AbstractEconomic resilience defines a community’s ability to prevent, withstand, and quickly recover from major disruptions to its economic base. Instead of having repeated damage and need for outside assistance, resilient communities proactively protect themselves against hazards, build self-sufficiency, and become more sustainable over the long term. Within these communities, small businesses are an important driver of economic growth and employment. However, small businesses are extremely vulnerable to natural disasters: about 40–60 percent of them never reopen their doors after a disaster. To gain an insight into the vulnerability and resilience of small businesses, we collected firm-level data through an online survey of primary decision-makers of small businesses located in 2017 Hurricane Harvey impacted counties. The questions in the survey covered five broad categories: general business characteristics; finance impact; operation impact; built environment impact; and mitigation actions. The analysis shows a small variation in recovery time between industry groups. However, the contrast between firms that invested in resilience and firms that did not is significant. We then modeled the small business recovery as a stochastic process and used the survey data to select probability models and then estimate model parameters. If firms chose to invest in resilience, the mean and median times could be reduced by 57% and 8.5%, respectively. Using the baseline provided, a firm could estimate the length of recovery expected and prepare a business continuity plan accordingly. In a hurricane’s aftermath, their performance can be benchmarked against that of their peers. The findings would serve as basis for public policies towards incentivizing prestorm mitigation and resilience-building actions.IntroductionThe interest in studying small business recovery from natural disasters roots in the fact that small businesses have long been an important driver of America’s economic growth and competitiveness, providing outsized contributions to employment, innovation, exports, and productivity growth. In 2016, there were 30.7 million small businesses, accounting for 99.9% of all businesses in the United States (SBA 2019). They employed 59.9 million workers, or 47.3% of the private workforce. The industry sectors with the highest share of small businesses were construction (82%), agriculture (84%), and service (85%). Small businesses are different from their larger counterparts with respect to agility, risk, and financing (Berger and Udell 1998). They tend to adapt quickly to a society’s changing needs in a competitive business environment (Rudenko et al. 2015). However, they face a higher level of survival risk. About one-fourth of new small business ventures dissolved within two years of commencement, and more than one-half cease operations within four years (Leach and Melicher 2011). They are often impacted the most and have little capacity to recover after a disaster (Asgary et al. 2013). Given their crucial role in the economy and higher vulnerability and survival risk, it is imperative to better understand the characteristics of small businesses and environmental factors in relation to disasters.Recovery from natural disasters is less understood in research and practice than emergency management and engineering design (Smith and Wenger 2007; Miles et al. 2019). The latter primarily focuses on ensuring public safety before a disaster hits and minimizing casualties when it does, which are relatively easier to verify or validate than the cascading and lasting effect in physical (e.g., infrastructure damage, service interruption) and socioeconomic (e.g., crime, unemployment) dimensions. Much of the economic literature centers on how disasters impact changes in macroeconomic conditions at aggregated temporal and spatial scales but offers fewer insights on specific risk reduction strategies for individual businesses. For example, Jerch et al. (2020) studied local government revenue, expenditure, and borrowing dynamics in the aftermath of hurricanes for the period from 1920 to 2010. They found that major hurricanes cause local revenues to fall by about 6%–7%, and such losses persist at least 10 years, leading to a 6% decline in expenditures on public goods and services and a significant increase in the risk of default on municipal debt. Using the same dataset, Boustan et al. (2020) concluded that major disasters increase out-migration rates at the county level by 1.5% and lower housing prices/rents by 2.5%–5.0%. FEMA reported that 40%–60% of small businesses never reopen their doors after a disaster (Tierney 2019). Recent administrative data reveal severe economic disruptions during the coronavirus pandemic (SBA 2020). In the five weeks following the issuance of a national emergency declaration on March 13, 2020, initial unemployment insurance claims totaled over 24 million. Job losses through the first half of March were primarily in small businesses.Comparing with macroeconomic studies, the existing (micro) literature on firm-level response to and recovery from disasters is scarce but has drawn growing attention. The Disaster Research Center (DRC) conducted large-scale mail surveys to examine key factors influencing business disaster preparedness, response, and recovery. Five thousand firms from five communities across the United States participated in this study (Dahlhamer and Tierney 1998; Webb et al. 2000). An analysis of 1,100 affected by 1994 Northridge Earthquake found that nonrecovered firms had fewer employees (median = 4) than the recovered ones (median = 6). This is consistent with the organizational research suggesting that smaller firms generally have less resources at their disposal during disasters (Alesch et al. 1993; Kroll et al. 1991). Young firms have a much higher probability to fail than mature one during nondisaster and disaster times (e.g., Carroll 1983). In addition, small, young firms were more likely to have a single location, lease their properties, and sustain physical damage. In a logistic model, receptance and use of postdisaster aid was a significant predictor for recovery in an opposite direction. The authors offered several plausible explanations, including financial weakness before the earthquake, hesitance to take loans, and difficulty in repaying them. Later, Webb et al. (2002) collected business recovery data