as worrying as the policies themselves are unpopular. Larry Fink, chief executive of BlackRock, the asset manager, argues that low rates prevent savers from getting the returns they need for retirement. As a result, they are forced to divert money from current spending into savings. Wolfgang Schäuble, Germany’s finance minister, has even put much of the blame for the rise of Alternative für Deutschland, a nationalist party, and on policies introduced by the European Central Bank. ‘Save the savers’ is an understandable complaint by an asset manager or finance minister of a creditor nation. But this does not mean the objection makes sense. The world economy is suffering from a glut of savings relative to investment opportunities. The monetary authorities are helping to ensure that interest rates are consistent with this fact….

The savings glut (or investment dearth, if one prefers) is the result of developments both before and after the crisis…. Some will object that the decline in real interest rates is solely the result of monetary policy, not real forces. This is wrong. Monetary policy does indeed determine short-term nominal rates and influences longer-term ones. But the objective of price stability means that policy is aimed at balancing aggregate demand with potential supply. The central banks have merely discovered that ultra-low rates are needed to achieve this objective…. We must regard ultra-low rates as symptoms of our disease, not its cause….

[But is] the monetary treatment employed… the best one[?]…. Given the nature of banking institutions, negative rates are unlikely to be passed on to depositors and… so are likely to damage the banks…. There is a limit to how negative rates can go without limiting the convertibility of deposits into cash…. And this policy might do more damage than good. Even supporters agree there are limits…. [Does] this mean monetary policy is exhausted? Not at all. Monetary policy’s ability to raise inflation is essentially unlimited. The danger is rather that calibrating monetary policy is more difficult the more extreme it becomes. For this reason, fiscal policy should have come into play more aggressively….

The best policies would be a combination of raising potential supply and sustaining aggregate demand. Important elements would be structural reforms and aggressive monetary and fiscal expansion…. Monetary policy cannot be for the benefit of creditors alone. A policy that stabilises the eurozone must help the debtors, too. Furthermore, the overreliance on monetary policy is a result of choices, particularly over fiscal policy, on which Germany has strongly insisted. It is also the result of excess savings, to which Germany has substantially contributed…

One way of looking at it is that two things went wrong in 2008-9:

• Asset prices collapsed.
• And so spending collapsed and unemployment rose.

The collapse in asset prices impoverished the plutocracy. The collapse in spending and the rise in unemployment impoverished the working class. Central banks responded by reducing interest rates. That restored asset prices, so making the plutocracy whole. But while that helped, that did not do enough to restore the working class.

Then the plutocracy had a complaint: although their asset values and their wealth had been restored, the return on their assets and so their incomes had not be. And so they called for austerity: cut government spending so that governments can then cut our taxes and so restore our incomes as well as our wealth.

But, of course, cutting government spending further impoverished the working class, and put still more downward pressure on the Wicksellian neutral interest rate r* consistent with full employment and potential output.

And here we sit.