Vulnerability Index. Haydar Kurban y and Mika Kato z. November 19, 2008

Transcription

1 Vulnerability Index Haydar Kurban y and Mika Kato z November 19, 2008 Abstract This paper develops an empirical method to measure the vulnerability of various population groups during a disaster. In our model, the degree of vulnerability depends on the nature of the disaster, i.e., its strength, duration and scope, and the household s ability to respond and recover. Vulnerability indices for various socio-economic groups are computed on the basis of riskaverse public perceptions. This study provides sound analytical and empirical guidance to decision makers regarding the most e ective and e cient way to allocate resources among cities to minimize social and economic vulnerability. Currently, methods are lacking for assessing and ranking vulnerabilities in a systematic and integrated manner. We estimated model parameters based on the socio-economic and loss data compiled from public and private sources after Hurricane Katrina. Our empirical method o ers a novel approach to quantify and rank vulnerability of population groups during a disaster. Key Words: vulnerability, disaster loss, recovery, homeowners insurance, Hurricane Katrina JEL Codes: Q56, Q54, Q58, D81 Paper presented at Southern Economic Association 78th Annual Meetings 2008, Washington, D.C. November 20-23, Introduction In this paper, we develop an empirical method to measure vulnerability of various population groups during a disaster. We propose a vulnerbility index that can be used We thank Alexis Miller for excellent research assistance. This research was supported by the United States Department of Homeland Security through the Center for Risk and Economic Analysis of Terrorism Events (CREATE) under grant number 2007-ST However, any opinions, ndings, and conclusions or recommendations in this document are those of the authors and do not necessarily re ect views of the United States Department of Homeland Security. y Department of Economics, Howard University; [email protected] z Department of Economics, Howard University; [email protected] 1

2 to assess vulnerability of individuals or groups in various economic status and di erent geographic locations in terms of how fast a population group recovers from losses caused by a disaster. Two points are emphasized in the index. First, vulnerability should be based not only on potential losses but also on potential ability of recovery. Second, vulnerability should also re ect the post-recovery welfare in relation to the minimum welfare. Speci cally, our index is made to emphasize vulnerability of individuals whose welfare falls below the mimimum welfare and discount vulnerability of those whose welfare is above the mimimum welfare. This is somewhat similar to maximizing the so-called risk-averse social welfare people maximizing this type of welfare tend to choose a society in which the minimum level of shelter and food are guranteed. Our study, therefore, may help to provide sound analytical and empirical guidance to emergency management agencies such as FEMA and SBA on the most e ective and e cient way of allocating the limited resources to di erent groups and individuals. Various factors a ect vulnerability of individuals. Not only the nature of disaster itself, i.e., size, duration and scope, but also the individual s ability to respond to a disaster plays an important role in explaining vulnerability. As Hurricane Katrina revealed, the lower income groups tend to be more vulnerable because they have limited access to private and public assets to respond to a disaster (Alwang, et al., 2001). The lower income groups are also vulnerable during the post disaster period as the recovery can be delayed due to limited economic resources and exclusion from social networks (Holzmann and Jorgensen, 2000). Social policy can reduce or eliminate some constraints by allocating resources according to the relative vulnerability of population groups during a disaster. To make the concept of vulnerability operational and useful, a socially accepted minimum has to be agreed upon for each risk and outcome. Vulnerability of the poor results from their closeness to the socially accepted minimum threshold level of well-being threshold. In fact, even if the lower income groups face similar risks, they are, ceteris paribus, more likely to fall below the threshold because of their inability to respond to losses in welfare. Our de nition of vulnerability also distinguishes between variability and vulnerability (Luers, et al., 2003). Even if everyone faces the same risks, some people are more vulnerable because of their inability to manage these risks. Although a higher income person might face more variability in wealth as a result of a disaster, vulnerability may be una ected since it is very unlikely that a higher income person will drop below the minimum level of well-being. On the other hand, a lower income household, closer to the minimum level of well-being, can easily fall below the minimum even if losses are smaller in magnitude. 2 De ning the Vulnerability Index Our interest is to create a vulnerability index that can capture not only the potential losses caused by an event, but also the potential recovery that can be made in the 2

