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Nonlinearities and Inactivity in Aggregate Investment: Some Theoretical Analysis and Time-Series Evidence


  • Corrado Luisa

    (University of Rome II “Tor Vergata”)

  • Holly Sean

    (Cambridge University)

  • Turner Paul

    (University of Sheffield)


The theoretical analysis of investment under uncertainty has been revolutionized over the last decade by the importation of ideas from finance. If investment is irreversible, there is a return to waiting. So although circumstances may suggest that it is profitable to invest, there may also be an incentive to postpone the decision until better opportunities arise. Identifying and valuing the option to invest has become the standard way to solve the firm's irreversible-investment problem. Empirical studies of investment that incorporate the insights of the real-options approach are now beginning to appear. These show that investment can have a nonlinear relationship to q and may show insensitivity for some threshold level to the shadow value of investment (Barnett and Sakellaris 1998). Abel and Eberly (1997) and Böhm and Funke (1999) have also shown how the real-options approach to investment can be combined with the traditional q approach. In this case the relationship between q and the rate of investment is discontinuous. Over a range of inaction there will be no investment, although q is in excess of one.This paper builds a theoretical model that explains the determinants of this investment discontinuity. In contrast to much of the literature, we use a mean-reverting stochastic process, of which the geometric Brownian motion process is a special case. Under the assumption of a production function with constant returns to scale and a specific functional form for the investment adjustment function, it is possible to derive a tractable analytical form for the shadow value of the investment project. We then analyze the comparative properties of the value of q under different assumptions about the stochastic process governing output. The advantage of using a mean-reverting process is that it better captures the undoubted persistence in the shocks that face firms, especially at the macroeconomic level.We then consider what the implications would be for the aggregate relationship between investment, q, and the business cycle. We first carry out Monte Carlo simulations of a discrete version of the theoretical model. We find that for many parameter values, aggregating suppresses any nonlinearities in the micro adjustment processes. Moreover, where we do detect nonlinearity at the aggregate level, it varies with the type of stochastic process. It is greatest when this is a random walkcorresponding to the Brownian motion in continuous timeand least when the stochastic process follows an i.i.d. process. Mean reversion lies in between. We turn finally to an empirical examination using aggregate data and explore how sensitive investment is to q in different regimes. To do this, we apply a generalization of the Granger-Lee method (Arden et al. 2000) that uses a linear spline function to approximate different regions for investment.

Suggested Citation

  • Corrado Luisa & Holly Sean & Turner Paul, 2002. "Nonlinearities and Inactivity in Aggregate Investment: Some Theoretical Analysis and Time-Series Evidence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 5(4), pages 1-21, January.
  • Handle: RePEc:bpj:sndecm:v:5:y:2002:i:4:n:2

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    References listed on IDEAS

    1. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    2. Abel, Andrew B. & Eberly, Janice C., 1997. "An exact solution for the investment and value of a firm facing uncertainty, adjustment costs, and irreversibility," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 831-852, May.
    3. Metcalf, Gilbert E. & Hassett, Kevin A., 1995. "Investment under alternative return assumptions Comparing random walks and mean reversion," Journal of Economic Dynamics and Control, Elsevier, vol. 19(8), pages 1471-1488, November.
    4. Cukierman, Alex, 1980. "The Effects of Uncertainty on Investment under Risk Neutrality with Endogenous Information," Journal of Political Economy, University of Chicago Press, vol. 88(3), pages 462-475, June.
    5. Hayashi, Fumio, 1982. "Tobin's Marginal q and Average q: A Neoclassical Interpretation," Econometrica, Econometric Society, vol. 50(1), pages 213-224, January.
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    Cited by:

    1. Munehisa Kasuya, 2003. "Investment with Uncertainty: Detection of Decomposed Uncertainty Factors Affecting Investment," Bank of Japan Working Paper Series 03-E-1, Bank of Japan.
    2. Yu-Fu Chen & Michael Funke, 2003. "Exchange Rate Uncertainty and Labour Market Flexibility under Fixed and Flexible Exchange Rates," Dundee Discussion Papers in Economics 149, Economic Studies, University of Dundee.
    3. Corrado, Luisa & Holly, Sean, 2003. "Nonlinear Phillips curves, mixing feedback rules and the distribution of inflation and output," Journal of Economic Dynamics and Control, Elsevier, vol. 28(3), pages 467-492, December.

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