in Santa Cruz County, California, eight years after the Loma Prieta Earthquake and in South Dade County, Florida, six years after Hurricane Andrew. Long-term recovery trajectories were shaped by industrial sector in which a business was operating, its age, disaster impacts, owner perceptions of the broader economic climate, among others. Effects by previous disaster experience, level of preparedness, and use of external sources of aid were not significant in the two study communities.Besides firm-level characteristics and decisions, business recovery is heavily influenced by local/regional economic trends and infrastructure conditions. For example, Watson et al. (2020) focused on the role of households in business recovery based on a case study of 2016 Hurricane Matthew. Both customer loss and labor interruption significantly lowered a business’ odds of full recovery. They also found that larger firms were better equipped to absorb, address, and withstand these issues. Furthermore, the failure to account for human (behavioral) adaptations to disaster outcomes such as power and water outages can lead to the misallocation of resources (e.g., Kendra et al. 2019). The difficulty in understanding disaster recovery and resource allocation may be further complicated by asymmetric information regarding private investment in mitigation activities (Yang et al. 2009).Our study aims to further examine the microlevel foundation of small business resilience. Considering the importance of small businesses to local communities and a need for expanding our understanding of their behaviors in the context of natural disasters, we opt for collecting more granular, firm-level data built upon findings from previous studies but with a more comprehensive set of questions relating to firm characteristics and strategies. As the result, the data enable us to parse a firm’s characteristics, financial and operational strategies, and preparedness and its dependence on essential infrastructures and services. Meanwhile, the focus on small businesses (rather than firms of all sizes) helps improve data reliability and usability. Furthermore, the model of uncertainty is explicitly quantified and then incorporated in the prediction. Another contribution of this study is the consideration of time to recover as a continuous dependent variable, as opposed to a binary indicator. Our goals are to: (1) identify the key drivers of survival and recovery of small businesses in the aftermath of hurricanes; (2) model the recovery performance of small businesses in relation to predisaster preparedness and disaster impact; and (3) suggest potential improvement to resilience-building decisions and public policies. Importantly, this study, by identifying the key microlevel drivers of small business recovery and resilience, lays the foundation for the macrolevel impact assessment and mitigation.The organization of the remaining part of the paper is as follows: the methodology for model development is introduced, followed by the description of data collected on Hurricane Harvey. Then, the results of parameter estimation and computer simulation are presented. The conclusion and future work are given in the end.MethodologyTraditionally, the mathematical modeling of disaster recovery has been of more interest to engineers, whereas issues such as unemployment, economic growth, migration, and disease spreading after a major crisis have been closely examined by social scientists, economists, and public health researchers. Most engineering approaches towards buildings and infrastructures are guided by the conceptual framework comprised of four sequential but overlapping postevent periods: emergency, restoration, reconstruction, and development (Kates and Pijawka 1977). Lindell (2013) offers a more in-depth recovery conceptualization involving four functions: assessment, short-term recovery, long-term reconstruction, and recovery management. Each of these functions varies in duration (from days to years) and in responsible parties (e.g., individual household, government, private business). Invariably, disaster recovery models in the engineering domain measure or represent the state of the study subject in response to a disaster at multiple time points. One of the common goals is to determine whether the subject returns to a preevent state or a counterfactual state. The state indicators shall be clearly defined and can be binary (e.g., habitable or inhabitable), discrete (e.g., minor, moderate, extensive damages), or continuous (e.g., percentage of full capacity available).Solutions to disaster recovery modeling could be grouped into eight categories: resource-constrained modeling, machine learning, dynamic economic impact modeling, system dynamics simulation, agent-based simulation, discrete-event simulation, stochastic simulation, and network modeling (e.g., Miles et al. 2019; Ouyang 2014; Tabucchi et al. 2010; Abdulla et al. 2019; Chang 2010). They are not mutually exclusive, and, very often, models combine two or more of these modeling approaches to leverage their respective modeling power. Furthermore, simulation is playing a more prominent role thanks to significant advancement and availability in computational capabilities.In our study, the recovery of small businesses after major hurricanes is modeled as a Poisson process in which recovery states of individual firms are randomly located in the time space. Other models have been used and implemented. For example, Watson et al. (2020) specified a logit function for predicting whether a business would recover based on damage, accessibility, business characteristics, owner/manager profile, and financial assistance. When modeling the case operation days, Aghababaei et al. (2021) applied a linear regress model with a log-log link function. Our rationale is that a Poisson process captures the essence of the phenomenon under examination in which independent and identically distributed (iid) arrivals enter a system. A foundational concept to econometric modeling is that industries, households, and governments in the economy are connected through buy-sell relationships. Therefore, the interruption at the individual firm levels could lead to a ripple of additional changes. Lee (2021) studied 1,150 local businesses in Aransas County, TX, after Hurricane Harvey and found evidence that the decision of business owners to reopen were influenced by the