3 Initial State of Wealth W0 An Event occurs (Hurricane, earthquake, etc.) Recovery Effort (Insurance pay, public and private assistance, etc.) Current State of Wealth W1 Time Immediate Loss, L, is determined Recovery, R, is made Net Loss, L R, is determined W1 = W0 L + R Figure 1: Order of Events future. Those who have ability to recover more of their loss will be considered less vulnerable regardless of the size of their loss while those who have less ability to recover the loss will be considered more vulnerable. 2.1 The Model We consider an individual (e.g., a household) with initial (pre-disaster) wealth W 0. We set up a simple time-line of events, as shown in Figure (1), which describes the experience of an a ected individual. When an event occurs, some or all of the initial wealth W 0 may be a ected. We assume, for simplicity, that the rate of loss depends only on the magnitude of an event, X. The rate of loss from the same X, however, may vary by physical and geographical conditions. For example, in case of hurricane Katrina, coastal areas and non-coastal areas have signi cantly di erent loss structures as we show later in Section 2. Therefore, we divide the a ected area in smaller groups so that each group should has a similar loss structure. Then the immediate loss L of an individual in group i is L = i (X) W 0 ; (1) where 0 < i (X) < 1 and i0 (X) > 0 for any X > 0. Various private and public e orts will be made to recover the loss. Among all, private insurance is most important to predict the individual s ability to recover losses. Typically, homeowners insurance protects individual s properties from disasters. To receive a higher coverage limit, an individual must pay a higher insurance premium with other conditions the same. The other factors, such as weather and landscape that are speci c to the area, also signi cantly a ect the relationship between insurance premium and the coverage limit According to the National Association of Insurance Commissioners (NAIC), the national average premium for homeowners insurance in 2005 is $764 while the top three most expensive states are Texas ($1,372), Louisiana ($1,144), and Florida ($1,083), those commonly exposed to severe storms and hurricanes. We therefore de ne the coverage limit function by area. The coverage limit C 3

4 of an individual in area j is C = C j (p) ; (2) where C j0 > 0. Assume that the amount of insurance premium that an individual is willing to pay is positively correlated with initial wealth W 0 p = p (W 0 ) ; (3) where p 0 (W 0 ) > 0. If one has an insurance policy that pays the coverage limit C, the actual loss covered by this insurance is equal to either the coverage limit C or the loss L, whichever the smallest. If one does not have insurance, then we assume that no recovery is made. Assume that the probability that an individual has insurance is and it depends on the wealth W 0. Then the actual amount of recovery R is R = (W 0 ) minfc; Lg, (4) where 0 (W 0 ) > 0. After all possible recovery is made, the post-recovery wealth W 1 of an individual in group i and area j is W ij 1 (X; W 0 ) W 0 L + R (5) = W 0 i (X) W 0 + (W 0 ) minfc j (p (W 0 )) ; i (X) W 0 g. 2.2 The Vulnerability Index Our vulnerability index measures and ranks the well-being of various population groups impacted by disasters. Speci cally, it computes the marginal change in afterrecovery wealth when an additional stress is given to an individual in group i and in area j with initial wealth W 0, ij 1 =@X. We also introduce an adjustment coe cient W =W ij 1 (X; W 0 ) to the index so that the vulnerability of individuals that fall below some poverty line of wealth W is emphasized while the vulnerability of individuals that are above W is discounted. De ne the vulnerability index for individuals in group i and area j ij V ij 1 (X; W 0 ) =@X (X; W 0 ) = W ij 1 (X; W 0 ) =W ; (6) where > 1 determines the degree of emphasis on vulnerability of people below the poverty level W. A larger implies that a policy puts higher priority on those who fall below W. Notice that this index depends only on the wind speed X and the pre-disaster wealth W 0. 4

