宏观经济理性预期主从递阶动态对策研究
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摘要
21世纪的科学突出学科之间的相互交叉和融合，人们一直在尝试将宏观经济系统中人的因素纳入到宏观经济建模理论中。为此本文将二次最优控制理论和宏观经济理性预期思想相结合，以邹至庄的定常目标函数下的二次最优理性预期简单模型和Sean Holly、Paul Turner的二次最优完全理性预期模型为基础，进行了二次最优完全理性预期模型的研究，并在此基础上构造了中央和地方对策模型，利用Stackelberg主从对策思想，进行了中央和地方对策模型的研究。首先，在宏观经济建模过程中，利用Chow、Sean Holly、Paul Turner的思想即将控制变量直接纳入到指标函数中，我们提出了完全理性预期概念。但是，由于经济系统本身的特殊性，在构造模型时，利用期望响应来构造二次最优完全理性预期模型是不合理的，这主要是由于经济系统固有的均衡轨道的存在。因此，我们将一致指数增长波动趋势纳入到目标函数中，基于二次最优动态叠加目标函数对模型进行一系列的研究。在上述的指标函数和动态叠加目标函数下建立二次最优完全理性预期模型，并通过最优化理论解决了闭环参数的估计问题。最后，从理论和仿真上证明了均衡轨道的存在，并定量地给出了动态叠加目标函数下均衡轨道的解析表达式，而且确定性均衡轨道仿真取得了较好的拟合结果。
由于传统经济学是在动力学理论的基础上构造宏观经济模型，主要是利用差分方程来描述，并且经济和社会系统是由会思考、有反应能力的智能体组成，因此，利用传统经济学研究宏观经济系统时必将丢失许多重要信息。为此我们基于多智能体构造宏观经济模型，通过Swarm仿真建立人工实验，确定了税率和信贷对宏观经济的作用，即税率可以调节和控制地方之间经济的波动相位；信贷能够控制宏观经济的波动幅度，并且会影响经济的发展速度。由此我们确定经济波动性的产生是由于企业的破产和重组，而通过控制信贷水平可以控制企业的破产规模，从而可以控制经济运行的大环境；另一方面，从长期来看，我们提出税率水平对经济发展的规模影响不大，但是，从短期看，它对经济发展过程中的波动相位影响较大即它会影响经济发展的速度和波动的幅度。基于上述思想，我们利用理性预期理论和Stackelberg主从对策思想构造了中央和地方对策模型的实验平台。在这实验平台上，我们进行了一系列中央和地方动态对策的人工实验。
本文力图较完整地把二次最优理性预期理论、多智能体建模思想和Stackelberg主从对策思想应用到宏观经济系统中，建立符合宏观经济理论思想、逼近客观实际的宏观经济模型，为宏观经济系统分析和决策提供理论依据，并为中央和地方经济动态对策建立理论基础。
It is emphasized that science intercross and syncretize each other in 21st century. People always try to bring human factors into modeling theory of macroeconomy. Therefore, this paper combines the theory of quadratic optimal control and the idea of rational expectation in macroeconomy. On the basis of Chow's simple model with rational expectation of quadratic optimum, Sean Holly and Paul Turner's model with complete rational expectation of quadratic optimal, we have done the study of the complete rational expectation model of quadratic optimal, and construct the game model between Central and Provinces. We have studied the game model between Central and Provinces by use of the idea of Stackelberg principal subordinate decreasing game.
Firstly, in the process of modeling macroeconomy, we bring forward the concept of complete rational expectation, based on the idea of Chow , Sean Holly and Paul Turner bringing control variables directly into target function. But on the account of the particularity and the existence of innate equilibrium paths of the economic system, it is unreasonable for us to construct the complete expectation model of quadratic optimal by the use of expecting response. So we bring uniform exponential growth into objective function and do a series of research based on the quadratic optimal dynamic adding objective function. Based on them, we construct complete rational expectation model. We solve the problem of estimation of the parameters of closed loop by the means of optimal theory. Finally, the existence of the equilibrium paths is proved theoretically and practically, and the analytic formulae of the equilibrium paths are derived under dynamic adding objective function. Furthermore, the simulation of definite equilibrium paths obtains quite good results.
