# Evaluating the Unconventional Monetary Policy of the Bank of Japan: A DSGE Approach

## Abstract

**:**

## 1. Introduction

## 2. Model

Assets are assumed to be imperfect substitutes for each other in wealth-owners’ portfolios. That is, an increase in the rate of return on any one asset leads to an increase in the fraction of wealth held in that asset, and to a decrease or at most no change in the fraction held in every other asset.

#### 2.1. Household

#### 2.2. Firm

#### 2.3. Fiscal and Monetary Authorities

#### 2.4. Analysis of Portfolio Rebalancing Mechanism

## 3. Calibration

#### 3.1. Calibration

## 4. Results

#### 4.1. Baseline Simulation

#### 4.2. QE Sensitivity Analysis

## 5. Concluding Remarks

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. The Steady State

## Appendix B. The Log-Linearized Model

## Notes

1. | Reith (2011) provided a good a comparison of QE in Japan and the US. Gupta and Marfatia (2018), and Gupta et al. (2019) also took the event-study approach to study the impact of unconventional monetary policy on stock markets. |

2. | Siranova and Kotlebova (2018) used a structural vector autoregression (SVAR) model to check ECB monetary-policy effects via the banking sector in Slovenia. Caraiani et al. (2020), and Huber and Punzi (2020) discussed the wealth channel of unconventional monetary policy. Caraiani et al. (2020) used a quantile structural vector autoregressive (QSVAR) model to analyze whether the impact of monetary-policy shocks on real housing returns in the United States was contingent on the initial state of housing-market sentiment. |

3. | For related studies, please refer to Olmo and Sanso-Navarro (2018), Kiss and Balog (2018), Chebbi and Derbali (2019). |

4. | For related studies, please refer to Harrison (2011, 2012), Falagiarda (2014), Cova et al. (2015), Del Negro et al. (2017), McKay et al. (2016) and Priftis and Vogel (2016, 2017). |

5. | Socci et al. (2018) used the calibrated dynamic computable general equilibrium (DCGE) model of the Italian economy to check the effects of the unconventional monetary policy of ECB. |

6. | This paper was written in 2015, and the conclusion is based on the situation of the Japanese economy in that time. |

7. | Indexation of each household is omitted because they are homogenous and identical. |

8. | This kind of classification in also used in model calibration, the steady state ratio of two kinds of bonds with different maturities relative to the total amount of government bonds. |

9. | ${B}_{L,t}^{H}$ means the long-term bonds held by households. |

10. | BoJ also purchases risky assets such as ETFs and J-REITs from the private sector, but the quantity of these purchases is much less than the purchased quantity of Japanese government bonds is. |

11. | |

12. | This is not true for a real economy because other financial institutions can hold government debt. In this model, financial intermediaries are neglected, and all private-sector households hold the remaining long-term bonds. |

13. | See Appendix B for log-linearization of the model. |

14. | See Appendix A. |

15. | Short-term debt ${b}_{S}$ includes bonds held by the central bank as the operation instrument in the interbank market plus bonds with maturity less than or equal to 1 year. |

16. | Long-term debt ${b}_{L}$ is calculated by subtracting its amount from total debt. |

17. | Data of Japanese government bonds can be obtained from http://www.mof.go.jp/jgbs/reference/appendix/index.htm accessed on 1 May 2021. |

18. | For other steady state values, see Appendix A. |

19. | The steady state of labor supply is calculated by assuming that the share of representative household’s time endowment spent on labor supply $\frac{L}{1-L}$ is equal to 0.3. |

20. | In similar research, this parameter was set to different values such as Chen et al. (2012) (0.015), Andres et al. (0.045), Harrison (2011, 2012) (0.1, 0.09). Following Falagiarda (2014), ${\phi}_{B}$ was set to 0.01, which means that 1% of household’s income is paid for the portfolio adjustment cost. Sensitivity analysis in the next section checks the role of this parameter in the portfolio-rebalancing channel of QE. |

21. | ${\phi}_{K}$ is derived from the steady state of the first-order conditions Equations (9) and (10). See Appendix A. |

