JAPANS LIQUIDITY TRAP

1
JAPANS LIQUIDITY TRAP
In this lecture I concentrate on the difficult
open economy aspects of the topic 1. Arbitrage
and the exchange rate (making sense of page 3 of
Krugmans Japanstill trapped Define E as the
nominal exchange rate in yen per so that a
depreciation of the yen is a rise in E Define e,
the real exchange rate, by eEP/P, where P is
the price of US goods and P is the price of
Japanese goods. So e is the relative price of US
goods. Denote the growth rate in percent of any
variable x by g(x). Suppose (a) no transactions
costs in international capital markets, (b)
risk-neutral agents who face no capital market
constraints. These two assumptions together add
up to what is called perfect capital mobility,
represented in the following equation.
2
The domestic rate of interest must equal the
foreign rate of interest plus the expected rate
of depreciation. The e superscript denotes
expectation. If this equation does not hold, then
under the assumption of perfect capital mobility
there would be an unlimited capital flow either
into or out of domestic assets. Now, we simply
use three identities relating (a) real to nominal
interest rates at home and abroad and (b) real
exchange rate expectations to nominal exchange
rate expectations and inflation expectations.
These allow us to convert the nominal arbitrage
condition above into a real arbitrage condition
(just substitute in and simplify).
The nominal arbitrage condition logically entails
the real arbitrage condition, even though the
real condition is less directly intuitive.
3
To develop some intuition, stick with the nominal
condition for a moment. It says, for instance,
that if (the one year maturity) i5 in and 3
in Euro, then the expected rate of depreciation
of the against the Euro must be 2 (well,
approximately 2, see below). Why? Because any
other expected rate of depreciation would cause
an unlimited flow of capital either into or out
of bonds. For instance, if the expected rate of
depreciation were zero, then arbitrageurs would
borrow to an unlimited degree in Euro at 3 and
lend the money at 5 in , making a risk-free 2
turn on the amount traded. Why approximately?
Well, because the arbitrage condition as
expressed is only exact for instantaneous
growth rates and interest rates (details in
Olivier Blanchards Macroeconomics 3rd edition,
Appendix 2, page A-7, proposition 3). In terms of
the numerical example above, 1 converted into
Euros and held in Euro assets for one year will
be expected to return, after conversion back
into , (10.03)(10.02). That comes to just a
little more than 1.05, as can be seen by
multiplying out the brackets. Finally, note that
another term for this arbitrage condition is
uncovered interest parity uncovered rather
than covered, because the above switch into Euros
does involve exchange rate risk.
4
How does monetary policy work under flexible
exchange rates and perfect capital mobility? The
answer is complicated because it all depends on
what we assume about exchange rate expectations.
Let us first review the analysis that was given
in second year macroeconomics (and based on
Burda/Wyplosz, 4th edition, chapter 10.7). There
it was assumed that exchange rate expectations
are static, in other words that the expected rate
of change of the exchange rate is always zero. In
that case, uncovered interest parity implies,
simply , that ii. This results in the IS/LM/CM
diagram below expansionary monetary policy (LM0
to LM1) causes an incipient capital outflow
that forces exchange rate depreciation, a rise in
net exports and a consequent IS shift (IS0 to
IS1) that restores ii.
LM0
LM1
i
CM
IS0
IS1
Y
5
Krugman makes a different assumption about
exchange rate expectations. He assumes that
agents know the long-run equilibrium real
exchange rate, e L, and that they expect a
fraction ? of the gap between the current and
long-run rates to be closed each year. This leads
to the following
Real interest rate gap equals expected rate of
real depreciation equals lambda multiplied by the
percentage gap between e and eL.
AA
Diagrammatically, we get a negative relationship
between r and e, as below. When rr, then ee
L. If r exceeds r, then e is below e L, as at
point C. For there to be expectations of real
depreciation, the exchange rate must be strong
now.
e
B
e L
C
r
r
6
NB Krugmans equation is a little different from
the one on the preceding slide this is because
he defines e as the natural logarithm of the real
exchange rate, not just the real exchange rate
itself. 2. Monetary policy, the exchange rate
and aggregate demand We now have a more
realistic method for analysing monetary policy
with a floating exchange rate and perfect capital
mobility. For a start, we can realistically
now think of the interest rate as the monetary
instrument. A cut of 1 in the interest rate
(nominal or real, provided that we think of
expected inflation as fixed) is going to
depreciate the exchange rate (real and nominal)
by 1/? , according to Krugmans equation. If
agents expect rather slow closing of the gap
between the current real exchange rate and the
long-run equilibrium exchange rate (so ? is
small, say 0.1), perhaps because they expect the
interest rate differential to be prolonged, then
the exchange rate effect will be large (10 in
this case). This corresponds to AA in the diagram
being rather steep.
7
We can finally make the step to Krugmans figure
4. All we need is to assume that net exports (NX)
depend on output, Y, and the real exchange rate e
- and that , for given output, NX increases with
e (the Marshall-Lerner condition is satisfied.
This implies a negative relationship between net
exports at full employment and the real rate of
interest. In other words
Goods market equilibrium implies YCIGNX,
while YCST is an identity, allowing the goods
market condition to be rewritten
(S-I)(T-G)NX. Ignoring government, for
simplicity, this becomes (S-I)NX, and leads to
the diagram which shows the real interest rate,
r0, consistent with full employment.
r
S-I
r0
A
NX
8
We have, finally, reached the conclusion of
Krugmans argument, which is that while interest
rate cuts certainly depreciate the exchange rate
and stimulate aggregate demand via expanded net
exports, this effect is finite and may - or may
not- allow full employment to be achieved. The
expected rate of inflation is vital if expected
inflation is negative, then the zero floor on the
nominal interest rate implies a positive floor on
the real interest rate. If, instead, expected
inflation is positive, then even point A in the
figure may be achievable. Some questions for
discussion 1. Would a temporary or a (more)
permanent interest rate cut cause a larger
exchange rate depreciation? Why? 2. What would
be the effect of fiscal expansion in Krugmans
diagram (assuming we generalize to allow for G
and T)? 3. How would a rise in r affect the
diagram?