Explicit investment setting in a Kaldor macroeconomic model with macro shock

Zhenzhen Wang, ,School of Mathematics, South China University of Technology, Guangzhou, 510640, China, Zhenghui Li, Shuanglian Chen, Zhehao Huang, ,Guangzhou International Institute of Finance and Guangzhou University, Guangzhou, 510405, China
2018 Discrete and Continuous Dynamical Systems. Series S  
2328 ZHENZHEN WANG, ZHENGHUI LI, SHUANGLIAN CHEN AND ZHEHAO HUANG where I is the investment function and S is the saving function. The economic variable Y represents the gross production and K represents the capital stock. Parameter α is the adjustment coefficient in the good market and q is the depreciation rate of the capital stock. Chang and Smyth [5] verified rigorously the generation of endogenous business cycle dynamics through the Poincare-Bendixson theorem. The result was consistent
more » ... was consistent with the hypothesis from Kaldor. Subsequently the macroeconomic dynamics, especially the cyclic fluctuation behaviors, were paid much attention by many authors, see e.g. [3, 12] and references therein. They have clarified that the underlying reasons causing the business cycles are against the exogenous periodic actions but the intrinsical endogeneity associated with the nonlinearity emerged by primary economic relationships. One popular modification for the Kaldor model is the introduction of delay effects motivated by Kalecki [11], who impacted the lag between the investment decision and the implementation. The unified model was developed by Krawiec and Szyd lowski [14] by means of delayed differential equations or equivalently an infinite-dimensional dynamic system, named the Kaldor-Kalecki model. In this model, time delay is responsible for the Hopf bifurcation to a limit cycle solution and for generating cycles. This is the primary difference between the Kaldor model and Kaldor-Kalecki model. In the former cycles are generated due to the nonlinear investment function. Nevertheless, the investment lag is addressed in the latter. Thereafter, various types of delay Kaldor model were pouring out. These works concentrated on the complex dynamics modeling macro economy, including the cycle and chaotic fluctuations led by delay effects and the transitions between them, see e.g. [9, 15] and references therein. As representative macroeconomic models, both the Kaldor model and Kaldor-Kalecki model neglect the effects of macro shocks. In reality, externally macro shocks are essential attributes in a macroeconomic system. Greenwood et al [8] investigated the impacts of shocks on the degree of economic cycle fluctuations and suggested the importance of shocks when considering macro economy. Generally, in macroeconomic models, macro shocks were embodied by random perturbations or stochastic elements introduced into the systems. Authors such as Brunnermeier and Sannikov [4], Kilmenko et al [13] and Phelan [20] constructed some macroeconomic models with macro shocks and investigated the equilibrium dynamics. Volatility effects and systematic risks caused by essential shocks were cared for in their works. Kaldor type macroeconomic models with shocks have been paid much attention by many authors as well. Mircea et al [18] studied the dynamics depicting the mean and variance of the system. The result suggests that the cyclic fluctuation is inherited by the mean and variance although perfect cyclic dynamics of the system has gone due to the shock. Li et al [16] applied the stochastic Kaldor model to modeling the financial business cycle. They investigated the bifurcation phenomena and the cyclic length. Bashkirtseva et al overcame the technique difficulty directly applying the Fokker-Planck-Kolmogorov equation, which is the most comprehensive probabilistic description for stochastic dynamics, through stochastic sensitivity function technique and investigated the complex dynamics of the shocked Kaldor models, mainly focusing on chaotic behaviors depicting economic crisis stage (see [1] and reference therein). Summarily, works on Kaldor models with shocks mostly concentrate on the dynamics addressing the effects of shocks on the economic system. Due to the inevitable occurrences of macro shocks on the macroeconomic system, in the current paper, the authors develop a Kaldor type macroeconomic model with
doi:10.3934/dcdss.2020093 fatcat:obeeyn5f7rcshd2kysqg4qlzu4