Updated on 2024/10/18

写真a

 
YOKOO Masanori
 
Organization
Faculty of Humanities and Social Sciences Professor
Position
Professor
Homepage
https://sites.google.com/site/masanoriyokoo71/
External link

Degree

  • Doctor of Economics ( Waseda University )

Research Areas

  • Humanities & Social Sciences / Economic theory

Education

  • Waseda University   大学院経済学研究科  

    1994.4 - 1999.9

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  • Waseda University   政治経済学部   経済学科

    1990.4 - 1994.3

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Research History

  • Okayama University   Graduate School of Humanities and Social Sciences   Professor

    2014.4

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  • Okayama University   Graduate School of Humanities and Social Sciences   Associate Professor

    2004.4 - 2014.3

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Papers

  • Controlling Chaotic Fluctuations through Monetary Policy Reviewed

    Takao Asano, Akihisa Shibata, Masanori Yokoo

    Studies in Nonlinear Dynamics and Econometrics   2024.1

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Walter de Gruyter GmbH  

    Abstract

    This paper applies the chaos control method (the OGY method) proposed by Ott, E., C. Grebogi, and J. A. Yorke. (1990. “Controlling Chaos.” Physical Review Letters 64: 1196–9) to policy-making in macroeconomics. This paper demonstrates that the monetary equilibrium paths in a discrete-time, two-dimensional overlapping generations model exhibit chaotic fluctuations depending on the money supply rate and the elasticity of substitution between capital and labor under the assumption of the constant elasticity of substitution (CES) production function. We also show that the chaotic fluctuations can be stabilized by controlling the money supply rate by using the OGY method and that even when the OGY method does not work due to periodic attractors, adding moderate stochastic shocks to the model can successfully stabilize the economy.

    DOI： 10.1515/snde-2023-0015

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    Other Link： https://www.degruyter.com/document/doi/10.1515/snde-2023-0015/pdf

  • Technology choice, externalities in production, and a chaotic middle-income trap Reviewed

    Takao Asano, Akihisa Shibata, Masanori Yokoo

    Journal of Economics   2023.10

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    Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    DOI： 10.1007/s00712-023-00844-9

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    Other Link： https://link.springer.com/article/10.1007/s00712-023-00844-9/fulltext.html

  • Middle-income traps and complexity in economic development Reviewed

    Takao Asano, Akihisa Shibata, Masanori Yokoo

    STUDIES IN NONLINEAR DYNAMICS AND ECONOMETRICS   2022.9

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：WALTER DE GRUYTER GMBH  

    In this paper, we develop a simple multi-technology overlapping generations model that exhibits a wide variety of economic development patterns. In particular, our numerical simulations demonstrate that for a given set of parameter values, various types of development patterns such as the middle-income trap, the poverty trap, periodic or chaotic fluctuations, and high-income paths can coexist, and which pattern is realized depends only on the initial value of capital. For another set of parameter values, we show that, due to the pinball effect, an economy starting at a middle-income level can take off to the high-income state or get caught in the poverty trap in a seemingly random way after undergoing transient chaotic motions. Our results can explain observed complicated patterns of economic development in a unified manner.

    DOI： 10.1515/snde-2021-0100

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  • Quasi-periodic motions in a two-class economy with technology choice: an extreme case Reviewed

    Takao Asano, Akihisa Shibata, Masanori Yokoo

    NONLINEAR DYNAMICS   110 ( 1 )   945 - 961   2022.9

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

    This paper constructs a simple overlapping generations (OLG) model with the working and capitalist classes and two types of production technologies. The behavior of agents belonging to the working class is basically the same as that in the standard Diamond (Am Econ Rev 55:1126-1150, 1965) type OLG model, whereas agents belonging to the capitalist class face two available technologies, select the one with a higher return on capital, and bequeath their assets to the next generation without supplying labor. Using techniques concerning the circle map in dynamical systems theory, we show that in an extreme case in which one technology is linear and the other is of the Leontief type, the economy exhibits bounded, non-periodic but non-chaotic motions for a large set of parameter values. We provide explicit formulas for the rotation number and the absolutely continuous invariant probability measure of the model.