5 3 Estimation In this section, we attempt to actually estimate the vulnerability index function (6) that is applicable to the areas impacted by Hurricanes Katrina and Rita. We use national, state, and county-level data to estimate functions i (X), p (W 0 ), C i (p), (W 0 ), and W that t to the impacted areas This helps us to predict vulnerability of individuals or a group of individuals with W 0 in group i and area j when an event with magnitude X occurs. 1. Loss Rate i (X) We estimate loss rate i (X) in (1). For the magnitude of an event X, we use the maximum wind speed, X = 1 ( 60 pmh), 2 (>60 pmh), 3 (>75 pmh), 4 (> 90 pmh), and 5 (> 100 pmh). We compiled the maximum wind speed data of 88 counties 1 in Alabama, Mississippi and Louisiana impacted by Hurricanes Katrina, Rita and Wilma. The storm maps created by NOAA is used to determine the maximum wind speed in each county that was in the path of Katrina. Table 2 in Appendix show the assignment of wind speed to each impacted county. 2 Table 1: Veri ed Losses To estimate the loss rate, we divide the 88 impacted counties into coastal counties and non-coastal counties. The loss structure of coastal counties is signi cantly di erent from that of non-coastal counties. This is so as damages in coastal counties are not only from strong wind but also from hurricane tidal surge ooding. We thus estimate the loss rate function for non-coastal counties nc (X) and that for coastal counties c (X) separately. 1 These counties were designated by the Federal Emergency Management Agency as eligible to receive individual and public assistance as of September 14, For Cameron Parish, LA and Vermilion Parish, LA, we use the maximum wind speed of Hurricane Rita, instead of that of Hurricane Katrina, as most of their losses reported in the Federal Emergency Management Agency (FEMA) and the Small Business Administration (SBA) were caused by Harricane Rita. 5

6 First, we estimate the dollar values of the full extent of housing damage in each of the 88 counties by using a special data set compiled by the Department of Housing and Urban Development (HUD). After Hurricane Katrina, the Federal Emergency Management Agency (FEMA) and the Small Business Administration (SBA) inspected the disaster area and identi ed three damage levels, minor, major and severe and 3 then estimated the dollar value of losses. We summarize, in Table 1, the mean veri ed losses for each damage level by state. We use Census 2000 data to nd the number of houses in each damage level in each county. We compute the county k s loss gure as P L k = 3 d k sn k s for k = 1; ::; 88; (7) s=1 where s = 1 (minor), 2 (major), 3 (severe) is the damage levels de ned by FEMA, d k s is the veri ed loss at damage level s in the state to which county k belongs from Table 1, and n k s is the number of houses in damage level s in county k from Census Next, we estimate the county s pre-disaster initial wealth W0 k. We compute the aggregate house value of county k as W0 k = W k 3P 0 n k s for k = 1; ::; 88; (8) s=1 where W k 0 is the pre-disaster mean house value of county k found in Census From Eqs. (7) and (8), the loss rate of county k can be computed by k Lk W k 0 = 3P d k sn k s s=1 3P W k 0 n k s s=1 for k = 1; ::; 88. (9) There are 72 non-coastal counties and 16 coastal counties. Thus we divide a ected counties into two groups as k = 1; :::; 72 (non-coastal); 73; :::; 88 (coastal) and regress the loss rate against the wind speed level X k = X k...for k = 1; :::; 72; 3 The O ce of the Federal Coordinator for Gulf Coast Rebuilding at the Department of Homeland Security, the Federal Emergency Management Agency, the Small Business Administration, and the Department of Housing and Urban Development have created a data set to assess the full extent of housing damage due to Hurricanes Katrina, Rita, and Wilma ( FEMA inspectors classi ed the damage levels as minor, major and severe. A subset of FEMA registrants with real property damage applied to the Small Business Administration for loans to repair their property. SBA inspectors then estimated veri ed loss for units assessed by the FEMA inspector to have either major damage or severe damage. We used SBA median veri ed loss tables, FEMA categories and the number of occupied housing units in each category to estimate total loss for 88 counties impacted by Hurricane Katrina. To estimate the aggregate damage level for each county, we multiplied the number of housing units in each damage category by the median veri ed losses. 6

