一类时滞Solow模型的动态周期波动分析

考虑到资本生产投资和污染治理投资的时滞性,为分析其对经济环境系统动态演化的影响机理,基于经典的Solow模型,引入环境净化和两个投资时滞参数.首次提出了带有环境净化的双时滞Solow模型,并分析了该模型的动态周期波动行为.结果表明:无论单个投资时滞还是两个投资时滞,均能诱发经济周期的产生;时滞越大,经济周期波动越强烈;通过调整投资决策可达到预期均衡目标,实现经济环境系统的周期稳定运行.     

山东省人力资本与经济增长关系的实证分析

利用有效劳动模型,选取1978—2016年山东省的统计数据,运用因子分析的方法测算人力资本存量,永续盘存费计算物质资本存量,分析山东省人力资本与经济增长之间的关系.结果表明,山东省人力资本对经济增长有促进作用,且已超过物质资本投资对经济增长的促进作用,但对经济增长的实际贡献率水平低于物质资本.为更好发挥人力资本对经济增长的促进作用,提出了提高教育投资,加快高等教育建设,采取柔性人才吸引政策、调整产业结构等建议.     

一个经济周期模型的稳定性及其近似解

以GDP为研究对象建立了一个新的经济周期模型.首先研究了经济周期模型在不动点处的稳定性以及分岔行为;解释了稳定极限环与经济周期之间的关系;然后利用多尺度摄动法得到了此模型的一阶近似解,分析了收入变量在一个经济周期中的波动过程.     

经济政策不确定性对中国生态农业上市公司投资的影响——基于2010-2017年季度数据的实证分析

从生态农业政策视角出发,选取2010-2017年A股生态农业上市公司季度数据作为研究样本,利用中国经济政策不确定性指数构建研究变量,实证检验经济政策不确定性对生态农业上市公司投资的影响.结果表明,在控制季度效应和季节效应下,EPU系数分别为-0.0029、-0.0030,均在1%的显著性水平下显著,说明经济政策不确定性会显著减少生态农业上市公司投资,且主要来自于投资不可逆转性较低、投资回报率较低的子样本.研究结果对于从生态农业投资的视角理解中国生态农业政策实施效果具有一定意义.提出面对经济政策变动时,生态农业上市公司应该充分考虑自身生产、经营的特征来优化投资决策以及国家经济政策制定机构应该根据生态农业上市公司面对经济政策不确定性时的反应,采取积极的措施,在稳定经济政策的基础上降低经济政策调整带来的不利影响.     

两部门内生增长模型中财政政策的短期分析

在一个两部门内生增长模型中,讨论政府财政政策变化对居民消费,资本积累以及经济增长的长期影响和短期影响.发现在短期内,政府增加资本收入税不仅可以增加居民消费,而且可以刺激人力资本积累,从而刺激短期经济增长.但是政府财政政策改变对长期经济增长不产生影响,而且资本收入税会降低长期的消费水平和资本存量.另外,从经济增长形态和消费者福利两个角度讨论了资本收入税的无效性.     

基于动力学视角的经济时间序列分析

基于1978~2014年中国教育发展水平、就业人数与实际资本存量的数据,应用动力学原理建立模型,讨论了模型均衡解的稳定性,同时分析了该经济系统受到外部扰动时的动力学行为.研究结果表明,外部扰动产生的系统混沌效应会影响经济系统的正常运行,从而管理者有必要对经济系统提出有效的应对策略.因此,基于动力学原理,本文为时间序列动力学特征的微观刻画提供了一个视角.     

政府花费改变对经济影响的理论分析

本文采用无限期内生时间偏好率模型,研究了政府花费对经济的影响.指出长期的政府花费增加可以使资本存量水平上升,消费水平下降和债券持有量上升;同时,短期分析表明政府花费增加可以减少初始投资率,增加政府债务率水平;但短期的政府花费增加同样导致资本存量水平上升,消费水平下降和债务水平的增加.     

一类具有双时滞的HIV感染模型的研究（英文）

本文主要研究具有时滞和毒性淋巴细胞(CTL)免疫反应的HIV感染模型的动力学行为.分别引入两类时滞:一类描述新感染的细胞开始产生病毒所需的时间,另一类是控制病毒复制的免疫反应出现所需的时间.通过分析时滞对平衡点稳定性的影响,建立了系统的无病平衡点P0,地方病平衡点P1的局部渐近稳定性.并且证明了在一定条件下,在地方病平衡点附近时滞可以诱导产生Hopf分支.     

