Updated on 2024/04/18


INABA, Toshio
Faculty of Education and Integrated Arts and Sciences
Job title
Professor Emeritus

Professional Memberships









Research Areas

  • Economic statistics


  • 年齢・世代効果を補正した需要弾力性の計測

    森宏, 石橋喜美子, 田中正光, 稲葉敏夫

    社会科学年報 専修大学   39   39 - 59  2005.03

  • 高齢化の進展の下で米・鮮魚の消費はどうなるかーコウホート分析

    森宏, 田中正光, 稲葉敏夫

    社会科学年報 専修大学   38 ( 38 ) 41 - 62  2004.03


  • 清酒およびビールの家計消費の将来予測-コウホート分析

    田中正光, 森宏, 稲葉敏夫, 石橋喜美子

    季刊 家計経済研究   61 ( 61 ) 50 - 61  2004.01


  • Re-estimating per Capita Individual Consumption by Age from Household Data

    M.Tanaka, H.Mori, T.Inaba

    Jpn. J. of Rural Econ.   6   20 - 30  2004

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    Mori and Inaba proposed an estimation method of deriving individual consumption by age from macro data classified by age of household head (HH), using quadratic programming, 1997. We replaced their approach by regression with weights which are determined by the magnitude of standardized residuals, following the leads of Huber, 1981 and Minotani, 1992. Using our revised method which provides objective statistics, the estimates of per capita individual consumption of fresh fruit and fresh fish, respectively, by non-adults are substantially larger and those for the young adults somewhat smaller in our studies than in previous studies. It seems quite apparent that Japanese children and young adults have decreased their at-home consumption of these products substantially in recent years. Those older than 50years of age seem to have maintained their consumption at relatively high levels.

    DOI CiNii

  • ビール・清酒消費の年齢・世代・時代効果

    日本統計学会    2002.09

  • Projection of At-home Fresh Fish Consumption by Cohort Approach

    日本農業経済学会    2002.03

  • Nonlinear Macroeconomic Dynamics: A Study of Noise Effects

    稲葉敏夫, 浅田統一郎, 三澤哲也

    電子情報通信学会・信学技報   NLP2001-64   79 - 88  2001.11

  • A Nonlinear Macroeconomic Dynamic Model: Its dynamics and Noise Effects

    The 7th International Workshop on Similarity in Diversity    2001.09

  • An Interregional Dynamic Model: The Case of Fixed Exchange Rates

    Toichiro Asada, Toshio Inaba, Tetsuya Misawa

    Studies in Regional Science   31 ( 2 ) 29 - 41  2001

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    In this paper, we consider a nonlinear macrodynamic model which describes the economic transaction between two regions. We suppose that the economic structures of both regions are characterized by the Kaldorian business cycle model with money, and two regions are connected through Interregional trade and interregional capital movement. We study the dynamic behavior of such a system under fixed exchange rates by means of analytical method and numerical simulations. © 2001, JAPAN SECTION OF THE REGIONAL SCIENCE ASSOCIATION INTERNATIONAL. All rights reserved.


  • An Inetrregional Dynamic Model

    日本地域学会    2000.11

  • Nonlinear Economic Dynamics in a Two-Country Model with Fixed Exchange Rates

    T.Asada,T.Inaba, T.Misawa

    Proceedings of International Symposium on Nonlinear Theory and its Applications   2   515 - 518  2000.09

  • Nonlinear Dynamics in a Two-Country Model

    The Second International Conference on Discrete Chaotic Dynamics in Nature and Society    2000.05

  • Chaotic dynamics in a flexible exchange rate system: A study of noise effects

    T Asada, T Misawa, T Inaba

    DISCRETE DYNAMICS IN NATURE AND SOCIETY   4 ( 4 ) 309 - 317  2000

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    In this paper, we investigate by means of analytical method and numerical simulations the properties of three-dimensional business cycle model, in which foreign exchange rate is flexible and a parameter is fluctuated by noise. The model is a discrete time version of Asada (Journal of Economics, 62, 239-269, 1995)'s continuous time open economy model without noise. We show (1) noise may suppress the burst of flexible foreign exchange rate when its behavior begins to burst as a bifurcation parameter (adjustment speed of the goods market) is increased, (2) the windows of cycles can be broken by noise, and (3) noise may reveal the hidden structures.

