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Public capital, private capital, and economic growth


  • Alberto BUCCI



An endogenous growth model is presented in which productive government expenditure takes the form of a stock. Private and public capital interact with each other in two different ways. The first takes place in the final output sector and depends on the specification of the aggregate production function (Cobb-Douglas vs. CES). The second has to do with the rates of investment in the two types of capital and arises from the law of motion of public capital. The share of public capital devoted to output production can be exogenous or endogenous. Our results suggest that when this share is exogenous along the balanced growth path the optimal growth rate of the economy depends positively on the degree of complementarity between the investments in the two kinds of capital, irrespective of the form of the aggregate production function. This is also true when the share of public capital devoted to output production is endogenous, as long as the inverse of the intertemporal elasticity of substitution in consumption is sufficiently large. When the technology for final output production is CES and the social planner can choose the fraction of public capital to be devoted to goods-production, optimal growth crucially depends on the elasticity of substitution between the two forms of capital in the production of goods. We analyze the conditions for an increase in this elasticity to yield either a positive, or a negative, or else an ambiguous effect on the economy’s optimal growth rate. Unlike Barro (1990), the relationship between optimal growth and the share of productive government expenditure in GDP is nonlinear and characterized by threshold-effects.

Suggested Citation

  • Alberto BUCCI, 2012. "Public capital, private capital, and economic growth," Departmental Working Papers 2012-08, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
  • Handle: RePEc:mil:wpdepa:2012-08

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    References listed on IDEAS

    1. Aiyar, Shekhar & Dalgaard, Carl-Johan, 2009. "Accounting for productivity: Is it OK to assume that the world is Cobb-Douglas?," Journal of Macroeconomics, Elsevier, vol. 31(2), pages 290-303, June.
    2. Guvenen, Fatih, 2006. "Reconciling conflicting evidence on the elasticity of intertemporal substitution: A macroeconomic perspective," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1451-1472, October.
    3. Kent Smetters, 2003. "The (Interesting) Dynamic Properties of the Neoclassical Growth Model with CES Production," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(3), pages 697-707, July.
    4. Lutfi Erden & Randall G. Holcombe, 2005. "The Effects of Public Investment on Private Investment in Developing Economies," Public Finance Review, , vol. 33(5), pages 575-602, September.
    5. Carlo Favero, 2005. "Consumption, Wealth, the Elasticity of Intertemporal Substitution and Long-Run Stock Market Returns," Working Papers 291, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    6. Attanasio, Orazio P & Browning, Martin, 1995. "Consumption over the Life Cycle and over the Business Cycle," American Economic Review, American Economic Association, vol. 85(5), pages 1118-1137, December.
    7. Duffy, John & Papageorgiou, Chris, 2000. "A Cross-Country Empirical Investigation of the Aggregate Production Function Specification," Journal of Economic Growth, Springer, vol. 5(1), pages 87-120, March.
    8. Duggal, Vijaya G. & Saltzman, Cynthia & Klein, Lawrence R., 2007. "Infrastructure and productivity: An extension to private infrastructure and it productivity," Journal of Econometrics, Elsevier, vol. 140(2), pages 485-502, October.
    9. Futagami, Koichi & Morita, Yuichi & Shibata, Akihisa, 1993. " Dynamic Analysis of an Endogenous Growth Model with Public Capital," Scandinavian Journal of Economics, Wiley Blackwell, vol. 95(4), pages 607-625, December.
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    More about this item


    Economic Growth; Complementarity/Substitutability; Public Capital; Private Capital;

    JEL classification:

    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • E60 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - General
    • H54 - Public Economics - - National Government Expenditures and Related Policies - - - Infrastructures


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