Estimating a Nonlinear New Keynesian Model with the Zero Lower Bound for Japan

• Published date: 01 September 2022
• Author: HIROKUNI IIBOSHI,MOTOTSUGU SHINTANI,KOZO UEDA
• Date: 01 September 2022
• DOI: http://doi.org/10.1111/jmcb.12908

DOI: 10.1111/jmcb.12908

HIROKUNI IIBOSHI

MOTOTSUGU SHINTANI

KOZO UE DA

Estimating a Nonlinear New Keynesian Model with

the Zero Lower Bound for Japan

Which type of monetary policy rule best describes the policy conducted by

the Bank of Japan (BOJ) during the period when the nominal interest rate

is constrained at the zero lower bound (ZLB)? What are the economic fun-

damentals that explain Japan’s prolonged stagnation? How important is in-

corporating nonlinearities in the analysis? We answer these questions by

estimating a small-scale nonlinear dynamic stochastic general equilibrium

(DSGE) model. Wend that: the BOJ conducted a threshold-based forward

guidance policy; adverse demand shocks explain Japan’s experience; and

nonlinear models are very useful in the analysis of the Japanese economy

during the ZLB period.

JEL codes C11, C13, C61, C63, E31, E43, E52

Keywords: Bayesian inference, DSGE model, Monte Carlo squared,

particle lter, sequential

J     stagnation, the so-called

“lost decades,” since the early 1990s. During the period of lost decades, Japan’s out-

We thank Ken West (the editor), two anonymous referees, Ryo Hasumi, Yasuo Hirose, Kazumasa

Iwata, Jinill Kim, Mariano Kulish, Taisuke Nakata, Frank Schorfheide, Naoto Soma, Nate Throckmor-

ton, TakayukiTsuruga, and the conference and seminar participants at the IAAE 2017, EEA-ESEM 2018,

SNDE 2018, Spring meeting of JEA 2019, Japan Center for Economic Research, Korea University, and

the University of Tokyofor their useful comments and suggestions. Iiboshi is grateful for nancial support

from the Japan Society for the Promotion of Science (JSPS, 18K01575). Shintani is grateful for nancial

support from the JSPS (17H02510 and 20H01482). Ueda is grateful for nancial support from the MEXT-

Supported Program for the Strategic Research Foundation at Private Universities (S1411025), the JSPS

(19H01491), and the Tokyo Center for Economic Research.

H I is a Professor at Faculty of Economics and Business Administration, Tokyo

Metropolitan University (E-mail: iiboshi@tmu.ac.jp). M S is a Professor at Faculty

of Economics, The University of Tokyo(E-mail: shintani@e.u-tokyo.ac.jp). K U is a Professor at

School of PoliticalScience and Economics, Waseda University (E-mail: kozo.ueda@waseda.jp).

Received October 1, 2018; and accepted in revised form December 31, 2020.

Journal of Money, Credit and Banking, Vol. 54, No. 6 (September 2022)

© 2022 The Authors. Journal of Money, Credit and Banking published by Wiley Periodicals

LLC on behalf of Ohio State University.

This is an open access article under the terms of the Creative Commons Attribution-NonCom-

mercial License, which permits use, distribution and reproduction in any medium, provided

the original work is properly cited and is not used for commercial purposes.

1638 :MONEY,CREDIT AND BANKING

put growth rate has been slow and the inationrate has been low, with occasional mild

deation. To stimulate the economy, the Bank of Japan (BOJ) lowered the short-term

nominal interest rate and set it at nearly zero for most of the time since 1995. In ad-

dition, the BOJ adopted a number of unconventional monetary policies, including a

forward guidance policy, for the purpose of inuencing the expectations of private

agents about the future course of monetary policy, and in turn, their behaviors in the

current period. However,despite the BOJ’s efforts, the Japanese economy has not yet

fully recovered from the period of stagnation.

In focusing on this experience, this paper intends to answer the following three

questions. The rst question is whether the forward guidance policy is most appro-

priate in describing the monetary policy conducted by the BOJ during the period when

the nominal interest rate was constrained by the zero lower bound (ZLB). The second

question is whether Japan’s experience of a long duration of zero interest rates can

be explained by economic fundamentals in the general equilibrium framework. The

third question is how important is incorporating nonlinearities and ZLB in the anal-

ysis of the Japanese economy. We address these questions by estimating a nonlinear

dynamic stochastic general equilibrium (DSGE) model, which incorporates both the

ZLB of nominal interest rates and a forward guidance policy during the zero inter-

est rate period. Unlike the typical analysis using linear DSGE models, however, we

focus on a small-scale DSGE model because computationally intensive methods are

required in solving and estimating the nonlinear DSGE model.

