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1. Introduction
Evaluating and forecasting the influence of investment in research and development (R&D) on economic growth can provide important guidelines for adjusting interest rates in banks and the tax rate in the market, optimizing the structure of industry, redistributing capital investment and forecasting new technological and social changes. Through massive studies, scholars have developed a series of classical econometric models. The Cobb-Douglas production function was proposed (Cobb and Douglas, 1928; Douglas, 1976) in 1928. It has been widely applied in assessing the impact of policies on gross domestic product (GDP) (Vilcu, 2011; Yuan et al., 2009). The Cobb-Douglas production function can be used to compute contributions to GDP, but it cannot forecast contributions to economic growth. Thus, Solow and Swan put forward the Solow-Swan model (also known as the Solow growth model) (Solow, 1956; Swan, 1956). This model and its improved versions performed well when analyzing the relations among capital, technology or knowledge, labor and total production (Durlauf et al., 2001; Rao, 2010; Schenk-Hoppe and Schmalfuss, 2001). These classical econometric models contribute immeasurably to the development of appropriate policies and economic market zones by the government.
However, these models seem relatively redundant when used to simply forecast GDP based on R&D because other variables, such as population and labor force, are usually relatively stable in cities such as Wuhan. The Lotka-Volterra model (or prey-predator model) was proposed when Lotka and Volterra attempted to explain population changes (Lotka, 1925; Volterra, 1926) and were able to show the predation, mutualism or competition between two organisms. Leslie offered the discrete time analytical expression of this model (Leslie, 1958), and May introduced delay into the model (May, 1973). Regarding the parameter estimation, scholars have developed a range of methods, such as the Bayesian approach (Putter et al., 2002), generalized smoothing approach (Ramsay et al., 2007), generalized profiling method (Cao and Ramsay, 2007) and nonparametric regression (Liang and Wu, 2008). Due to its simple mechanism and clear explanation of parameters, the Lotka-Volterra model has been increasingly applied in a series of econometric forecasting systems, such as those concerning the dynamics of market share (Wijeratne et al., 2009), industrial clusters (Bischi and Tramontana, 2010), the silicon wafer market (Chiang, 2012), and the dynamic estimation of...