    DOI： 10.1007/s11071-022-07643-9

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    Other Link： https://link.springer.com/article/10.1007/s11071-022-07643-9/fulltext.html

  • A simple model of growth cycles with technology choice Reviewed

    Yosuke Umezuki, Masanori Yokoo

    JOURNAL OF ECONOMIC DYNAMICS & CONTROL   100   164 - 175   2019.3

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    In this study, we develop a simple, computable overlapping generations model that exhibits endogenous fluctuations. The key assumption is that a firm can choose from multiple technologies of production. Since the model reduces to a piecewise linear map on the unit interval, it allows us to conduct an in-depth analysis of its dynamic properties. Particularly, this piecewise linearization reveals the ability of the model to exhibit periodic attracting cycles of an arbitrarily large period as well as non-periodic attractors. Furthermore, it is demonstrated that the occurrence of periodic patterns is completely characterized by the rotation number or the "devil's staircase." (C) 2019 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.jedc.2018.11.006

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  • Chaotic dynamics of a piecewise linear model of credit cycles Reviewed

    Takao Asano, Masanori Yokoo

    JOURNAL OF MATHEMATICAL ECONOMICS   80   9 - 21   2019.1

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE SA  

    We develop a simple piecewise linear overlapping generations model exhibiting endogenous business cycles, which is based on Matsuyama's (2007) model of credit cycles. Some sort of "noise" representing information imperfection is shown to transform the Matsuyama model into a continuous, eventually expanding, piecewise linear map on the interval, which is tractable enough to investigate the dynamics in depth by using the techniques of the Frobenius-Perron operators to find observable chaos. While, according to the analysis of Asano et al. (2012), the Matsuyama model exhibits periodic cycles of arbitrarily large period, it is essentially not capable of chaotic dynamics. However, our model exhibits ergodic chaos with some robustness. (C) 2018 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.jmateco.2018.11.001

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  • Misperception-driven chaos: Theory and policy implications Reviewed

    Masanori Yokoo, Junichiro Ishida

    JOURNAL OF ECONOMIC DYNAMICS & CONTROL   32 ( 6 )   1732 - 1753   2008.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    In a large economy, it is extremely difficult, if not impossible, to immediately grasp the state of our surrounding environment with precision since we normally have access only to a subset of relevant information. In this paper, we introduce this information imperfection into an ordinary model of endogenous business cycles and examine how it would affect the dynamic nature of the model. We, in particular, present a mechanism by which observation errors result in chaotic fluctuations in a model that would behave regularly otherwise, thereby indicating the importance of potential misperception about the current state in a qualitative sense. Also, our model is tractable enough to explicitly derive a policy index of chaotic fluctuations under some conditions. This feature of the model allows us to draw some policy implications regarding the observability of macroeconomic state variables. (C) 2007 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.jedc.2007.06.013

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  • Threshold nonlinearities and asymmetric endogenous business cycles Reviewed

    J Ishida, M Yokoo

    JOURNAL OF ECONOMIC BEHAVIOR & ORGANIZATION   54 ( 2 )   175 - 189   2004.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    This paper presents a model of endogenous business cycles in the presence of knowledge spillovers and a time-to-build restriction. There are two key assumptions that characterize the model: (i) the payoff to each firm depends on the aggregate state of knowledge, and (ii) the innovation of a project is time-consuming. Under those assumptions, a simple structure is shown to be described by a piecewise linear difference equation with a discontinuity. We show that the resulting dynamics generated by such a dynamical system leads to an asymmetric periodic cycle of arbitrary period that appears to switch repeatedly between different regimes. (C) 2004 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.jebo.2003.04.006

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  • Stability, chaos and multiple attractors: a single agent makes a difference Reviewed

    T Onozaki, G Sieg, M Yokoo

    JOURNAL OF ECONOMIC DYNAMICS & CONTROL   27 ( 10 )   1917 - 1938   2003.8

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    This paper provides an example in which a slight behavioral heterogeneity may fundamentally change the dynamical properties of a nonlinear cobweb market with a quadratic cost function and an isoelastic demand function. We consider two types of producers; cautious adapters and naive optimizers. In a market of naive optimizers a single cautious, adapter stabilizes the otherwise exploding market. In a market of cautious adapters a single naive optimizer may destabilize the market; without him there exists at most one periodic attractor in the market but with him there may appear many (and even infinitely many) coexisting periodic attractors. (C) 2002 Elsevier Science B.V. All rights reserved.

