资本之谜（英）

Thecapitalpuzzle by Eduardo AmaralMonetary and Economic Department September 2025 JEL classification: E43, E52, E58Keywords: monetary policy, New Keynesian Model,natural interest rate BISWorking Papers are written by members of the Monetary and EconomicDepartment of the Bank for International Settlements, and from time to time by othereconomists, and are published by the Bank. The papers are on subjects of topicalinterest and are technical in character. The views expressed in them are those of theirauthors and not necessarily the views of the BIS. This publication is available on the BIS website (www.bis.org). ©Bank for International Settlements 2025. All rights reserved. Brief excerpts may bereproduced or translated provided the source is stated. The Capital Puzzle Eduardo G. C. Amaral*a,b aBanco Central do Brasil (BCB): eduardo.amaral@bcb.gov.brbBank for International Settlements (BIS): eduardo.amaral@bis.org August 27, 2025 Abstract Can a central bank tighten monetary policy and real interest rates fall under mone-tary dominance? Introducing endogenous capital into the New Keynesian model allowsreal interest rates to move in any direction at the impact of a positive persistent mone-tary policy shock. This raises concerns that the real interest rate channel is only obser-vational — not structural — in these models. This paper demonstrates that the puzzlegoes beyond capital. It emerges when the elasticity of an endogenous state variable toa persistent shock is high enough to sink inflation expectations, inducing the endoge-nous (or systematic) component of the monetary policy rule to sufficiently offset itsexogenous component. The channel is indeed structural, but conventional definitionsof the natural interest rate (r-star) and real interest rate gap can be misleading, particu-larly following events that significantly disrupt investment, such as pandemics, financialcrises or trade wars.As an alternative sign-consistent gauge of the monetary policystance, I propose the real interest rate gap that neutralizes the effect of shocks on en-dogenous state variables.From 1965Q1 to 2023Q3, it was often a better predictor offuture inflation and helped telling the history of monetary policy in the United States. Keywords:Monetary Policy, New Keynesian Model, Natural Interest Rate JEL Classification:E43; E52; E58. *The views in this paper are those of the author and do not necessarily reflect those of the BCB or the BIS. Aprevious version of this paper was released as Amaral (2024). I thank Carlos Viana de Carvalho, Eduardo Loyo,Ricardo Reis, André Minella, Diogo Guillén, Jon Frost, Ilhyock Shim, and two anonymous referees for theirvaluable comments, as well as Frank Smets, Raf Wouters and Johannes Pfeifer for providing helpful codes.I gratefully acknowledge the Economics Department of the London School of Economics for its hospitalityduring the 2018/2019 academic year. Finally, I thank the Banco Central do Brasil, CAPES, and the EconomicsDepartment of PUC-Rio for their support. The author declares there are no conflicts of interest that could haveappeared to influence the work reported in this paper. All remaining errors are the author’s sole responsibility. 1Introduction Can a central bank tighten monetary policy and real interest rates fall under monetary dom-inance? In a recent paper, Rupert and Šustek (2019) challenged the existence of a real inter-est rate channel of monetary policy transmission in textbook New Keynesian models, e.g.,Woodford (2003a) and Galí (2015). They showed that introducing endogenous capital intosuch models allows the real interest rate to move in any direction after a positive persistentmonetary policy shock,ξmt.1Figure 1 displays the effect of that shock under two differentspecifications for its persistence coefficient,ρm.The real interest rate rises immediatelyafter a transitory shock (ρm=0.0) but falls when the latter is just mildly persistent (ρm=0.5),while inflation falls and investment slumps in both cases. Rupert and Šustek (2019) argue that these puzzling impulse response functions wouldprove that the real interest rate channel is only observational — not structural — in NewKeynesian models. A channel that is not robust to the Lucas (1976) critique raises seriousconcerns regarding the reliability of these models for policy recommendations. For example,the interpretation of the mechanisms behind their impulse response functions becomes de-batable. It would also be quite problematic to assume the real interest rate channel for theidentification of vector autoregression (VAR) models, whether through sign restrictions, asin the method proposed by Uhlig (2005); through sequentially ordering nominal and realrates, as in a Cholesky decomposition; or by selecting real rates instead of nominal onesas part of a reduced model’s endogenous variables. The importance of this identificationproblem is straightforward, yet significant, to the extent that it has recently been evo