6 In the US, assistance from the Department of Housing and Urban Development (HUD) plays an essential role 7 in supporting the post-disaster recovery of states with unmet housing needs. HUD requires data on unmet needs 8 to appropriate recovery funds. Ground truth data are not available for months after a disaster, however, so HUD 9 uses a simplified approach to estimate unmet housing needs. State authorities argue that HUD’s simplified approach 10 underestimates state’s needs. This paper presents a methodology to estimate post-disaster unmet housing needs that 11 is accurate and relies only on data obtained shortly after a disaster. Data on the number of damaged buildings are 12 combined with models for expected repair costs. Statistical models for aid distributed from the Federal Emergency 13 Management Agency (FEMA) and the Small Business Administration (SBA) are then developed and used to forecast 14 funding provided from those agencies. With these forecasts, the unmet need to be funded by HUD are estimated. 15 The approach can be used for multiple states and hazard types. As validation, the proposed methodology is used to 16 estimate the unmet housing needs following disasters that struck California in 2017. California authorities suggest 17 that HUD’s methodology underestimated the state’s needs by a factor of 20. Conversely, the proposed methodology 18 can replicate the estimates by the state authorities and provide accounts of losses, the amount of funding from FEMA 19 and SBA, and the total unmet housing needs without requiring data unavailable shortly after a disaster. Thus, the 20 proposed methodology can help improve HUD’s funding appropriation without delays. 21 1 Introduction 22 Studies of housing recovery after previous disasters have identified that disadvantaged persons are more likely to 23 occupy deteriorated homes in hazard-prone neighborhoods and have the least resources to restore their livelihoods. 24 *Corresponding author: Rodrigo Costa, rccosta@stanford.edu 1 These conditions have led to an unequal distribution of disaster impacts due to income [e.g., 27, 38, 41], race [e.g., 25 3, 12, 25], homeownership [e.g., 16, 18, 22, 39], and other demographic factors. To partly address inequalities in 26 disaster impacts, governmental disaster assistance programs are often designed to assist the most vulnerable [e.g., 27 5, 17, 20, 42]. In the US, the Department of Housing and Urban Development (HUD) has increasingly supported 28 the recovery of uninsured, low-income, disaster-affected families. As HUD’s role in supporting disaster recovery 29 in communities increased over the last decades, criticisms have been raised regarding their limited and slow funding 30 disbursement. In some cases, for reasons sometimes beyond their control, HUD’s role in disaster recovery was deemed 31 to have worsened socioeconomic inequalities [14, 23, 32]. 32 One way HUD’s recovery assistance programs negatively impact recovery outcomes is the strict criteria to estimate 33 the funds needed by a disaster-struck state. HUD defines unmet housing needs as the difference between the home re- 34 pair costs (i.e., losses) and the funding a state is expected to received from insurance, Federal Emergency Management 35 Agency (FEMA), or the Small Business Administration (SBA) for housing repairs. HUD uses the number of FEMA 36 funding applications as a proxy for the number of households with unmet housing needs. This approach has been 37 criticized because it implicitly assumes those who do not apply for FEMA assistance do not have any unmet needs 38 [4]. However, the FEMA assistance application is complicated, results in small grants, and many are disincentivized 39 from applying. Previous research with Black households identified that they did not apply because FEMA ‘was not for 40 them’; other research points to racial minorities’ distrust in government institutions which can lead to the households 41 not seeking needed resources [2, 7]. Another problem is that HUD limits its assistance to renter-occupied homes 42 that are affordable to low-income renters. In areas with high costs of living, most housing may not be affordable to 43 low-income persons. However, without assistance landlords may not be able to repair, reducing the available rental 44 housing and further increasing rental costs [27]. Combined, these factors lead to an under-estimation of unmet needs 45 [4, 11]. 46 However, obtaining better estimates of post-disaster unmet housing needs is challenging. HUD must combine 47 information from FEMA with detailed data from other sources, including other federal agencies, private insurance 48 claims payments, and possibly charitable assistance, to have a clear picture of unmet needs. Often, these data are 49 unavailable for months after a disaster. For this reason, HUD grantees must produce an Action Plan for using the 50 HUD funding, which includes re-calculating unmet needs conducted months after the disaster. Although the Action 51 Plans still rely on often inaccurate or insufficient data, they provide a better representation of the unmet needs [21]. A 52 problem is raised if there is a significant discrepancy between the HUD-allocated funding and the grantee-estimated 53 needs. For example, after the 2017 California Wildfires, a survey was conducted to assess homeowners’ needs and 54 define priorities resulting in delays in funding disbursement [4]. From this perspective, estimating unmet housing 55 needs shortly after a disaster can help HUD allocate appropriate funding and communities to better plan their disaster 56 recovery. 57 2 This paper presents a methodology that uses computational simulations to estimate post-disaster unmet housing 58 needs using data that can be collected shortly after a disaster. Computational simulations have provided a multilevel 59 understanding of relationships between factors influencing disaster impacts [24]. Disaster financing data from the 60 Federal Emergency Management Agency Individual Assistance Program (FEMA IAP) and the Small Business Ad- 61 ministration Homeowner and Personal Property Loan (SBA HPPL) programs are used to build probabilistic models 62 to estimate the expected approval rate and approved amount for these programs. The models account for hazard type 63 (e.g., flood, wildfire, earthquake), state, and applicant demographics (e.g., income, insurance status, home-ownership, 64 and residence type). These models are combined with a methodology to estimate housing reconstruction costs based 65 on FEMA guidelines and used to estimate post-disaster unmet housing needs. Thus, this paper provides two contri- 66 butions. First, we develop statistical models to probabilistically estimate post-disaster assistance from the FEMA IAP 67 and SBA HPPL programs. Second, we develop an improved methodology to estimate post-disaster housing needs that 68 utilized only data available shortly after a disaster. A case study application of the methodology to the 2017 California 69 wildfire-related disasters shows that the proposed approach can replicate the losses, assistance, and unmet housing 70 needs following these disasters. 