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Prospect Theory: a Global Income Elasticity for Disaster Risk.

JEL C10 * D00 * D80 * F01 * O50 * G32

An income elasticity for disaster risk is derived from prospect theory and estimated using country-level data. There is some debate as to the sign of the income elasticity for disaster risk (e.g. Toya and Skidmore, Economics Letters, 2007; Kellenberg and Mobarak, Journal of Urban Economics, 2008). If the sign was negative, an increase in incomes that occurs with economic development could be relied upon by policymakers to automatically mitigate the adverse impact of disasters. If instead the sign were positive, the reasons must be identified and appropriate measures undertaken.

In relation to prospect theory (Kahneman and Tversky, Econometrica, 1979), disaster risk can be derived as the probability of a loss associated with the value of an extreme outcome. If the prospect-theory equation were held unchanged and the riskless component were treated as a constant, the income elasticity becomes equal to the ratio of a percentage change in the probability of a loss, to a percentage change in the potential loss. The numerator is a marginal utility expressed as the first derivative of the utility function multiplied by the decision weight and the value of the potential loss. The denominator is a marginal weight expressed as the first derivative of the decision function multiplied by the probability of a loss and its utility.

This income elasticity was estimated using annual country-level data released for the year 2016 by a global provider of disaster risk information, the Index for Risk Management ( Following convention, a variable for disaster risk was made equal to the product of a natural-hazard index (0.1 to 8.4), a socioeconomic-vulnerability index (0.1 to 9.6) and an infrastructure-vulnerability index (0.4 to 9.6). The natural hazard index considered the frequency of past disasters, the number of people affected and the extent of damage. The socioeconomic index considered poverty, inequality and aid-availability. The infrastructure index considered access to basic services and government effectiveness against disasters. The mean for Disaster-Risk was 67.68, with a standard deviation of 80.6. The minimum was 0.024 (Norway) and the maximum was 574.46 (Somalia). A variable for potential loss was made equal to year 2016 GDP per capita, the mean and standard deviation being 18,439 and 20,382 U.S. dollars, respectively.

An ordinary least-squares regression of the logarithm of disaster risk against the logarithm of gross domestic product (GDP) resulted in an income elasticity estimate of -1.21, significant at a t-statistic of 18.36. This estimate changed to -1.23 (t-stat = 19.99) when controlling for population size (not significant) and land area (significant). To capture the possible effect of human capital, the 2016 values for GDP per capita were replaced by same-year values for the Human Capital Index. This changed the income elasticity estimate to -5.99 (t-stat= 16.72). The change supported the hypothesis that including human capital as part of potential loss increased the absolute magnitude of the effect upon disaster risk.

As a final check, the possibility of reverse-causality (that disaster risk affects potential loss rather than vice-versa) was controlled for. We use two-stage least-squares regression algorithms of GDP per capita and the Human Capital Index as an instrument of the INFORM variable and percent improvements in sanitation. The results were an income elasticity estimate of-1.24 for GDP per capita and -5.71 for the Human Capital Index, significant, each with t = 12.

These estimates complement the finding of an income elasticity of-1.1 for local government data where disaster risk was instead represented by fatalities and potential loss was represented by income per capita (Yonson, PhD Dissertation, Victoria University of Wellington, 2017). They also support the finding in that study of a compounding effect if human capital was included in the regression.

Thus, for prospect theory, the income elasticity for disaster risk is probably negative. There is greater than a 1 % change in marginal utility for a 1% change in marginal weight. This finding suggests that mitigating risk using preventive measures is either a luxury gain or a luxury loss, depending on whether the reference point is a current state of economic development or an unattained aspiration. Either way, an increase in incomes that comes with economic development coupled with an increased share on spending for risk prevention can be relied upon by policymakers as a form of implicit insurance against the adverse impacts of disasters (e.g., Kahn, Review of Economics and Statistics, 2005).

Acknowledgments Gratitude is extended to Rio Yonson for helpful comments, suggestions and references.

Antong Victorio (1)

(1) Victoria University of Wellington, Wellington, New Zealand

Antong Victorio


Published online: 1 February 2018
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Title Annotation:RESEARCH NOTE
Author:Victorio, Antong
Publication:International Advances in Economic Research
Article Type:Abstract
Date:Feb 1, 2018
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