decisions of their neighbors. However, the assumption of iid events could still be valid for the narrow application and timeframe presented in this study. In the wake of a disaster, the intrafirm relationship during the recovery could be considered weaker than the firm-community relationship. In addition, the effect of spatial dependence among small businesses would be further minimized when a short time step of simulation (i.e., one month) is set.In many ways, the Poisson process the continuous version of the Bernoulli process that only allows arrivals to occur at positive integer increments. In comparison, arrivals may occur at arbitrary positive times, and the probability of an arrival at any particular instant is zero. The Poisson process has been successfully applied to model random events in time and space in numerous disciplines such as business, economics, telecommunication, biology, and ecology. Furthermore, the Poisson process and associated functions have well known properties and ready-to-use solvers.The Poisson distribution with a constant rate function fails the Chi-squared goodness-of-fit test. We then make the rate function {λ(t),t≥0} stochastic, leading to a nonhomogeneous Poisson process. The time-varying rate is more consistent with observation that the probability of small businesses to recover after a disaster can weigh heavily on the left: at the beginning, firms that sustained minimal/minor impact return to normal operation quickly. The longer they wait, the more likely that they would never return. Conceptually, the rate function should be decreasing with t, in an either concave or convex form.In this study, we model a firm’s recovery time t with a probability function RT (e.g., lognormal, exponential) with a cumulative distribution function (CDF) of (1) where t = random variable for recovery time; the parameter vector β is estimated with sample observations.At time t, the arrival rate per unit time is a recovery probability density function (or hazard function as conventionally termed) conditional on recovery not yet attained [i.e., Pr (T>t)] (2) where fRT(t) = recovery probability density function. Note that there could be a single λ(t) for all firms, or multiple ones for multiple strata. Once λ(t) is specified, we can use Eq. (2) to simulate the small business recovery trajectories under various scenarios.DataHurricane Harvey and Its ImpactsHurricane Harvey was a Category 4 hurricane that made landfall on August 25, 2017, between Port Aransas and Port O’Connor with sustained winds over 130 mph (GLO 2020). It caused catastrophic flooding and 68 direct deaths. The economic loss is estimated at $120 billion (2017 USD), primarily from flooding in the Houston metropolitan area and southeast Texas, where many areas received more than 40 inches (1,000 mm) of rain over a four-day period. Fig. 1 shows 39 counties in Texas eligible to receive individual assistance (IA) and public assistance (PA) as the part of this presidentially declared disaster (4332-DR).The storm displaced more than 30,000 people, prompted more than 17,000 rescues, and shut down ports, trade, tourism, agricultural production, and general businesses across most of the Texas coast. The effects on oil and gas production rippled across the nation, with a gas price spike averaging about $0.33 a gallon (Energy Information Administration 2018). FEMA’s National Flood Insurance Program (NFIP) received over 92,000 claims and disbursed more than $8.92 billion to claimants (FEMA 2019). The Small Business Administration (SBA) has disbursed over $2.7 billion in home loans and almost $291 million in business loans to assist disaster recovery efforts. The cost of Harvey’s destruction was offset by an increase in business activities related to emergency repair, reconstruction, and restoration efforts, combined with an influx of funding from federal aid and insurance payments. In its aftermath, cars and trucks damaged or destroyed by flooding must be repaired or replaced, lifting sales in the auto industry. Many businesses, in addition to repairing damaged facilities, replaced some or all of their equipment and inventory. Meanwhile, thousands of evacuees stayed in hotels or rental units before returning to their flood-damaged homes, and purchasing furniture, household goods, electronics, and clothes. Memberships (to clubs, sports centers, parks, theaters, and museums), telecommunication services and entertainment were among the industries hit the hardest, whereas health services, food and beverages, rental housing, motor vehicles, furniture, and clothing sectors fared better.Furthermore, 71% of manufacturing firms reported revenue and/or production losses from Harvey and an average closure of 5.5 days. In addition, 27% expected more difficulties in finding and hiring workers over the subsequent six months (Federal Reserve Bank of Dallas 2017). Overall, the net effect on the state’s economy may be much less severe than many have expected (Texas Comptroller of Public Accounts 2018).Online SurveyThe aim of the survey is to collect firm-level data on operations, storm impact, resilience, and recovery of small businesses impacted by Hurricane Harvey. The survey instrument was submitted to and approved by the Human Research Protection Program of Texas Tech University (IRB2019-463). The survey was administered through Qualtrics Panels, a 3rd-party survey vendor (Qualtrics) over two waves.Respondents were recruited directly through Qualtrics based on the following inclusion criterion: 1.Employed in a small business located in one of the 42 counties in the greater Houston area impacted by Hurricane Harvey.2.Self-reported that they were a primary decision maker for the business.3.Self-reported that they had input and influence over key financial and operation decisions.4.Must have worked at the company for 12 months leading up to Hurricane Harvey.5.Must have worked for the company for at least 6 months following Hurricane Harvey.This criterion ensures that respondents had intimate and detailed knowledge of the key operational and financial characteristics of businesses. Moreover, by requiring at least 12 months of tenure prior to and 6 months poststorm, we ensure that respondents are qualified to report on decisions related to both preparation and recovery. Prior to launching the survey, Qualtrics ran a prelaunch analysis to evaluate and possibly improve aspects of the