71 2 Summary of Post-disaster Housing Recovery Financing in the US 72 Multiple sources of financing are available to support reconstruction of privately-owned housing following a disaster. 73 These sources differ in their approval criteria, maximum amount, and disbursement time. The following briefly reviews 74 the primary sources of post-disaster housing recovery financing in the US. 75 Insurance against disasters is an add-on to a standard homeowner’s insurance policy and often the first source of 76 coverage for disaster losses. Insurance coverage varies by hazard. Homeowners exposed to perils perceived more 77 frequently tend to have higher insurance coverage [40]. In some at-risk regions, disaster insurance is a requirement for 78 a mortgage. Insurance covers the home’s reconstruction cost minus a deductible, usually between 10% and 25% of the 79 reconstruction cost. However, the insurer assesses the home reconstruction cost and does not account for post-disaster 80 price surges or any required improvements [19, 26]. As consequence, even insured households may rely on other 81 sources of financing to repair their homes [4]. 82 The Federal Emergency Management Agency (FEMA) provides small grants to homeowners with uninsured or 83 under-insured needs due to a disaster through its Individuals Assistance Program [33]. After a disaster, FEMA inspects 84 the impacted homes and assesses FEMA Verified Losses (FVL). The FVL reflects the funds needed to repair the home 85 to an occupiable state rather than to reestablish its pre-disaster state. These grants are capped at $36,000 per applicant 86 and are aimed at low-to-moderate income persons [9]. Homeowners deemed able to repay a loan are steered away 87 from FEMA IAP assistance and recommended to seek loans. 88 3 The Small Business Administration (SBA) Home and Personal Property Loans (HPPL) program provides low- 89 interest loans to cover losses not fully covered by insurance or other means [28]. The interest rate is capped at 4% for 90 applicants unable to obtain credit elsewhere, and 8% for those who can obtain credit elsewhere. Unlike the FEMA IAP 91 grants, SBA loans are aimed at repairing homes to their pre-disaster state, and the maximum SBA loan is $200,000. 92 These loans are designed to be more accessible than bank loans, but household income and credit history are still 93 considered in the decision process. 94 Households may procure a private bank loan if an SBA loan is insufficient. These loans have more strict approval 95 criteria: borrowers must demonstrate the capacity to repay the loan, e.g., through their credit history or by providing 96 collateral. The interest rates for these loans can significantly exceed those of the SBA loans. Hence, bank loans are 97 more accessible to higher-income homeowners who are more likely to be approved, have assets to provide as collateral, 98 and can obtain shorter maturity loans with lower interest rates. Because the estimate of unmet housing needs is focused 99 on homeowners of lower socioeconomic status, bank loans are generally not included in the calculation. 100 Homeowners unable to cover their losses using the abovementioned programs may rely on federal funding from 101 the Department of Housing and Urban Development (HUD), which is provided through the Community Development 102 Block Grants for Disaster Recovery (CDBG-DR). HUD’s CDBG-DR program is the backstop for many homeowners 103 and can be the only financing mechanism available to uninsured, low-income homeowners [21]. Congress allocates 104 CDBG-DR funding based on the losses and the impacted region’s demographics [1]. It requires the approval of an 105 Action Plan developed by state housing authorities. However, the approval of CDBG-DR funds can be slow, often 106 taking more than a year for homeowners to receive the first payments [15, 30]. To determine the amount of funding to 107 be provided, HUD relies on an estimate of the unmet housing needs for the disaster [36]. In the following, we discuss 108 how unmet housing needs are currently calculated by HUD and by state authorities. 109 2.1 HUD’s Post-disaster Unmet Housing Needs Estimation 110 To estimate post-disaster unmet housing needs, HUD uses the FEMA Verified Losses to categorize each building into 111 one of five damage categories: (1) minor, (2) minor high, (3) major low, (4) major high, or (5) severe damage. HUD 112 considers that only buildings at major low, major high, or severe damage categories have unmet housing needs. Among 113 owner-occupied homes, only uninsured homeowners are eligible. Among renter-occupied homes, only those that are 114 affordable to households with income below 50% of the area median income are eligible. Thus, using HUD’s criteria, 115 the serious unmet housing needs in a disaster-impacted community are 116 U=LT−Finsurance −FFEMA−FSBA (1) where LTare the total housing losses for the eligible homes, and Finsurance ,FFEMA , and FSBAare the funding coming 117 4 from insurance, FEMA, and SBA, respectively. Note that under HUD’s criteria, Finsurance is zero since only uninsured 118 homeowners are assumed to have unmet needs. 119 The challenge for HUD is that FFEMA andFSBAare not known by the time funds need to be appropriated because 120 homeowners may not apply for FEMA and SBA immediately after a disaster and because these applications take 121 weeks-to-months to be processed. Thus, HUD’s initial appropriation employs a simplified approach in which the 122 serious unmet housing are estimated as 123 U∗=5 ∑ dc=3Hdc·Mdc (2) where Hdcis the number of FEMA IAP applicants in each damage category dc, and the multiplier Mdcis the amount 124 of unmet needs per home, empirically estimated by HUD. The multipliers Mdcare defined per state and per year. In 125 2017, the minimum cost multipliers across all Major Disasters were M3= $40,323, M4= $55,812, and M5= $77,252. 126 2.2 Limitations of the HUD Methodology 127 HUD’s simplified method (Eq. 2) has been criticized by CDBG-DR grantees. Eq. 2 implicitly assumes that homeown- 128 ers who do not apply for FEMA IAP assistance do not have any unmet needs. However, the FEMA IAP application 129 can be complicated and often results in grants smaller than $5,000, as we demonstrate later. These factors lead to an 130 under-representation of disaster impacts if unmet needs are estimated by Eq. 2 [4, 11]. Recent disasters in Texas, 131 Florida, and California show that the grantee-calculated unmet needs (using Eq. 1) can be between 3 and 20 times 132 higher than the initial HUD estimate (Eq. 2). In a recent review of multiple CDBG-DR programs, [21] suggests that 133 improved certainty about unmet needs and federal resources could improve the initial allocation and disbursement time 134 without compromising the quality of the programs. These limitations of the current approach and the observations by 135 [21] motivate the current study. 