# Contents of My Paper¶

**Habit formation, equilibrium yield curve, and interest rate lower bound**¶

**Work in progress**(Aug 2022).

**Abstract:**

**The model**

**Main figures:**

**Optimal irreversible monetary policy** [1]¶

*European Economic Review*134, 103707, May 2021.

Real-world central banks have a strong aversion to policy reversals. Nevertheless, theoretical models of monetary policy within the dynamic general equilibrium framework normally ignore the irreversibility of interest rate control. In this paper, we develop a formal model that incorporates a central bank’s discretionary optimization problem with an aversion to policy reversals. We show that, even under a discretionary regime, the optimal timing of liftoff from the zero lower bound is characterized by its history dependence, which arises from the option value to waiting, and there exists an optimal degree of policy irreversibility at which the social loss is minimized.

**The model:**

**Central bank with policy reversal aversion:**

Notes

**How robustness can change the desirability of speed limit policy** [2]¶

*Scottish Journal of Political Economy*68(5), 553-570, 2021.

This paper investigates a robust monetary policy under speed limit policy when a central bank fears model misspecification. We show that the persistence of the output gap becomes small with the robust speed limit policy. The low persistence of the output gap contributes to mitigating the variance of the output gap. Also, with a robust policy, social losses are lower under the speed limit policy than under precommitment. Our results suggest that adding the growth of the output gap to the central bank’s objectives is effective when the worst-case scenario is realized.

**The model (Walsh, 2003)**

*Robust control problem:*

**Analyses in an extended model:**

Notes

Previous title: “Speed limit policy and Knightian uncertainty.”

\(\phi\) denotes degree of inflation persistence.

SLT, PLT, and NIT denote speed limit targeting regime, price-level targeting regime, and nominal income targeting regime, respectively.

**Trend growth and robust monetary policy**¶

*The B.E. Journal of Macroeconomics*(Contributions) 21(2), 449-472, 2021.

**The model (Mattesini and Nistico, 2010)**

*The robust control problem:*[5]

**Proposition 2.**

*In the worst-case scenario, a higher trend growth decreases the effect of the central bank’s model uncertainty on the inflation rate, the output gap, and the policy rate under Assumptions 1 and 2.*

*Proof.*[…] Combining these conditions, we determine the signs of the cross-derivative as follows: [6]

Notes

\(\gamma\) denotes trend growth.

\(c_j\) for \(j = \pi, x, i\) denotes a coefficient of policy function in response to the cost-push shock.

**A note on robust monetary policy and non-zero trend inflation** [7]¶

*Macroeconomic Dynamics*24(6), 1574-1594, 2020.

*Robustness*, Princeton University Press] robust control techniques into a New Keynesian model with non-zero trend inflation. We reveal the following three points. First, we find that robust monetary policy responds more aggressively. This aggressiveness increases with trend inflation. Second, as the trend inflation rises, the response of macroeconomic variables is larger under robust policy. Third, stronger robustness tends to lead to indeterminate equilibrium as trend inflation increases. Consequently, the economy might be volatile when trend inflation is high due to robustness from the view of both variance and determinacy. We interpret the results as indicating that the model uncertainty might be the one of the factors causing large macroeconomic fluctuations when trend inflation is high.

**The model (Sbordone, 2007, Cogley and Sbordone, 2008, and Alves, 2012 and 2014)**

*Robust control problem:*

where

**Proposition 1.**

*In the worst-case scenario, Eqs. (11) - (16) show that stronger policy robustness increases sensitivity in inflation, output gap, and policy rate in response to cost-push shock and natural rate shock under Assumption 2.*

**Proposition 2.**

*In the worst-case scenario, Eqs. (18) - (21) show that the amount of change in sensitivity in inflation, output gap, and policy rate depend on trend inflation.*

Notes

This work is inspired by Kobayashi, T., and Muto, I. (2013) “A note on expectational stability under non-zero trend inflation,” *Macroeconomic Dynamics* 17(3), 681-693.

**Role of expectations in a liquidity trap** [8]¶

*Journal of the Japanese and International Economies*52, 201-2015, 2019.

**The model:**

Notes

Published in *Special Section on Unconventional Monetary Policy in Japan.*

**The liquidity effect and tightening effect of the zero lower bound**¶

*Japanese Journal of Monetary and Financial Economics*2(2), 1-15, 2014.

**The model:**