Inflation Target As a Buffer Against Liquidity Trap

IMES DISCUSSION PAPER SERIES

Inflation Target as a Buffer against Liquidity Trap

Shin-Ichi NISHIYAMA

Discussion Paper No. 2003-E-8

INSTITUTE FOR MONETARY AND ECONOMIC STUDIES

BANK OF JAPAN

C.P.O BOX 203 TOKYO 100-8630 JAPAN

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Inflation Target as a Buffer against Liquidity Trap

Shin-Ichi NISHIYAMA*

Abstract

In times of low-inflation, conventional monetary policy is perpetually exposed to the risk of being caught by the liquidity trap. As a part of a pre-emptive monetary policy to avoid the liquidity trap, many economists have pointed out that this risk can be possibly circumvented by targeting a small but positive inflation rate - i.e., so-called the ‘buffer’ role of an inflation target. In this paper, based on the stylized framework of a central bank's linear-quadratic dynamic optimization problem taking into account the zero lower-bound constraint on the nominal interest rate, we analyze the role of an inflation target in reducing the long run stabilization cost stemming from the liquidity trap. We prove the existence of the ‘buffer’ role of small but positive inflation in the presence of a liquidity trap. Moreover, we analytically show that a central bank's loss function evaluated at the steady state is decreasing and convex function of an inflation target. Finally, these analytical properties of an inflation target are verified by a numerical method. Sensitivity analyses suggest that, in the presence of a liquidity trap, a central bank faced with volatile macroeconomic shocks should consider the ‘buffer’ role of an inflation target seriously.

Key words: Deflation; Inflation Target; Liquidity Trap; Zero-Bound

JEL classification: E52, E58, C63

* Research Division 1, Institute for Monetary and Economic Studies, Bank of Japan (E-mail: [email protected])

I would like to thank Steve Cecchetti, Kentaro Iwatsubo, Ryo Kato, Yukinobu Kitamura, Jun Nagayasu, Masao Ogaki, Akihisa Shibata, Raphael Solomon, Dan Thornton, and the staff members at the Institute for Monetary and Economic Studies and the Research and Statistics Department for their valuable comments. Any remaining errors are, of course, my own. The views expressed in this paper are those of the author and do not necessarily reflect those of the Bank of Japan or the Institute for Monetary and Economic Studies. wkhuh duh vhyhudo phdvxuhv wkdw wkh Ihg +ru dq| fhqwudo edqn, fdq wdnh wr uhgxfh wkh ulvn ri idoolqj lqwr gh dwlrq1 Iluvw/ wkh Ihg vkrxog wu| wr suhvhuyh d exhu }rqh iru wkh lq dwlrq udwh/ wkdw lv/ gxulqj qrupdo wlphv lw vkrxog qrw wu| wr sxvk lq dwlrq grzq doo wkh zd| wr }hur1 Prvw fhqwudo edqnv vhhp wr xqghuvwdqg wkh qhhg iru d exhu }rqh1 Iru h{dpsoh/ fhqwudo edqnv zlwk h{solflw lq dwlrq wdujhwv doprvw lqyduldeo| vhw wkhlu wdujhw iru lq dwlrq deryh }hur/ jhqhudoo| ehwzhhq 4 wr 6 shufhqw shu |hdu1 Pdlqwdlqlqj dq lq d0 wlrq exhu }rqh uhgxfhv wkh ulvn wkdw d odujh/ xqdqwlflsdwhg gurs lq djjuhjdwh ghpdqg zloo gulyh wkh hfrqrp| idu hqrxjk lqwr gh dwlrqdu| whuulwru| wr orzhu wkh qrplqdo lqwhuhvw udwh wr }hur1 Jryhuqru Ehq V1 Ehuqdqnh lq uhpdunv wlwohg Gh dwlrq= Pdnlqj Vxuh Lw Grhvq*w Kdsshq Khuh +Qryhpehu 54/ 5335,1 Dw wkh vdph wlph/ wkh Jryhuqlqj Frxqflo djuhhg wkdw lq wkh sxuvxlw ri sulfh vwdelolw| lw zloo dlp wr pdlqwdlq lq dwlrq udwhv forvh wr 5( ryhu wkh phglxp whup1 Wklv fodul fdwlrq xqghuolqhv wkh HFE*v frpplwphqw wr surylgh d vx!flhqw vdihw| pdujlq wr jxdug djdlqvw wkh ulvnv ri gh dwlrq1 HFE Suhvv Uhohdvh= Wkh HFE*v Prqhwdu| Srolf| Vwudwhj| +Pd| ;/ 5336,1

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61415 Surshuwlhv ri Vwhdg| Vwdwh Orvv Ixqfwlrq zlwk uhvshfw wr dq Lq dwlrq Wdujhw