On account of that macroeconomic model is modeled based on the theory of kinetics, that the economic and social system is composed of agents who can think and response, much information will be neglected by the use of conventional economics. Therefore, we model macroeconomic model based on multi-agents. Through the artificial experiment in Swarm, It's certain that revenue and loan play
part on Macroeconomy, namely revenue can adjust and control the fluctuating phase of Provinces economy and loan can control the fluctuating scope of economy , furthermore it will affect the speed of economic development. we are assured that the economy fluctuation occurs because of the bankrupt and organization of the enterprises. We can control the bankrupt scale of the enterprise through the control of the credit level. On the other hand, we believe that the level of revenue has slight impact on the development of economy in the long run, however in the short run, it has heavy impact on the fluctuation phase of economy and will affect the development pace of economy. Based on above ideas, we construct the interface of the game model between Central and Provinces through the use of rational expectation theory and the idea of Stackelberg principal subordinate decreasing game, and we do a series of artificial experiments about Central and Provinces.
This paper tries to completely apply rational expectation theory of quadratic optimal, the idea of modeling based on multi-agents and Stackelberg principal subordinate game to macroeconomic system. So we can model macroeconomic fit for dynamic game between central and districts , furthermore, the model accords with macroeconomic theory and reality.
由于传统经济学是在动力学理论的基础上构造宏观经济模型，主要是利用差分方程来描述，并且经济和社会系统是由会思考、有反应能力的智能体组成，因此，利用传统经济学研究宏观经济系统时必将丢失许多重要信息。为此我们基于多智能体构造宏观经济模型，通过Swarm仿真建立人工实验，确定了税率和信贷对宏观经济的作用，即税率可以调节和控制地方之间经济的波动相位；信贷能够控制宏观经济的波动幅度，并且会影响经济的发展速度。由此我们确定经济波动性的产生是由于企业的破产和重组，而通过控制信贷水平可以控制企业的破产规模，从而可以控制经济运行的大环境；另一方面，从长期来看，我们提出税率水平对经济发展的规模影响不大，但是，从短期看，它对经济发展过程中的波动相位影响较大即它会影响经济发展的速度和波动的幅度。基于上述思想，我们利用理性预期理论和Stackelberg主从对策思想构造了中央和地方对策模型的实验平台。在这实验平台上，我们进行了一系列中央和地方动态对策的人工实验。
本文力图较完整地把二次最优理性预期理论、多智能体建模思想和Stackelberg主从对策思想应用到宏观经济系统中，建立符合宏观经济理论思想、逼近客观实际的宏观经济模型，为宏观经济系统分析和决策提供理论依据，并为中央和地方经济动态对策建立理论基础。
It is emphasized that science intercross and syncretize each other in 21st century. People always try to bring human factors into modeling theory of macroeconomy. Therefore, this paper combines the theory of quadratic optimal control and the idea of rational expectation in macroeconomy. On the basis of Chow's simple model with rational expectation of quadratic optimum, Sean Holly and Paul Turner's model with complete rational expectation of quadratic optimal, we have done the study of the complete rational expectation model of quadratic optimal, and construct the game model between Central and Provinces. We have studied the game model between Central and Provinces by use of the idea of Stackelberg principal subordinate decreasing game.
Firstly, in the process of modeling macroeconomy, we bring forward the concept of complete rational expectation, based on the idea of Chow , Sean Holly and Paul Turner bringing control variables directly into target function. But on the account of the particularity and the existence of innate equilibrium paths of the economic system, it is unreasonable for us to construct the complete expectation model of quadratic optimal by the use of expecting response. So we bring uniform exponential growth into objective function and do a series of research based on the quadratic optimal dynamic adding objective function. Based on them, we construct complete rational expectation model. We solve the problem of estimation of the parameters of closed loop by the means of optimal theory. Finally, the existence of the equilibrium paths is proved theoretically and practically, and the analytic formulae of the equilibrium paths are derived under dynamic adding objective function. Furthermore, the simulation of definite equilibrium paths obtains quite good results.
