DP
RIETI Discussion Paper Series 03-E-002
Price Level Dynamics in a Liquidity Trap
IWAMURA Mitsuru
Waseda University
WATANABE Tsutomu
RIETI
The Research Institute of Economy, Trade and Industry
http://www.rieti.go.jp/en/
RIETI Discussion Paper Series 03-E-002
Price Level Dynamics in a Liquidity Trap
Mitsuru Iwamura and Tsutomu Watanabe
December 2002
Abstract
This paper studies the dynamic behavior of the general price level when the natural rate of interest
declines substantially. Particular attention is paid to two constraints: the non-negativity constraint of
nominal interest rates, and the government's intertemporal budget constraint. In a normal situation,
nominal bond prices rise in response to the shock, which restores equilibrium. However, if the
non-negativity constraint is binding, nominal bond prices cannot rise sufficiently. Equilibrium can
then be restored only by a sufficient fall in the current price level. The required fall is greater when
the maturity of government debt is shorter. To avoid deflation, the government must coordinate with
the central bank by committing itself to reducing the current and future primary surplus.
Price Level Dynamics in a Liquidity Trap
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NB
NB
NB
NB
NB
NB
NB
NB
NB
NB
NB
NB
NB
NB
Dˆ j , j +1
0.010
0.008
0.006
0.004
0.002
0.000
-10
0
10
20
30
40
50
60
70
80
90
100
Qˆ j , j +1
0.012
0.010
Optimal path
Taylor rule
0.008
0.006
0.004
0.002
0.000
-10
0
10
20
30
40
50
60
70
80
90
100
90
100
Pˆ j − Pˆ j −1
0.010
0.000
-0.010
-0.020
Optimal path
Taylor rule
-0.030
-0.040
-0.050
-0.060
-10
0
10
20
30
40
50
60
70
80
Figure 1
Optimal responses when the natural rate of interest stays above zero
Dˆ j , j +1
0.016
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.000
-10
0
10
20
30
40
50
60
70
80
90
100
Qˆ j , j +1
0.012
0.010
Optimal path
Taylor rule
0.008
0.006
0.004
0.002
0.000
-10
0
10
20
30
40
50
60
70
80
90
100
90
100
Pˆ j − Pˆ j −1
0.010
-0.010
-0.030
-0.050
Optimal path
Taylor rule
-0.070
-0.090
-0.110
-10
0
10
20
30
40
50
60
70
80
Figure 2
Optimal responses when the natural rate of interest falls below zero
Qˆ j , j +1
0.012
s_hat=0
s_hat=1/3
s_hat=2/3
s_hat=3/3
0.010
0.008
0.006
0.004
0.002
0.000
-10
0
10
20
30
40
50
60
70
80
90
100
80
90
100
Pˆ j − Pˆ j −1
0.005
0.000
-0.005
s_hat=0
s_hat=1/3
s_hat=2/3
s_hat=3/3
-0.010
-0.015
-0.020
-0.025
-0.030
-0.035
-10
0
10
20
30
Figure 3
40
50
60
Optimal policy mix
70