    DOI： 10.1016/S0165-1889(02)00090-8

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  • Chaotic dynamics in a two-dimensional overlapping generations model Reviewed

    M Yokoo

    JOURNAL OF ECONOMIC DYNAMICS & CONTROL   24 ( 5-7 )   909 - 934   2000.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    This paper investigates the global dynamics of a two-dimensional Diamond-type overlapping generations model extended to allow for government intervention. Using a singular perturbation method, we identify conditions under which transverse homoclinic points to the golden rule steady state are generated. For a parametric example with a CES production function, the occurrence of complicated dynamics (e.g. strange attractors) associated with homoclinic bifurcations is demonstrated. (C) 2000 Elsevier Science B.V. All rights reserved. JEL classification. E32.

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  • Complex dynamics in a cobweb model with adaptive production adjustment Reviewed

    T Onozaki, G Sieg, M Yokoo

    JOURNAL OF ECONOMIC BEHAVIOR & ORGANIZATION   41 ( 2 )   101 - 115   2000.2

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    Chaos occurs in a nonlinear cobweb model with normal demand and supply, naive expectations and adaptive production adjustment. The model differs from existing ones in that it includes adaptive production adjustment instead of adaptive expectations. The model exhibits observable chaos (strange attractors) as well as topological chaos (horseshoes) associated with homoclinic points. As numerical simulations show, the faster suppliers adjust their production and the more inelastic demand is, the more likely the market behaves chaotically. (C) 2000 Elsevier Science B.V. All rights reserved.

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  • Chaos, complex transients and noise: Illustration with a Kaldor model Reviewed

    A Dohtani, T Misawa, T Inaba, M Yokoo, T Owase

    CHAOS SOLITONS & FRACTALS   7 ( 12 )   2157 - 2174   1996.12

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：PERGAMON-ELSEVIER SCIENCE LTD  

    In the present paper two-dimensional discrete Kaldor-type models are investigated. First, a sufficient condition for the existence of topological chaos of the model is derived analytically for a special parameter set. Second, the influences of noise on the Kaldor model are examined numerically. We show that noise may not only obscure the underlying structures, but also reveal the hidden structures, for example, the chaotic attractors near a window of chaos or the periodic attractors near a small chaotic parameter region. Copyright (C) 1996 Elsevier Science Ltd.

    DOI： 10.1016/S0960-0779(96)00077-X

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Books

  • 進化ゲームの理論

    Weibull, Jörgen W., 三澤, 哲也, 赤尾, 健一, 大阿久, 博, 横尾, 昌紀, 大和瀬, 達二

    オフィスカノウチ,文化書房博文社 (発売)  1998.3  （ ISBN:4830108207 ）

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    Total pages：xviii, 342p   Language：Japanese

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MISC

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Research Projects

  • 非線形経済変動現象の研究

    Grant number：21K01388  2021.04 - 2026.03

    日本学術振興会  科学研究費助成事業 基盤研究(C)  基盤研究(C)

    横尾 昌紀

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    Grant amount：\4160000 （ Direct expense: \3200000 、 Indirect expense：\960000 ）

    主に下記の研究論文をDPとして発行し，学術誌に投稿した．
    ①"Technology Choice, Externalities in Production, and Chaotic Middle-Income Traps," KIER Discussion Paper Series No.1075, Institute of Economic Research, Kyoto University, 2022.②"Quasi-Periodic Motions in a Polarized Overlapping Generations Model with Technology Choice," KIER Discussion Paper Series No. 1070, Institute of Economic Research, Kyoto University, 2021.③"Middle-Income Traps and Complexity in Economic Development," , KIER Discussion Paper Series No. 1049, Institute of Economic Research, Kyoto University, 2020.
    上記の論文はすべて浅野貴央氏（岡山大学）と柴田章久氏（京都大学）との共著である．特徴として，技術選択により発生した非線形性によってもたらされる複雑な景気循環ないし，成長循環について書かれた理論研究である．①は外部性と技術選択の相互作用により，中所得の罠でカオスが発生するメカニズムを研究している．②は２クラスの経済主体と技術選択の相互作用で，かつ，技術が特殊な場合，準周期的な変動が生じるメカニズムを研究している．③はCES生産関数の範囲での技術選択が貧困の罠，中所得の罠，高度成長などの同時発生をもたらし，かつ中所得の罠ではカオス的変動が起こることをシミュレーションで示した．