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46 vwdelol}dwlrq frvw lq wkh orqj uxq1 Khuh/ wkh whup cvwdelol}dwlrq frvw lq wkh orqj uxq* pd| kdyh glhuhqw phdqlqjv iru glhuhqw uhvhdufkhuv1 Wr dyrlg dpeljxlw|/ zh gh qh cvwdelol}dwlrq frvw lq wkh orqj uxq* dv wkh ydoxh ri orvv ixqfwlrq hydoxdwhg dw wkh vwhdg| vwdwh ru/ vwhdg| vwdwh orvv ixqfwlrq iru vkruw1 Pruh suhflvho|/ wkh vwhdg| vwdwh orvv ixqfwlrq lv gh qhg dv/ 4 4 O77 @ +|77,2 +77 W,2> +4;, 5 5 zklfk fdq eh lqwhusuhwhg dv wkh vwhdg| vwdwh frxqwhusduw ri ht1 +4,1 Wkxv/ lq wklv sdshu/ wkh uhodwlrqvkls ehwzhhq wkh orqj uxq vwdelol}dwlrq frvw dqg lq dwlrq wdujhw lv dfwxdoo| sur{lhg e| wkh uhodwlrqvkls ehwzhhq wkh vwhdg| vwdwh orvv ixqfwlrq dqg lq dwlrq wdujhw1 Lq sduwlfxodu/ zh vd| wkdw wkhuh h{lvw wkh exhu uroh ri dq lq dwlrq wdujhw zkhq wkh vwhdg| vwdwh orvv ixqfwlrq lv ghfuhdvlqj lq wkh lq dwlrq wdujhw1 Nhhslqj wklv lq plqg/ zh qrz vwdwh wkh pdlq sursrvlwlrq ri wklv sdshu l1h1/ wkh h{lvwhqfh ri wkh exhu uroh ri dq lq dwlrq wdujhw lq wkh suhvhqfh ri d oltxlglw| wuds1

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67 Figure 1: Inflation in Industrial and Emerging Market Economies

18 16 US CAN 14 FR 12 GER IT 10 UK 8 JP Swiss Annual % 6 4 2 0 -2 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

25 HK KOR 20 Malay. Singa. Thai 15 PRC

10 Annual %

-5 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

Source: IMF, International Financial Statistics Figure 2: Money Market Rates in Industrial and Emerging Market Economies

25 US CAN 20 FR GER IT 15 UK JP Swiss Annual % 10

0 Jan-80 Jan-81 Jan-82 Jan-83 Jan-84 Jan-85 Jan-86 Jan-87 Jan-88 Jan-89 Jan-90 Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02

30 HK 25 KOR Malay. Singa. 20 Thai PRC 15 Annual %

0 Jan-80 Jan-81 Jan-82 Jan-83 Jan-84 Jan-85 Jan-86 Jan-87 Jan-88 Jan-89 Jan-90 Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02

Source: IMF, International Financial Statistics Phase Diagram Illustration: Intuition behind the Buffer Role of an Inflation Target

π ∆y=0 ∆π=0 (Zero-bound Non-Binding)

π πSS = E1

Conventional Monetary Policy Zone

* E2 i=0 Risk of falling into Controllable Liquidity Trap Zone deflationary spiral Zone from steady state. Deflationary Spiral Zone Saddle Path ∆y=0 (Zero-bound Binding)

y=0 y

Figure 3

Note: The monetary authority can reduce the risk of falling into a deflationary spiral by raising the inflation target in the long-run. Note that steady-state inflation is an increasing function of the inflation target. Figure 4: Interpolated Value Function without Zero-Bound (π*=0, σ=1)

Figure 5: Interpolated Value Function with Zero-Bound (π*=0, σ=1) Figure 6: Horizontal View of Figure 4 (π*=0, σ=1)

Long-run Cost-to-Go =

2.61

Figure 7: Horizontal View of Figure 5 (π*=0, σ=1=1)

Long-run Cost-to-Go =

3.27 Figure 8: Relationship between Long-run Cost-to-Go and Inflation Target ( Given σ = 1 )

Long-run Cost-to-Go with Liquidity Trap

Long-run Cost-to-Go without Liquidity Trap

Note: The solid curve represents the long-run Cost-to-Go in the presence of a liquidity trap as a function of the inflation target, while the dashed curve represents the long-run Cost-to-Go in the absence of a liquidity trap. As can be seen from the figure, the long- run Cost-to-Go is a decreasing-convex function of the inflation target, which implies that a central bank’s stabilization cost could be reduced by setting a higher inflation target in the long-run – i.e., the buffer role of an inflation target. It should be noted that this buffer role of an inflation target is non-existent when there is no liquidity trap in the economy. In other words, the long-run Cost-to-Go is invariant to the level of the inflation target when there is no liquidity trap. Figure 9: Relationship among LR Cost-to-Go, Inflation Target, and Volatility (No Liquidity Trap)

Figure 10: Relationship among LR Cost-to-Go, Inflation Target, and Volatility (With Liquidity Trap) Figure 11: Difference in LR Cost-to-Go with and without Liquidity Trap

Note: The figure represents the portion of long-run Cost-to-Go solely arising from the risk of falling into a liquidity trap. It should be noted that this particular cost approaches zero, as the inflation target is set higher. As can be seen from the figure, the buffer role of an inflation target becomes more substantial as the economy becomes more volatile.