survey to optimize the quality of the responses. Based on their evaluation, Qualtrics estimated a predicted duration of 13.5 min for the survey. The fact that an actual average response time was 12 min indicates that respondents in our survey were spending the amount of time consistent with the expectation.Wave 1 data collection was conducted in November 2019, generating 260 unique and random survey responses. The subsequent analysis allowed us to refine certain questions and identify coverage gaps. As the result, Wave 2 data were collected between October 2020 and November 2020, and consisted of 360 additional unique survey responses. Overall, across both waves the total sample is 620 respondents. Based on self-reported zip code, about 200 different zip codes from within the 39 impacted counties are represented across the sample (see Fig. 1). As seen in Fig. 1, the geographic area comprising all survey respondents spans a large area of the 39 impacted counties. Overall, we view this sample a providing reasonable representation of the geographic area most impacted by Hurricane Harvey.After consenting and meeting the inclusion criterion, respondents were first asked some general demographic questions about themselves including how long they had been working at the company prior to Hurricane Harvey, if they were still working at the same company (if not, how long after Harvey they worked there), how many people worked under their management, and how many people were at a more senior level. Next, they provided general characteristics about the business itself including industry, annual gross revenues, number of employees, and number of locations. We then asked them a series of questions about their business operations and financing, followed by questions about the financial impact of Hurricane Harvey and questions about the company’s level of preparedness and investments in resilience. The last set of questions related to the built environment and infrastructure. The mean time spent on the survey were roughly 12 min, indicating that respondents did spend sufficient time to provide thoughtful responses.Summary StatisticsNote that the inclusion criterion required these respondents to report being in a managerial role and having input and influence over key decision-making. In Table 1, one sees that the vast majority of respondents (78%) had at least four other people under their management, with 37% reporting having over 10 people under their management. Moreover, a majority of respondents (63%) also reported having at most three people more senior than them, with 25% reporting having no one else more senior to them (see Table 2). We view this as corroborating evidence that indeed these individuals assumed managerial roles in their respective companies. Whereas they were required to work at the company for a year leading up to Hurricane Harvey and at least six months after, the average tenure at the time of Harvey was 7.5 years, and most respondents (90%) reported still working for the same company at the time they were surveyed. It is also worth noting that 48% of them were self-employed.Table 1. Characteristics of surveyed respondents (N=620): people under managementTable 1. Characteristics of surveyed respondents (N=620): people under managementNumber of people under respondent’s management% of sampleNone41–3184–6227–1019Over 1037Table 2. Characteristics of surveyed respondents: people more seniorTable 2. Characteristics of surveyed respondents: people more seniorNumber of people more senior than respondent% of sampleNone251–3384–6207–107Over 1010Tables 3–5 present some key characteristics of small businesses represented in our study. As shown in Table 3, more than half of the firms (57%) had annual revenues of less than $1M. The mean (median) number of employees in these firms was 84 (36). As for the industry category, our sample is a relatively diverse mix with the sample being roughly uniformly split over the reported categories. The survey form initially classified small businesses into 21 industry sectors as defined in the North American Industry Classification System (NAICS). They include: Agriculture, Forestry, and Fishing and Hunting; Construction; Manufacturing; Transportation and Warehousing; Wholesale Trade; Retail Trade; Finance and Insurance; Mining, Quarrying, and Oil and Gas Extraction; Information; Accommodation and Food Services; Other Services (except Public Administration); Professional, Scientific, and Technical Services; Real Estate and Rental and Leasing; Health Care and Social Assistance; Administrative, Support, and Waste Management; Arts, Entertainment, and Recreation; Educational Services; and Utilities. Following convention in the economics literature, the categories were consolidated into eight broader industry sectors (as displayed in Table 4) which has the effect of increasing statistical power (Ewing and Wunnava 2004; Bureau of Economic Analysis 2017). In addition, we regrouped across the two waves of the survey to account for small differences in the categorical industry choices. In terms of how many locations their business had, a majority of those surveyed (54%) reported their company had just one location (see Table 5).Table 3. Characteristics of surveyed small businesses (N=620): annual gross revenueTable 3. Characteristics of surveyed small businesses (N=620): annual gross revenueAnnual gross revenue% of sampleLess than $125k22$125k–$250k12$250k–$500k11$500k–$1M12$1M–$2M9$2M–$4M6$4M–$6M6$6M–$8M5$8M–$10M4$10M or more9Do not know3Table 4. Characteristics of surveyed small businesses: industry categoryTable 4. Characteristics of surveyed small businesses: industry categoryIndustry category% of sampleConstruction15Manufacturing, production, and utilities14Trade, transportation, and warehousing11Finance, insurance, and real estate10Health care and education services8Hospitality, food, and entertainment services12Admin, professional, and tech services18Information and other services12Table 5. Characteristics of surveyed small businesses: locationTable 5. Characteristics of surveyed small businesses: locationNumber of locations% of sample15421431044556372819110 or more6Tables 6–9 report key characteristics elicited on financial operations of the surveyed small businesses. A majority of the surveyed firms reported having access to some kind of bank funding (65%), with about half also reporting access to