Let us provide in more detail the background behind each question. Regarding

the rst question on the type of monetary policy, the BOJ claims that the forward

guidance policy was implemented during the ZLB period.1However, based on the

observation that the ination rate had increased to a certain level, the BOJ twice de-

cided to end the zero-rate policy, rst in 2000 and then in 2006. Since such pol-

icy changes have been followed by the recessions in 2001 and 2007, respectively,

one may view that the BOJ’s forward guidance policy was neither clearly stated nor

consistently implemented. For this reason, several studies consider whether the term

“forward guidance policy” appropriately describes the BOJ’s actual policy (e.g., Ito

and Mishkin 2004). In contrast, Hayashi and Koeda (2019) have estimated a regime-

switching vector autoregressive (VAR) model and provide evidence that the BOJ im-

plemented a type of forward guidance policy. In particular, their model incorporates

the threshold-based forward guidance policy, in the terminology of Boneva, Harri-

son, and Waldron (2018), in which an ination rate needs to be sufciently high to

exit from the zero-rate policy. We aim to provide further evidence on this issue by

estimating a DSGE model that not only allows the ZLB but also several monetary

policy rules, including a threshold-based forward guidance rule.2

1. The BOJ announced in April 1999 that the “zero rate will be maintained until deationary concerns

are dispelled,” and in March 2001 that the BOJ’seasing policy continues to be in place “until the consumer

price index (excluding perishables) registers stably a zero percent or an increase year on year.”

2. There are a number of studies on monetary policy during the ZLB period. Aoki and Ueno (2012) use

forward rate curves to take into account the effects of the ZLB for Japan, while estimating a linear DSGE

model. Kulish, Morley, and Robinson (2017) estimate the duration of the ZLB for the United States by

HIROKUNI IIBOSHI, MOTOTSUGUSHINTANI, AND KOZO UEDA :1639

Providing the evidence for the rst question brings us to the second question. It

is natural to ask why the zero interest rate period has continued for more than two

decades, and why the ination rate has remained low despite the BOJ’s efforts to

conduct unconventional monetary easing policies, including the forward guidance

policy. According to the macro-economic theory, the prolonged stagnation can be

explained either by adverse shocks to economic fundamentals (e.g., Summers 2013,

Eggertsson, Mehrotra, and Robbins 2019, Katagiri, Konishi, and Ueda 2020) or by the

presence of a sunspot equilibrium (e.g., Benhabib, Schmitt-Grohé, and Uribe 2001,

Benigno and Fornaro 2018). For the latter explanation, several studies provide sup-

porting evidence by estimating DSGE models of a sunspot equilibrium.3In contrast,

evidence for the former explanation based on the DSGE model does not seem to be

sufcient, partly because of technical reasons. Indeed, estimating a nonlinear DSGE

model incorporating the ZLB can be very difcult when the duration of episodes of

zero interest rates becomes longer. In this regard,the fact that our solution and estima-

tion algorithm is successful in describing the Japanese economy is a benet. Without

relying on a sunspot equilibrium, our approach can demonstrate the extent to which

economic fundamentals can account for Japan’s experience. For the purpose of un-

derstanding the role of fundamentals, we focus specically on the estimated natural

rate of interest (see, e.g., Wicksell 1936, Krugman 1998, Woodford 2003). We com-

pare the estimated natural rate of interest with the real interest rate, and then seek the

reason for Japan’s prolonged stagnation by historically decomposing the natural rate

of interest with structural shocks.

For the third question, we evaluate the usefulness of incorporating nonlinearities

and ZLB to describe the Japanese economy over the past few decades. It is well-

known that the presence of the ZLB on the nominal interest rate often changes the

policy implications of DSGE models (see Eggertsson 2011, Fernández-Villaverde

et al. 2015, Boneva, Braun, and Waki 2016, Nakata 2017, among others). However,

for computational convenience, linearized DSGE models have commonly been em-

ployed in the analysis of the Japanese economy (e.g., Sugo and Ueda 2008, Fujiwara,

Hirose, and Shintani 2011, Hirakata et al. 2016). Indeed, Hirose and Inoue (2016)

assuming that it is foreseen perfectly in each period and then assess the time-varyingpolicy functions, given

the estimated duration of the ZLB. In the nance literature, based on the partial-equilibrium approach, a

shadow rate is estimated to evaluatethe effects of unconventional monetary policy on the yield curve (see,

e.g., Ichiue and Ueno 2006, Kim and Singleton 2012, Krippner 2013, Bauer and Rudebusch 2016, Wuand

Xia 2016, Ueno 2017). Kim and Pruitt (2017) use forecasters’ surveys to estimate a monetary policy rule

in the United States. A partial-equilibrium approach and structural VARmodel may enable us to identify

a monetary policy rule by estimating the response of nominal interest rates to economic disturbances. In

contrast, our estimation based on a DSGE model takes into account not only the response of nominal

interest rates to economic disturbances but also the effects of monetary policy on the economy. Thus, if

the forward guidance puzzle is signicant (Del Negro, Giannoni, and Patterson 2015, McKay,Nakamura,

and Steinsson 2016, i.e., if the theoretical power of forward guidance is too strong;), then our estimation

unlikely supports the threshold-based forward guidance rule.

3. See, for example, Hirose (2008), Aruoba, Cuba-Borda, and Schorfheide (2018), and Cuba-Borda

and Singh (2019). Aruoba, Cuba-Borda, and Schorfheide (2018) construct a model, in which the economy

uctuates between a normal determinate equilibrium and a deationary indeterminate equilibrium. They

estimate the model without the ZLB and then generate data and conduct simulations that incorporate the

ZLB. Cuba-Borda and Singh (2019) estimate a model with the ZLB by assuming a permanent liquidity

trap and estimating parameters only associated with shocks.