  • A nonlinear macrodynamic model with fixed exchange rates: Its dynamics and noise effects

    T Asada, T Inaba, T Misawa

    DISCRETE DYNAMICS IN NATURE AND SOCIETY   4 ( 4 ) 319 - 331  2000

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    In this paper, we formulate a discrete time version of the Kaldorian macrodynamic model in a small open economy with fixed exchange rates. The model is described by a system of the three-dimensional nonlinear difference equations with and without stochastic disturbances (noise effects). We study the local stability/instability properties analytically by using the linear approximation method, and chaotic dynamics with and without noise effects are investigated by means of numerical simulations, In general, it is believed that the effect of the noise is to obscure the basic structure of the system. But, this is not necessarily the case. We show by means of numerical analysis that the noise can reveal the hidden structure of the model contrary to the usual intuition in some situations.

  • Window Ipmplies Chaos while Chaos Implies Cycles

    Proceedings of International Symposium on Nonlinear Theory and its Applications   2,pp.539-542  1999.12

  • 変動相場制のマクロ動学分析;カオス的変動とノイズ効果

    中央大学経済研究所年報   30;pp.63-77  1999.03

  • Nonlinear business cycle model with flexible foreign exchange rates: noise effects on the dynamics

    Proceedings of International Symposium on Nonlinear Theory and its Applications   3,pp.1209-1212  1998.09

  • ノイズ摂動が3次元非線形景気循環モデルの挙動に及ぼす影響

    日本統計学会大会報告(共同研究)    1998.07

  • 開放経済における非線型マクロ動学モデル:数値シミュレーション分析

    経済学論纂(中央大学経済学部)   38巻;5,6合併号/P181-200  1998.03

  • Nonlinear business cycle model in an open economy : noise effects on the dynamics

    Proceedings of International Symposium on Nonlinear Theory and its Applications   vol.1/P505-508  1997.12

  • Estimating individual fresh fruits consumption by age,1979 to 1994

    農業経済研究(農業経済学会)   69巻;3号/P175-185  1997.12

  • 景気循環モデルにおけるカオス

    理論・計量経済学会    1997.09

  • 非線形景気循環モデルにおけるノイズ摂動の影響

    日本統計学会65回大会    1997.07

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Research Projects

  • Restructuring Economics Education for the Connection between Senior High School and University and an International Comparative Study of Students' Economic Literacy

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :


    YAMAOKA Michio, MANO Yoshiki, HIGUCHI Kiyohide, INABA Toshio, ASANO Tadayoshi, ABE Shintaro, TAKAHASHI Keiko

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    Disconnection of the contents of economic education between senior high school and university in Japan was examined, and the problems of curriculum in universities for effective and efficient economics learning for students were pointed out. The personal financial literacy test was conducted for senior high school and university students in Japan, and the results were analyzed. The common economic literacy test for university students was administered in Japan, the US, Korea, the Philippines and New Zealand, and the test results made Japanese students' economic understanding clearer.

  • Interdisciplinary Study on Reconstruction of Oligopoly and Duopoly theory based on Nonlinear Dynamic theory

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :


    MATSUMOTO Akio, KAWASAKI Yasuo, ASADA Toichoro, ISHIKAWA Toshiharu, YABUTA Masahiro, INABA Toshio

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    This study extends the traditional dynamics study on Oligopoly and Duopoly models in two directions : one is to consider the effects caused by strong nonlinearities on dynamics, using the nonlinear economic dynamics theory and the other is to consider the effect caused by spatial factors.
    The main results that we obtain are the followings.
    1.Construction of attractor sets that trajectories converge when a stationary point is locally unstable.
    2.Clarification of the relation between parameters values and the structure of basin in a case of multistability.
    3.Construction of analytical solutions when a stationary state is locally stable.
    4.Possible occurrence of complex dynamics when spatial elements are introduced into the traditional regional model.
    5.Comparison of the effect caused by a delayed stabilization policy with the effect caused by spatial elements.

