Using Disaster Surveys to Model Business Interruption

This paper relied on data collected from face-to-face surveys in Lumberton, North Carolina after Hurricane Matthew. Hurricane Matthew made landfall in the US in South Carolina on October 8, 2016, as a Category 1 Hurricane with 139–143 km/h (75–77 kt.) winds and torrential rainfall (Stewart 2017). Rainfall was particularly heavy in eastern North Carolina; some areas received more than 38 cm (15 in.). The resulting flooding was exacerbated by heavy rains in September from Tropical Storm Hermine, which had saturated the ground, and riverine flooding continued days after the hurricane passed back toward the Atlantic Ocean (Armstrong 2017; van de Lindt et al. 2018).

In particular, Lumberton (population. approximately 21,000) was severely impacted by Hurricane Matthew and the resulting heavy rains. The Lumber River that bisects Lumberton experienced a historic flood crest of 6.7 m (22 ft)⁠ on October 9—1.2 m (4 ft) higher than the previous maximum flood level, set in 2004 (USGS 2018). Much of the area south of the river was flooded, as were some isolated areas in the northern part of the city (North Carolina Emergency Management 2017). In addition to the inundation of buildings, several utilities were disrupted. Electric power was disrupted due to downed trees and substation flooding, and Lumberton’s sole water treatment plant also was inundated. A boil water advisory was in effect for slightly more than 1 week after service resumed (van de Lindt et al. 2018). Although the flooding was more severe for businesses in the southern commercial corridors, the utility disruption was experienced by businesses across Lumberton. The river receded to below flood stage [4 m (13 ft)] by about October 23 (USGS 2018).

The business survey effort was part of a larger interdisciplinary effort and longitudinal field study in Lumberton (van de Lindt et al. 2018, 2020; Sutley et al. 2021). The authors used a phone-verified business database downloaded from ReferenceUSA (now Data Axle Reference Solutions) for the sample frame. An inundation shapefile that was created at the University of Alabama through modeling that combined a digital elevation model and the hydrograph from the stream gauge in Lumberton (USGS 02134170) was used in the sample generation: all 218 businesses that were within the inundation area or a 100-m buffer were included, in addition to a random sample of businesses in the 100-year floodplain north of the Lumber River, to obtain to a total of 380 businesses. A map of the sample and study area is presented in Fig. 1. To protect the privacy of individual respondents, the sample is displayed as a heat map of the density of individual businesses.

The survey data were collected through in-person visits to the businesses in January 2018, about 15 months after Hurricane Matthew. The survey instrument was deliberately brief (two pages front and back) and asked businesses questions related to their damage and operations, business characteristics, recovery status, financial assistance, and owner or manager demographics. Survey questions were informed by a systematic review of the business and disaster literature, and were modified from previous business survey efforts if possible (Xiao and Peacock 2014; Xiao et al. 2018). Prior to use in the field, the survey was subjected to a comment period by an interdisciplinary group of researchers at NIST and the NIST-funded Center for Risk-Based Community Resilience Planning.

Questions about the business’s damage corresponded to damage states developed by a team of engineers on the project. These ranged from DS0 to DS4 for building structural damage, content and inventory damage, and machinery and equipment damage. These damage states generally are no damage (DS0), minor damage (DS1), moderate damage (DS2), severe damage (DS3), and complete damage (DS4). The damage states and survey instrument have been published on DesignSafe for reference (Xiao et al. 2020).

Survey teams were multidisciplinary, and had at least one engineer to assist businesses in categorizing their damage in the field; laminated description sheets of each damage state were given to the business to review during the survey. Managers, owners, and employees with enough knowledge to be able to answer questions on the financial decisions of the business were asked to complete the survey. If no one was available at the time of the initial survey team visit, teams scheduled follow-up visits, left a paper survey, or followed-up with phone calls after field deployment. Of the 380 businesses that were sampled, the authors received 164 survey responses, a response rate of 43%, with a sector distribution that matched the Lumberton business population. More detailed information on the sampling strategy and survey methodology were presented by Sutley et al. (2021).