On account of that macroeconomic model is modeled based on the theory of kinetics, that the economic and social system is composed of agents who can think and response, much information will be neglected by the use of conventional economics. Therefore, we model macroeconomic model based on multi-agents. Through the artificial experiment in Swarm, It's certain that revenue and loan play
part on Macroeconomy, namely revenue can adjust and control the fluctuating phase of Provinces economy and loan can control the fluctuating scope of economy , furthermore it will affect the speed of economic development. we are assured that the economy fluctuation occurs because of the bankrupt and organization of the enterprises. We can control the bankrupt scale of the enterprise through the control of the credit level. On the other hand, we believe that the level of revenue has slight impact on the development of economy in the long run, however in the short run, it has heavy impact on the fluctuation phase of economy and will affect the development pace of economy. Based on above ideas, we construct the interface of the game model between Central and Provinces through the use of rational expectation theory and the idea of Stackelberg principal subordinate decreasing game, and we do a series of artificial experiments about Central and Provinces.
This paper tries to completely apply rational expectation theory of quadratic optimal, the idea of modeling based on multi-agents and Stackelberg principal subordinate game to macroeconomic system. So we can model macroeconomic fit for dynamic game between central and districts , furthermore, the model accords with macroeconomic theory and reality.
引文
1 盛昭瀚.主从递阶决策论——Stackelberg问题.科学出版社,1998：28~32
2 Soren Johansen，Anders Rygh Swensen. Testing exact rational expectations in cointegrated vector autoregressive models. Journal of Econometrics. 1999，(93)：73~91
3 吴国富等. 经济系统的预期不确定性与模型选择. 系统工程理论与实践. 1999，19(12)：48~51
4 苏丽等. 二次最优完全理性预期Riccati稳态方程.哈尔滨理工大学学报. 2001，（5）： 92-95
5 罗汉. 诺贝尔获奖者演说文集——经济学奖（1969年-1995年）（上、下）. 上海：上海人民出版社出版，1999：78~19
6 G.C.Chow. 经济计量学. 郑宗成. 北京：中国友谊出版公司，1988：139~141
7 Hans M. Amman，David A. Kendrick. Computing the steady state of linear quadratic optimization models with rational expectation. Economics Letters. 1998，(58)：185~191
8 司春林. 经济控制论. 北京：中国展望出版社，1989：250~251
9 李卓立. 实用经济计量学. 北京：清华大学出版社，1987：321~327
10 CHOW G C.用控制方法进行计量经济分析. 侯先荣等译.北京：中国友谊出版公司,1987：375~377
11 张守一. 现代经济对策论. 北京：高等教育出版社，1998：421~424
12 Luna ，Benedikt Stefansson. Economic Simulations in Swarm：Agent-Based Modelling and Object Oriented Programming. Kluwer Academic publishers. 2000：123~132
