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Mcdonald and Siegel Meet Laibson: Dynamic Investment Strategies with Time-Inconsistent Preferences

The real options framework has been used extensively to analyze the timing of investment under uncertainty. The ability to defer decisions under evolving uncertainty provides the investor with a valuable option to wait. While real options models assume that agents possess a constant rate of time preference, there is substantial evidence that decision makers are very impatient about choices in the short-term, but are quite patient when choosing between long-term alternatives. We extend the real options framework to model the investment timing decisions of entrepreneurs with such time-inconsistent preferences. Two opposing forces determine investment timing: while evolving uncertainty induces investors to defer investment in order to take advantage of the option to wait, their present-biased preferences motivates them to invest earlier in order to avoid the time-inconsistent behavior they will display in the future. We find that the precise trade-off between these two forces depends on such factors as whether investors are sophisticated or naive about their future time-inconsistent behavior, as well as whether the payoff from investment occurs all at once or over time. We extend the model to consider equilibrium investment behavior for an industry comprised of time-inconsistent entrepreneurs. Equilibrium involves the dual problem of agents playing dynamic games against others as well as against their own future selves.