136 3 Unmet Housing Needs after the 2017 Disasters in California 137 Once HUD funding is approved by Congress and allocated to the state authorities, the grantees must design an Action 138 Plan which includes a thorough estimate of unmet housing needs. To do so, grantees estimate the number of impacted 139 homes and their respective losses and compare that to the state’s funding from insurance claims, FEMA grants, and 140 SBA loans. In this section, we discuss the Action Plans designed in response to the 2017 Disaster in California to 141 exemplify this process. 142 In October 2017, a series of wildfires spanned from the north coast of the San Francisco Bay Area to the northern 143 Central Valley and Orange County in California. More than 200,000 acres burned, and 8,922 structures were destroyed. 144 5 In response to the fires, FEMA issued Major Disaster Declaration DR-4344 in October 2017. In December of the same 145 year, another series of wildfires burned 308,383 acres across Southern California. The wildfires were followed by 146 heavy rains, mudflows, and debris flows which compounded the devastation. In December 2017, FEMA issued Major 147 Disaster Declaration DR-4353 in response to these events. The disaster declarations led to a Presidential Disaster 148 Declaration and the subsequent Congressional Appropriation of Funds, and on August 14th, 2018, HUD published the 149 Federal Register allocating $124 million to California [35]. These funds were destined for three programs. The Owner 150 Occupied Housing Rehabilitation and Reconstruction Program received $47.63 million to repair single-family owner- 151 occupied homes. The Multifamily Housing Program received $66.7 million to be used for reconstructing apartment 152 complexes and mixed-use developments, with preference given to displaced individual renter households. Lastly, $3.5 153 million was destined to repair critical infrastructure via the FEMA-Public Assistance Match Infrastructure Program. 154 3.1 HCD’s Post-disaster Unmet Housing Needs Estimation 155 In response to the 2018 HUD allocation, the California Department of Housing and Community Development (HCD) 156 prepared an Action Plan for Disaster Recovery [4], published on March 15th, 2019. The HCD obtained data from the 157 California Department of Forestry and Fire Protection (CAL FIRE), which identified that 7,640 homes were impacted: 158 137 severely damaged and 7,503 destroyed. The HCD estimated the average replacement cost for a home in California 159 to be $300,000. The HCD assumed that the repair costs are a fraction of the replacement costs, between 50% and 75% 160 for severely damaged homes and 100% for completely damaged homes. With this, the HCD estimated the total losses 161 per county as 162 LT=$300 ,000·NS ∑ i=10.75+0.5 2+NC ∑ i=j1 (3) where NSandNCare the number of severely and completely damaged homes, respectively. Using this approach, the 163 HCD estimated the total losses to be $2.283 billion. The HCD identified that many homeowners were not insured or 164 held policies that did cover the total building replacement costs. Some fully insured homeowners had significant unmet 165 needs due to increased materials and labor costs. Moreover, HCD advocated that HUD’s criteria limiting the analysis 166 to homes affordable to low-income households did not reflect the high-living-cost areas involved in these disasters. 167 Thus, the HCD included all losses in calculating unmet housing needs. The HCD collected data from FEMA and SBA 168 to estimate funding from these sources, i.e., FFEMA =20.7 million and FSBA=163.2 million. However, more than a year 169 after the disasters, the HCD could not collect reliable data on insurance funding, and so estimated the upper bound of 170 the unmet housing needs using Finsurance =0. Thus, Eq. 1 provided an unmet needs estimate of 171 6 U=$2.283 billion −$0−$20.7 million −$163 .2 million (4) =$2.098 billion (5) Comparatively, applying Eq. 2 using HUD’s simplified approach with its more restricted criteria yields $80 million 172 in unmet housing needs. Due to the mismatch of unmet needs and available funding, HCD implemented a program 173 survey period before launching its Owner Occupied Rehabilitation and Reconstruction Program to accurately measure 174 owner households with unmet housing recovery needs. The survey was necessary but incurred delays in the funding 175 allocation process. 176 Figure 1 presents a timeline of events following the 2017 Disasters in California. The highlighted period between 177 the FEMA 4353 Disaster Declaration and the Notice of Appropriation could have been reduced if the HUD appropri- 178 ation of funds was completed more quickly. The second highlighted period, between the approval of the State Action 179 Plan and the Initial Program Awards, could have been reduced if the initial appropriation provided sufficient funding 180 and the survey period was unnecessary. 181 Effective Date of Federal Register NoticeAug/2018Mar/2019HUD approved State Action PlanOct/2017FEMA 4344Nov/2019Launch Homeowner SurveySpring/2020Initial Program AwardsApril/2018Notice of Appropriation $124 millionDec/2017FEMA 4353Period that can be minimized with better estimates of unmet housing needsPeriod that can be minimized if unmet housing needs estimates do not depend on FEMA and SBA application results Figure 1: Timeline of CDBG-DR funding allocation following FEMA Disasters 4344 and 4353. 3.2 Limitations of the HCD Methodology 182 The HCD methodology accounts for community and disaster-specific contexts and yields unmet housing needs es- 183 timates more representative of the impacts of the 2017 Disasters. However, there are some limitations to the HCD 184 approach. First, it could not consider financing from insurance, so it only estimates the upper bound of the unmet 185 housing needs. Second, the HCD estimated the average replacement cost for any home is $300,000. However, home 186 values in California vary significantly per county. For example, the average home value is $167,300 in Lake County, 187 but $503,000 in Napa County [34]. Third, the HCD approach requires data on processed FEMA grants and SBA loans, 188 which only become available several months after a disaster. Thus, the HCD approach cannot be applied shortly after 189 a disaster to inform HUD funding appropriation. 190 7 4 Proposed Approach to Estimate Post-disaster Unmet Housing Needs 191 This section introduces the proposed approach to estimating unmet housing needs, which overcomes some of the 192 limitations of the Department of Housing and Urban Development (HUD) and California Department of Housing and 193 Community Development (HCD) approaches. Fig. 2 presents a schematic representation of the three approaches. 