13 R.B. Carroll，D.A. Brask. A practical implementation for solutions to the algebraic matrix Riccati equation in a LQCM setting. Journal of Economic Dynamics and Control. 1998，(23)：1~7
14 景旭等. 二次最优合理预期模型. 数量经济技术经济研究. 1997，(3)： 45~52
15 景旭等. 宏观增长经济二次最优Riccati稳态方程. 哈尔滨理工大学学报. 1999，(3)：81~84
16 景旭等. 宏观非一致增长波动经济二次最优完全控制模型. 哈尔滨理工大学学报. 2000，(5)：68~72
17 景旭等. 宏观经济二次最优合理预期简单模型. 哈尔滨理工大学学报. 2000，(6)：64~67
18 景旭等. 一致增长波动趋势二次最优闭环模型. 电机与控制学报. 2001，(1)： 11~15
19 薛楠等. 宏观增长波动经济均衡轨道. 哈尔滨理工大学学报. 2001，(5)：89~91
20 何维凌，邓英淘. 经济控制论. 成都：四川人民出版社出版，1984：12~23
21 朱延福，蔡玲，胡雪萍. 宏观经济学. 北京：统计出版社，1995：432~441
22 罗伯特.E.霍尔，约翰.B.泰勒. 宏观经济学—理论运行和政策. 北京：中国经济出版社，1992：115~132
23 张钟俊等. 经济控制论——控制理论在经济管理中的应用. 西安：西安电子科技大学出版社，1991：37~52
24 贺允东. 经济控制论. 成都：西南交通大学出版社，1988：321~342
25 曾云宝等. 罚函数乘子的初值选取和多步长问题. 哈尔滨理工大学学报. 2003，(1)：20~22
26 吴沧浦. 最优控制的理论与方法. 北京：国防工业出版社，2000：129~135
27 薛毅. 最优化理论与方法. 北京：北京工业大学出版社，2001：354~376
28 张金水. 经济控制论——动态经济系统分析方法与应用. 北京：清华大学出版社，1999：18~32
29 朱延福. 论宏观经济运行的常态——兼评均衡轮与非均衡论之争. 东 岳论丛. 1992，(6)：40~46
30 Hans M. Amman，David A. Kendrick. Computing the steady state of linear quadratic optimization models with rational expectation. Economics Letters. 1998，(58)：185~191
31 Andrew Hughes Hallett. Analyses in Macroeconomic Modelling. Kluwer Academic Publishers. 1999：57~64
32 吴广玉，范钦义，姜复兴，汪德辉. 系统辩识与自适应控制. 哈尔滨：哈尔滨工业大学出版社，1987：412~436
33 符曦. 系统最优化及控制. 北京：机械工业出版社，1995：13~21
34 庆凯，王肇明. 优化与最优控制中的计算方法. 北京：科学出版社， 1986：321~346
35 陈宝林. 最优化理论与算法. 北京：清华大学出版社，2000：523~540
36 G.C.Chow.The Lagrange Method of Optimization with Applications to Portfolio and Investment Decisions.Journal of Economic Dynamics and Control.1996 20(1-3):1~18
37 G.C.Chow. Optimal control without solving the Bellman equation. J. Economic Dynamics & Control.1993 17(4):621-630
38 Yum K. Kwan. Chow's method of optimal control : A numerical Solution.J.Economic Dynamics And Control.1997 21(4-5):739~752
39 Michael Reiter.Chow's method of optimal control.Joural of Economic Dynamics And Control.1997 21(4-5):723~737
40 Luca Fanelli. A new approach for estimating and testing the linear quadratic adjustment cost model under rational expectations and I(1) variables.J.Economic Dynamics And Control.2002 26(1):117~139
41 欧阳莹之.复杂系统理论基础.上海：上海科技教育出版社,2002：327~335
42 苏丽. 二次最优完全理性预期模型. 哈尔滨理工大学硕士学位毕业论文, 2002
2 Soren Johansen，Anders Rygh Swensen. Testing exact rational expectations in cointegrated vector autoregressive models. Journal of Econometrics. 1999，(93)：73~91
3 吴国富等. 经济系统的预期不确定性与模型选择. 系统工程理论与实践. 1999，19(12)：48~51
4 苏丽等. 二次最优完全理性预期Riccati稳态方程.哈尔滨理工大学学报. 2001，（5）： 92-95
5 罗汉. 诺贝尔获奖者演说文集——经济学奖（1969年-1995年）（上、下）. 上海：上海人民出版社出版，1999：78~19
6 G.C.Chow. 经济计量学. 郑宗成. 北京：中国友谊出版公司，1988：139~141
7 Hans M. Amman，David A. Kendrick. Computing the steady state of linear quadratic optimization models with rational expectation. Economics Letters. 1998，(58)：185~191
