### Scott Kelly

#### Abstract

A cornerstone of economic growth and development is a robust and functioning national infrastructure system. Concerns arising from the effects of infrastructure failure on the economy are beginning to raise important questions about the risks associated with infrastructure failure and, importantly, the wider economic costs that these failures might have on a national economy. This research explores the interdependencies of infrastructure failure and estimates economic loss probabilistically. A MonteCarlo I-O model is proposed for estimating total economic loss when there is uncertainty around direct economic loss estimates. Results show that when impacts fall in the tails of distributions, the range of loss estimates can be four to five times more than the expected loss when a deterministic model used. Economic impact analyses that employ deterministic estimates of economic loss may therefore be misleading and are therefore encouraged to include estimates of uncertainty when presenting economic losses.

Hazards are probabilistic events that can lead to disasters that vary in magnitude from minor incidents that cost little, to large catastrophic events that cause widespread harm and cost billions. The economic impact of disasters is therefore highly uncertain and varies significantly from one hazard to the next. Despite the probabilistic nature of natural hazards and therefore the stochastic nature of the economic consequences, the majority of disaster related research still use deterministic inputs when estimating economic loss. When historical analyses are conducted, indirect economic losses are typically estimated using deterministic ex-post estimates of direct economic impact. On the other hand when impacts from future events are estimated, probabilistic hazard models are sometimes employed to stochastically estimate the magnitude and location of potential hazards, but deterministic economic loss estimates are still used in I-O models to estimate direct and indirect economic loss.

In order to understand the effect that different probability distributions may have on economic loss estimates, this research compares losses across five probability distributions (uniform, triangular, normal, log-normal and Cauchy). For comparison purposes, each probability distribution is created with the same expected impact representing a decrease in direct economic output (final demand) of 10% [E(x) = 0.1]. Each probability distribution represents a sample size of 1 million entries from which unique samples can be drawn at random (see Figure 1). A MonteCarlo simulation is then performed 10,000 times on each of the five distributions. Each time a new sample is taken from the distribution it contains nine values representing the level of shocked final demand for each of the nine infrastructure sectors. The direct economic impact of the disaster on all remaining economic sectors is assumed to be zero and therefore the only effect on these sectors occurs indirectly through impacts occurring through infrastructure disruption. This is done so that direct and indirect economic impacts of infrastructure failure can be properly analysed for each sector of the economy. Each time a sample is drawn at random from each probability distribution, it represents the direct economic impact from a single disaster. Thus 10,000 samples represent 10,000 unique disasters but with an expected impact of 10% disruption. Each sample (disaster) contains nine independent draws from a probability distribution representing each of the nine infrastructure sectors, thus each infrastructure sector is shocked by a unique value. Using well established IO methods both direct and indirect and economic losses are estimated for each sector of the economy.

The cost of cascading failure: risk and resilience within UK infrastructure networks (pdf, 3.2 MB). *The future of national infrastructure systems & economic prosperity conference, *Cambridge, UK, March 27–28, 2014.

#### Authors

Kelly, S., Tyler, P. and Crawford, D.B.