22. | This calibration was conducted by checking the impulse response of ${\tilde{x}}_{t}={\rho}_{x}{\tilde{x}}_{t-1}+{\mu}_{t}^{x}$ through trial and error. Just like parameter ${\phi}_{B}$, ${\rho}_{x}$ and ${\sigma}_{x}$ were also assumed to be important in the portfolio-rebalancing channel of QE. Sensitivity analysis is given in the next section. |

## References

- Andres, Javier, J. David López-Salido, and Edward Nelson. 2004. Tobin’s Imperfect Asset Substitution in Optimizing General Equilibrium. Journal of Money, Credit and Banking 36: 665–90. [Google Scholar] [CrossRef] [Green Version]
- Angrick, Stefan, and Naoko Nemoto. 2017. Central Banking Below Zero: The Implementation of Negative Interest Rates in Europe and Japan. Asia Europe Journal 15: 417–43. [Google Scholar] [CrossRef]
- Bernanke, Ben, Vincent Reinhart, and Brian Sack. 2004. Monetary Policy Alternatives at The Zero Bound: An Empirical Assessment. Brookings Papers on Economic Activity 2: 1–100. [Google Scholar] [CrossRef] [Green Version]
- Calvo, Guillermo A. 1983. Staggered Prices in A Utility-Maximizing Framework. Journal of Monetary Economics 12: 383–98. [Google Scholar] [CrossRef]
- Caraiani, Petre, Gupta Rangan, Lau Chi Keung Marco, and Hardik A. Marfatia. 2020. Effects of Conventional and Unconventional Monetary Policy Shocks on Housing Prices in the United States: The Role of Sentiment. Journal of Behavioral Finance. [Google Scholar] [CrossRef]
- Chebbi, Tarek, and Abdelkader Derbali. 2019. US Monetary Policy Surprises Transmission to European Stock Markets. International Journal of Monetary Economics and Finance 12: 3–14. [Google Scholar] [CrossRef]
- Chen, Han, Cúrdia Vasco, and Ferrero Andrea. 2012. The Macroeconomic Effects of Large-Scale Asset Purchase Programmes. The Economic Journal 122: F289–F315. [Google Scholar] [CrossRef]
- Cova, Pietro, Pagano Patrizio, and Pisani Massimiliano. 2015. Domestic and International Macroeconomic Effects of the Eurosystem Expanded Asset Purchase Programme. Economic Working Papers No. 1036. Rome: Bank of Italy, Economic Research and International Relations Area. [Google Scholar]
- Vasco, Curdia, and Woodford Michael. 2011. The Central-Bank Balance Sheet as An Instrument of Monetary Policy. Journal of Monetary Economics 58: 54–79. [Google Scholar] [CrossRef] [Green Version]
- Del Negro, Marco, Eggertsson Gauti, Ferrero Andrea, and Kiyotaki Nobuhiro. 2017. The Great Escape? A Quantitative Evaluation of The Fed’s Liquidity Facilities. American Economic Review 107: 824–57. [Google Scholar] [CrossRef] [Green Version]
- Eggertsson, Gauti B., and Woodford Michael. 2004. Optimal Monetary and Fiscal Policy in a Liquidity Trap. NBER Working Papers No. 10840. Cambridge: National Bureau of Economic Research, Inc. [Google Scholar]
- Falagiarda, Matteo. 2014. Evaluating Quantitative Easing: A DSGE Approach. International Journal of Monetary Economics and Finance 7: 302–27. [Google Scholar] [CrossRef] [Green Version]
- Falagiarda, Matteo, and Massimiliano Marzo. 2012. A DSGE Model with Endogenous Term Structure. Working Papers wp830. Bologna: Universita’ di Bologna. [Google Scholar]
- Fukuda, Shin-ichi. 2018. Impacts of Japan’s Negative Interest Rate Policy on Asian Financial Markets. Pacific Economic Review 23: 67–79. [Google Scholar] [CrossRef] [Green Version]
- Galí, Jordi. 2015. Monetary Policy, Inflation and The Business Cycle: An Introduction to The New Keynesian Framework and Its Applications. Jersey: Princeton University Press. [Google Scholar]