考虑资本闲置的多年时滞人力资本投入占用产出模型

人力资本理论强调的是由教育所新增的人力资本对经济增长的决定作用.为了规划与中国经济持续增长相适应的人力资本需求,建立了一个新颖的考虑资本闲置的多年时滞投入占用产出模型.为了考虑人力资本时滞长的特点以及人力资本占用的损耗补偿,在斯通人口投入产出模型和Leontief动态投入产出模型基础上,提出了多年时滞人力资本投入占用产出模型.将LDS模型推广为考虑资本闲置的多年时滞人力资本投入占用产出模型,以便考虑影响教育产出的外生因素,并推导出既适于产出增加也适于产出减少的正解.应用上,预测至2015年的各种教育水平人力资本的总量和部门需求,发现高级人力资本短缺和人才行业结构不合理是经济发展需要解决的重要问题.     

气候政策的经济环境效应分析与比较—基于碳税、许可交易和总量控制的动态微分博弈

基于产品差别化假设,建立双寡头动态微分博弈模型,比较碳税和许可交易以及总量控制3种气候政策的经济环境效应.研究发现,不同气候政策对两国的经济效应不同.进一步研究还发现,在企业产品差别化竞争时,从碳排放流量来看,碳税政策和许可交易政策与总量控制政策之间没有严格的优劣之分;碳排放存量对碳税政策最敏感.从碳存量对政策的边际影响来看,许可交易政策与总量控制政策是相同的,而碳税政策与之相反.当两国生产的产品完全同质时,从均衡碳排放流量和碳排放存量来看,许可交易政策最优,总量控制政策次之,碳税政策最差.若政府单纯以控制碳排放量为目的,许可交易政策是最佳选择.     

Nonlinear oscillations in business cycle model with time lags

In this paper we analyse the dynamics of the Kaldor–Kalecki business cycle model. This model is based on the classical Kaldor model in which capital stock changes are caused by past investment decisions. This lag is connected with time delay needed for new capital to be installed. The dynamics of the model is reduced to the form of damped oscillator with negative feedback connected with lag parameter and next it is analysed in terms of bifurcation theory. We find conditions for existence and persistence of oscillatory behaviour which is represented by limit cycle on some central manifold in phase space, i.e., single Hopf bifurcation. We demonstrate that the Hopf cycles may be exhibited for nonzero measure set of the parameter space. The conditions for bifurcation of co-dimension two connected with interaction of bifurcations as well as bifurcation diagrams are also given. Finally, we obtain numerical values describing an amplitude and a period of oscillation for different parameter of the system. It is also proved that while the investment function is not nonlinear a quasi-periodic solution (a 1:2 resonant double Hopf point) can appear. The source of such a behaviour is rather a consequence of time lag than nonlinearity of the investment function. Our results confirm the existence of asymmetric (two periodic) cycles in the Kaldor–Kalecki model with time-to-build.     

Dynamics of a delayed business cycle model with general investment function

The aim of this paper is to study the dynamics of a delayed business cycle model with general investment function. The model describes the interaction of the gross product and capital stock. Furthermore, the delay represents the time between the decision of investment and implementation. Firstly, we show that the model is well posed by proving the global existence and boundedness of solutions. Secondly, we determine the economic equilibrium of the model. By analyzing the characteristic equation, we investigate the stability of the economic equilibrium and the local existence of Hopf bifurcation. Also, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theory. Moreover, the global existence of bifurcating periodic solutions is established by using the global Hopf bifurcation theory. Finally, our theoretical results are illustrated with some numerical simulations.     

Optimal dynamic investment with learning by doing in the adjustment cost function

In an optimal control model of a firm's dynamic investment policy, we analyze the effects of including learning by doing in the adjustment cost function (the larger the existing capital stock, the smaller the cost of installing an additional unit of capital stock).The authors wish to thank two anonymous reviewers for valuable comments. The research of the second author was sponsored by a fellowship of the Royal Netherlands Academy of Arts and Sciences.     

Construction of a regulator for the hamiltonian system in a two-sector economic growth model

We consider an optimal control problem of investment in the capital stock of a country and in the labor efficiency. We start from a model constructed within the classical approaches of economic growth theory and based on three production factors: capital stock, human capital, and useful work. It is assumed that the levels of investment in the capital stock and human capital are endogenous control parameters of the model, while the useful work is an exogenous parameter subject to logistic-type dynamics. The gross domestic product (GDP) of a country is described by a Cobb-Douglas production function. As a utility function, we take the integral consumption index discounted on an infinite time interval. To solve the resulting optimal control problem, we apply dynamic programming methods. We study optimal control regimes and examine the existence of an equilibrium state in each regime. On the boundaries between domains of different control regimes, we check the smoothness and strict concavity of the maximized Hamiltonian. Special focus is placed on a regime of variable control actions. The novelty of the solution proposed consists in constructing a nonlinear stabilizer based on the feedback principle. The properties of the stabilizer allow one to find an approximate solution to the original problem in the neighborhood of an equilibrium state. Solving numerically the stabilized Hamiltonian system, we find the trajectories of the capital of a country and labor efficiency. The solutions obtained allow one to assess the growth rates of the GDP of the country and the level of consumption in the neighborhood of an equilibrium position.     