owner funding (48%), and about a quarter (28%) having access to investor funding (as seen in Table 6). We also asked about lines of credit, and 71% reported having access to a line of credit, and 74% of those reported using it (as shown in Tables 7 and 8). Last, we measured business exposure to the Houston market by asking respondents to report the fraction of sales generated from the Houston area, and the fraction of suppliers located in the Houston area. On average, about 65% of sales were from the Houston area, and 64% of their suppliers were located in the Houston area, as indicated in Table 9.Table 6. Characteristics of financial operations of surveyed small businesses: funding sourceTable 6. Characteristics of financial operations of surveyed small businesses: funding sourceSources of fundinga% of sampleBank65Investor28Owner/partner48Table 7. Characteristics of financial operations of surveyed small businesses: access to line of creditTable 7. Characteristics of financial operations of surveyed small businesses: access to line of creditAccess to line of credit% of sampleYes71No24Do not know5Table 8. Characteristics of financial operations of surveyed small businesses: use of line of creditTable 8. Characteristics of financial operations of surveyed small businesses: use of line of creditUsing line of credit% of sampleYes74No21Do not know5Table 9. Characteristics of financial operations of surveyed small businesses: local market exposureTable 9. Characteristics of financial operations of surveyed small businesses: local market exposureLocal market exposure% of sampleAverage percentage of sales from Houston area65Average percentage of suppliers located in Houston area64In terms of recovery, most of the firms (87%) reported that the business fully recovered after Hurricane Harvey. Of those firms that did recover, one sees in Table 10 that there is substantial variation in the time reported to recover. Here, we provided categorical choices, as a common practice, to shorten the response time and reduce recall bias (e.g., Asgary et al. 2013). Many firms recover quickly (37% reported recovering within three months), whereas others take much longer (22% reported taking 10 months or longer). In Collier et al. (2020), about 50% reported that they had not recovered within a year. Note that the question on business recovery was open to respondent’s own definition/interpretation, which would vary greatly. Some might base their answer on return of revenue or profit in comparison to prestorm levels and others on restoration of key production capacities (e.g., equipment, employees, and utilities). It is also expected that comparison could be made to one’s peers affected by the same storm. Such variability in how recovery is defined and how it relates to business characteristics was further examined in a follow-up study through interviews of small construction contractors in Houston, TX (see preliminary result in Sahu et al. 2022). In terms of preparedness which reflects a business owner/manager’s own assessment of their coping capability and outlook of possible consequence, Table 11 illustrates substantial variation in whether the surveyed individual felt the company was prepared for Harvey; this ranged from about 26% reported A great deal of preparedness, to 18% reporting A little preparedness, down to 9% reporting Not at all prepared. In a more objective manner, the most popular mitigation measures adopted were backing up of computer files, use of emergency generators, installing flood barriers, and performing a review of their property.Table 10. Preparedness, recovery, and damage of surveyed small businesses: recovery timeTable 10. Preparedness, recovery, and damage of surveyed small businesses: recovery timeTime to recover% of sample1–3 months374–6 months287–9 months1310–12 months10More than 1 year12Table 11. Preparedness, recovery, and damage of surveyed small businesses: level of preparednessTable 11. Preparedness, recovery, and damage of surveyed small businesses: level of preparednessReported level of preparedness% of sampleA great deal26A lot19A moderate amount28A little18Not at all9About half of the respondents reported that the company proactively made investments in resilience leading up to Harvey. To ensure consistency in their understanding of resilience, we included a robust checklist of 14 common mitigation measures ranging from install storm shutters, to backup computer files, to procure additional insurance coverage. These measures represent three broad categories of actions: physical, operational, and financial., in terms of building damage, 63% reported that the business sustained some building damage because of Hurricane Harvey. In addition, utility outages were very commonly reported (as seen in Table 12): 83% reported power outages, 68% reported water outages, 82% reported internet outages, and 90% reported transportation disruptions.Table 12. Preparedness, recovery, and damage of surveyed small businesses: utility outageTable 12. Preparedness, recovery, and damage of surveyed small businesses: utility outageUtility outages by the storma% of samplePower83Water68Internet82Transportation90ResultsModel Selection and Parameter EstimationWe first verify the independence of observed recovery time from a variety of class variables as defined or derived from a firm’s characteristics, action, and impact. Using the Pearson’s chi-squared test, the null hypothesis that the frequency distribution of recovery time has no association with a given class would be rejected when the test statistic, χ2, exceeds the critical value at a significant level with a certain degree of freedom. In such cases, this class variable could be a candidate to stratify the sample and differentiate recovery functions. We ask the respondents to select from a set of categories (i.e., first column in Table 13 below). Use of intervals in survey allow for quicker response, fewer data entry error, and/or increased response rate. This is generally accepted best-practice for survey implementation of large-scale panels. For example, in the 2020 FEMA National Household Survey (FEMA 2020), rather than entering an exact amount, the respondent was asked to give a ballpark figure for the amount they have set aside for emergency by selecting from the following ranges: $1 to $99; $100–$399; $400–$699; $700–$999; $1,000–$1,499; $1,500–$2,999; $3,000–$5,000; more than $5,000. In studying the impact of COVID19, Pierel et al. (2021) asked small businesses to indicate their recovery time in less than 1 week, 1–4 weeks, 2–3 months, 4–6 months, 7 months–1 year, 1–2 years, or longer than 2 years. As with any survey design, some ex-ante subjective judgment is required when formulating questions. However, these specific bins were selected with the aim of balancing the appropriate level of granularity while also spanning a reasonable recovery timeframe for most small businesses (e.g., Lee 2019). High concentration of data points in certain bins may call for setting closer thresholds and vice versa. However, we note that our examination of the data reveals we did not have such an issue with too much/little concentration in any single bin (the frequency ranged from 37% in the largest bin of 1–3 months to 10% in the smallest bin of 10–12 months). Overall, we view this as ex-post support that our threshold choices for recovery time were reasonable. For statistical analysis, we convert the categorical recovery times as reported to the numerical values as midpoints for parameter estimation (i.e., model fitting). When the recovery time is greater than 12 months, we approximate it to 18 months (the midpoint between 12 months and 26 months when the first wave survey was initialized).Table 13. Rescaling of recovery times (all numbers are in months)Table 13. Rescaling of recovery times (all numbers are in months)Recovery time (from online survey)Recovery time (in parameter estimation)1–324–657–9810–1211>1218Not recoveredRight censoredThe class variables we examined include industry sector, investment in resilience, levels of preparedness, line-of-credit, power outage, and building damage ratings.The observed count of firms corresponding to the recovery time and its industry sector classification are tabulated and analyzed. For example, 10 out of 92 (or 10.9%) construction firms report in our survey that they recovered within 7–9 months after the storm. For the same timeframe, only three out of 77 (or 3.9%) small businesses in hospitality, food, and entertainment services recovered. Results from the Pearson’s chi-squared [χ2(35)=41.12, p=0.22] fail to reject the null hypothesis at 95% significant level. Thus, the recovery time of firms appears independent from the industry sectors to which they belong. We are able to draw a similar conclusion when comparing individual sectors with the entire sample. The closest exception, though, is hospitality, food and entertainment services sector [χ2(5)=10.58, p=0.06] in which a large number of firms are on the two extreme of recovery spectrum: 45.5% recovered within the first 3 months, whereas 16.9% had not recovered at the time of survey. Our findings echo a similar conclusion in Webb et al. (2002) about the absence of significant effect of economic sectors on long-term business recovery. Therefore, we do not stratify the sample based on industry sectors.Investment in resilience, levels of preparedness, line-of-credit, power outage, and building damage have significant association with reported outcome of recovery time as shown in Table 14. Among them, building damages appears to be the strongest driver: 55.8% of firms with none or minor damage recovered within 3 months, and 76.6% did so within 6 months. In contrast, only 8.9% and 28.6% of those with major building damages recovered within 3 months and 6 months, respectively. The correlation between building damage and business recovery was also observed in the Northridge Earthquake (Dahlhamer and Tierney 1998), the Loma Prieta Earthquake, and Hurricane Andrew (Webb et al. 2002). However, content damage, not building damage, was found to be a strong predictor in Hurricane Matthew (Watson et al. 2020). Note that the question on level of preparedness was purposely designed to be vague, allowing for open interpretation by respondents based on the small business’ unique traits and contexts. Because of the diversification of small businesses and industries represented in our sample, we opted for such a general question with an intent to capture the mixed effect of perceptions of threats, protective actions, and stakeholders that ultimately drive decision making in disasters (Lindell and Perry 2012). It is similar to a question in FEMA National Household Survey (FEMA 2020): How confident are you that you can take the steps to prepare for a disaster in your area, not at all confident, slightly confident, somewhat confident, moderately confident, or extremely confident?Table 14. Result of Pearson’s chi-squared test for different class variablesTable 14. Result of Pearson’s chi-squared test for different class variablesClass variableValueNDFPearson’s chi-squaredp-valueInvestment in resilienceYes/no620528.167<0.0001Line of creditYes/no620524.261<0.0002Level of preparednessLittle/some/lot6201040.015<0.0001Power outageYes/no620548.945<0.0001Building damageMajor/some/minor-none62010151.631<0.0001Then, we fit the data to various life distribution functions for both the entire sample and the split samples based on class variables. The unrecovered firms are right-censored. The Frechet and lognormal functions are best-fit in comparison. We adopt the lognormal models for its better-known qualities. Hence, the recovery cumulative distribution function (FRT) and the recovery probability density function (fRT) are specified as (3) FRT(t;μ,σ)=Φ(ln(t)−μσ),t>0(4) fRT(t;μ,σ)=1tσϕ(ln(t)−μσ),t>0where μ and σ>0 = location and scale parameters of the distribution; Φ and ϕ are CDF and PDF of standardized normal distribution [i.e., N(0,1)]. The maximum likelihood estimators (5) (6) σ^2=∑(ln(rti)−μ^)2n−1where rt1,rt2,…,rtn = sample’s recovery time as reported in the online survey.We estimated μ and σ for the whole sample (N=620) and, for brevity, the split sample based on whether or not a firm made investment in resilience before Hurricane Harvey. Note that e[μ+(σ2/2)] and eμ are the mean and median recovery times, respectively.We then set the time step as 1 month. Thus, the arrival rate function λ(t) as shown in Eq. (6) is calculated and shown in Fig. 2.When firms are considered as a single population, the conditional probability of recovery in the first month (i.e., t=1) stands at 9%. In other words, about 1 out of 11 firms affected by the hurricane is expected to recover to the prestorm level. The probability reaches its peak value of 12% in month 3 before