Production, Growth and Business Cycles: Technical Appendix


The methods used in our two survey papers on real business cycles (King,Plosser and Rebelo, 1988a,b) are detailed in this document. Our presentationof the basic neoclassical model of growth and business cycles is broken intothree parts. First, we describe the model and its steady state, discussing:the structure of the environment including government policy rules; the natureof optimal individual decisions and the dynamic competitive equilibrium;technical restrictions to insure steady state growth; comparable restrictionson preferences and policy rules; stationary levels and ratios in the steadystate; and the nature of a transformed economy. Second, we detail methods forstudying near steady-state dynamics, considering: the linear approximationapproach; the rational expectations solution algorithm; the nature ofalternative 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 aneoclassical economy that is sufficiently flexible to permit: (a) exogenoussteady state growth; (b) distorting tax rules of various sorts; and (c) timevarying government spending. Although we do not focus on all of these issuesin the present discussion, other investigations in progress will utilize thisframework. The appendix is divided into three main parts. Part A describes theartificial economy under study and analyses its steady state, Part B developsmethods to study approximate dynamics around the steady state, and Part Cderives a set of formulas for generating population moments. This technicalappendix is designed to serve two functions. First, it develops thetheoretical 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 computingdynamic equilibria, written by King and Rebelo in the Spring of 1987. Notationin programs and the technical appendix has been detailed as closely asfeasible.

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  1. Blanchard, O. and Kahn, C. (1980). The solution of linear difference models under rational expectations. Econometrica, 48, 1305–1311.

    Google Scholar 

  2. Cass, D. (1965). Optimum growth in an aggregative model of capital accumulation. Review of Economic Studies, 32, 233–240.

    Google Scholar 

  3. Chow, G. (1975). Analysis and Control of Dynamic Economic Systems. Wiley, New York.

    Google Scholar 

  4. Ferguson, C. (1964). Microeconomic Theory. Irwin, New York.

    Google Scholar 

  5. Hansen, L. and Sargent, T. (1980). Formulating and estimating dynamic linear rational expectations models. Journal of Economic Dynamics and Control, 2, 7–46.

    Google Scholar 

  6. Hansen, L. and Sargent, T. (1981). Linear rational expectations models for dynamically interrelated variables. In R.E. Lucas, Jr. and T.J. Sargent (eds.), Rational Expectations and Econometric Practice. Minneapolis Univ. Press, Minneapolis.

    Google Scholar 

  7. Harvey, A. (1981). Time Series Models. Phillip Allan, Oxford.

    Google Scholar 

  8. King, R.G. (1987). Business cycles and economic growth, lectures on macroeconomics. Unpublished. University of Rochester.

  9. Koopmans, T. (1965). On the concept of optimal economic growth. The Econometric Approach to Development Planning. Rand-McNally, Chicago.

    Google Scholar 

  10. Phelps, E. (1966). Golden Rules of Economic Growth. Norton, New York.

    Google Scholar 

  11. Prescott, E. (1986). Theory ahead of business cycle measurement. Carnegie-Rochester Conference Series on Public Policy, 25, 11–66.

    Google Scholar 

  12. Romer, P. (1986). Increasing returns and long run growth. Journal of Political Economy 94, 1002-1037.

    Google Scholar 

  13. Romer, P. and Sasaki, H. (1984). Monotonically decreasing natural resources prices under perfect foresight. Rochester Center for Economic Research Working Paper No. 19.

  14. Romer, P. and Shinotsuka, T. (1987). The Kuhn Tucker Theorem Implies the Growth Transversality Condition at Infinity. Unpublished. University of Rochester.

  15. Swan, T. (1964). Growth Models of Golden Ages and Production Functions. In Kenneth Berril (ed.), Economic Development with Special Reference to East Asia, Macmillan, London.

    Google Scholar 

  16. Vaughan, D.R. (1970). A non recursive algorithm solution for the discrete Ricatti equation. IEEE Transactions on Automatic Control, AC-15, 597–599.

    Google Scholar 

  17. Weitzman, M. (1973). Duality theory for infinite time horizon convex models. Management Science, 19(7), 738–789.

    Google Scholar 

  18. Wynne, M. (1987). The effects of government spending in a perfect foresight model. Unpublished. University of Rochester.

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King, R.G., Plosser, C.I. & Rebelo, S.T. Production, Growth and Business Cycles: Technical Appendix. Computational Economics 20, 87–116 (2002).

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  • specifications
  • steady state
  • solutions
  • algorithm
  • key elements