The Two Sector Endogenous Growth Model and the Intertemporal Elasticity of Substitution: An Atlas

We extend the Lucas (1988) endogenous growth model to include sector-specific external effects and depreciation in both sectors. We derive analytically, the restrictions on the parameter space that are necessary and sufficient for the existence of balanced growth paths and equilibria. We demonstrate that in contrast to the original model, with the addition of an external effect and depreciation in the production the human capital sector, the Lucas model can be made consistent with the high degrees of intertemporal elasticities of substitution increasingly estimated in the empirical literature. Finally, we offer empirical evidence using Canadian and U.S. data suggesting that the intertemporal elasticity of substitution may be higher than conventionally assumed.