Liquidity traps and unconventional monetary policy

With all this talk about a zero lower bound and unconventional monetary policy I was keen to refresh myself on “liquidity traps” – as I remember people chatting away about these when I was at university.  So what is a liquidity trap, how does it refer to what is going on now, and how can I think about monetary policy when we are in that situation?

Liquidity trap
The term liquidity trap comes from thinking about the money market and the central banks ability to “stimulate” the economy.  A liquidity trap suggests that the bank is unable to ease monetary policy through its actions – by increasing the real money supply or reducing the nominal interest rate – when interest rates get sufficiently low.  We would be in such a trap when the overnight cash rate is close to zero, market interest rates are very low (especially the yield on government bonds), and measures of the money stock become elevated.
In order to think about this it is useful to use the IS-LM model shown in this old Krugman article.
This model assumes that prices are fixed in the economy, and it works by finding the situation where – for that given price – the goods market and money markets are in equilibrium.  The IS curve slopes downward in nominal interest rates, as when nominal interest rates decline people shift consumption and investment forward – thereby increasing aggregate expenditure and from there income.  The LM curve slopes upwards, as increases in real output increase demand for money which, for a fixed money supply drives up interest rates.  Another way of thinking about this is that the interest rate determined in the money market determines the interest rate faced by people making choices in the goods market – which is why they determine the level of output together.
In this simplistic way of looking at things the central bank manages to stimulate expenditure by cutting the interest rate – and they cut the interest rate by increasing the money supply (by buying government bonds).  A liquidity trap is when interest rates are so low that they can no longer reduce interest rates through this process of “open market operations” (in other words .  This seems like the end of the story – is the central bank can’t cut interest rates what can it do!
Unconventional policies and the liquidity trap
It is worth thinking about some thought experiments here.  Money and bonds have become perfect substitutes, and both are held as a store of value (money demand is perfectly elastic).  Increasing the stock of money does nothing.  However, is there really no way the central bank can increase expenditure that don’t involve the interest rate?  In other words, is there really no way that the central bank can shift the IS curve?  This is the thought experiment Krugman used in the past when describing what a central bank could do and it was this motivation that was behind my previous post on forward guidance.
Importantly, monetary policy needs friends when this happens.  Government spending and tax policy provides an important way to help support expenditure when it is flagging, and when the central bank is struggling with its own liquidity trap.  Although the private sector may just sit on money, the government most certainly doesn’t need to – and the fact that government is spending will, if it helps to support demand, allow the central bank to keep interest rates above zero.