Dynamic Macroeconomics

20.7.1 The Liquidity Trap
Such a situation was referred to as a theoretical possibility by Keynes in the
General Theory
and has since been known as a 
liquidity trap
. Keynes
[1936, p. 187] argued
There is the possibility … that, after the rate of interest has fallen to a certain level, liquidity-
preference may become virtually absolute in the sense that almost everyone prefers cash to holding
a debt which yields so low a rate of interest. In this event the monetary authority would have lost
effective control over the rate of interest. But whilst this limiting case might become practically
important in future, I know of no example of it hitherto.
The liquidity trap was analyzed by Modigliani [1944] as a special case of
the Keynesian model in which the LM curve becomes flat, and monetary
policy is thus ineffective. In such a case, a monetary expansion would fail to
further reduce nominal and real interest rates, increase aggregate demand,
and counteract deflation and recession.
The liquidity trap can be analyzed with the help of 
figure 20.2
. Assume
that the economy is at an initial equilibrium 
E
, and that a negative shock to
aggregate demand shifts the IS curve to the left. Short-run equilibrium output
moves from 
Y
E
to 
Y
E
′
, and the nominal interest rate shifts from 
i
E
to zero.

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Figure 20.2
The liquidity trap.
The central bank cannot counteract the contraction in aggregate demand by
increasing liquidity. Increases in liquidity cannot result in further reductions
in nominal interest rates, because households and firms prefer to hold money
(which has a zero nominal yield) to bonds (which would have a negative
nominal yield). Hence, conventional open market operations, in which the
central bank increases liquidity by exchanging money for short-term bonds,
would have no effect on nominal interest rates. Commercial banks and the
nonbank public would be quite happy to exchange zero-yield bonds or
deposits for cash, without any effect on the price or yield of these bonds.