The Dynamic Properties of Endogenous Growth Models

Abstract

This paper explores the dynamics of semiendogenous versus fully endogenous growth models in “lab equipment” specifications of the models with expanding sectors. Capital is allowed to accumulate and is used, together with other inputs, to produce new knowledge. The stability of the steady state path is found to be determined by the inequality and/or knife-edge restrictions needed to produce steady state growth. This paper takes the ratio of the shadow price of capital to knowledge and the level of consumption as jump variables. Semiendogenous growth models lead to a 4 × 4 dynamic system where the sign of the coefficient matrix of the log linearized dynamic system is indefinite, leading to a potential for both stable and unstable equilibria. The knife-edge restrictions needed to generate policy influences on growth are shown to be restrictions that reduce the system to 3 × 3 with a positive definite coefficient matrix, thereby guaranteeing a globally stable equilibrium. Implications for empirical testing are addressed.

A Note on Skill-Structure Shocks, the Share of the High-Tech Sector, and Economic Growth Dynamics

“…Parameter values are the same as in Figure 6. eects in secular trend, while acknowledging their role over transitional dynamics (e.g., Jones, 1995;Jones, 2002;Sedgley andElmslie, 2010, 2013). Similarly, our quantitative results underline the role of scale eects in the medium term, in particular given the relatively short time span of the time-series data that we used in our calibration.…”

“…Potential entrants can devote resources to either horizontal or vertical R&D, and dithree-dimensional stable manifold irrespective of the degree of scale eects. 9 In fact, scale eects over transitional dynamics obtain in several theoretical models; see, e.g., Jones (1995), Dinopoulos and Thompson (1998); Jones (2002), and Sedgley and Elmslie (2013).…”

“…The complete removal of scale eects as sometimes posited in the theoretical growth literature is a knifeedge case, as Peretto and Smulders (2002) have recently stressed. Indeed, the existence of scale eects at the aggregate level is disputed, with the empirical results rejecting it in secular trend but not over transitional dynamics (e.g., Jones, 1995;Jones, 2002;Sedgley and Elmslie, 2010), whereas early empirical studies clearly indicate the existence of scale eects at the industry (manufacturing) level (e.g., Backus, Kehoe, and Kehoe, 1992). Thus, because the literature does not oer a clear cut answer to the issue of the existence of scale eects, we consider a number of scenarios, from no scale eects on growth (only price-channel eects exist) to full scale eects (only market-size-channel eects exist).…”

Economic Growth With Endogenous Economic Institutions

“…Youcai (2008) embodies endogenous institutional variable into the endogenous economic growth model, making a theoretical analysis how institution as an endogenous variable affected the economic growth equilibrium path, but without empirical analysis. Sedgley and Elmslie (2013) explored the dynamics of semiendogenous versus fully endogenous growth models in "lab equipment" specifications of the models with expanding sectors. Gómez (2015) analyzed the dynamics of an endogenous growth model with external habit formation and elastic labor supply.…”

Tax policy implications for a two‐engine growing economy

“…In most models featuring an R&D‐capital setup, as stressed by Lloyd‐Ellis and Roberts (2002), only one of the driving forces acts as a primary engine of endogenously sustainable growth and the other is either exogenous or is driven by the necessity of the primary engine. Specifically, physical capital exhibits decreasing marginal returns as in the standard neoclassical growth model while it acts as a complement to R&D which is a primary engine of endogenously sustainable growth (e.g., Romer, 1990; Howitt and Aghion, 1998; Howitt, 2000; Sedgley and Elmslie, 2013; Gil et al ., 2017; Gil and Iglésias, 2020). Since capital accumulation is necessary for growth to be sustained in the long run, capital accumulation and R&D are complementary mechanisms, giving rise to only one sustained growth rate in such a setting 8…”