Stochastic Optimal Control of Economic Growth Model under Research and Development Investment with Kalman Filtering Approaches

Yue Yuin Lim, Sie Long Kek, Wah June Leong

Abstract

This article examines an economic growth model that expresses the interaction between production, technology stock, and research and development (R&D) investments. The goal of this study is to maximize production. Considering the presence of Gaussian white noises, this model is reformulated as a stochastic optimal control problem, where the R&D investment rate is defined as the control input. We aim to explore the efficiency of Kalman filtering approaches for solving this problem. Here, the extended Kalman filter (EKF) and unscented Kalman filter (UKF) are applied for state estimation. The state equation linearization is made in the EKF, while the unscented transform is taken in the UKF for generating a set of sigma points. These approaches aim to estimate the state dynamics from different perspectives. With these state estimates, two different computational algorithms are proposed, the EKF for state-control (EKF4SC) and UKF for state-control (UKF4SC) algorithms. The optimal control policy is designed to minimize the cost function. For illustration, the model's parameters are considered in the simulation experiment. The simulation results showed that the UKF has higher accuracy in the state estimation with the smallest mean squares of error compared with the EKF. Moreover, the optimal control policy based on the state estimate generated from the UKF could optimize the cost function of the problem. Hence, the results show the efficiency of the algorithms proposed. In conclusion, the application of the Kalman filtering algorithms to the economic growth model is presented. The significance of this study is to provide a stochastic optimal control model for the economic growth problem and to suggest an efficient computational approach for solving this stochastic optimal control problem.  

  

Keywords: economic growth model, research and development investment, nonlinear stochastic optimal control, state estimation, Kalman filtering.

 

https://doi.org/10.55463/issn.1674-2974.49.6.13


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References


LIU C., & XIA G. Research on the Dynamic Interrelationship among R&D Investment, Technological Innovation, and Economic Growth in China. Sustainability, 2018, 10(11): 4260. https://doi.org/10.3390/su10114260

JONES C. I., & WILLIAMS J. C. Too Much of a Good Thing? The Economics of Investment in R&D. Journal of Economic Growth, 2000, 5(1): 65-85. https://doi.org/10.1023/A%3A1009826304308

RESHMIN S. A., TARASYEV A. M., and WATANABE C. Optimal Trajectories of the Innovation Process and Their Matching with Econometric Data. Journal of Optimization Theory and Applications, 2002, 112(3): 639-655. https://doi.org/10.1023/A%3A1017924301798

INEKWE J. N. The Contribution of R&D Expenditure to Economic Growth in Developing Economies. Social Indicators Research, 2015, 124(3): 727-745. https://doi.org/10.1007/S11205-014-0807-3

GRIGORIEVA E. V., & KHAILOV E. N. Optimal Control of a Nonlinear Model of Economic Growth. Discrete and Continuous Dynamical Systems, Supplement 2007: 456-466. http://dx.doi.org/10.3934/proc.2007.2007.456

YEGOROV I., BRATUS A., and TODOROV Y. Synthesis of Optimal Control in a Mathematical Model of Economic Growth under R&D Investments. Applied Mathematical Sciences, 2015, 9(91): 4523-4564. https://doi.org/10.12988/AMS.2015.55404

TARASYEV A. M., & WATANABE C. Optimal Dynamics of Innovation in Models of Economic Growth. Journal of Optimization Theory and Applications, 2001, 108(1): 175-203. https://doi.org/10.1023/A%3A1026422223814

VLAD S., & BALAN I. Kalman Filters for Estimating the Potential GDP. Journal of Applied Computer Science & Mathematics, 2018, 12(25): 39-43. https://doi.org/10.4316/JACSM.201801006

MUNGUÍA R., DAVALOS J., and URZUA S. Estimation of the Solow-Cobb-Douglas Economic Growth Model with a Kalman Filter: An Observability-Based Approach. Heliyon, 2019, 5(6): e01959. https://doi.org/10.1016/j.heliyon.2019.e01959

ZAINUDIN A., & NURBAIZURA B. Examining Time-Varying Economic Impacts on Tourism Demand for Malaysia: A Kalman Filter Approach. AIP Conference Proceedings, 2019, 2184: 050031. https://doi.org/10.1063/1.5136419

ARABMAZAR YAZDI A., MOHAMMADI T., TAKLIF A., and JALALPANAHI R. Balance of Payments Constraint and Economic Growth: Evidence from the Thirlwall’ s Law in Developing Oil Countries (ARDL and Kalman Filter Approach). Iranian Economic Research, 2020, 25(85): 1-34.

JULIER S. J., & UHLMANN J. K. New Extension of the Kalman Filter to Nonlinear Systems. Proceedings Volume 3068, Signal Processing, Sensor Fusion, and Target Recognition VI, 1997, 3068: 182-193. https://doi.org/10.1117/12.280797

BRYSON A. E., & HO Y. C. Applied Optimal Control. Hemisphere, Washington, District of Columbia, 1975.

CHONG E. K. P., & ZAK S. H. An Introduction to Optimization. 4th ed. John Wiley & Sons, Hoboken, New Jersey, 2013.

KIRK D. E. Optimal Control Theory: An Introduction. Dover Publications, Mineola, New York, 2004.

LEWIS F. L., VRABIE V., and SYMOS V. L. Optimal Control. 3rd ed. John Wiley & Sons, New York, 2012.

TEO K. L., LI B., YU C., and REHBOCK V. Applied and Computational Optimal Control: A Control Parametrization Approach. Springer, Cham, 2021. https://doi.org/10.1007/978-3-030-69913-0


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