194 The top panel shows HUD’s methodology, which estimates unmet housing needs based on FEMA IAP data and the 195 multipliers dependent on damage categories. The center panel presents the methodology used by the HCD, which uses 196 data from multiple sources to estimate unmet housing needs using Eq. 5. In Fig. 2, the shaded boxes indicate data 197 unavailable for some months after a disaster. The boxes associated with damage information are half shaded because 198 rapid damage assessments tools exist for specific hazards [e.g., 37]. 199 Damage DataDamage Data B:damage buildings𝜹:damage ratios𝑳: losses𝑭𝑭𝑬𝑴𝑨: FEMA funding𝑭𝑺𝑩𝑨: SBA Funding 𝑼𝑯𝑵:unmet housing needsUnmet Housing Needs𝑈=Σ𝐻'⋅𝑀()FEMA IAP Data𝐻!UHN multipliers𝑀"# PROPOSEDHUDHCDHCD Loss ModelFEMA IAP DataSBA HPPL DataUnmet Housing Needs𝑈=𝐿*− 𝐹+,-.−𝐹/0.𝐿$B,𝛿𝐹%&'(𝐹)*(Loss Model(e.g., Hazus)FEMA IAP Model𝐴!"#$%=f(𝑆,𝑿)𝐹!"#$%=𝐸[𝐹!"#$|𝑆,𝑿,𝐿]SBA HPPL Model𝐴&'$%=f(𝐻,𝑆,𝑿,𝐿)𝐹&'$%~f(𝑎(,…,𝑎);𝑝(,…,𝑝)|𝐻,𝑆,𝑿,𝐿)Unmet Housing Needs𝑈=𝐿*−𝐹+,-.−𝐹/0. 𝐿+={𝐿,,…,𝐿-}𝐿$B,𝛿𝐹%&'(𝐹)*( Expected number of applicants Figure 2: Overview of the unmet housing needs methodologies. Orange boxes indicate required input data. Green boxes are models that replace the need for input data. The bottom panel in Fig. 2 shows the proposed approach and shares the reliance on damage estimates in the HCD 200 approach. The proposed approach also depends on an estimate of the number of households expected to apply for 201 FEMA and SBA funding. We discuss the implications of this dependency and alternative ways to obtain these data 202 later in this communication. The FEMA IAP Model estimates the approval rate, Ah FEMA, and the amount of financing 203 8 received Fh FEMAby approved households. Similarly, Ah SBAandFh SBArepresented the approval rate and expected amount 204 received by a household from the SBA HPPL program. The sum of the losses and the total funding from FEMA IAP 205 and SBA HPPL across all households are used to estimate the total unmet housing needs in the community. We note 206 that the proposed approach does not include a model for insurance funding, similar to the HCD approach. Later in this 207 communication, we discuss potential alternatives to overcome this limitation. 208 4.1 Loss Model 209 The first step in analyzing the unmet housing needs is to determine losses. While collecting data on the number of 210 buildings damaged can be done quickly after a disaster, estimating losses is not trivial due to the variability in the 211 building portfolio. Here, we employ a methodology developed by the Federal Emergency Management Agency to 212 estimate the replacement costs of homes in the United States. The methodology was designed to be used within 213 FEMA’s Hazus Loss Assessment tools [8] and is henceforth called the Hazus Loss Model. The replacement cost is the 214 cost of repairing a structure to its pre-disaster state. It is often smaller than the home value, which includes land value 215 and appreciation. Using the Hazus methodology, the replacement cost for a building ( Brc) is 216 Brc(county ) =Amain·Cmain(county ) +111bsm·Absm·Cbsm(f,county ) +111g·Ag·Cg(f,county ) (6) where Amain,Absm,Agare the areas of main floor, basement, and garage in square feet, Cmain(county ),Cbsm(f,county ) 217 andCg(f,county )are the cost to replace one square foot of main area, basement, and garage based on the quality 218 of the finish, f, and 1 11bsmand 111gare an indicator functions which return the unity if the home has a basement or 219 garage, or they return zero otherwise. The replacement costs are based on 2018 RSMeans estimates [6]. Note that the 220 replacement costs vary per county, making the building replacement cost a function of the county where the building 221 is located. Tables that are used to determine Amain,Absm,Ag,Cmain(county ),Cbsm(f,county )andCg(f,county )are 222 available in [8] for all regions of the US. 223 4.2 The FEMA Individual Assistance Program (IAP) Model 224 Data on recent Major Disaster Declarations from the OpenFema portal [10] are used to estimate the funding coming 225 from the FEMA IAP grants. These data include accounts of losses, assistance received, and some basic demographic 226 information on the applicants impacted by Hurricanes Harvey, Irma, Maria, Laura, Ida, Michael, and the 2021 Texas 227 Winter Storm. We exclude entries where the verified losses are missing, zero, or the building type is ’Mobile Home.’ 228 Entries for Puerto Rico are also removed, as the median applicant income for Puerto Rico is $12,000, less than half 229 that of the state with the lowest median applicant income ($25,200 in Louisiana) and about one-third of the median 230 income for applicants in the continental US ($34,000). The final data set contains 430,908 FEMA IAP applications. 231 9 In our data set, 38.4% of all applications with any amount of verified losses received some assistance from FEMA 232 IAP. The maximum assistance one household can receive for repairs or replacement is about $36,000. However, 53% 233 of the successful applicants in our data set received less than $5,000, and 3.8% received more than $30,000. Figure 3 234 provides a breakdown of the amount received by FEMA IAP applicants for repairs and replacement. 235 010 20 30 40 FEMA IAP assistance for repair or replacement [$ 1000]010000200003000040000Count Figure 3: FEMA IAP funding received by successful applicants impacted by Hurricanes Harvey, Irma, Maria, Laura, Ida, Michael, and the 2021 Texas Winter Storm to repair or replace housing. In Fig. 4, we evaluate the influence of multiple variables on approval rates and households’ approved amounts. In- 236 sured households tend to receive more on average. Except for condominiums, there is also a tendency for high-income 237 households to receive more assistance. The residence type appears to have a negligible effect on the amount received. 238 However, the residence type has a strong effect on the approval rate. Houses and duplexes have slightly higher rates 239 of approval overall. The positive correlation between income and home value can explain these observations since, 240 all else equal, losses are a consequence of home value. Income has a minor effect on approval rates, and insurance 241 decreases one’s approval rate. These observations reinforce the idea that higher approved amounts for higher income 242 households are tied to these households experiencing higher losses. 