This study used closure to measure business interruption. Although businesses can remain partially open and experience interruption losses, many studies have operationalized business interruption as closure, or have used initial closure as a key business resilience metric (Chang and Falit-Baiamonte 2002; Orhan 2014; Ortiz et al. 2021; Sultana et al. 2018). This paper used three approaches to explore how variable choice, variable measurement, and time dynamics affected interruption modeling in the Lumberton case. First, we regressed interruption—i.e., days of closure—on a comprehensive set of damage and utility variables commonly used in descriptive studies, but less common in statistical models. We also did this for sets of control variables, to inform model selection and establish a baseline full model for comparison with the literature. All analyses followed the general formwhere Y = dependent variable, in this case interruption days; $B_0$ is the intercept; $B_n$ is the regression or slope coefficient for the $n$th independent variable, $X_n$; and $\epsilon$ is an error term. Independent variables damage indicators, utility disruption indicators, and other control variables are described in more detail in the next section. For reporting purposes, beta coefficients were translated to percentage change in $y$ using

Second, we examined how correlation, significance, and model fit was affected by different measures of damage and utility variables, and updated the full model with the controls. Lastly, we recoded the days of interruption dependent variable to represent binary open or closed status at weekly intervals, and ran correlations with the different damage, utility, and control variables to determine how variable relationships change when time is considered for both the dependent and independent variables.

Survey weights were used in the analysis because businesses in the sample had different probabilities of being selected depending on whether they were in the predicted inundation area. Therefore, the study used probability weights ($N/n$), where $N$ is the number of businesses in the population, and $n$ is the number of sample businesses, to ensure that the coefficients were not biased. This was done for each regression using the survey design commands in Stata version 17 (StataCorp 2021); although the number of observations may vary, they were all adjusted by a probability weight to represent a consistent population of 508. To facilitate analysis, the damage states were transformed into damage percentages ranging from 0% to 100% (Xiao and Peacock 2014) where Damage states 0–4 were recoded into 0%, 25%, 50%, 75%, and 100%, respectively. There also were outliers in the interruption and utility variables that exerted a large amount of influence on the regression analyses. Therefore, log transformations were used for days of interruption as the dependent variable and days of utility disruptions as independent variables. To preserve zeros in the data, a constant value of 1 was added to all values of the variable before taking the log. Lastly, because damage and utility losses are all related to hazard severity, the variance inflation factor (VIF) of the variables was checked after running each model to identify issues of multicollinearity. The highest VIFs were 3.09 and 2.99, for percentage machinery damage and percentage building damage, in the final full model (Model 22). Although there is no standard threshold, these were below most rule-of-thumb values used to identify cause for concern (James et al. 2013).

Descriptive statistics of the sample are presented in Table 2. Almost 40% of businesses in the sample were in the retail or wholesale sector, and 7% were in manufacturing or construction. About 30% were a branch of a larger firm, and about half rented their premises. The size of businesses, measured by number of part- and full-time employees, in the sample ranged from 1 to 250 employees, with an average of 16 at a given facility. Owners, managers, and senior employees who were interviewed had an average of 16 years of business experience, and 40% identified as other than non-Hispanic White.

In terms of impacts from Hurricane Matthew, businesses in Lumberton were interrupted (i.e., closed for business) for 17 days, on average; the maximum length of interruption was 300 days. By 1 week postflooding, only 45% of businesses in Lumberton had reopened. This percentage rose to 71% after 2 weeks and to 85% after 4 weeks. After 6 weeks, most (91%) of businesses had reopened.

In general, more businesses experienced contents damage (11%) than building (36%) or machinery (15%) damage. Businesses also were more likely to report higher damage levels for their contents than for their building or machinery; businesses reported 17% and 10% damage for their building and machinery, but 25% damage for contents. Content loss can be related to utility loss, and almost all businesses in Lumberton lost electricity and water. Whereas only 12% lost natural gas, 38% lost sewer, and 28% lost cell phone service, 98% lost electricity at some point, and 91% lost water. Figs. 2 and 3 illustrate the restoration of utilities and operations over time during the first 90 days. Most businesses regained their utilities and operations in the first few weeks after the flooding. Businesses waited the longest time to resume service for water; respondents cited an average of close to 12 days without water access. Sewer loss was similar, with an average of almost 12 days with no service. Electricity, natural gas, and telecommunications were disrupted for an average of approximately 7, 3, and 4 days, respectively. However, there were outliers of businesses experiencing very long down times for these services, and some businesses had not had the utility restored at the time of the survey.

Beyond the more physical impacts of Hurricane Matthew, businesses also experienced a variety of impacts related to customers, employees, and their ability to work at and access the business. Approximately 48% of businesses experienced accessibility issues related to street and sidewalk closure, and 61% experienced a loss of customers. Employees were likely to be unable to come to work due personal home damage (50% of businesses). Issues related to childcare and schooling caused employees to be unable to come to work in approximately 25% of businesses, and health problems caused staffing disruption in approximately 7% of the business sample.

Businesses in Lumberton had a variety of insurance coverage types to deal with the flooding impacts. Building insurance was the most commonly held insurance, with 65% of businesses reported having coverage. Content insurance was the second most common, with 58% of businesses in the sample maintaining coverage. Only 34% of businesses had insurance for business interruption. Insurance variables had the highest number of missing values out of the various variables categories. This was due both to managers being unaware of the types of coverage the company had, and to a higher unwillingness to share financial information with the survey team compared with other types of questions. Therefore, we anticipate that these numbers likely were higher because businesses were more likely in the field to respond that they did not know (coded as missing) unless they were sure they had coverage.

