According to Eggertsson, monetary policy is setting short term interest rates. The variable representing the nominal interest rate has a side constraint--greater than or equal to zero.
Eggertsson shows that aggregate demand doesn't simply depend on the current value of the interest rate, but rather on its expected future value. He claims that this means that demand depends on long term interest rates. However, he manages this with a model that only has "the" short term interest rate. It turns out to be crucial, because long term interest rates don't show up as the yields on long term bonds, but rather are all about expectations of future monetary policy.
Eggertsson also notes that there is an implication for the quantity of money in all this. He gives a money demand function, which presumably determines the quantity of money. He explains that the quantity of money is indeterminate at the zero nominal bound because zero-interest government bonds and money are perfect substitutes. (I never fully trusted the figures provided by the Federal Reserve, but I feel sorry for the statisticians, having to calculate something that cannot even be determined!)
Monetary policy, (setting the short term interest rate,) is assumed to be aimed at avoiding output gaps or deviations of inflation from target. The "modern" liquidity trap exists because the central bank cannot credibly promise to keep interest rates at a low level after a deflationary shock passes and generate an inflationary boom. Real output collapses and price deflation results because no one believes that the central bank will allow real output to rise above target and prices to rise faster than the long run trend during future periods.
It all becomes clear. The Fed is doing its job. It promises to keep the federal funds rate low for a good long time. If people have faith in the Fed, this will bring recovery. But this is faith in the Fed generating an inflationary boom at some future time. Maybe that future Fed will instead revert to its 2% inflation target. And so the Great Recession.
According to Eggertsson, aggregate supply is driven by changes in inflation. I guess this means that if aggregate demand falls, and prices fall, this creates deflation, and leads to an output gap--a recession. If aggregate demand rises, and prices rise again, then this leads to inflation and a boom.
I don't think so. Suppose prices aren't just sticky, but stuck. Falling demand results in lower output, and the current price level is above its now lower equilibrium value. If aggregate demand increases, then output rises again, the economy recovers, and the equilibrium price level rises back up to its existing level.
Suppose some prices are flexible. Those prices fall with aggregate demand. And if aggregate demand recovers, those prices rise again. It isn't that the deflation caused output to fall, and reversing the deflation isn't going to cause an inflationary boom. While real output may grow more quickly than usual, it is just returning to his natural level in a prompt fashion.
In my view, a scenario of falling nominal expenditure (like 4th quarter 2008 and 1st quarter 2009) has this sort of effect. Modeling in terms of inflation and expected inflation may be best when trying to explain a boom due to more rapid growth of demand, or even a recession due to slower growth of aggregate demand. But aggregate demand falling and then, hopefully, rising back to where it should have been?
These models fail. Or maybe they describe the behavior of a blind and foolish central bank.
Suppose that the central bank targets a growth path of nominal expenditure. There are implications for the output gap and inflation, of course. But with that goal, there is no reason for the central bank to prevent whatever inflation that results from a return of nominal expenditure to its targeted growth path.
The liquidity trap described by Eggertsson, (as best I can tell) is that the assumed deflationary shocks push the price level down. For some reason, the central bank wants the price level to grow from that low level at a targeted rate. Why?
Further, the central bank manipulates long term interest rates by making promises about future short term interest rates. What about purchasing long term bonds? Why can't the central bank manipulate long term rates directly buy purchasing long term bonds? Does demand depend on the short term interest rates set by monetary authority in the future? Or do decreases in long term interest rates in the present, rates that are not at the zero bound, impact demand directly? In my view, quantitative easing is about purchasing long term bonds if necessary, not about making promises to keep short term interest rates low in the future to generate inflation in the future.
What is the supposed arbitrage that keeps short term rates above zero? Obviously, it is arbitrage between zero interest currency and bonds, but there is no explicit discussion of currency at all. Money is identified with currency, even though most of it takes the form of deposits that pay interest. Why nothing about this? Well, it is easy with money is thrown in as an afterthought.
In my view, Eggertsson's version of the liquidity trap is really a story about a model--a class of models. Did we suffer a Great Recession because central bankers pay too much attention to these models?