243 Considering the insights from Fig. 4, we estimate the approval rate for a household of interest ( AFEMA ,h) in state 244 Sh, with loss Lh, and demographics Xh(i.e., income, housing type, and insurance status), as 245 AFEMA ,h(Sh,XXXh,Lh) =∑N i=1111(Si=Sh)·111(XXXi=XXXh)·1(Li∼Lh)·1(FFEMA ,i>0) ∑N i=1111(Si=Sh)·111(XXXi=XXXh)·1(Li∼Lh)(7) where N=430,908 is the number of FEMA IAP applicants in the OpenFEMA database, and 1 (·)is an indicator function 246 10 Figure 4: Summary of approval rates (left) and approved amount (right) by household and housing characteristics that returns 1 if the condition within the parenthesis is true and 0 otherwise. The condition 1 11(Si=Sh)if household i 247 has is in the same state as the household of interest, h. The condition 1 11(XXXi=XXXh)is true when households iandhhave 248 the same income, housing type, and insurance status. The condition 1 (Li∼Lh)indicates that the losses experienced 249 by households iandhare similar, namely, within a $5,000 range. FFEMA ,iis the FEMA IAP funding received by 250 household i. 251 Using a similar approach, we estimate the amount of FEMA IAP financing that a household is expected to get, 252 FFEMA ,h, as 253 FFEMA ,h(Sh,XXXh,Lh) =∑N i=1111(Si=Sh)·111(XXXi=XXXh)·1(Li∼Lh)·FFEMA ,i ∑N i=1111(Si=Sh)·111(XXXi=XXXh)·1(Li∼Lh)·1(FFEMA ,i>0)(8) and the expected total amount of FEMA IAP assistance across all impacted households is 254 FFEMA =H ∑ h=1AFEMA ,h(Sh,XXXh,Lh)·FFEMA ,h(Sh,XXXh,Lh) (9) where His the total number of households that apply for FEMA IAP in the community. 255 4.3 The SBA Home and Personal Property Loans (HPPL) Model 256 We collected two data sets to gain insights into the approval rates and amounts for SBA loans. The first data set was 257 obtained and made publicly available by [13] through the Freedom for Information Act. This data set, henceforth 258 called the Goldstein data set, contains only individual SBA applications. However, in areas with few applicants, the 259 SBA aggregates data at the zip code level to protect privacy. Thus, the Goldstein dataset contains a subset of all SBA 260 loans from 2001 through 2018. Moreover, the Goldstein data set is split into approved and denied applications and 261 does not contain data on the losses. Thus, this data set helps calculate approval rates, ASBA, but does not provide 262 11 insights on the loan-to-loss ratios. Figure 5 provides an overview of the approved loans in the Goldstein data set, 263 showing that loans below $50,000 are the most common. 264 050100 150 200 Approved SBA loan amount [$ 1000]0200004000060000Count Figure 5: SBA approved loan amounts in the Goldstein data set. The second data set was collected from the OpenSBA portal [29]. The OpenSBA data contains all approved loans 265 between 2008 and 2019. This data set includes entries representing individual applicants (like the Goldstein data set) 266 and aggregated entries that protect applicants’ privacy. The entries representing individual applicants in the OpenSBA 267 data set contain data on losses and loans received, allowing us to derive loan-to-loss ratios. Figure 6 shows the loan- 268 to-loss ratios for different hazards. The dots indicate the mean loan-to-loss ratio, and their size represents the number 269 of loan applications available for a hazard-state pair, i.e., sample size. The vertical lines are bounded between the 10th270 and 90thquantiles. The shading of each dot indicates the state. For example, the leftmost dot shows that SBA loans 271 to repair earthquake damage have only come from California. The loan-to-loss ratios are between 0.55 and 1.0, and 272 fewer than 300 applications match this hazard-state pair. 273 Table 1 summarizes the data available from each data set. The Goldstein data set covers 18 years compared to 274 the 11 years in the OpenSBA data. For this reason, the Goldstein data set across all disasters represents a higher total 275 approved amount. When focusing on FEMA declarations 4344 and 4353, it is noticeable that the Goldstein data set is 276 not comprehensive, with $60 million of approved funds compared to $152 million from OpenSBA. 277 Table 1 highlights the issue with aggregation in the OpenSBA data set. For example, for the 2017 Disaster there 278 are only 105 entries that represent individual applications. To obtain more individual application data, we employ the 279 procedure described in Fig. 7. For a given hazard Hand state S(e.g., wildfire and California), we create a histogram 280 12 EarthquakeFireFlood Hurricane Severe Storm(s)Tornado00.250.500.751Approved Loan / Verified LossSample size (0, 300] (300, 600] (600, 900] State CA FL IL LA NC NJ NY TXFigure 6: Approved loan vsverified loss by hazard from the OpenSBA dataset. Table 1: Summary of SBA data. SBA Goldstein (2001-2018) OpenSBA (2008-2019) Entries Approved amount Entries Approved amount Disasters Mean[$] Total[$million] Mean[$] Total[$ million] All 553,471 54,886 15,200 16,842*– 9,890 California 7,738 64,427 260 183*– 630 FEMA 4344 & 4353 966 96,405 60 105*– 152 *some entries represent multiple applicants. as the one in Fig. 5 and describe the probability that the loan amount for a given approved loan, LSBA, is within a 281 $25,000-interval. That is, the amount received from SBA, LSBA, is approximated as a multinomial distribution given 282 by 283 LSBA∼f(a1,..., an;p1,..., pn|H,S) (10) where the probability that the amount received is in the interval a∗(e.g., a1=[$0, $25,000) and a2=[$25,000, $50,000)) 284 isp∗. Next, the OpenSBA data is separated into individual and aggregated entries. Entries with approved loan amount 285 larger than $200,000 are considered to represent more than one successful applicant, i.e., an aggregated entry. Using 286 the OpenSBA individual loans, for a given hazard, H, state, S, and eligible loss L, the loan-to-loss ratio, RLL, is 287 13 modeled as a multinomial distribution, that is 288 Rind LL∼f(a1,..., an;p1,..., pn|H,S,L) (11) Certain H-Scombinations may yield small sample sizes and result in poor models for LSBAandRLL. To avoid these 289 situations, one of the conditions the data grouping may be relaxed, for example by using data from all hazards for one 290 state S. 291 The last step is splitting the aggregated loans into the OpenSBA data set. Consider an aggregated entry with a 292 total loan amount of Lagg=$2 million. First, a loan amount is sampled from the Eq. 10 LSBAdistribution (e.g., LSBA,1293 =$150,000). Next, a loan-to-loss ratio with distribution RLL(Eq. 11) is assigned to LSBA,1. The loan LSBA,1is then 294 added to a list of split loans. The loan amount for LSBA,1is subtracted from Lagg, and the process is repeated until 295 Laggis completely split into loans smaller than $200,000. The procedure is performed for all aggregated entries in 296 the OpenSBA data set. Finally, all split loans are combined with the original list of individual loans. This procedure 297 expands the number of loan data points available for the 2017 California disaster from 97 to 12,769, while ensuring 298 that the loans split from aggregated entries have statistical characteristics that are consistent the the individual loan 299 data. Note that the procedure in Fig. 7 assumes that in the OpenSBA data set, the individual and aggregated loans are 300 identically distributed. 