gradually trending down. If a firm still has not recovered after 3 years, the chance of recovery after that is as low as 5%. Meanwhile, the divergence between two groups of small businesses—those made investment in resilience (hereinafter referred to as resilient firms) and those that did not (nonresilient firms) is quite pronounced. For resilient firms, the conditional probability of recovery rises sharply during the immediate aftermath of the hurricane, peaking in month 5. After that, they are 50%–60% more likely to recover than the nonresilient ones.Simulation of Recovery TrajectoriesThe lognormal models described in the preceding section could be most useful when establishing certain benchmarks for specified business characteristics. The ability to compare itself with its peers under normal and crisis conditions is important to many business owners. In a related study, we interviewed 15 small construction contractors and saw a strong desire for tracking their own performance against that of their competitors after Hurricane Harvey (Keeler et al. 2022). Such an alternative (or supplementary) definition of business recovery could be useful only if peers or industry benchmarks are available. Underperformance, if detected, would call for a deeper analysis of its risk profile and possibly corrective actions. However, the averages (i.e., recovery time, recovery probability) given in these models only capture a part of the recovery process. Especially at the community level, a strong interest is to examine both the aggregated pattern of recovery and the uncertainty associated with it. To that end, we choose to create a synthetic community with a fixed number of small businesses each of which could be different in its financial, operational, physical property, and other attributes. When a hurricane hits, their recovery trajectories are likely to be unique but governed by a common nonhomogeneous Poisson process.Fig. 3 below uses the arrival rate functions and plots the recovery process of 100 firms for the purpose of uncertainty quantification. These firms are randomly sampled from the lognormal distribution with parameters specified in Table 15. Each line in Figs. 3(a, c, and e) on the first column represents a single realization of the nonhomogeneous Poisson process in terms of the accumulative number of firms recovered from the hurricane in each month. Fig. 3(a) considers all firms having the same rates of recovery, whereas Figs. 3(c and e) are for resilient and nonresilient firms, respectively. Based on 100 realizations, Figs. 3(b, d, and f) show the percentages of firms that have recovered, accumulatively, in forms of mean, 5th-percentile, and 95th-percentile.Table 15. Result of parameter estimation for recovery times using lognormal modelsTable 15. Result of parameter estimation for recovery times using lognormal modelsSampleParameter estimationEstimateStandard errorLower limit 5%Upper limit 95%All firms (N=620)μ^1.900.051.811.99σ^ in resilience (N=301)μ^1.860.061.751.97σ^0.960.040.891.05No investment in resilience (N=319)μ^1.940.071.802.09σ^ years after the hurricane, about 90% of all firms would have recovered. For resilient firms, the percentage is in the range of 93%–96%. In comparison, among nonresilient firms, that range from 87% to 89%. At the 12-month mark, 78% of resilient firms have recovered, whereas it is only 69% for nonresilient firms.The model uncertainty is represented by 5th-percentile, and 95th-percentile bounds. The gap between the two bounds tends to expand as time elapses before contracting towards the end. Alternatively, we plot the coefficients of variance (CV) for the first 12 months. Nonresilient firms are shown to have the greatest variability in relation to their means. This could be attributed to larger uncertainties in model parameters for nonresilient firms. In practice, nonresilient firms may behave in a less predictive manner. Such high volatility, in a financial term, would correspond to higher risk to business performance or valuation.ConclusionsA better understanding of the capability of small businesses to withstand the shock of a natural disaster, recover from it, and adapt to the new market conditions are of significance to local communities and policy makers. In their seminal paper, Bruneau et al. (2003) expressed seismic resilience on the community scale in robustness, rapidity, resourcefulness, and redundancy. Those measures are then integrated into the technical, organizational, social, and economic dimensions for various types of physical and organizational systems. While increasing disaster resilience is a national imperative, collaborative efforts of government agencies and local communities are required (National Research Council 2012). Specifically, application of the resilience framework to small businesses must first overcome several challenges, including extensive heterogeneity among small businesses and lack of firm-level data, particularly with respect to mitigation and resilience investments. Moreover, very often the dynamics of recovery are an important dimension that is overlooked.In this study, we model the small business recovery as a stochastic process and use a unique survey data set to select probability models and then estimate model parameters. We find that when taken as a whole, the mean and median times for small businesses to recover from hurricane are 12.6 months and 6.7 months, respectively. If firms opt to invest in resilience, the mean and median times could decrease significantly to 10.2 months and 6.5 months, respectively. The accelerated recovery is likely to lead to several benefits at the firm level, such as larger profit, increased market share or competitiveness, and lower employee turnover. It puts the resilient business at a competitive advantage and may lead to a more sustainable local economy. In a community, the contribution of small businesses can often be amplified beyond economic matrices. For instance, closure of a beloved local restaurant is unlikely to have a material impact on a city’s tax base or unemployment rate but could be perceived by many as a troubling sign. Similarly, quick reopening of businesses after a storm will help instill the confidence among residents who had either stayed or evacuated. To that end, we yet have means and methods to reliably capture the effect of success and failure of small businesses on social capital and equity.For