7 L/W0 = X Loss Rate (L/W0) L/W0 = X Coastal Noncoastal Wind Speed (X) Figure 2: Wind Speed and Rate of Loss and k = X k...for k = 73; :::; 88; where X k is the maximum wind speed in county k as reported in Table 2 in the Appendix. Figure 2 shows the average loss rates plotted against wind speeds. We nd that: 1. the average loss rate is higher in coastal counties at any level of wind speed, and 2. the marginal losses from additional wind speed is much higher in coastal counties and thus di erence in losses between the two groups tends to enlarge as wind speed increases. The estimated loss rate function for non-coastal counties is and that for coastal counties is 2. Coverage Limit Function C j (p) nc (X) = 0: :0195X; (10) c (X) = 0: :1753X. (11) We estimate the area (state in our case)-speci c coverage limit function in Eq. (2) for Alabama, Mississippi, and Louisiana. However, data on coverage limit and premium are available at the national level, not at the state level. Thus, we take two steps to derive the state-speci c coverage limit function. First, we estimate the national coverage limit function using a linear form C na (p) = + bp. (12) We use real insurance coverage data and average premium data compiled from National Association of Insurance Commissioners report (NAIC, 2000). The NAIC report is based on the data collected from insurance regulatory o cials. Since the 7

8 $500,000 $450,000 $400,000 Coverage Limit (USD) $350,000 $300,000 NAP $250,000 LAP $200,000 MAP $150,000 $100,000 Cna(p) = p Cal(p) = 412.5p AAP Cms(p) = p $50,000 Cla(p) = p $ Annual Premium (USD) Figure 3: Annual Premium and Coverage Limit NAIC gures are based on actual policy forms, they re ect the actual nationwide coverage limit and premiums paid. The estimated function is C na (p) = :32p. (13) As aforementioned, applying the national coverage limit function (13) to an individual state j may be inappropriate. Insurance premium re ects state-speci c factors such as landscape and weather that determine the likelihood of disaster occurrence. Therefore, the insurance premium for identical policies can vary largely by state. We con rm this point in Table 3 in the Appendix. It shows that the average premium of the most commonly written insurance package HO-3 4 varies signi cantly by state and that states constantly a ected by disasters tend to have higher premiums. Second, we de ne the national average premium as p na and the state j s average premium as p j and assume that state j s homeowners pay p j =p na of national premium for any level of coverage limit. This assumption allows us to de ne the state j s coverage limit function for a given national coverage limit function (12) as p C j n (p) = a + b p: (14) From Table 3 in the Appendix, the average premium for an HO-3 insurance package in Alabama is p al = 847, that of Mississippi is p ms = 939, and that of Louisiana is p la = 1144, and the nationwide average is p na = 764. Thus using the estimated national coverage limit function (13), we may derive the coverage limit function of Alabama as p j C al (p) = :5p, (15) % of homeowners insurance are this type. HO-3 is an open perils policy that covers any direct damage to the house or other structures on the property unless it is speci cally excluded. However the coverage for personal property is for named perils only. 8

9 1400 Annual Premium (USD) p(w 0) = W $0 $100,000 $200,000 $300,000 $400,000 $500,000 $600,000 Home Value (USD) Figure 4: Home Value and Annual Premium that of Mississippi as and that of Louisiana as C ms (p) = :09p, (16) 3. Premium function p (W 0 ) C la (p) = :41p. (17) We estimate the premium function p (W 0 ) in Eq. (3) by regressing annual homeowners insurance payments on home value data compiled from American Housing Surveys 1999 National Sample. Not surprisingly, Figure 4 and Eq. (18) show that homeowners with higher home values are willing to pay a higher annual premium. For every $10,000 increase in home value, annual insurance payments increase by $ Insured Homeowners Rate (W 0 ) p (W 0 ) = 0:0018W :39: (18) We estimate insured homeowners rate (W 0 ) in Eq. (4). The data for this variable, again, come from American Housing Surveys 1999 National Sample. We constructed this variable by dividing the number of owner-occupied housing units with homeowners insurance by the total number of owner-occupied housing units in the sample.in Figure 5, di erent purchasing patterns are observed between homeowners with a home value < $100,000 and homeowners with a home value $100,000. The rate of insured homeowners when home value is less than $100,000 is (W 0 ) = 0:2327W 0: for 0 W 0 < 100; 000; (19) and the rate of insured homeowners when home value is $100,000 or more is approximately constant at = 0:97 for W 0 100; 000. (20) 9