301 Finally, the expanded OpenSBA data set containing split and individual loans is used to estimate the amount of 302 funding a household in state Swill received from SBA as result of Leligible losses incurred by hazard Has 303 FSBA,h∼f(a1,..., an;p1,..., pn|H,S,L) (12) 14 Approved loan amountCountsGoldstein SBA data Loan, $[0,50]Loan-to-loss ratio, %Loan,$[50,100]Loan,$[100,150]OpenSBAindividual loans Loan,$[150,200]𝐿!"#~f(x$,…,𝑥%;𝑝$,…,𝑝%|𝐻,𝑆)𝑅&&'%(~f(x$,…,𝑥%;𝑝$,…,𝑝%|𝐻,𝑆,𝐿)OpenSBAaggregated loans 𝐿!"#,%< 200k𝐿!"#,&< 200k𝐿!"#,'< 200k…For each aggregated loan, 𝐿!"" Individual loansSplit loansAll loans𝐴!"#=𝑓(𝐻,𝑆,𝐿 ) Individual Losses andLoans 𝐹!"#,*~f(x$,…,𝑥%;𝑝$,…,𝑝%|𝐻,𝑆,𝐿)Figure 7: SBA data processing. Individual loan amounts from the Goldenstein data set and the loan-to-loss ratio from the OpenSBA data set are used split aggregated data in the OpenSBA data set into individual loans. 4.4 Insurance 304 As discussed earlier, HUD does not include insured homeowners in their estimate of serious unmet housing needs 305 (see 2), and state authorities face difficulties obtaining reliable insurance data, even several months after a disaster. 306 Unlike federal grants and loans, insurance coverage may vary significantly by location and hazard. For example, while 307 Californians in flood-prone areas may be required to purchase flood insurance, only 13% of the homes in California 308 have earthquake insurance [31]. Even if county-level insurance statistics are available, these may not be sufficient (e.g., 309 for wildfires, insurance penetration may differ in wildland-urban interface areas). Thus, developing an Finsurance model 310 for Eq. 1 that can be employed soon after a disaster is challenging. However, because the proposed approach provides 311 detailed estimates of the building replacement costs (e.g., Eq. 6), it can be used to estimate insurance financing 312 probabilistically as 313 Finsurance ,h(county ) =P(I|B,H,S,XXX)·I(B|H,S,XXX)·Brc(county ) (13) where P(I|B,H,S,XXX)is the probability that a home is insured conditioned on building type ( B), hazard ( H), location 314 15 S(e.g., state or county), and demographics of the owner household ( XXX), and I(B|H,S,XXX)is the insurance coverage as 315 a percentage of the building value. For applications to specific disasters, the values of P(I|B,H,S,XXX)andI(B|H,S,XXX) 316 should be defined by the state authorities in collaboration with community and insurance-sector specialists. Note 317 that although Finsurance ,hcould be integrated into the HCD methodology, Eq. 1, the assumption that the building 318 replacement cost is homogeneous within the state (i.e., $300,000) would limit the accuracy of the estimates. Thus, the 319 possibility to calculate Finsurance ,h(county )using Brc(county )is another improvement of the proposed approach. 320 5 Application to the 2017 California Fires 321 We employ the proposed methodology to hindcast the impact and unmet housing needs following the 2017 California 322 Disasters (FEMA Disaster Declarations 4344 and 4353). Although the disaster events are months apart and affected 323 different counties, we evaluate their collective impact because they resulted in a single funding allocation by HUD. 324 The proposed methodology (Fig. 2) is employed to estimate losses, funding from FEMA IAP and SBA HPPL, the 325 subsequent unmet housing needs, and to compare the results with the findings and estimates provided by the California 326 Department of Housing and Community Development (HCD). Only FEMA and SBA data from 2017 or earlier (i.e., 327 data available at the time of the disasters) are used to fit the models to replicate the available data after the disasters. 328 Table 2 lists the inputs to the case study. The limitations incurred by the need for this information and alternatives to 329 improve the model are discussed later. 330 Table 2: Input parameters from 2017 California disasters required by the proposed approach. Parameter Value Source Severely damaged buildings 137 CAL FIRE Completely damaged buildings 7,503 CAL FIRE FEMA IAP applicants with verified loss 3,048 FEMA, reported by HCD SBA HPPL applicants with verified loss 3,971 SBA, reported by HCD Table 3 lists the empirical outputs that we aim to replicate using the proposed approach. The values come from 331 FEMA and SBA directly or from data collected and reported by the HCD in their Community Development Block 332 Grant-Disaster Recovery Action Plan published on March 2019 [4]. We emphasize that these data require the pro- 333 cessing of FEMA IAP and SBA HPPL applications and are not available for months after a disaster. The proposed 334 approach is probabilistic as the approval rates and approved amounts are uncertain. To gain insights on the variability 335 of the results, the workflow in Fig 2 is run 1,000 times; that is, 1,000 estimates are collected for each variable. The 336 results are presented in the following sections. 337 16 Table 3: Impact of FEMA 4344 & 4353 disasters and financing received by California. Parameter Value Source Total housing loss $2,283,300,000 Estimated by HCD $2,578,607,000 Estimated by SBA, reported by HCD Total FEMA IAP funding $15,247,000 OpenFEMA Total SBA funding $152,000,000 OpenSBA* Unmet housing needs $2,584,349,091 – *total for 2018 5.1 Estimated Losses 338 We estimated losses using the the number of damaged buildings, replacement costs, and estimated loss ratios. The 339 replacement costs are estimated using Eq. 6 with one modification due to the data available for the case study being 340 compiled at the County level, not at the Census tract level. Without Census tract-level data, the building replacement 341 costs estimated with Eq. 6 do not capture the variability across all counties investigated. To partially correct this, we 342 adjust the estimated replacement costs in each county based on the home values available from the 2020 American 343 Community Survey [34]. The adjusted building replacement cost is 344 Bad j rc(county ) =Brc(county )·HVACS(county ) HVACS(CA)(14) where HVACS(county )andHVACS(CA)are the home values for the county and for California, respectively. Table 4 345 compares the loss estimates provided by the HCD (i.e., Eq. 3) to the estimates yielded by the proposed approach. Two 346 empirical data are provided for comparison: (i) home values from the American Community Survey (ACS), and (ii) 347 total losses reported by SBA. The ACS home values include the value of land and appreciation. Thus the replacement 348 costs should be consistently smaller than home values. The proposed approach yields results between 45% and 80% of 349 the ACS home values. Conversely, the HCD approach yields replacement costs up to 166% of the ACS home values. 350 The HCD approach is not designed to yield accurate results at the county level; hence this finding is not surprising. 