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Measuring Monetary Policy Under Zero Interest Rates With a Dynamic Stochastic General Equilibrium Model

: An Application of a Particle Filter

September 2010
Tomiyuki Kitamura *1

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Abstract

This paper proposes an empirical dynamic stochastic general equilibrium (DSGE) framework to measure the degree of monetary policy accommodation when the nominal interest rate is zero. The framework employs a hypothetical DSGE model in which the nominal interest rate can be lowered below zero because, for instance, the central bank can impose a 'carry tax' on currency. We call the model's nominal interest rate the 'shadow rate.' When the shadow rate is positive, it is observed as the actual nominal interest rate set by the central bank. When it is negative, however, it deviates from the actual nominal interest rate which remains at its lower-bound of zero. In the model, it is not the actual nominal interest rate but the shadow rate that affects the economy when the two rates deviate. The hypothetical DSGE model can be fit to data using a version of particle filters, and the historical movements of the shadow rate can be estimated. As an application, we estimate a small New Keynesian model using Japanese data. The results suggest that the shadow rate was well below zero during the period when the nominal interest rate was zero in the early 2000s.

JEL classification
E30; E52

Keywords
Monetary policy; Dynamic stochastic general equilibrium; Zero lower-bound of nominal interest rate; Particle filter; Shadow rate

I am grateful to Hiroshi Fujiki, Yasuo Hirose, Shigeru Iwata, Sohei Kaihatsu, Ryo Kato, Takushi Kurozumi, Kazuo Monma, Jouchi Nakajima, Masashi Saito, Toshitaka Sekine, Jeffrey Sheen, Tomohiro Sugo, Shu Wu, and the participants at the Reserve Bank of Australia Research Workshop for their comments. I have also greatly benefited from discussions with Hibiki Ichiue and Toyoichiro Shirota. I also thank Koiti Yano for the seminar at the Bank of Japan on particle filtering, which gave me the opportunity to learn the technique. The views expressed in this paper are those of the author and are not reflective of those of the Bank of Japan.

  •   *1 Research and Statistics Department, Bank of Japan
    E-mail: tomiyuki.kitamura@boj.or.jp

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