Abstract
The precautionary principle justifies postponing the implementation of development projects to await better information about their environmental impacts. But if implementation capacity is congestible, as is often the case in practical settings, a postponed project may have to vie for implementation priority with projects that arrive later. Limitations of implementation capacity create two risks. First, it may sometimes not make sense to go back to a postponed project, even if it is later revealed to be a good one. Second, the planner may find it worthwhile to go back to it, but at the expense of undesirable delay of subsequent projects. We consider a planner facing a sequence of projects that vary stochastically in their (1) importance and (2) improvability, but knowing that implementation capacity is congestible. The scope for congestion implies a ‘bonus’ for earlier-than-otherwise decisions, in common parlance ‘keeping the desk clear’, which works against the well-understood option value that encourages postponement. The optimal decision rule depends upon the stochastic environment whereby future projects are generated, in ways that are not obvious. The value of the bonus is increasing in the expected importance of future projects but decreasing in their expected improvability. Higher variability of the importance of projects, in the sense of mean-preserving spread, increases the size of the bonus, but variability in their improvability has a generally ambiguous impact. We characterize the adjusted decision rule and note its implications for the conduct of cost-benefit informed policy.
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Notes
See Atkinson et al. (2006). In Arrow & Fisher (1974), Henry (1974), and most of the subsequent literature choice-relevant information is assumed to arrive with passage of time. An alternative strand of research treats decision-makers as active gatherers of information. See, for example, Che & Mierendorff (2018), and references therein.
Readers may recognize a parallel phenomenon at individual level – ‘mental bandwidth’ is limited (Mullainathan & Shafir, 2013) such that an individual can only do so many things effectively at one time. Among management scholars the notion of organizational bandwidth being congestible is widely acknowledged (see, for example, Nunamaker et al. (2001) and the associated journal special issue Enhancing Organizations’ Intellectual Bandwidth). The congestion may be driven by a number of factors, but by way of caricature, “... the chief executive can only do so many things at once” (Geanakoplos & Milgrom, 1991).
To simplify a comparison of costs and benefits, we report all values in terms of the present discounted value in the initial period. We could capture intertemporal discounting explicitly in the model by writing \(\eta = \rho H\) where \(\rho \in [0,1]\) is the discount factor and H the contemporary value of future benefits.
Our findings continue to hold if we allow \(\omega _{0}\) to be positive, as long as \(\omega _{0}<\eta\).
We do not require that uncertainty is totally resolved by any date, though that is what we will assume. It would be sufficient to regard \(\omega\) and \(\omega _{0}\) as the conditional expected values of the natural resource, contingent on the arrival of some binary signal.
To see why, note that given discount factor \(\rho \in [0,1]\), we have \(\eta = \rho H\) as the discounted value of future payoff H of development and \(\omega = \rho W\) as the discounted value of state-contingent future payoff W of preservation, respectively. If so, we can write \(\pi ^*(\rho ) = \frac{\tau +\rho H }{\rho W }\) and \({\hat{\pi }}(\rho )= \frac{\tau }{\rho (W -H) }\). Both values are decreasing in \(\rho\), so that a smaller value of \(\rho\) raises these thresholds. If the future matters less, early implementation is more likely, except when there is a very high risk that the lost resource will later be revealed to be valuable.
A softer version of (2) would be to make implementation not subject to an absolute constraint but rather congestible. In other words, an increase in the number of projects ‘on the go’ at any one time would reduce the efficacy of implementation – less than perfect scalability in implementation activities.
The attentive reader will also note that this formulation implies that project opportunities expire or have a ‘shelf-life’ of two periods – the first project cannot be implemented in period 3. This is for tractability, as it ensures no more than one unimplemented project from a past round can be carried over.
A richer setting could allow the structure of returns to sequential projects to vary more generally. Our simplified structure allows us to focus on the impact of the likely size of future projects without distorting qualitative insights.
As all payoffs are scaled by a common multiple s, the critical threshold \({\hat{\pi }}\equiv \tau /(\omega -\eta )\) is invariant to s.
Our modeling assumption is that abandoning a legacy project immediately releases implementation capacity for current projects. In real settings, even abandonment could demand decision-making resources.
To see that this does not imply loss of generality, observe that we could allow \({\tilde{s}}_{2}\) to take one of any multiple values, and then partition the set of projects into two sub-sets: those that are small vs those that are large, with \(\frac{\eta }{\tau }\) being the dividing line. In effect, \(s_{\ell }\) and \(s_{h}\) can be regarded as expected values conditional on that partition.
To see why serial postponement is optimal in this case, note that it delivers a payoff of \(\eta\) from implementing Project 1 in period 2 and at least \(\eta s_{\ell }\) from an optimal decision in period 3 for Project 2. Implementing Project 2 immediately, with payoff \((\tau +\eta )s_{\ell }\) would require abandoning Project 1 altogether. Given \(s_{\ell }<(\eta /\tau )\) the total payoff from sequential postponement is higher.
This additional restriction avoids trivialities. If \(a > {\hat{\pi }}\), then the second period opportunity is always sufficiently improvable to merit postponement of a decision to period 3, eliminating any potential congestion in decision. If \(b < {\hat{\pi }}\), then the second period opportunity is never improvable enough to merit postponement of a decision, reducing the sequential decision problem to a single period choice.
The optimal social rate of discount on environmental projects is a controversial issue.
The formal details are sketched out in a separate note.
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Heyes, A., Kapur, S. The precautionary principle when project implementation capacity is congestible. Theory Decis 95, 691–711 (2023). https://doi.org/10.1007/s11238-023-09934-y
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DOI: https://doi.org/10.1007/s11238-023-09934-y