A dynamic IS-LM business cycle model with two time delays in capital accumulation equation

In this paper, we analyze a augmented IS-LM business cycle model with the capital accumulation equation that two time delays are considered in investment processes according to Kalecki’s idea. Applying stability switch criteria and Hopf bifurcation theory, we prove that time delays cause the equilibrium to lose or gain stability and Hopf bifurcation occurs.     

Neimark–Sacker bifurcation for the discrete-delay Kaldor model

We consider a discrete-delay time, Kaldor nonlinear business cycle model in income and capital. Given an investment function, resembling the one discussed by Rodano, we use the linear approximation analysis to state the local stability property and local bifurcations, in the parameter space. Finally, we will give some numerical examples to justify the theoretical results.     

Zero-Hopf bifurcation analysis of a Kaldor-Kalecki model of business cycle with delay

The zero-Hopf singularity of a Kaldor-Kalecki model of business cycle with delay in both the gross product and the capital stock is investigated. By computing the normal forms for the system, the bifurcation diagrams such as saddle-node, pitch-fork, and Hopf bifurcations are obtained. A major obstacle is to solve singular linear systems when the third order terms in the normal form are computed. Some examples are presented to confirm the theoretical results.     

Stabilizing the Hamiltonian system for constructing optimal trajectories

An infinite-horizon optimal control problem based on an economic growth model is studied. The goal in the problem is to optimize the mechanisms of investment in basic production assets in order to increase the growth rate of the consumption level. The main output variable-the gross domestic product (GDP)-depends on three production factors: capital stock, human capital, and useful work. The first two factors are endogenous variables of the model, and the useful work is an exogenous factor. The dependence of the GDP on the production factors is described by the Cobb-Douglas power-type production function. The economic system under consideration is assumed to be closed, so the GDP is distributed between consumption and investment in the capital stock and human capital. The optimal control problem consists in determining optimal investment strategies that maximize the integral discounted relative consumption index on an infinite time interval. A solution to the problem is constructed on the basis of the Pontryagin maximum principle adapted to infinite-horizon problems. We examine the questions of existence and uniqueness of a solution, verify necessary and sufficient optimality conditions, and perform a qualitative analysis of Hamiltonian systems on the basis of which we propose an algorithm for constructing optimal trajectories. This algorithm uses information on solutions obtained by means of a nonlinear regulator. Finally, we estimate the accuracy of the algorithm with respect to the integral cost functional of the control process.     

利用多变量马尔科夫转移因子模型对我国经济周期波动的经验研究

本文应用多变量动态马尔科丈转移因子模型对我国1991年1月以来的经济周期波动进行研究。通过选取两组与经济景气一致的宏观经济指标进行实证分析,结果表明多变量动态马尔科夫转移因子模型对不同组指标的分析是一致的;根据模型所构造出的景气指数与一致合成指数的对比分析,我们发现这两个指数不论从变动趋势和峰谷转折点,还是波动幅度上都极其相似;通过对经济周期转折点测定,并与我国经济运行状况对比,我们认为用多变量动态马尔科夫转移因子模型刻画经济周期的特征是有效的。     

A multi‐stage ‘infection’ model of stock investors' reaction to new product announcement signal

Drawing on viral dynamics theory, this paper presents a differential equations model with time delay to investigate the stock investor behavior driven by new product announcement (NPA) signal. Visually, we look upon investors in stock market as cells in vivo and the NPA signals as free virus. The potential investors will be ‘infected’ by the dissociative NPA signal and then make investment decisions. In order to better understand the ‘infection’ process, we extract and establish a multi‐stage process during which NPA signal is delivered and ‘infects’ the potential investors. A time‐delay effect is employed to reflect the evaluation stage at which potential investors comprehensively evaluate and decide whether to invest or not. In addition, we introduce a set of external and internal factors into the model, including information sensitivity and investor sentiment, and so on, which are pivotal for examining investor behavior. Equilibrium analysis and numerical simulations are employed to check out the properties of the model and highlight the practical application values of the model. Copyright © 2016 John Wiley & Sons, Ltd.