The first set of analyses tested how empirical models of business interruption may be improved through the inclusion of more-comprehensive damage and utility variables used in more-descriptive studies. Table 3 presents a series of models regressing days of interruption on variable groupings of damage and utilities, in addition to transportation, customer, employee, business characteristic, owner or manager profile, and insurance variables that frequently have been used in past studies (Table 1).

Models using damage and utility variables were able to explain more of the variation in the (log) number of days a business was closed than were models using other variable categories. Model 1, which included indicators of building, content, and machinery damage, had an $R^2$ value of 0.345. All three types of damage were significantly and positively related to length of business interruption in the Lumberton case. Businesses that experienced building damage, contents damage, and machinery damage were closed for 18%, 3%, and 261% more days, respectively, than businesses that did not report that type of damage. Model 2, which included indicators of electricity, water, natural gas, sewer, and cell phone service outages, had an $R^2$ value of 0.146. Natural gas loss was the only individually significant variable. Businesses experiencing gas loss were interrupted for 493% more days than those without gas loss.

Models 3 and 4, which included transportation disruption and customer loss indicators, also had significant variables. Businesses that experienced accessibility issues with respect to road and sidewalk closure were closed for 211% more days than businesses that did not experience accessibility issues. Similarly, businesses that lost customers were closed for 111% more days than businesses without customer loss. Models 3 and 4, which included access loss and customer loss alone, had $R^2$ values of 0.146 and 0.083, respectively. However, models using business characteristic variables, owner or manager profile variables, and insurance coverage variables did not have any individually significant variables, and the models were insignificant, taken as a whole.

Model 9 was the full model, and included variables in all models with significant $F$-tests (Models 1–4). All utility variables were included from Model 2, despite only natural gas being significant, because many utilities, such as water and sewer, are interdependent. The significance and model fit of each individual utility variable is explored further in the following section. The significance of the individual variables did not change in the full model, with the exception of building damage, which changed from significant in Model 1 to insignificant in Model 9. Contents damage, machinery damage, natural gas loss, access loss, and customer loss all significantly increased interruption duration for Lumberton businesses. The significance of contents and machinery damage compared with building damage highlights the importance of including multiple dimensions of damage in business disruption models, and natural gas loss is rarely if ever included in empirical models. However, including these variables led to the final model having an $R^2$ value of 0.460.

The previous set of analyses showed the importance of including multiple dimensions of damage and utility disruptions, even if only by using binary indicators. However, these variables can be measured and quantified in many ways. For example, surveys can collect detailed information such as days of downtime and level of damage based on damage states. Secondly, given the interdependence of some of the utility provisions and the likelihood that damage severity is related across different physical assets of the business, it is possible that knowing the maximum damage state and days of utility loss across these variables would be sufficient. Therefore the following sets of models explore variable measurements of damage and utilities on interruption, comparing dichotomous measures for damaged–undamaged and lost service–had service with damage state and service disruption duration. Table 4 presents the correlation and the beta coefficient, $p$-value, and model $R^2$ for models regressing days of interruption on each variable individually.

The results in Table 4 suggest that interruption models are sensitive to more-imprecise measurements in utility disruption, but comparatively less so for damage. For example, the weighted correlations between damage variables and log days of interruption and the beta coefficients when using each damage variable in a simple regression model with log days of interruption were significant regardless of whether the percentage damage based on damage state or binary measure was used. However, for utility disruption, using log days instead of the binary measure led to changes in significance in both the correlations and the beta coefficients in the case of electricity, water, and sewer loss. Whereas the binary measure was insignificant in these cases, the log days of disruption to those utilities was significantly related to log days of interruption. For natural gas and cell phone loss, both the binary and continuous measures were significant and insignificant, respectively.

Across the damage and utility variables, the $R^2$ value generally was higher when percentage damage and log days of utility outages were used in the simple regression models. This was most pronounced for building damage and electricity loss. For building damage, a simple regression model using the binary measure had an $R^2$ value of 0.115, whereas a simple regression model using percentage damage based on the damage state had an $R^2$ value of 0.268. For electricity loss, the difference was greater: a simple regression model using the binary measure had an $R^2$ value of $<0.001$, whereas a simple regression model using the duration of electricity loss had an $R^2$ value of 0.263. However, the $R^2$ values cannot be compared directly.

