Abstract
This work presents a novel approach for estimating the Solow-Cobb-Douglas economic growth model. In this case, an Extended Kalman Filter is used for estimating, at the same time, the time-varying parameters of the model and the system state, from subsets of partially available economic data measurements. Different from traditional econometric techniques, the proposed EKF approach is applied directly to a state-space representation of the original nonlinear model, where all the model parameters are treated as time-varying parameters. An extensive nonlinear observability analysis was carried out in order to investigate the different subsets of measurements that can be used for estimating the state of the system, and also, in order to find out theoretically necessary conditions to achieve the observability system property. Experiments with real macroeconomic data are presented in order to validate the proposed approach. While the observability analysis offer theoretically conditions for system observability, the experimental results suggest that between the subsets of available economic data, some specific economic data are more relevant than others for better estimating the model.
Highlights
One of the most important models of economic endogenous growth is the Solow-Swan model [1, 2]
The Solow-Swan model tries to explain the dynamics of long-run economic growth, as a result of investment capital, labor or population growth and the increment of productivity, known as productivity factor or technological progress
In order to apply the Extended Kalman Filter (EKF), and since the economic data is obtained in a discrete manner, a discrete-stochastic system model must be defined from the continuous dynamics x_ 1⁄4 fðxÞ
Summary
One of the most important models of economic endogenous growth is the Solow-Swan model [1, 2]. The Solow-Swan model is considered to have attractive mathematical properties It consists in a single nonlinear ordinary differential equation that models the evolution of the per capita stock of capital. Balistreri et al [6] used time series with the objective of estimating in a consistent way a complete set of capital-labor substitution elasticities for the United States economy. Their calculations revealed the possibility of an aggregation bias, suggesting a reconsideration of averaging methods in flexible aggregation models. While Deniz et al [10] through a principal components analysis, concluded that the variables that capture the effects of human and physical capital generally produce a positive impact on the growth of 73 countries of the sample during the period of 1960–2014
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