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  • Research on models of economic dynamics using dynamical systems theory

    Grant number：20730133  2008 - 2011

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)  Grant-in-Aid for Young Scientists (B)

    YOKOO Masanori

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    Grant amount：\4030000 （ Direct expense: \3100000 、 Indirect expense：\930000 ）

    From the perspective of nonlinear dynamics, I studied foreign exchange rate dynamics including external, periodic economic fluctuations. Furthermore, I examined the overlapping generations model with government that holds real assets, discussing how to stabilize, by birth control, the fluctuating economic paths in the presence of chaos.

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  • 力学系理論によるマクロ動学モデルの研究

    Grant number：17730134  2005 - 2007

    日本学術振興会  科学研究費助成事業 若手研究(B)  若手研究(B)

    横尾 昌紀

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    Grant amount：\3400000 （ Direct expense: \3400000 ）

    経済動学の専門学術誌Journal of Economic Dynamics and Control(以下JEDC) に掲載予定である石田潤一郎との共同論文"Misperception-driven chaos:Theory and policy implications"では以下のような研究を公表した. 一般にマクロ経済の諸変数を経済主体が正確に観測したり認識したりすることは困難である. この一種の不確実性を,Ishida and Yokoo (2004,Journal of Economic Behavior and Organization: 以下JEBO)に発表した内生的景気循環モデルに導入した場合, どのような動学的変化が生じ,またどのような政策的含意が得られるのかを理論的に検証した.JEBO論文では,ある条件下で経済が不連続性を持つ区分線形の差分方程式で表現でき,かつ任意の長さの周期の周期解がパラメータの変化に応じて発生することを示した.JEDC論文では,上記の不確実性(異質性とも解されえる)が導入されることで,非常に緩い条件下でも位相的カオス(弱い意味でのカオス)的景気循環が発生することを示した.また,やや特定化された状況(システムが区分線形となるような)では,観測可能なカオス(強い意味でのカオス)的景気循環が典型的現象としてに発生することを示した.強いタイプのカオスは観測可能性をもつので,実際の非周期的な経済変動現象を表現していると解釈できる.JEDC論文ではさらに,特殊なパラメータのもとで経済活動水準を測る政策的指標がカオス的変動下でも計算可能であることを示した.さらにある区分線形のクラスの摂動に対し,その政策指標が頑健性をもつことを示した.この結果はカオス的変動をしている経済を特殊な区分線形モデルで近似できる可能性を示唆しているという意味で重要である.

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  • 教育選択と非線形マクロ経済変動モデル分析及び最適教育政策

    Grant number：15653018  2003 - 2005

    日本学術振興会  科学研究費助成事業 萌芽研究  萌芽研究

    古松 紀子, 横尾 昌紀

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    Grant amount：\3200000 （ Direct expense: \3200000 ）

    昨年度の研究成果をもとに以下の研究を引き続き行った.
    まず,合理的期待形成仮説のもとでの経済モデルの動学的振る舞いと,他の適応的期待形成仮説のもとでの経済モデルの動学的振る舞いをの違いを検討し,それらの異なった期待形成仮説のもとでの教育政策への影響についての検討を行った.その中で,カオスが発生している場合の比較の方法をFrobenius-Perron作用素を利用した不変測度に関する諸結果を用いての開発を試みた.また,同一の期待形成過程を有する経済主体の集団に異質な期待形成過程を有する経済主体の集団が僅かに混入した場合に,動学的挙動がどのような定性的変化を蒙るかを調べると同時に,教育政策にどのような変更を加えるべきか,あるいは,既存の教育政策が異質性の混入に対しどれだけ頑健であるかを検討した.動学モデルを構築した後は,その分析の際に,非線形力学系理論を援用してモデルのカオス的な動学的振る舞いを特徴付けることに重点を置いた.解析的には観測可能な複雑性を導くホモクリニック分岐やヘテロクリニック分岐の発生条件の導出,数値解析的には,パラメータ空間での分岐曲線の追跡プログラムと安定多様体/不安定多様体の精度保証付き計算プログラムの開発に主眼を置いた.さらに,カオスや複数アトラクターなど動学的な複雑性が存在する場合の教育政策の検討を行った.

