Here is a post by Matt Yglesias, my version goes like this:
1. If there is something akin to a liquidity trap, one can expect that a broader aggregate such as M2 has collapsed. Accelerating the velocity of currency (say through a negative nominal interest rate, enforced through money stamping) may be a highly imperfect substitute for all the lost credit. (Not all AD is created equal.) Currency is usually small relative to M2, it is sector-specific, and the demand for currency can be slow to respond to relative prices.
2. If currency disappeared, how might negative nominal interest rates come about? The market won’t do it automatically. Let’s say we start with zero price inflation and the real rate of return goes negative. Competitive banks won’t impose negative nominal rates, rather the equilibrium is that they stop further real investments and pay zero on the balances. One constraint is that some form of withdrawals may always be possible, the more important constraint is simply that “storing balances” costs almost nothing at the margin and so competition will bring a zero rather than negative nominal return, adjusting for costs of transacting of course.
3. There is another way to get negative nominal interest. We could imagine a government-engineered reserve requirement, the shutting down of competing networks for trading reserves, and then the government raises the tax on those reserves to bring about negative nominal interest rates. This can be done with or without the existence of zero-interest-bearing currency. (Converting large quantities of reserves to currency, by the way, might be quite costly, given costs of transport and storage.)
4. Conclusion: getting rid of zero-interest-bearing currency doesn’t provide a new weapon against a liquidity trap. Tsiang (JMCB, 1974), by the way, went to an extreme and argued that getting rid of zero-interest-currency meant you were in a liquidity trap all the time, because arguably the money-bonds distinction disappears. I don’t agree, but the presumption lies in that direction.
5. Most generally, the problem in liquidity trap scenarios is that the economy is making an attempt to move from riskier assets to safer assets, and in the face of that attempted adjustment economic expansion is unlikely, no matter what the policy response. Changing one of the properties of one of the safest assets (i.e., allowing currency to bear interest) probably won’t make the reequilibration process much easier if at all. In broad outlines it will be pretty much the same.