10 Figure 5: Home Value and Insured Homeowners 5. Poverty Line W To estimate poverty line of an individual s wealth W in (6), we use below poverty level median house value as proxy for the socially accepted minimum level of well being. According to American Housing Survey s 1999 National Sample the median housing value of those that earned less than below poverty level income was $86,643. W = (21) 4 Simulation Based on the estimated loss rate functions, Eqs. (10) and (11), the coverage limit functions Eqs. (15)-(17), the premium function (18), the rates of insured homeowners, Eqs. (19) and (20), and the poverty line (21), we can predict vulnerability of an individual with given initial home value W 0 in group i (non-coastal or coastal) and in state j (AL, MS, or LA) when wind speed X occurs. For actual accessment of vulnerbility, > 1, the degree of emphasis on vulnerability of people who fall below the poverty level W, has to be determined. It should re ects the public interest and consensus on priority rank. A larger emphasizes vulnerbility of the poor under W 0 more. We use = 1 and = 2 in our simulation to see the e ect of the choice of on vulnerability. Figures 7, 9, and 11 show the estimated vulnerability functions for non-coastal and coastal counties in Alabama, Mississippi, and Louisiana respectively when = 1 and Figures 7, 9, and 11 show those when = 2. The height of the function shows the scale of vulnerability, and the initial home value W 0 in the rage of $20,000-$300,000 and the wind speed level in the range of 1-8 are taken on the oor.several important implications can be derived from the simulation results. 1. Homeowners with initial wealth under $100,000 in non-coastal counties in AL, MS, and LA show some vulnerability. Vulnerabilty is higher for a lower initial 10

11 Figure 6: Coverage Limit to Home Value Ratio wealth. Vulnerbility of less wealthy homeowners is, however, much higher when = 2 as shown in Figures 8, 10, and 12 than that when = 1 as shown in Figures 7, 9, and 11 as a higher policy parameter emphasizes those under the poverty line more. For wind speeds between 1-8, losses do not exceed the coverage limit. Thus if a homeowner has insurance, all losses should be covered. Vulnerability is, however, higher for less wealthy individuals as the rate of insured homeowners declines with decreases in home value. 2. Homeowners with initial wealth in the range of $100,000-$300,000 in non-coastal counties in AL, MS, and LA, seem little a ected as they are mostly insured (97%) and their losses, when wind speed is between 1 and 8, are covered by insurance. 3. Vulnerability of coastal counties is higher than that of non-coastal counties. As wind speed increases, for a given home value, losses eventually exceed the home value and this increases vulnerability. 4. In coastal counties, vulnerability, for a given wind speed, increases when home value rises when = 1, that is, less emphasis is put on vulnerability of homeowners under the poverty line. Welthier homeowners are assessed more vulnerble as they tend to have larger uninsured losses. This comes from the fact that the coverage limit to home value ratio tends to decline as home value increases as shown in Figure 6, derived from Eqs. (15)-(18). When = 2, on the other hand, vulnerability decreases when home value rises as the policy parameter discounts vulnerability for the welthier homeowners more and emphasizes that for the poor homeowners more. 5. In coastal counties, Louisiana is most vulnerable, Mississippi is second-most vulnerable, and Alabama is least vulnerable among the impacted three states. This re ects the fact that Louisiana is the most expensive state and Alabama is 11

12 Figure 7: Vulnerability Functions for Alabama with = 1 Figure 8: Vulnerability Functions for Alabama with = 2 12

13 Figure 9: Vulnerability Functions for Mississippi with = 1 Figure 10: Vulnerability Functions for Mississippi with = 2 13

14 Figure 11: Vulnerability Functions for Louisiana with = 1 Figure 12: Vulnerability Functions for Louisiana with = 2 14