351 The SBA losses are calculated from the reported losses by applicants. Figure 8 shows that the loss estimates using 352 the proposed approach partially capture the trends in the SBA data. Each dot in Fig. 8 represents one county in Table 353 4. The size of the dot reflects the number of damaged buildings in the county. The proposed loss model yields better 354 results for Sonoma county, which had the most damaged buildings. In consequence, the proposed approach total loss 355 estimates (e.g., $2.812 billion) are closer to the values reported by the SBA (e.g., $2.782 billion) when compared to 356 the HCD total estimated losses (e.g., $2.658 billion). 357 17 Table 4: Comparison of losses from empirical data and two estimation models. ACS SBA Loss model Insured home total HCD Hazus buildingsavalue loss RCbTotal loss RCbTotal loss County Buildings [count (%)] [$ 1,000] [$ 1,000] [$ 1,000] [$ 1,000] [$ 1,000] [$ 1,000] Butte 38 16 (42) 229 5,092 300 6,115 103 3,844 Lake 131 97 (74) 167 20,174 300 15,436 74 9,657 Los Angeles 75 63 (84) 465 11,775 300 23,457 267 19,533 Mendocino 313 200 (64) 319 75,746 300 70,344 141 43,802 Napa 626 472 (75) 503 199,694 300 221,237 403 251,823 Nevada 29 32 (1) 356 5,249 300 7,269 220 6,105 San Diego 116 70 (60) 455 25,636 300 36,900 267 31,144 Santa Barbara 255 42 (16) 480 71,655 300 73,909 283 62,015 Sonoma 5,154 4,963 (96) 465 1,850,286 300 1,685,488 373 1,919,231 Ventura 762 627 (82) 481 287,274 300 256,575 388 292,851 Yuba 143 107 (75) 191 26,026 300 19,201 113 16,307 All 7,642 6689 – 2,578,607 – 2,415,932 – 2,656,314 athe number of insurance claims is used as a proxy for the number of insured buildings. bper-building replacement cost. 100 200 300 400 Estimated repair cost per building [$1000]100200300400SBA repair cost per building [$1000]Loss model HCD Hazus Buildings (0,100] (100-500] >500 Figure 8: Comparison between SBA reported losses and estimates using the HCD loss model and the proposed loss model. Each point in the figure represents per-building losses for a single county. 5.2 Funding from Insurance 358 There are limited data regarding housing insurance for these disasters. The best information available was provided 359 by the California Department of Insurance (CDI) to the HCD. These data consist of the total sum of all insurance 360 claims (i.e., residential, personal property, life, and automotive) and counts of the residential insurance claims per 361 18 county, shown in Table 4. Thus, there is no available information on the amount of insurance funding provided for 362 housing reconstruction. In the face of these limitations, three scenarios are tested regarding insurance penetration. The 363 ‘None Insured’ scenario represents the extreme case where no resident has insurance. Conversely, the ’All insured’ 364 scenario considers all residents are insured with coverage equal to 85% of their home repair costs, i.e., full coverage 365 for expenses that exceed a deductible of 15%. These two scenarios capture extreme cases and have the advantage of 366 not requiring any further empirical data. The third ’CDI-based’ scenario assumes that the number of insurance claims 367 provided by the CDI (Table 4) represents the number of insured homes. This assumption overestimates the number 368 of insured buildings since, in some counties, e.g., Nevada County, insurance claims exceed the number of damaged 369 buildings. For this scenario, we assume that insurance will cover 50% of the repair costs. This assumption reflects 370 the findings from the HCD regarding the issues with underinsurance. Because this scenario uses data that would not 371 otherwise be available shortly after a disaster, it is presented as a benchmark. That is, it can be used to test whether the 372 more rapidly available ’None Insured’ or the ’All Insured’ scenarios better represent the empirical results. 373 5.3 Funding from FEMA’s Individual Assistance Program 374 The model described in Section 4.2 is used to generate 1,000 estimates of the FEMA IAP funding received by Califor- 375 nians following the 2017 Disasters. Figure 9 shows the results obtained from all insurance scenarios. For reference, 376 the vertical dashed line shows the empirical estimate of $15.3 million in assistance obtained from the OpenFEMA 377 portal. The results show that at least one simulation from the ’CDI-based’ and the ’None insured’ scenarios replicate 378 the empirical results. However, the empirical result is a relatively extreme value for both distributions. This finding 379 can be explained by the fact that the wildfires caused complete damage to most homes, which would be expected to 380 result in the maximum FEMA IAP funding of about $34,000. However, Fig. 3 demonstrated that only 3.8% of FEMA 381 IAP applicants received more than $30,000. Lastly, the ’All insured’ scenario does not replicate the empirical results, 382 showing that the assumptions in this scenario do not represent the reality of the households impacted by the 2017 383 Disasters in California. 384 19 1012.51517.520 Estimated FEMA IAP funding [$ million]050100150Count Empirical results All insuredCDI- based None insuredFigure 9: Results from 1,000 estimates of the total FEMA IAP funding received by California in response to FEMA Disasters 4344 and 4353 using the proposed approach. The vertical dashed line indicates empirical results after the event, as collected from the OpenFEMA portal [10]. 5.4 Funding from SBA’s Homeowner Personal Property Loan Program 385 Figure 10 shows the results from 1,000 simulations of the SBA funding using the method described in Section 4.3. 386 Because SBA loans exclude losses covered by insurance, the SBA estimates are strongly influenced by assumptions 387 regarding insurance penetration. The dashed vertical line indicates the empirical value obtained after the event (2,371 388 successful SBA applicants from California received $152 million between 2017 and 2018, according to the OpenSBA 389 portal [29]). The results in Fig. 10 indicate that the ’All insured’ scenario underestimates SBA funding by a factor 390 of 3. Although consistently overestimated, the ’None insured’ results are significantly closer to the empirical values. 391 Lastly, the mode of the results from the ’CDI-based’ scenario perfectly matches the empirical results. These results 392 indicate that most who applied for an SBA loan following the 2017 Disasters were either uninsured or underinsured, 393 i.e., had significant remaining losses after insurance payments were received. 394 The OpenSBA data are also available per-county basis allowing us to assess the proposed approach in finer detail. 395 Figure 11 compares the SBA funding per county estimated using the proposed approach (on the abscissa axis) to the 396 OpenSBA data (on the ordinate axis). The ’None insured’ results are not presented due to the low accuracy shown in 397 Fig. 10. The size of the dots indicates the number of damaged buildings per county. Combined with the results in Fig. 398 20 050100 150 200 Estimated SBA funding [million 2021 dollars]0100200300400500Count Empirical resultsAll insuredNone insuredCDI- basedFigure 10: Results from 1,000 estimates of the total SBA HPPL funding received by California in response to FEMA Disasters 4344 and 4353 using the proposed approach. The vertical dashed line indicates empirical results collected from the OpenSBA portal [29]. 