Macroeconomic Dynamics, 17, 2013, 1118–1134. Printed in the United States of America. doi:10.1017/S1365100512000119 THE DYNAMIC PROPERTIES OF ENDOGENOUS GROWTH MODELS NORMAN SEDGLEY Loyola University in Maryland BRUCE ELMSLIE University of New Hampshire 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. Keywords: Endogenous Growth, Dynamic Properties, Transitional Dynamics, Stability 1. INTRODUCTION The dynamics outside of the steady state and the stability of the steady state growth rate have been studied for first-generation versus semiendogenous growth models by Eicher and Turnovsky (1999, 2001). The purpose of this paper is to study the dynamic properties of semiendogenous versus fully endogenous growth models and the relationship between the stability of the equilibrium steady state rate of growth and the inequality restrictions and/or knife-edge restrictions needed to produce semiendogenous and fully endogenous growth when the economy accumulates capital and ideas. The results of the model developed here have strong implications for empirical testing of the various models that allows the use of the full time series properties of the data. To date, most testing of endogenous growth models has assumed a steady state, which ignores the non–steady state dynamics of the various models, making empirical testing problematic (Zachariadis, 2003, 2004; Ha and Howitt, We are grateful for the tremendous comments provided by an anonymous referee. Address correspondence to: Norman Sedgley, Department of Economics, Sellinger School of Business and Management, Loyola University in Maryland, Baltimore, MD 21210, USA; e-mail: nsedgley@loyola.edu. c  2013 Cambridge University Press 1365-1005/13 1118