- Gertler, Mark, and Peter Karadi. 2011. A Model of Unconventional Monetary Policy. Journal of Monetary Economics 58: 17–34. [Google Scholar] [CrossRef]
- Gertler, Mark, and Peter Karadi. 2013. QE 1 vs. 2 vs. 3...: A Framework for Analyzing Large-Scale Asset Purchases as A Monetary Policy Tool. International Journal of Central Banking 9: 5–53. [Google Scholar]
- Gertler, Mark, and Nobuhiro Kiyotaki. 2010. Financial Intermediation and Credit Policy in Business Cycle Analysis. In Handbook of Monetary Economics. Amsterdam: Elsevier, vol. 3, pp. 547–99. [Google Scholar]
- Gupta, Rangan, and Hardik A. Marfatia. 2018. The Impact of Unconventional Monetary Policy Shocks in The US on Emerging Market REITs. Journal of Real Estate Literature 26: 175–88. [Google Scholar] [CrossRef]
- Gupta, Rangan, Lau Chi Keng Marco, Liu Ruipeng, and Hardik A. Marfatia. 2019. Price Jumps in Developed Stock Markets: The Role of Monetary Policy Committee Meetings. Journal of Economics and Finance 43: 298–312. [Google Scholar] [CrossRef] [Green Version]
- Harrison, Richard. 2011. Asset Purchase Policies and Portfolio Balance Effects: A DSGE Analysis. In Interest Rates, Prices and Liquidity: Lessons from the Financial Crisis. Cambridge: Cambridge University Press, pp. 117–43. [Google Scholar]
- Harrison, Richard. 2012. Asset Purchase Policy At The Effective Lower Bound for Interest Rates. Bank of England Working Papers 444. London: Bank of England. [Google Scholar]
- Huber, Florian, and Maria Teresa Punzi. 2020. International Housing Markets, Unconventional Monetary Policy, and The Zero Lower Bound. Macroeconomic Dynamics 24: 774–806. [Google Scholar] [CrossRef] [Green Version]
- Joyce, Michael, David Miles, Andrew Scott, and Dimitri Vayanos. 2012. Quantitative Easing and Unconventional Monetary Policy—An Introduction. The Economic Journal 122: F271–88. [Google Scholar] [CrossRef] [Green Version]
- Kiyotaki, Nobuhiro, and John Moore. 2012. Liquidity, Business Cycles, and Monetary Policy. NBER Working Papers No. 17934. Cambridge: National Bureau of Economic Research, Inc. [Google Scholar]
- Kiss, Gábor Dávid, and Enikő Balog. 2018. Conventional and Unconventional Balance Sheet Practices and Their Impact on Currency Stability. International Journal of Monetary Economics and Finance 11: 76–94. [Google Scholar] [CrossRef]
- Krippner, Leo. 2013. Measuring The Stance of Monetary Policy in Zero Lower Bound Environments. Economics Letters 118: 135–38. [Google Scholar] [CrossRef] [Green Version]
- Krugman, Paul R., Kathryn M. Dominquez, and Rogoff Kenneth. 1998. It’s Baaack: Japan’s Slump and The Return of The Liquidity Trap. Brookings Papers on Economic Activity 1998: 137–205. [Google Scholar] [CrossRef] [Green Version]
- Lars, Ljungqvist, and Thomas J. Sargent. 2012. Recursive Macroeconomic Theory, 3rd ed. Cambridge: MIT Press. [Google Scholar]
- Leeper, Eric M. 1991. Equilibria under “Active” and “Passive” Monetary and Fiscal Policies. Journal of Monetary Economics 27: 129–47. [Google Scholar] [CrossRef]
- McKay, Alisdair, Nakamura Emi, and Steinsso Jón. 2016. The Power of Forward Guidance Revisited. American Economic Review 106: 3133–58. [Google Scholar] [CrossRef] [Green Version]
- Meier, Andre. 2009. Panacea, Curse, or Nonevent? Unconventional Monetary Policy in The United Kingdom. Working Paper No. 09/163. Washington: International Monetary Fund. [Google Scholar]
