{Update: Preface: Is it possible that an economy could find itself in an absolute liquidity trap because the natural rate of interest went negative? Or is it only possible if mistakes in monetary policy caused expected inflation to go negative?]
We argue that the nominal rate of interest cannot be negative. If it were, people would just store cash under the mattress.
We could equally argue that the real rate of interest cannot be negative. If it were, people would just store cans of beans under the mattress.
Unlike paper money, the demand for cans of beans is part of the demand for newly-produced goods and services, and so is part of Aggregate Demand. The demand to store newly-produced goods is part of investment demand. If the real rate of interest ever became negative, the demand for cans of beans would become infinitely large. So the equilibrium, or natural real rate of interest, could never be negative. So any argument for an absolute liquidity trap based on a negative natural rate of interest must be false. The IS curve cannot drop below the x axis.
If you don't like beans: try clothes, furniture, towels, landscaping, wine, scotch, copper, insulation, tobacco, dentistry, cutlery, steel, bricks, canoes, lumber, art, education, books, guitars,…., whatever. At negative real interest rates, why wait? Why not buy them now?
Two immediate objections arise: storage costs; and the risk of a fall in relative price of the good you store.
(Currency has storage costs too, and I worry more about being robbed of currency than cans of beans).
If it costs 5% of the value of the beans to store them per year, then real interest rates would have to fall below minus 5% before it would pay to store beans.
Also, if you expect that the relative price of beans would fall by 5% per year, then real interest rates would have to fall below minus 5% before it would pay to store them.
But if you expect the relative price of beans to fall, you must expect the relative price of some other goods to rise. So store one of those other goods instead.
Suppose we hit the zero lower bound on nominal interest rates. As long as there is one good whose expected rate of inflation is higher than its storage costs, demand for that good will be indefinitely large. And if that good is newly-produced, demand for that good will be part of aggregate demand.
Macroeconomics is so much easier if we assume there's only one good produced, so that demand for that one good is aggregate demand. But that won't work here, unfortunately. Some goods are easily stored, and others aren't. And labour is not always easily switched from one good to another. We might hit full employment in producing easily-stored goods, but have excess supply and unemployment elsewhere, because interest rates cannot go low enough.
But is that a macroeconomic problem of insufficient aggregate demand? Or a microeconomic problem of resource reallocation?
That is not a rhetorical question.
Worthwhile Canadian Initiative 
Nick,
Targets are not always acchievable.
Nick, agreed that perfect substitutibility in production combined with some storables allows the transfer of consumption from now to later. However, you need relative prices and wages to change today to cause the factors of produciton to all get moved into making storables today. Presumably sticky prices in aggregate comes from sticky prices at the single good level so you really are talking about a fundamentally different model. If you take away both nominal frictions (sticky prices/wages) and real frictions (imperfect substiutibility of factors) then of course there’s no recession! I do, however, feel a real vs nominal frictions post might be in order.
Nick:
Think of an economy without currency. All money is deposits. Monetary policy keeps inflation zero. The real interest rate is the nominal interest rate. There is no zero nominal bound.
Think about negative nominal and real interest rates. No inflation. Relative prices can change.
So, negative nominal and real interest rates are possible. Producing consumer goods now and storing them and selling them in the future is an investment project.
Nominal interest rates not keeping up with expected inflation so that people store goods as inflation hedges–well, OK. But I think that the cashless payments system with price level stability and negative nominal and real interest rates is the best way to get a pure “take” on what happens.
Bill: good to see you commenting here!
Yes, the cashless economy might be a good way to think about this question. Or a pure barter economy. And storing consumer goods is investment.
But if all produced goods could be costlessly stored, I take it you agree that real interest rates could not go negative? The only question is: are there enough cheaply storable goods whose relative prices would be expected to rise for other reasons without storage, to satisfy the excess demand for savings, of a magnitude that might empirically occur?
You can earn a positive carry by “investing in inflation”, when real rates are negative and the nominal (borrowing) rate is less than the inflation rate.
Can you also earn a positive carry by “investing in deflation”, when real rates are positive and the nominal (borrowing) rate is less than the real rate?
Is this problem symmetric or asymmetric? Why?