Scott Sumner writes
Now as we all know, [Krugman’s] model is wrong. It predicts that core inflation will plummet steadily lower when in a liquidity trap. If the Fed is targeting inflation, then there is no liquidity trap, no paradox of thrift, no paradox of toil, no fiscal multiplier, no “Depression economics.” And as we saw in 2010, when the Fed observes core inflation fall below their 2% target they do policies like QE, and extended promises of low interest rates, in order to raise core inflation back up near 2%
I am not sure exactly which model Scott is referring to, but in Paul’s standard story concerning Japan the liquidity trap comes about because the Central Bank is targeting inflation or at least people believe it to be.
Indeed, in that model if the central bank were willing and able to target Nominal GDP then the liquidity trap would disappear.
c = y = D-1 y* (P*/P) (1+i)-1
where c is consumption, y is real income P is the price level, D is the discount factor, i is the nominal interest rate and * indicates long run values as opposed to current values.
NGDP targeting implies P*/P = y/y*
c = y = D-1 y* (y/y*) (1+i)-1 = D-1(1+i)-1y =>
D = (1+i)-1 =>
If D < 1 then i > 0
and so there is a non-negative nominal interest rate that clears the goods market.
In the current context the interpretation would go like this. The Fed would assure the public that NGDP would grow at 5%. Thus, if for any reason real GDP collapsed by 6% in 2008 – 2009, the Fed would produce 11% inflation so as to ensure that Nominal GDP did not fall.
However, knowing that 11% inflation was coming real GDP would likely not fall as much. If I am reading Scott right then he suggests that the real GDP would not fall at all.
My take would be that both real GDP and inflation would likely fall in the face of something like the banking failure. However, the promise by the Fed to bring nominal spending back to path as soon as possible would cause a more rapid turnaround than we saw because there would have been an even more aggressive expansion of business investment and faster recovery in the stock market.