- Olmo, Jose, and Marcos Sanso-Navarro. 2018. Unconventional Monetary Policies and The Credit Market. International Journal of Monetary Economics and Finance 11: 480–98. [Google Scholar] [CrossRef] [Green Version]
- Priftis, Romanos, and Lukas Vogel. 2016. The Portfolio Balance Mechanism and QE in The Euro Area. The Manchester School 84: 84–105. [Google Scholar] [CrossRef]
- Priftis, Romanos, and Lukas Vogel. 2017. The Macroeconomic Effects of The ECB’s Evolving QE Programme: A Model-based Analysis. Open Economies Review 28: 823–45. [Google Scholar] [CrossRef]
- Reith, Matthias. 2011. Unconventional Monetary Policy in Practice: A Comparison of “Quantitative Easing” in Japan and The USA. International Journal of Monetary Economics and Finance 4: 111–34. [Google Scholar] [CrossRef]
- Siranova, Maria, and Jana Kotlebova. 2018. SVAR Description of ECB Monetary Policy Effects via Banking Sector in Individual EA Countries: Case of Slovenia. International Journal of Monetary Economics and Finance 11: 56–75. [Google Scholar] [CrossRef]
- Socci, Claudio, Severini Francesca, Pretaroli Rosita, Ahmed Irfan, and Ciaschini Clio. 2018. Unconventional Monetary Policy Expansion: The Economic Impact through A Dynamic CGE Model. International Journal of Monetary Economics and Finance 11: 140–62. [Google Scholar] [CrossRef]
- Svensson, Lars E.O. 2003. Escaping from A Liquidity Trap and Deflation: The Foolproof Way and Others. Journal of Economic Perspectives 17: 145–66. [Google Scholar] [CrossRef] [Green Version]
- Taylor, John B. 1993. Discretion versus Policy Rules in Practice. In Carnegie-Rochester Conference Series on Public Policy. Amsterdam: Elsevier, vol. 39, pp. 195–214. [Google Scholar]
- Tobin, James. 1969. A General Equilibrium Approach to Monetary Theory. Journal of Money, Credit and Banking 1: 15–29. [Google Scholar] [CrossRef]
- Tobin, James, and William C. Brainard. 1963. Financial Intermediaries and The Effectiveness of Monetary Controls. American Economic Review 53: 383–400. [Google Scholar]
- Ugai, Hiroshi. 2007. Effects of The Quantitative Easing Policy: A Survey of Empirical Analyses. Monetary and Economic Studies-Bank of Japan 25: 1. [Google Scholar]
- Vayanos, Dimitri, and Jean-Luc Vila. 2009. A Preferred-Habitat Model of The Term Structure of Interest Rates. NBER Working Papers No. 15487. Cambridge: National Bureau of Economic Research, Inc. [Google Scholar]
- Wang, Rui. 2019a. Unconventional Monetary Policy in US: Empirical Evidence from Estimated Shadow Rate DSGE Model. International Journal of Monetary Economics and Finance 12: 361–89. [Google Scholar] [CrossRef]
- Wang, Rui. 2019b. Unconventional Monetary Policy in Japan: Empirical Evidence from Estimated Shadow Rate DSGE Model. Journal of International Commerce, Economics and Policy 10: 1950007. [Google Scholar] [CrossRef] [Green Version]
- Woodford, Michael. 2003. Interest and Prices: Foundations of A Theory of Monetary Policy. Princeton: Princeton University Press. [Google Scholar]
- Wu, Jing Cynthia, and Fan Dora Xia. 2016. Measuring The Macroeconomic Impact of Monetary Policy at The Zero Lower Bound. Journal of Money, Credit and Banking 48: 253–91. [Google Scholar] [CrossRef]
- Zagaglia, Paolo. 2013. Forecasting Long-Term Interest Rates with a General-Equilibrium Model of the Euro Area: What Role for Liquidity Services of Bonds? Asia-Pacific Financial Markets 20: 383–430. [Google Scholar] [CrossRef]