10, the results Fig. 11 provide two insights. First, the proposed approach can capture the overall expected funding 399 and its county distribution. Second, the proposed methodology can estimate the expected SBA funding with relative 400 accuracy by using the ’None insured’ assumption. 401 21 1e5 1e6 1e7 1e8 1e9 Estimated SBA funding per county [$]1e51e61e71e81e9Empirical SBA funding per county [$]Insurance assumption CDI-based None insured Buildings (0,100] (100-500] >500Figure 11: Comparison of the SBA funding received per county estimated using the that assumption all applicants are insured to empirical data from the OpenSBA portal considering all approved loans in 2018. 5.5 Estimated Unmet Housing Needs 402 Finally, the losses summarized in Table 4 are combined with the results from Figs 9 and 10 to estimate the total 403 unmet housing needs. Figure 12 presents the mean unmet housing needs estimated using the proposed approach 404 and compares it to the $2.58 billion unmet housing needs calculated by the HCD and the $124 million total CDBG- 405 DR funding in HUD’s initial allocation. The ’All insured’ and the ’CDI-based’ scenarios reinforce the empirical 406 evidence that the HUD-estimated unmet housing needs underestimate reality. Even under optimistic assumptions in 407 these scenarios, the results in Fig. 12 show that the HUD significantly underestimated the unmet housing needs for the 408 2017 Disasters. On the other hand, the results from the ’None insured’ scenario closely replicate the HCD estimates. 409 However, the proposed approach could produce these estimates shortly after the disaster and does not require data 410 from FEMA or SBA. Thus, the proposed approach can significantly expedite the estimation of unmet housing needs 411 without significantly reducing the accuracy of the current HCD approach. 412 22 0 1 2 3 Estimated unmet housing needs [$ billion]02505007501000Count CDBG-DR funding allocated HCD-estimated unmet housing needsAll insuredNone insuredCDI- basedFigure 12: Results from 1,000 estimates of the unmet housing needs using the proposed approach. The vertical dashed line represents the estimate by the California Department of Housing and Community Development. 5.6 Limitations 413 Although the proposed approach presents significant advantages compared to existing methodologies, it has limitations 414 in addressing a complex problem. The proposed methodology does not include a model to estimate the funding 415 from insurance payments directly–a limitation also present in the existing methodologies. Insurance penetration and 416 coverage are community-dependent and hazard-dependent. Thus, developing a generic model for insurance funding 417 may not be feasible. However, if local authorities have data on insurance penetration and coverage for specific hazards, 418 the proposed methodology can incorporate this information. The methodology also requires information about the 419 number of persons expected to apply for FEMA and SBA assistance - not the result of the applications. Future work 420 may be devoted to evaluating previous disasters and establishing relationships between the number of impacted persons 421 and the number of FEMA and SBA applicants. Alternatively, the impacted population may be quickly surveyed after 422 a disaster to establish their intention of applying for FEMA and SBA assistance. Surveying this information would 423 still be considerably faster than waiting for FEMA and SBA to process the applications and report results. 424 23 6 Conclusions 425 This study proposes a methodology to estimate post-disaster unmet housing needs in U.S., accounting for losses and 426 funding from the Federal Emergency Management Agency (FEMA) and the Small Business Administration (SBA). 427 Rapid estimates of unmet housing needs are essential for the Department of Housing and Urban Development (HUD) 428 to allocate Community Development Block Grants for Disaster Recovery (CDBG-DR) funding. However, current ap- 429 proaches to accurately estimate unmet needs rely on data not available until months after a disaster. The methodology 430 proposed in this paper uses data from the OpenFEMA and OpenSBA portals regarding assistance provided after major 431 disaster in the US in the last 20 years to build predictive models for the approval rate and approved amount from each 432 agency. Thus, the proposed methodology can be used shortly after a disaster and provides accuracy equivalent to the 433 state-of-the-art approaches. We envision that the proposed methodology can be used by state housing authorities after 434 a disaster to gain insights into the magnitude of unmet housing needs or to inform the appropriation of funds by HUD. 435 The methodology could also be used with regional loss estimation tools to assess the unmet housing needs following 436 hypothetical disasters and inform pre-disaster recovery planning initiatives. Thus, the proposed methodology can help 437 communities better prepare and respond to a disaster by providing accurate and quick estimates of unmet housing 438 needs. 439 A case study methodology application is used to estimate unmet housing needs after a combination of disasters 440 that struck California in 2017 (i.e., FEMA DR-4344 and FEMA DR-4353). Unmet housing needs estimates provided 441 by the California Department of Housing and Community Development (HCD) using data collected about one year 442 after the disaster are used as benchmarks. The case study demonstrates that the proposed methodology can replicate 443 the HCD estimates while using only data available much sooner after the Disasters. Moreover, while the HCD results 444 are only accurate if aggregated over all impacted counties, the proposed methodology provides accurate per-county 445 estimates of loss and funds received. One of the challenges of the case study is that although insurance was the 446 primary source of housing recovery financing, even a year after the disaster, the HCD could not obtain accurate data 447 regarding insurance. We demonstrate that with basic information regarding the insurance penetration rate and average 448 coverage, the accuracy of the proposed methodology is increased significantly. This finding reinforces the confidence 449 in the proposed approach but also suggests that collecting and maintaining information regarding housing insurance 450 can significantly help communities understand their residents’ recovery needs after a disaster. 451 7 Funding 452 Funding for this for this work was provided by the Stanford Urban Resilience Initiative. 453 24 8 Data Availability 454 All data used in this study are publicly available from the referenced sources. These data and the code to run the 455 analyses described in this paper are provided here. 456