Tables 5 and 6 present the result of using continuous measures in place of the indicator variables, using partial $F$-tests to determine whether these additions can improve the $R^2$ value significantly. Adding more-precise measures of utility disruption significantly improved the $R^2$ in Table 5, whereas using the indicator measures did not. The $R^2$ value increased by 0.107 in Model 12 ($F=3.92$, $p=0.003$) and 0.083 in Model 15 ($F=3.14$, $p=0.011$) when adding log days of utility loss and increased by 0.061 in Model 11 ($F=1.63$, $p=0.157$) and 0.039 in Model 14 ($F=1.13$, $p=0.349$) when adding the indicator measures. Adding the percent damage variables and damage indicator measures both significantly improved the $R^2$ value in Table 6. The $R^2$ value increased by 0.294 in Model 18 ($F=26.29$, $p=0.000$) and by 0.162 in Model 21 ($F=15.85$, $p=0.000$) when adding percentage damage, and it increased by 0.239 in Model 17 ($F=15.05$, $p=0.000$) and by 0.109 ($F=13.10$, $p=0.000$) when adding the indicator measures. Overall, the results suggest that adding nonbinary variables can increase the model goodness-of-fit more than adding the binary variables. It also changed the significance of some of the variables: both electricity loss and building damage gained significance when using days of utility loss and percentage damage, respectively.

Lastly, the bottom two rows in the Table 4 present the interruption correlations and simple regression results with the maximum percentage damage across the building, machinery, and contents, and the longest (logged) days of utility outage across electricity, water, gas, sewer, and cell phone service for each business. The $R^2$ values were 0.18 and 0.27 for maximum damage and maximum utility outage duration, respectively. These measures may be an efficient alternative for smaller samples, because they use only one degree of freedom.

The analysis in the section titled “Variable Measurement Considerations” displayed the particular importance of examining utility outage durations rather than basic indicators when modeling business interruption, and indicate that there is some relationship between utilities, closure, and time. Additionally, the significance of individual utilities is different depending on whether the duration or indicator measure was used. Therefore the final analysis explored this more deeply by examining how variable measures behave over time (Table 7). Business interruption was measured using binary indicators in previous studies (see Table 1); therefore, this analysis explores the importance of capturing time in both dependent and independent variables.

The days of interruption variable was used to create a series of binary indicators for whether the business had reopened each week, starting from Week 1 and ending at Week 6, at which time most (91%) of the sample had resumed their operations. Days of utility outage information was recoded to create a series of binary indicators for whether the business had that particular utility restored in the same periods (denoted “in period” in Table 7). These variables were included along with the initial binary loss measure for the utilities, the binary measure for damage, the damage state measures, customer loss, and access loss used in previous analyses.

The results in Table 7 further support the conclusions presented in the “Variable Measurement Considerations” section and clarify some of the variable significance discrepancies. The percentage damage measures had greater correlations with business reopening at all time periods than did the damage indicator measures. However, the biggest differences involved the utility loss measures. Natural gas was the only variable that was significantly correlated with reopening across the different periods when considering only the initial utility loss, which corroborates its significance in the first full model (Model 9). However, examining utility restorations in the different periods indicates that all the utility services except cell phone service were significantly correlated with business reopening in one or more periods. The correlations also indicate how the effects of the utilities differed depending on the time since the initial flooding, and likely capture different rates of restoration. Electricity had a very high correlation with reopening in the first few weeks, but became insignificant at 5 weeks. Conversely, sewer and gas had stronger correlations in later weeks than in earlier weeks. Some businesses experienced very long disruptions to these utilities in particular, as indicated by the high maximum values and standard deviations in Table 2. It is possible that certain utilities became the limiting factor to reopening as time went on, even as other utilities were restored. This is supported by the $R^2$ value of 0.179 for the model that used the maximum utility loss variable alone (Table 3) and the chart of reopenings and utility restorations after Day 30 (Fig. 2).

The final interruption model is presented in Table 8. This model included all variables significantly related to interruption (Table 3) and the measurement improvements in the dependent and independent variables explored in Tables 4–7. In the final model, building damage, machinery damage, electricity loss, access loss, and customer loss were significantly associated with length of interruption. For each additional percentage of building damage and machinery damage, businesses were interrupted for 1% and 0.7% more days, respectively, controlling for all other variables. For each additional 1% increase in days of electricity loss, businesses were interrupted for 42% more days, controlling for other variables. Finally, businesses experiencing customer loss and access loss were interrupted for 62% and 55% more days, respectively, controlling for damage and utility losses. Although contents damage was significant in previous models, the $p$-value for this variable was 0.120 in the final model using a two-tailed test. Although this approached significance at the 0.1 level, it ultimately was insignificant. Altogether, variables in the final model were able to explain approximately 54% of the variation in (log) interruption days.