8 司春林. 经济控制论. 北京：中国展望出版社，1989：250~251
9 李卓立. 实用经济计量学. 北京：清华大学出版社，1987：321~327
10 CHOW G C.用控制方法进行计量经济分析. 侯先荣等译.北京：中国友谊出版公司,1987：375~377
11 张守一. 现代经济对策论. 北京：高等教育出版社，1998：421~424
12 Luna ，Benedikt Stefansson. Economic Simulations in Swarm：Agent-Based Modelling and Object Oriented Programming. Kluwer Academic publishers. 2000：123~132
13 R.B. Carroll，D.A. Brask. A practical implementation for solutions to the algebraic matrix Riccati equation in a LQCM setting. Journal of Economic Dynamics and Control. 1998，(23)：1~7
14 景旭等. 二次最优合理预期模型. 数量经济技术经济研究. 1997，(3)： 45~52
15 景旭等. 宏观增长经济二次最优Riccati稳态方程. 哈尔滨理工大学学报. 1999，(3)：81~84
16 景旭等. 宏观非一致增长波动经济二次最优完全控制模型. 哈尔滨理工大学学报. 2000，(5)：68~72
17 景旭等. 宏观经济二次最优合理预期简单模型. 哈尔滨理工大学学报. 2000，(6)：64~67
18 景旭等. 一致增长波动趋势二次最优闭环模型. 电机与控制学报. 2001，(1)： 11~15
19 薛楠等. 宏观增长波动经济均衡轨道. 哈尔滨理工大学学报. 2001，(5)：89~91
20 何维凌，邓英淘. 经济控制论. 成都：四川人民出版社出版，1984：12~23
21 朱延福，蔡玲，胡雪萍. 宏观经济学. 北京：统计出版社，1995：432~441
22 罗伯特.E.霍尔，约翰.B.泰勒. 宏观经济学—理论运行和政策. 北京：中国经济出版社，1992：115~132
23 张钟俊等. 经济控制论——控制理论在经济管理中的应用. 西安：西安电子科技大学出版社，1991：37~52
24 贺允东. 经济控制论. 成都：西南交通大学出版社，1988：321~342
25 曾云宝等. 罚函数乘子的初值选取和多步长问题. 哈尔滨理工大学学报. 2003，(1)：20~22
26 吴沧浦. 最优控制的理论与方法. 北京：国防工业出版社，2000：129~135
27 薛毅. 最优化理论与方法. 北京：北京工业大学出版社，2001：354~376
28 张金水. 经济控制论——动态经济系统分析方法与应用. 北京：清华大学出版社，1999：18~32
29 朱延福. 论宏观经济运行的常态——兼评均衡轮与非均衡论之争. 东 岳论丛. 1992，(6)：40~46
30 Hans M. Amman，David A. Kendrick. Computing the steady state of linear quadratic optimization models with rational expectation. Economics Letters. 1998，(58)：185~191
31 Andrew Hughes Hallett. Analyses in Macroeconomic Modelling. Kluwer Academic Publishers. 1999：57~64
32 吴广玉，范钦义，姜复兴，汪德辉. 系统辩识与自适应控制. 哈尔滨：哈尔滨工业大学出版社，1987：412~436
33 符曦. 系统最优化及控制. 北京：机械工业出版社，1995：13~21
34 庆凯，王肇明. 优化与最优控制中的计算方法. 北京：科学出版社， 1986：321~346
35 陈宝林. 最优化理论与算法. 北京：清华大学出版社，2000：523~540
36 G.C.Chow.The Lagrange Method of Optimization with Applications to Portfolio and Investment Decisions.Journal of Economic Dynamics and Control.1996 20(1-3):1~18
37 G.C.Chow. Optimal control without solving the Bellman equation. J. Economic Dynamics & Control.1993 17(4):621-630
38 Yum K. Kwan. Chow's method of optimal control : A numerical Solution.J.Economic Dynamics And Control.1997 21(4-5):739~752
39 Michael Reiter.Chow's method of optimal control.Joural of Economic Dynamics And Control.1997 21(4-5):723~737
40 Luca Fanelli. A new approach for estimating and testing the linear quadratic adjustment cost model under rational expectations and I(1) variables.J.Economic Dynamics And Control.2002 26(1):117~139
41 欧阳莹之.复杂系统理论基础.上海：上海科技教育出版社,2002：327~335
42 苏丽. 二次最优完全理性预期模型. 哈尔滨理工大学硕士学位毕业论文, 2002
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