Notation | Description | Steady State Value18 |
---|---|---|

Y | Output | 1 (normalization) |

C | Consumption | 0.6114 |

I | Investment | 0.2173 |

L | Labor supply19 | 0.2308 |

G | Government Expenditure | 0.119 |

T | Lump-sum Tax | 0.1196 |

${R}_{S}$ | Gross short-term interest rate | 1.01 |

${R}_{L}$ | Gross long-term interest rate | 1.0201 |

$\mathsf{\Pi}$ | Gross inflation rate | 1.0039 |

${b}_{S}+{b}_{L}$ | Total debt | 1.5493 |

${b}_{S}$ | Total short-term debt | 0.0869 |

${b}_{L}$ | Total long-term debt | 1.4624 |

${b}_{L}^{CB}$ | Long-term debt held by central bank | 0.2296 |

${b}_{L}^{H}$ | Long-term debt held by private sector | 1.2328 |

${\kappa}_{B}$ | Steady state ratio of $\frac{{b}_{L}^{H}}{{b}_{S}}$ | 14.1864 |

x | Steady state ratio of $\frac{{b}_{L}^{CB}}{{b}_{L}}$ | 0.1570 |

Notation | Description | Value |
---|---|---|

$\alpha $ | Capital share | 0.36 |

$\delta $ | Depreciation rate | 0.025 |

$\beta $ | Discount factor | 0.994 |

$\theta $ | Habit formation | 0.7 |

$\varphi $ | Fixed cost in production | 0.2 |

$\chi $ | Inverse of Frisch elasticity of labor supply | 5 |

$\sigma $ | Inverse of intertemporal substitution (risk aversion) | 2 |

$\xi $ | Interest-rate semielasticity of money demand | 4 |

$\eta $ | Calvo type price rigidity | 0.75 |

$\gamma $ | Price indexation | 0.5 |

$\u03f5$ | Steady state mark-up Rate | 0.2 |

${\phi}_{B}$ | Portfolio Adjustment Friction20 | 0.01 |

${\phi}_{K}$ | Investment Adjustment Friction21 | 770.6056 |

$\tau $ | Steady state lump-sum tax | 0.1196 |

${\tau}_{S}$ | Response to short-term debt deviation | 0.3 |

${\tau}_{L}$ | Response to long-term debt deviation | 0.3 |

${\phi}_{Y}$ | Response to output | 0.25 |

${\phi}_{\pi}$ | Response to inflation | 1.5 |

${\rho}_{R}$ | Monetary-policy smoothing | 0.995 |

QE Persistence | Output | Investment | Inflation | Long-Team Interest Rate |
---|---|---|---|---|

${\rho}_{x}=0.76$ (4 years) | 0.38% | 0.97% | 0.26% | −50.84 bp |

${\rho}_{x}=0.83$ (6 years) | 0.51% | 1.29% | 0.41% | −49.46 bp |

${\rho}_{x}=0.88$ (8 years) | 0.68% | 1.71% | 0.62% | −47.56 bp |

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**MDPI and ACS Style**

Wang, R.
Evaluating the Unconventional Monetary Policy of the Bank of Japan: A DSGE Approach. *J. Risk Financial Manag.* **2021**, *14*, 253.
https://doi.org/10.3390/jrfm14060253

**AMA Style**

Wang R.
Evaluating the Unconventional Monetary Policy of the Bank of Japan: A DSGE Approach. *Journal of Risk and Financial Management*. 2021; 14(6):253.
https://doi.org/10.3390/jrfm14060253

**Chicago/Turabian Style**

Wang, Rui.
2021. "Evaluating the Unconventional Monetary Policy of the Bank of Japan: A DSGE Approach" *Journal of Risk and Financial Management* 14, no. 6: 253.
https://doi.org/10.3390/jrfm14060253