15 the least expensive state for the HO-3 type homeowners insurance, and homeowners in Louisiana tend to be underinsured. We can con rm this point in Figure 6. 5 Conclusions This paper developed a novel approach to measure and rank the vulnerability of various population groups during and after a disaster. In our model, the degree of vulnerability depends on the nature of the disaster, i.e., its severity, duration and scope, and the household s ability to respond and recover. Our study contributes to the vulnerability literature by developing an index that is consistent with utility maximizing consumer behavior and risk-averse public perceptions. Given that natural catastrophes have been occurring with greater frequency and severity in the last decade, this study provides sound analytical and empirical guidance to decision makers regarding the most e ective and e cient way to allocate resources among the cities in order to minimize social and economic vulnerability. Currently, methods are lacking for assessing and ranking vulnerabilities in a systematic and integrated manner. Our model parameters were estimated based on the socioeconomic and loss data compiled from public and private sources. As seen during Hurricane Katrina, a lack of such models can lead to tremendous costs and su ering for vulnerable populations and national economy. Our simulation indicates that less wealthy individuals in non-coastal counties are more vulnerable as there is a negative relationship between home values and rate of insured homeowners. The homeowners with home value above $100,000 face less vulnerability because about 97 percent of homeowners purchase insurance. For non-coastal counties we observe overall higher degrees of vulnerability as losses exceeds the coverage limit. We observe that vulnerbility tends to be higher for wealthier homeowners. The reason is that while the coverage limit increases as the home value rises, it does not increase as much as the home value. Of the coastal counties impacted, the most vulnerable counties are in Louisiana and the least vulnerable ones are in Alabama. This re ects the fact that Louisiana is the most expensive state and Alabama is the least expensive state for the HO-3 type homeowners insurance among the three states. This implies that homeowners in Louisiana tend to be underinsured. The empirical method developed and applied to Hurricane Katrina can easily be extended to other types of disasters in the states other than Alabama, Louisiana, and Mississippi. Our model parameters were estimated based on national level information on insurance coverage level, tenure, homeowners insurance premium and whether homeowners have insurance coverage or not. Given information on pre-disaster level wealth, the type of disaster, its impact area and its severity, one can estimate the vulnerability for various population groups in coastal and non-coastal communities. 15

16 References [1] Alwang, J. P. B. Siegel and S.I. Jorgensen Vulnerability: a new from di erent disciplines Social Protection Discussion Paper No. 0115, World Bank [2] Congressional Research Service Hurricane Katrina: Social-Demographic Characteristics of Impacted Areas. [3] Holzmann, Robert; Steen Jorgensen "Social risk management: A new conceptual framework for social protection, and beyond." World Bank. [4] Liu, Amy, Matt Fellowes, and Mia Mabanta Katrina Index: Tracking Variables of Post-Katrina Recovery. Brookings Institution. [5] Luers, Amy L., David B. Lobell, Leonard S. Sklar, C. Lee Adams, and Pamela A. Matson A method for quantifying vulnerability, applied to the agricultural system of the Yaqui Valley, Mexico. Global Environmental Change 13: [6] Logan, John R The Impact of Katrina: Race and Class in Storm- Damaged Neighborhoods. [7] Louisiana Department of Health and Hospitals Louisiana Health and Population Survey, Survey Report November 28, [8] National Association of Insurance Commissioners Homeowners Insurance Results, NAIC Research Quarterly, Vol. VI, Issue 2: [9] Newberger, Robin, and Michelle Coussens Insurance and Wealth Building among Lower-income Households. Chicago Fed Letter, June 2008: 1-4. [10] Pielke Jr., Roger A., and Christopher W. Landsea Normalized Hurricane Damages in the United States. Weather and Forecasting 13: [11] Smith, Kerry V., Jared C. Carbone, Jaren C. Pope, Daniel G. Hallstrom, and Michael E. Darden Adjusting to Natural Disasters. Journal of Risk and Uncertainty 33: [12] U.S. Census Bureau Special Population Estimates for Impacted Counties in the Gulf Coat Area. Release/www/emergencies/impacted_gulf_estimates.html. [13] U.S. Department of Housing and Urban Development s Of- ce of Policy Development and Research Current Housing Unit Damage Estimates Hurricanes Katrina, Rita and Wilma. 16

17 [14] Viscusi, W. Kip and Patricia Born The Catastrophic E ects of Natural Disasters on Insurance Markets. NBER Working Paper No. W

18 Appendix: Data Table 2: Damage in 88 counties impacted by Hurricane Katrina 18

19 Table 3: Average Premium by State 19