government agencies, a risk assessment instrument specifically designed for small businesses can be used to help allocate recovery resources. Businesses with higher potential of closure or slow recovery could receive targeted outreach effort and technical assistance in the aftermath of a disaster. Because some of risk factors are mitigatable (e.g., line-of-credit, building damage) and others are not (e.g., business size, industry sector), these policies and programs should pay close attention to moral hazard and not to reward bad behaviors. Meanwhile, the restoration of public infrastructure and services could be prioritized by types and geographical areas when the risk profile of small businesses is considered. A more effective approach towards resilience is to inform small businesses about their vulnerability and available mitigation measures. To that end, federal agencies such as Federal Emergency Management Agency (FEMA) and Department of Housing and Urban Development (HUD) can play a bigger role in enacting predisaster grant programs supporting evidence-based best practices and actions.The firm-level, time-dependent approach we adopted is consistent with an increasing emphasis on access to timely (or even real-time), high-spatial resolution information on consumer spending and business performance to inform economic policies. The existing government surveys (e.g., Business Employment Dynamics, Quarterly Census of Employment and Wages) may be too coarse to study localized or short-lived economic shocks. As an alternative approach to fill these information gaps, Aladangady et al. (2019) used anonymized transactions data from a large electronic payments technology company to create daily estimates of retail spending at detailed geographies. When applied to Hurricanes Harvey and Irma in 2017, they found that spending at building materials stores ramped up before the hurricane and rebounded afterwards, such that the net effect for this category is positive (12% for the month). Spending at grocery stores also ramped up before the hurricane but did not rebound afterwards so that the net effect was negative (−3.5% for the month). Other retail categories (e.g., restaurants, clothing stores) showed no evidence of a ramp up or a quick make-up. The spending lost during the storm appears to be largely foregone. Another recent study examined the credit reports of 8,219 businesses and a detailed survey of 273 businesses in the area affected by Hurricane Harvey (Collier et al. 2020). They found that Hurricane Harvey increased credit delinquencies, especially short-term delinquencies. Firms that most commonly reported recovery use earnings and the owner’s personal resources. This research is consistent with ongoing work focusing on community resilience (e.g., core metrics of population, economic, social services, physical services, and governance stability) and efforts (e.g., the COVID-19 demographic and economic resources dashboard and data hub).Our study complements the findings of others, and advances our understanding of how small businesses’ operations evolve after a hurricane. However, the study has several limitations. The probability models are derived from the survey on a single event and location (i.e., Hurricane Harvey of 2017 affecting Houston, TX) and therefore they may not be readily extended to other disasters or regions without further study. As such, the cross-sectional analysis we plan to conduct would help to validate the generality of model forms and parameters. Control variables accounting for regional and disaster differences will be introduced. The survey itself may contain several biases. For example, the current survey design only allowed us to collect data on firms that have survived the storm, not on the ones that had failed, a group that is arguably much more difficult to find and track. As a result, the rates of survival and recovery based on this truncated sample would likely be overstated, the exact extent of which is unknown. Accordingly, our findings should be interpreted in this context, that is, conditional on firm survival. Remedies may involve collecting and examining registration, credit, and tax records of businesses in affected areas, and perhaps estimating survival rates. Proxy indicators of business activities could also be introduced, such as foot traffic and social media presence, some of which may involve various types of remote sensing technologies. Furthermore, investment in resilience and level of preparedness are self-reported by respondents and could be further cross-validated. The statistical significance ascertained simply points to the linkage between subjective evaluations of small business owners and manager prior to the storm and the ensuring recovery process after it. From an implication standpoint, this type of general questions could be very useful as indications to quickly canvas hurricane prone areas efficiently gauge how vulnerable these areas might be. Unpacking the causal relationship would require the inclusion of questions on specific mitigation actions taken.Data Availability StatementSome or all data, models, or code generated or used during the study are proprietary or confidential in nature and may only be provided with restrictions. As survey responses could reveal the identity of businesses who participated in the study, information on their finances, operations, and impacts can only be made available, upon request, for reuse in aggregated forms. Survey instrument and statistical models that do not contain confidential information on individual businesses are available from the corresponding author upon reasonable request.AcknowledgmentsThis material is based upon work supported by the National Institute of Standards and Technology (under Award # 70NANB19H061) and Center for Risk-Based Community Resilience Planning) and Economic Development Administration (under Project # 08-79-05280) of US Department of Commerce. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the sponsors.References Abdulla, B., A. Mostafavi, and B. Birgisson. 2019. “Characterization of the vulnerability of road networks to fluvial flooding using network percolation approach.” In Computing in civil engineering 2019: Smart cities, sustainability, and resilience, 428–435. Reston, VA: ASCE. Aladangady, A., S. Aron-Dine, W. Dunn, L. Feiveson, P. 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