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Investment Under Alternative Return Assumptions: Comparing Random Walks and Mean Reversion


  • Gilbert E. Metcalf
  • Kevin A. Hassett


Many recent theoretical papers have come under attack for modeling prices as Geometric Brownian Motion. This process can diverge over time, implying that firms facing this price process can earn infinite profits. We explore the significance of this attack and contrast investment under Geometric Brownian Motion with investment assuming mean reversion. While analytically more complex, mean reversion in many cases is a more plausible assumption, allowing for supply responses to increasing prices. We show that cumulative investment is generally unaffected by the use of a mean reversion process rather than Geometric Brownian Motion and provide an explanation for this result.

Suggested Citation

  • Gilbert E. Metcalf & Kevin A. Hassett, 1995. "Investment Under Alternative Return Assumptions: Comparing Random Walks and Mean Reversion," NBER Technical Working Papers 0175, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberte:0175 Note: PE

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    References listed on IDEAS

    1. Pindyck, Robert S, 1982. "Adjustment Costs, Uncertainty, and the Behavior of the Firm," American Economic Review, American Economic Association, vol. 72(3), pages 415-427, June.
    2. Pindyck, Robert S, 1988. "Irreversible Investment, Capacity Choice, and the Value of the Firm," American Economic Review, American Economic Association, vol. 78(5), pages 969-985, December.
    3. Lund Diderik, 1993. "The Lognormal Diffusion Is Hardly an Equilibrium Price Process for Exhaustible Resources," Journal of Environmental Economics and Management, Elsevier, vol. 25(3), pages 235-241, November.
    4. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 707-727.
    5. Avinash Dixit, 1992. "Investment and Hysteresis," Journal of Economic Perspectives, American Economic Association, vol. 6(1), pages 107-132, Winter.
    6. Bertola, Giuseppe, 1998. "Irreversible investment," Research in Economics, Elsevier, vol. 52(1), pages 3-37, March.
    7. Abel, Andrew B, 1983. "Optimal Investment under Uncertainty," American Economic Review, American Economic Association, vol. 73(1), pages 228-233, March.
    8. John V. Leahy, 1993. "Investment in Competitive Equilibrium: The Optimality of Myopic Behavior," The Quarterly Journal of Economics, Oxford University Press, vol. 108(4), pages 1105-1133.
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    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • E2 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment

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