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  • 力学系理論による経済変動モデルの研究

    Grant number：14730016  2002 - 2004

    日本学術振興会  科学研究費助成事業 若手研究(B)  若手研究(B)

    横尾 昌紀

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    Grant amount：\2700000 （ Direct expense: \2700000 ）

    "Threshold nonlinearities and asymmetric endogenous business cycles"と題した石田潤一郎氏(信州大学経済学部助教授)との共同論文が査読付学術雑誌Journal of Economic Behavior and Organization, vol.54,pp.175-189,2004に掲載された.また,この論文のひとつの発展として,石田氏とともに執筆した"Heterogeneity-induced chaos : an example"という論文(岡山大学経済学部Discussion Paper Series I-47)は改定中である.
    『地域間労働移動と内生的経済変動の発生』(北東アジア経済研究創刊号)では,地域(例えば岡山市)の人口の社会増加数の激しい変動に着目し,世代重複モデルを基礎に,それ変動を説明することが可能な数理モデルを構築し,そのモデルについてシミュレーション分析をおこなった.結果,労働移動を考慮しない経済では定常状態に単調に収束する経済変動パターンしか発生しない経済とは異なり,労働移動の可能性(および経済間の異質性)により,実態経済と整合的とみなしうるような内生的経済変動(周期変動,準周期変動,カオス変動)が生じることが数値計算により明らかとなった.
    "Contribution cycles and preferable incentive schemes", Okayama Economic Review36,では,金銭的なインセンティブを目当てに雑誌に論文を投稿する一定数の経済主体を想定し,論文1本あたりのインセンティブが一定な場合と,インセンティブの総額が一定で,それらを投稿者の間で分け合う戦略的な場合とで,どのような投稿論文数の時系列が生じ,またどちらのインセンディブスキームが望ましいかを検討した.結果後者の場合,カオス的な投稿循環が発生することが示された.また,後者のスキームが,インセンティブのための予算が少なく,特,にカオスが発生する場合は,論文数に関してより効果的であることが示された.
    "On dynamic effects of the number of players in a commons game : a tragedy of nutria in Okayama", forthcoming in Okayama Economic Review,では補助金により有害獣であるヌートリアの駆除をおこなう岡山市の取り組みを例に,この補助金スキームを捕獲者をプレーヤー,ヌートリア個体群をrenewable resourceとする一種の「共有地問題」としてモデル化し,そこでのヌートリアの個体群動態を力学系理論的手法を用いて分析した.結果,捕獲者の数の変化に応じて,個体群が定性的および定量的な変動パターンの変化をきたすことが例示された.特に,捕獲者数が中くらいの場合,観測可能なカオス的が生じることが示された.

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  • 力学系理論による経済変動モデルの研究

    Grant number：99J06130  1999 - 2000

    日本学術振興会  科学研究費助成事業 特別研究員奨励費  特別研究員奨励費

    横尾 昌紀

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    Grant amount：\1000000 （ Direct expense: \1000000 ）

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  • Introduction to Macroeconomics （2023academic year） 3rd and 4th semester  - 金10

  • Seminar on Macroeconomics （2023academic year） Late  - 火2

  • Macroeconomics 1 （2023academic year） Prophase  - 火2

  • Macroeconomics 2 （2023academic year） Late  - 火2

  • Macroeconomic Theory （2023academic year） Prophase  - その他

  • Seminar on Macroeconomic Theory 1 （2023academic year） Late  - その他

  • Seminar on Macroeconomic Theory 2 （2023academic year） special  - その他

  • Graduation Research Seminar （2023academic year） 1st and 2nd semester  - その他7～8

  • Graduation Research Seminar （2023academic year） 3rd and 4th semester  - その他7～8

  • Seminar （2023academic year） 1st and 2nd semester  - 月7～8

  • Seminar （2023academic year） 3rd and 4th semester  - 月7～8

  • Basic Seminar （2023academic year） Third semester  - 火7～8

  • Special Seminar 2(Division of Economic Theory and Policy) （2023academic year） Late  - その他

  • Challenge Seminar 1(Division of Economic Theory and Policy) （2023academic year） Prophase  - その他

  • Challenge Seminar 2(Division of Economic Theory and Policy) （2023academic year） Late  - その他