  • Economic Reseach on Global Environmental Problems

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :


    MATSUMOTO Akio, INABA Toshio, YOKOYAMA Akira, ANIKA Yuji, MISAWA Tetsuya

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    The study constrocts multi-dimensional nonlinear dynamic economic models that are useful for considering the long-run dynamic phenomenon observed in not only economics but also other areas such as ecology, biology, global warming, etc.
    This study has three parts. The first part investigates an economic implication of chaotic fluctuations that are observed in a nonlinear economic dynamic model. To this end, it constructs a nonlinear discrete time Cournot duopoly model in which firms have U-shaped or inverted U-shaped reaction functions due to production externality and shows that chaotic output fluctuations can arise for strong nonlinearities. Two main results are the following: (1) it is theoretically as well as numerically confirmed that one of the duopolists can benefit in the sense that the long-run average profit taken along a chaotic trajectory is higher than the profit taken at an equilibrium point, while the rival is disadvantaged if both duopolists are homogeneous; (2) is it verified with numerical simulations that both duopolists can benefit from chaotic trajectories if they are heterogeneous.
    The second part of this study focuses on the stable fixed point and derives the particular analytic solutions, as well as general solutions of the Cournot adjustment process of output. Since there are, in general, difficulties in finding analytical solutions in a discrete time system, it is worthwhile to present the existence conditions for analytical solutions.
    The last part constructs a two (agricultural and manufactured) sector general equilibrium model and studies the dynamic path of the economy and the global temperatures. It is numerically demonstrated that the dynamic interaction between the stable climate system and the stable market adjustment process can generate various dynamics ranging from periodic cycle to chaotic fluctuations

  • Study of Economic Fluctuations Using the Method of Nonlinear Dynamics

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :


    INABA Toshio, TANAKA Hisanori, WARAGAI Tomoki, SASAKURA Kazuyuki, MISAWA Tetsuya, MATSUMOTO Akio

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    (1) One Dimensional Models
    Chaos occurs in a nonlinear cobweb model with normal demand and supply, naive expectations and adaptive production adjustment. We demonstrates the possibility that chaotic fluctuations may be preferable to a steady state for a simple macro disequilibrium model in which inventory can be chaotically fluctuated.
    (2) High Dimensional Models
    We investigate the global dynamics of two-dimensional Diamond-type overlapping generations model extended to allow for government intervention. We identify conditions under which transverse homoclinic points to the golden rule steady state are generated. We examine by mean of analytical method and numerical simulations the properties of three-dimensional Kaldor-type business cycle models in which a parameter is fluctuated by noise. It is shown that noise may not obscure the underling structures, but also reveal the hidden structures.
    (3) New Numerical Approximation Schemes
    Composition methods for autonomous stochastic differential equations (SDEs) are formulated to produce numerical approximation schemes for the equations. The new schemes are advantageous to preserve the special character of SDEs numerically and are useful for approximations of the solutions to stochastic nonlinear equations
    (4) Alternative Approaches and Models
    We investigate various alternative approaches and models. For example, percolation theory is employed to model stock price fluctuations.


Overseas Activities

  • 非線形経済動学の研究と食糧消費の分析


    オーストリア   国際応用システム分析研究所

Internal Special Research Projects

  • 非線形動学の方法による経済変動の研究


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     貿易と資本移動を通じて相互依存の関係にある2国経済モデル(5次元非線形差分方程式体系)の動学的性質を数値シミュレーションによって調べた。モデルはカルドア型の不均衡マクロモデルを想定した。 固定相場制および変動相場制の下で,景気循環の同期現象・非同期現象をはじめとして,多様な関連があり得ることを数値例によって示した。2国の所得調整速度が同一であれば,多くの場合景気は同じ動きを示し,同期するが,初期値を変更することによって2国の好況・不況の関係が完全に逆転し,逆相現象が現れることもあり得る。2国間の資本移動の流動性の程度を表すパラメータがノイズによって摂動されると系の挙動が大きく変わることも示された。2国間の所得調整速度の差異が大きくなればなるほど,短期的な同期現象は崩れ,逆相現象が顕著になるものの,中・長期的な波としては同期現象見られることが示された。 また、2国モデルの拡張として固定相場制の下での3国モデルについても試みた。

