Nanyang Business School Forum on Risk Management and Insurance
Should We Do More When We Know Less? Optimal Risk Reduction Under Technological Uncertainty
Technological uncertainty (TU) arises whenever the effects of risk mitigation depend on exogenous factors or are subjectively perceived to be uncertain. For example, a sprinkler system might operate more or less reliably when a fire breaks out. The benefits of climate change mitigation depend on a variety of environmental factors, over which there is considerable scientific disagreement. While economists commonly assume that the benefits of risk mitigation are precisely known at the time a decision is made, we argue that many, if not all forms of risk reduction are characterized by TU. In this paper, we study the effects of TU on self-insurance (the reduction of the magnitude of a loss) and self-protection (the reduction of the probability of a loss) for a risk-averse, expected utility maximizing decision maker.
We first study individuals’ willingness to pay (WTP) for risk reduction. TU reduces the WTP for self-insurance because it introduces risk into the agent’s endowment. An increase in TU has the same effect because either change makes the risk-averse agent worse off. As a result, self-insurance increases her welfare by less than if TU were absent. TU compromises the effectiveness of self-insurance, which is reflected in a lower WTP. On the contrary, TU has no impact on the WTP for self-protection because expected utility is linear in probability. Switching to a better technology, as represented by a first-order stochastic dominant (FSD) improvement, raises the WTP for both activities. Such an FSD improvement reduces the expected loss, which is always desirable for the agent and therefore leads to a higher WTP.
We then direct our attention to the agent’s optimal demand for both activities. While the results on WTP are straightforward, the impact of TU on optimal demand is jointly determined by the agent’s risk preferences and measures of risk-reduction effectiveness. We identify conditions for TU, FSD improvements and increases in TU to have unambiguous comparative statics.
For a prudent agent, TU increases optimal self-insurance as long as large losses can be mitigated more effectively than small ones, for instance, when the installation of a higher-quality airbag system makes the magnitude of a potential accident depend to a lesser extent on the carefulness of the driver. This result is in line with the precautionary principle, which calls for more investment in the face of higher uncertainty as proposed in the Rio declaration. However, we also identify conditions under which TU reduces optimal self-insurance, i.e. when the agent is imprudent and when a better-performing technology enhances the gain from additional effort. The latter result would imply that lack of scientific knowledge can be a reason to invest less in climate change mitigation, consistent with the opinion of some skeptics. The assumptions needed to justify such a reasoning find much less support empirically than those that generate the opposite prediction. When it comes to FSD improvements and increases in TU, we derive similar sets of conditions involving how the agent’s degree of relative risk aversion compares to unity for FSD improvements, and how her degree of relative prudence compares to two for increases in TU.
TU and increases in TU have no impact on optimal self-protection for the same reason they do not affect the WTP for self-protection. The effect of an FSD improvement, on the other hand, depends on whether the cost of self-protection is separable from the agent’s utility function. For example, if self-protection effort involves a disutility, the cost is separable and the effect of an FSD improvement is independent of the agent’s preference. Instead, it relies entirely on how the performance of the technology affects the gain from more effort. If self-protection comes at a monetary cost, it is non-separable from the agent’s utility, and the agent’s risk aversion comes into play.
Our theory can be applied in a variety of settings. We provide the first systematic analysis of the effects of TU on optimal risk mitigation. Second, we determine conditions on the agent’s preferences and on risk reduction effectiveness that yield clear comparative statics. We thus derive new hypotheses about the optimal use of self-insurance and self-protection. While a lot is known about the empirical validity of certain preference traits such as prudence or relative risk aversion, there is still a gap in the empirical literature when it comes to our proposed technology measures. This motivates their measurement in the lab and in the field. Third, TU can increase or decrease the optimal level of the available risk reduction activity. It can serve as an explanatory variable in those cases where conventional theories have a hard time explaining why observed demand for risk mitigation deviates from predicted demand. Our analysis makes the simple wisdom precise that the benefits of risk reduction lie “in the eye of the observer”, allowing differences in behavior to be attributed to heterogeneity in perception.
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