  • Challenge Seminar3(Division of Economic Theory and Policy) （2023academic year） Prophase  - その他

  • Challenge Seminar4(Division of Economic Theory and Policy) （2023academic year） Late  - その他

  • Game Theory （2022academic year） 1st and 2nd semester  - 月3～4

  • Macroeconomics （2022academic year） Prophase  - 水2

  • Introduction to Macroeconomics （2022academic year） 3rd and 4th semester  - 金3～4

  • Introduction to Macroeconomics （2022academic year） 3rd and 4th semester  - 水10

  • Seminar on Macroeconomics （2022academic year） Late  - 水2

  • Macroeconomics 1 （2022academic year） Prophase  - 水2

  • Macroeconomics 2 （2022academic year） Late  - 水2

  • Macroeconomic Theory （2022academic year） special  - その他

  • Seminar on Macroeconomic Theory 1 （2022academic year） special  - その他

  • Seminar on Macroeconomic Theory 2 （2022academic year） special  - その他

  • Graduation Research Seminar （2022academic year） 1st and 2nd semester  - その他

  • Graduation Research Seminar （2022academic year） 3rd and 4th semester  - その他

  • Seminar （2022academic year） 1st and 2nd semester  - 木7～8

  • Seminar （2022academic year） 3rd and 4th semester  - 月7～8

  • Basic Seminar （2022academic year） Third semester  - 火7～8

  • Challenge Seminar 1(Division of Economic Theory and Policy) （2022academic year） Prophase  - その他

  • Challenge Seminar 2(Division of Economic Theory and Policy) （2022academic year） Late  - その他

  • Game Theory （2021academic year） 1st and 2nd semester  - 月1～2

  • Macroeconomics II （2021academic year） 3rd and 4th semester  - 月1～2

  • Introduction to Macroeconomics （2021academic year） 3rd and 4th semester  - 金10

  • Introduction to Macroeconomics （2021academic year） 3rd and 4th semester  - 金10

  • Seminar on Macroeconomics 1 （2021academic year） Prophase  - 火4

  • Seminar on Macroeconomics 2 （2021academic year） Late  - 月2

  • Macroeconomic Theory （2021academic year） special  - その他

  • Seminar on Macroeconomic Theory 1 （2021academic year） special  - その他

  • Seminar on Macroeconomic Theory 2 （2021academic year） special  - その他

  • Graduation Research Seminar （2021academic year） 1st and 2nd semester  - その他

  • Graduation Research Seminar （2021academic year） 3rd and 4th semester  - その他

  • Seminar （2021academic year） 1st and 2nd semester  - 木7～8

  • Seminar （2021academic year） 3rd and 4th semester  - 木7～8

  • Seminar （2021academic year） 3rd and 4th semester  - 木7～8

  • Basic Seminar 1(Division of Economic Theory and Policy) （2021academic year） Prophase  - その他

  • Basic Seminar （2021academic year） Third semester  - 火7～8

  • Challenge Seminar 1(Division of Economic Theory and Policy) （2021academic year） Prophase  - その他

  • Game Theory （2020academic year） 1st and 2nd semester  - [第１学期]月5,月6, [第２学期]月1,月2

  • Introduction to Macroeconomics （2020academic year） Second semester  - 金3,金4

  • Introduction to Macroeconomics （2020academic year） 1st and 2nd semester  - 水10

  • Macroeconomics 1 （2020academic year） Prophase  - 水2

  • Macroeconomic Theory （2020academic year） special  - その他

  • Seminar on Macroeconomic Theory 1 （2020academic year） special  - その他

  • Seminar on Macroeconomic Theory 2 （2020academic year） special  - その他

  • Graduation Research Seminar （2020academic year） 1st and 2nd semester  - その他

  • Graduation Research Seminar （2020academic year） 3rd and 4th semester  - その他

  • Basic Seminar （2020academic year） 1st semester  - 月7,月8

  • Basic Seminar （2020academic year） Second semester  - 月7,月8

  • Challenge Seminar 1(Division of Economic Theory and Policy) （2020academic year） Prophase  - その他

  • Challenge Seminar 2(Division of Economic Theory and Policy) （2020academic year） Prophase  - その他

  • Challenge Seminar 2(Division of Economic Theory and Policy) （2020academic year） Late  - その他

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