透过镜子大厅的自然利率.pdf

The Natural Rate of Interest Through a Hall of Mirrors

∗

Abstract

Prevailing justifications of low-for-long interest rates appeal to a secular decline in

the natural interest rate, or r-star, due to factors outside monetary policy’s control.

We propose informational feedback via learning as an alternative explanation for

persistently low rates, where monetary policy plays a crucial role. We extend the

canonical New Keynesian model to an incomplete information setting where the central

bank and the private sector must learn about r-star and infer each other’s information

∗

We thank Claudio Borio, Jenny Chan, Giovanni Favara, Etienne Gagnon, Ben Johannsen, Afrasiab

Mirza, Hyun Song Shin, Min Wei, and participants at the conference on Expectations in Dynamic Macroe-

conomic Models at the Czech National Bank, the CEF 2021 conference, the EEA Annual Congress 2021, the

52nd MMF Annual Conference, the Bank for International Settlements and Federal Reserve Board for helpful

comments. All remaining errors are ours. The views herein are solely the responsibility of the authors and

should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System,

the Bank for International Settlements, or of any other person associated with the Federal Reserve System

or the Bank for International Settlements.

†

natural rate of interest, or r-star—the real interest rate consistent with output equaling

potential and stable inflation. Since the 1980s, real interest rates in advanced economies

have fallen by more than 5 percentage points. The great financial crisis (GFC) in 2008

prompted major central banks to cut their policy interest rates to record lows in a bid to

support economic recovery. Global inflation has nonetheless remained subdued for over a

decade. Standard macroeconomic theory can rationalise the co-existence of persistent lack

of price pressure and very low interest rates by a decline in r-star. A fall in r-star to very

low levels poses a problem because, given an effective lower bound on the nominal interest

rate, it limits the scope of monetary policy accommodation that central banks can provide.

Such concerns have led some central banks to introduce unconventional policy measures, and

level of real interest rate. Empirically, there is little consensus, however, on the relative

importance of these factors. The literature that provides an independent empirical evaluation

of these competing explanations is relatively scant, and tends to find only limited explanatory

power of various saving-investment factors consistently over long samples (see Borio et al.

(2017) and Lunsford and West (2019)). The lack of solid empirical evidence is perhaps

not surprising given the inherent identification challenge: Not only is r-star unobservable,

but it is also a theoretical construct—it can only be estimated by taking a stand on the

correct model of the economy. This leaves open the possibility that other factors may well

be relevant secular drivers of real interest rates.

This paper proposes an alternative explanation of persistent movements in r-star that

which central banks infer r-star at least partly from macroeconomic and financial market

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rates at least partly from current interest rates and policy communications.

While our extension is simple, its implications are not. We show that r-star—which

is really the private sector’s belief of long-run real rates— now becomes endogenous, in

particular to monetary policy. Furthermore, when both sides overestimate the quality of the

information of the other, the mutual learning process can lead both astray. We characterise

this misperception equilibrium and show that it implies persistent overreaction of r-star

beliefs to noise, in particular to purely cyclical macroeconomic shocks. This overreaction

effect can be likened to a hall of mirrors. As an example, suppose that, in a recession,

effects of their own actions as genuine information: They are staring into a hall of mirrors.

Despite its simplicity, our model is capable of explaining a range of salient empirical

facts in the post-GFC period, including some that are otherwise difficult to rationalise. In

particular, the excess sensitivity of long-term forward real rates to short-term interest rate

movements runs counter to the natural rate hypothesis, which postulates a convergence of

real interest rates to r-star in the long run. Such sensitivity is a general property of our

model, as the private sector (i.e. financial market participants) learns about the long-run

real rate from the central bank’s actions. Moreover, the model can quantitatively explain

the evolution of several macroeconomic variables after the GFC, including the entire decline

of US real interest rates between 2008 and 2019.

it believes r-star to have fallen, it not only lowers the short-term interest rate, but also its

expected long-run level, thus weakening the degree of policy accommodation. Our model thus

calls for greater recognition of the unintended consequences of policy communications. These

consequences are more severe the more the private sector and the central bank overestimate

each other’s knowledge of the economy.

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sector are learning about uncertain long-run economic fundamentals from each other. The

macroeconomic literature has extensively studied cases in which only the central bank learns

about economic fundamentals from the private sector. Prominent contributions in this area

are Orphanides (2003), Cukierman and Lippi (2005) and Primiceri (2006) and Nimark (2008).

Orphanides and Williams (2007, 2008) additionally allow for imperfect information on behalf

of the private sector, though only about the short-run dynamics of the economy. On the

empirical side, the well-known r-star estimation procedures of Laubach and Williams (2003)

and others (e.g. Holston et al., 2017; Johannsen and Mertens, 2021) also belong in this

documented empirically by Nakamura and Steinsson (2018). On the theory side, there have

been several structural models of the information channel, for example Tang (2015), Melosi

(2016), Angeletos and La’O (2020) and Angeletos et al. (2020). Our paper forms a bridge

between these two strands of the literature by considering the case in which the information

sets of the central bank and the private sector are not nested within each other, thus giving

rise to learning by both sides.

An older literature in monetary economics has discussed informational feedback between

the private sector and the central bank that are related to the hall-of-mirrors effect. Bernanke

and Woodford (1997) argue that if the central bank targets private sector inflation forecasts

to steer actual inflation, indeterminacy can obtain from a positive feedback loop between

Our model also relates to an emerging literature on the possibility that r-star could

be endogenous to monetary policy. In Rungcharoenkitkul et al. (2019), a monetary policy

regime that focuses unduly on short-term output can exacerbate the financial boom-bust

cycle, resulting in lower equilibrium output and interest rates in the long run. In Mian et al.

(2020), the natural rate of interest is lower when demand is constrained by over-indebtedness,

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Meh (2021), low interest rates can push the economy into an ELB trap in which r-star is

endogenously low. In our model, r-star is endogenous not because of fundamental economic

mechanisms, but because of mutual learning and endogenous information acquisition. The

notorious practical difficulties in assessing r-star speak to the importance of having a model

where learning is a central feature.

Finally, the analysis in our paper shares some features with Caballero and Simsek (2021),

who discuss the setting of optimal monetary policy when the central bank and the private

sector disagree about the state of the economy. In their model, disagreement arises from

The remainder of this paper is organised as follows. The next section discusses motivating

empirical evidence. Section 3 sets up the basic macroeconomic framework modified to

accommodate incomplete information, and establishes the modified r-star concept. Section

4 builds intuition by analysing a tractable static version of the model and deriving key

qualitative results. The full dynamic version of our model is laid out in Section 5, and

Section 6 discusses our quantitative simulation results. Section 7 concludes.

2 Motivating evidence

Is our proposed hall-of-mirrors effect on r-star simply a theoretical curiosity with no relevance

in practice? The answer would be yes if the natural rate hypothesis and the rational

expectations hypothesis both held true. The natural rate hypothesis states that the short-

term real interest rate will converge in the long run to a natural rate that is independent of

changes in monetary policy have a surprisingly strong effects on forward real interest rates

in the distant future. Hanson and Stein (2015) explain this by movements in term premia.

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