Production, Growth and Business Cycles: Technical Appendix

Abstract

The methods used in our two survey papers on real business cycles (King, Plosser and Rebelo, 1988a,b) are detailed in this document. Our presentation of the basic neoclassical model of growth and business cycles is broken into three parts. First, we describe the model and its steady state, discussing: the structure of the environment including government policy rules; the nature of optimal individual decisions and the dynamic competitive equilibrium; technical restrictions to insure steady state growth; comparable restrictions on preferences and policy rules; stationary levels and ratios in the steady state; and the nature of a transformed economy. Second, we detail methods for studying near steady-state dynamics, considering: the linear approximation approach; the rational expectations solution algorithm; the nature of alternative solutions; and the special case of the fixed labor model. Third, we discuss the computation of simulations, moments and impulse responses. The objective of this appendix is to provide a detailed analysis of a neoclassical economy that is sufficiently flexible to permit: (a) exogenous steady state growth; (b) distorting tax rules of various sorts; and (c) time varying government spending. Although we do not focus on all of these issues in the present discussion, other investigations in progress will utilize this framework. The appendix is divided into three main parts. Part A describes the artificial economy under study and analyses its steady state, Part B develops methods to study approximate dynamics around the steady state, and Part C derives a set of formulas for generating population moments. This technical appendix is designed to serve two functions. First, it develops the theoretical material in Sections 2 and 3 of the main text in more depths. Second, it serves as a detailed guide to PC-MATLAB programs for computing dynamic equilibria, written by King and Rebelo in the Spring of 1987. Notation in programs and the technical appendix has been detailed as closely as feasible.