How robustness can change the desirability of speed limit policy
| Published date | 01 November 2021 |
| Author | Kohei Hasui |
| Date | 01 November 2021 |
| DOI | http://doi.org/10.1111/sjpe.12268 |
Scott J Polit Econ . 2021;68:553–570. wileyonlinelibrary.com/journal/sjpe
|
553
© 2021 Scottish Ec onomic Society
1 | INTRODUCTION
Minimizing socia l welfare loss is one of the mos t important topics i n monetary policy. In a st andard forward-lo ok-
ing New Keynesian mo del, a central bank mini mizes the quadratic ter ms of inflation rate and out put gap.1 In terms
of minimizing socia l welfare losses, it has b een pointed out that opt imal precommitment u nder a timeless per spec-
tive is effect ive.
However, when central banks in the actu al world are considered, several problems arise in m onetary policy
design. Firs t, the precommitment is di fficult to implement , because it requires a cent ral bank to be extremel y pa-
tient. This lea ds to a normative analys is of how the policy maker c an improve welfare losse s under discretion wh en
the policy make r does not have a commitment te chnology. Since pure opti mal discretionary p olicies are inferior to
1Woodford (200 3) derives this q uadratic los s function by ap proximating ho useholds' uti lity in the seco nd order.
Accepted: 11 Decem ber 2020
DOI: 10 .1111/sjpe.1 2268
ORIGINAL ARTICLE
How robustness can change the desirability of
speed limit policy
Kohei Hasui
Faculty of Econo mics, Matsuyam a
University, Matsuyama, Ehime, Japan
Correspondence
Kohei Hasui, Faculty of Economics,
Matsuyama University, Bunkyo-cho,
Matsuyama, Ehime, Japan.
Email: khasui@g.matsuyama-u.ac.jp
Funding information
Matsuyama University Center Project,
JSPS KAKE NHI, Grant/Award Num ber:
16K03920 and 17K13768
Abstract
This paper investigates a robust monetary policy under
speed limit polic y when a central bank fears mod el misspeci-
fication. We reveal several points. First, the persistence of
the output gap becomes small with the robust speed limit
policy. The low persistence of the output gap contributes
to mitigating the variance of the output gap. Second, for a
robust policy, social losses are lower under the speed limit
policy than unde r precommitment. Our results sug gest that
adding the growth of the output gap to the central bank’s
objectives is effective when the worst-case scenario is
realized.
KEYWORDS
monetary policy, speed limit policy, robust control
JEL CLASSIFI CATION
E31; E52; E58; E61
554
|
HASUI
precommitment in welfare performance, private sector and government delegate various objectives to the central
bank under discretion. This is called an optimal delegation policy.2
Many papers have an alyzed optimal deleg ation problems in New Keyne sian models.3 As one desirable delega-
tion policy, Walsh’s (2003) “speed limit policy” is frequently referred to in the literature on optimal delegation
policy. He sugges ts that central bank s include growth of t he output gap among t heir targets. Th e basic idea behind
the speed limit p olicy is that the growth of o utput can produce desir able policy inertia s uch as a precommitment.
In particula r, Walsh (2003) shows that the spee d limit policy achieves sup erior social welfare com pared with pure
discretion, an d it is even sometimes super ior to precommitment.
Second, another problem arises when we consider an actual economy, namely model misspecification and
model uncertainty. The central bank has difficulty designing a policy because it has imperfect knowledge of
the true model, and therefore seeks to design a robust policy supposing that a model misspecification might
exist. It has be en pointed out that these mo del misspecifications h ave profound implications fo r monetary policy
(Dennis, 2010, 2014; Giorda ni & Söderlind, 200 4; Leitemo & Söderströ m, 2008a, 2008 b).
Taking this backgrou nd into account, we arrive at the fo llowing question: How does th e desirability of speed
limit policies ch ange under robust monet ary policy? Walsh (2003) shows t he desirability of spee d limit policies in
a situation wher e the central bank can fully c apture the true model. We relax t his assumption of perfect k nowl-
edge by introduci ng Hansen and Sargent’s (20 08) robust control te chnique. Their appro ach assumes that the tru e
model lies in the n eighborhood of a so-called re ference model.4 The deviation b etween the true model and th e
reference mode l is called misspecificati on. It is assumed that a policy maker c annot formulate the probabi lity of
the model misspecification (Knightian uncertainty). Therefore, the central bank designs a policy supposing the
worst-case outcom es. This approach incl udes a wide variety of m odel uncertaint y, such as parameter uncer tainty,
distorted ex pectations, and m ore adverse shocks. T hough most previous s tudies mainly have focus ed on whether
the robust pol icy responds cautiousl y or aggressively, we focus on both the p olicy response and welfare p erfor-
mance of the robus t speed limit policy.
We obtained sever al results that were diffe rent from those of previous s tudies. First, unde r the robust speed
limit policy, the out put gap responds cautiousl y to the lagged output gap; that is, the persistence of the output
gap becomes small. The policy function of the output gap under the speed limit policy depends on the lagged
output gap, be cause the objective func tion includes the quadrat ic terms of growth of the output ga p. However,
we found that this p ersistence of the outp ut gap was mitigated un der the robust spee d limit policy. This is beca use
the central ban k does not have the power to control th e expectations in the pr ivate sector under the spe ed limit
policy. Under the r obust speed limit po licy, model misspecifi cation makes the outp ut gap respond to the cos t-push
shock more aggressively. This resul t is consistent with those of Giordani and Söderlind (2004) and Lei temo and
Söderström (2008a, 20 08b). Therefore, the cost-push shock causes greate r fluctuation under the robust speed
limit policy. Unde r these circumstance s, the social welfare wors ens more if the persiste nce of the output gap also
increases, be cause the fluctuati on of the output gap increas es. Since the central bank k nows this scenario, it mit-
igates the aggr essive response of the outp ut gap to the lagged outpu t gap.
However, the persistence of the output gap is amplified under precommitment with robustness.5 Since pre-
commitment has t he power to control the expect ations, the central bank mi nimizes the social loss by control ling
2The delegat ion is often expr essed by retrof itting the ob jective func tions of centra l banks. It is note d that the objec tive functio n under delegat ion is
not always cons istent with the f unction of mic ro-founded soc ial welfare loss . Social welfa re is evaluated wi th the micro-fou nded functio n of social
welfare.
3Vestin (200 6) shows that a price -level targeti ng rule mimics o ptimal precom mitment polic y and achieves lo wer welfare los ses than pure
discretion ary policy. Jen sen (2002) arg ues that monet ary policy mi ght achieve a desi rable social we lfare outcome w hen the centra l bank targets t he
growth of nominal income.
4We refer to the spe ed limit polic y under a robust p olicy as the “rob ust speed limi t policy”. Analo gously, we refer to th e price-level ta rgeting rule
under the rob ust policy as t he “robust PLT rule.”
5We call the prec ommitment und er robust poli cy “precommit ment policy wi th robustnes s.”
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