  • 非線形経済モデルの挙動にノイズが及ぼす影響


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     5次元非線形差分方程式で記述される、開放経済系2国モデルの動学的性質を調べた。次元が高いため解析的取り扱いは困難であるので、数値計算によって挙動を分析した。2国はともにカルドアタイプで記述されるものと想定し、財市場に不均衡の調整過程を導入した。2国は財・サービスの輸出入および資本の移動を通じて相互依存の関係にある。簡単化のために固定相場制の場合を扱った。2国間に貿易も資本移動も共にない場合、2国の国民所得はそれぞれの均衡点に単調に収束する。しかし貿易および資本移動を通じて関連しあう場合、多様な挙動が作り出されることが示された。2国が同一の経済構造を有するときは2国の景気循環は完全に同期し、しかも周期的な動きをする。ところが一方の国の所得調整速度を若干高めると2国は全く逆の景気の動きをする、つまり一方の国が好景気のとき他国は不景気の状態にある。所得調整速度をさらに高めると再び2国の景気の動きは同期する。所得調整速度を増加させるに従い、2国の景気の動きにはタイムラグが現れ、景気循環の周期も大きくなる。やがて周期的な動きが崩れカオス的な振る舞いが現れる。 ノイズが2国の景気循環に及ぼす影響を調べるために、2国間の資本移動の容易さを示すパラメータに摂動(確率的ノイズ)を付加した。ノイズがなければ同期を示していた2国の景気状態は逆転し、一方が好景気のとき他方は不景気となる。また高い周期でタイムラグを伴いながら変動していた2国の景気は僅かなノイズによって不規則な景気循環を示すようになる。以上のように、パラメータに摂動が加わることによって2国の経済変動の関係が大幅に変化する、不安定性があることが示された。

  • 非線形景気循環モデルの挙動にノイズが及ぼす影響の研究


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  • 非線形経済系の挙動に及ぼすノイズの影響の研究


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  • 経済現象における非線形性の分析


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  • 経済現象における非線形性の分析


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    幾らか周期性があるものの不規則的挙動を示すことの多い経済時系列を,非線形性の観点から分析した。主として以下の2点に焦点を絞って研究した。一つは,経済変数間の動学的関係の抽出であり,他の一つはノイズが非線形関係に及ぼす影響である。 経済変数間の動学的関係の抽出については,四半期国民所得系列データの多数の系列の3次元埋め込みを行い,軌道を再構築し,それらのポアンカレ断面及び断面上の性質を調べた。その結果,国内総生産,民間設備投資そして民間住宅投資のデータに関しては決定論性,とりわけカオスの可能性があることが示された。従来時系列データにおけるカオスの判定は相関次元,リャプノフ指数などが使用されてきたが,それら指標について問題点が指摘されていることもあり,本研究においては従来とは異なった観点からデータの性質を判定した。 経済系が社会システムにおけるサブシステムに過ぎないのであれば,政治などの他のサブシステムとは独立しているとは考え難い。他のサブシステムからの不断の影響を受けていると考えた方が自然であろう。その様な不断の影響をノイズとしてとらえ,非線形の経済系の挙動がノイズによって如何に影響を受けるかを調べた。これまで幾つかのシミュレーションによって示されていることは,周期的な軌道はそれほど大きくないノイズによって周期性が弱まりはするが周期そのものは保存される。また非周期的な軌道にあっては不規則性が一層強くなることである。 これに対して,周期アトラクターの窓での周期は極めて小さなノイズによってさえもカオテイックとなることがあるのを示した。また不規則生の極めて強い状態においてノイズは規則性を強めることをも示した。

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