These hypotheses are examined by way of three models that vary by the spatial units and time units employed. The first model examines the effect of hazard damage at the county level using annual data. The second model is at the state level also using annual data and the third model is at the state level but uses quarterly data. The models can be characterized as follows. Model 1: refined spatial scale with broad temporal scale; Model 2: broad spatial scale and broad temporal scale; Model 3: broad spatial scale with refined temporal scale.
Comparing the results of these three models also reveals the effect of examining the impacts of hazards at different spatiotemporal units. Thus, a third hypothesis, regarding spatiotemporal scale, is examined:
4.1 Regression
This study used the models presented by Thomas and Helgeson (
2021), which employ a Cobb–Douglas production function. Research from Shughrue et al. (
2020) and Koks and Thissen (
2016) confirmed that damages grow nonlinearly, which suggests that nonlinear models such as the Cobb–Douglas may more accurately measure the effects of hazards. The effects of damages are multiplicative and exponential, as discussed in Thomas and Helgeson (
2021). The Cobb–Douglas model was selected because it both captures the multiplicative/exponential relationship and facilitates using lagged dependent variables in place of capital, labor, and technology components. However, since the models in this study do not strictly follow a Cobb–Douglas production function, it might also simply be considered a logarithmic transformation (Kennedy
2003).
The models used in this study contain 10 variable groupings plus two individual variables: (1) lagged dependent variables; (2) local hazard damage; (3) local hazard count; (4) interaction of local hazard damage and the dependent variable; (5) interaction of hazard count and the dependent variable; (6) hazard damage supply chain variable; (7) hazard count in the supply chain; (8) zero local damage indicator; (9) zero count indicator; (10) indicator for each quarter (only for the quarterly model); (11) indicator for 2012 and earlier; (12) indicator for negative GDP growth nationally. Below is a discussion on why each variable is included.
The Cobb–Douglas production function uses capital, research and development, labor, and technological progress. To control for these items, our models use lagged values of the dependent variable, manufacturing GDP. Because GDP follows seasonal patterns, we use indicator variables for the second, third, and fourth quarters. Additionally, to prevent economic downturns from creating spurious correlations, we include an indicator variable for when national GDP declines.
The first group of variables that we are interested in is local hazard damage, measured in US dollars, and we examine the effect the damage has for up to 2 years. Supply chains can be years long, as Thomas and Kandaswamy (
2015) demonstrate, which is why we examine the impact for up to 2 years. Hazard events can have both positive and negative effects on GDP through local hazards. For instance, there is a positive economic impact when companies and consumers increase spending to replace damaged property, but there is a negative impact when hazards damage infrastructure needed to facilitate production activities. A count variable is intended to capture any positive effects of a hazard (for example, expenditures on repairs or public aid) while the damage variable is intended to capture negative effects. However, it is not possible to completely separate positive and negative effects; thus, any measured negative effects are potentially a lower bound, as some positive effects may be countering the negative ones. Note that we are primarily interested in the negative effects. Although there may be some establishments that benefit from a hazard, that is little consolation for those that did not benefit and whose business is disrupted or damaged. Generally, the businesses that benefit are those that receive funds or an increase in purchases to address or replace losses. Those that suffer are the ones that have losses to replace and those who have disruptions in their supply chain. Gross domestic product represents the economic activity of all firms in a geographic location over a specified period of time, regardless of whether they benefited or suffered from a hazard. We are examining the GDP in the location of a hazard and that of those that receive a significant amount of the supplies from the location of the hazard (that is, those in the downstream supply chain). Downstream losses suggest the potential for a misalignment of incentives, as the firm that experiences the hazard does not bear all the losses, resulting in an underinvestment in resilience. Each lag of the count and damage variable is interacted with manufacturing GDP to account for the scale of damage relative to the level of production at a given location.
A variable representing hazard damage in the supply chain was developed by taking the damage at each of the FAF supply chain zones in the top 20% for a location, multiplying the damage by the proportion of domestic shipments, and summing the product. For instance, consider Frederick County in the State of Maryland. The supply chain variable for hazard damage (that is, \({\mathrm{SUPCHN}}_{t-m,x}\) described below, where \(x\) is Frederick County at time \(t-m\) where \(t\) is in years) for this location is the amount shipped to that FAF zone from the largest supplier (excluding self-supply) divided by the total shipped to the region from all US locations (including FAF region self-supply). This proportion is multiplied by total hazard damage in the FAF supplier zone. This calculation is made for each of the top 20% of FAF zones for Frederick (that is, top 25 locations) and summed together. Moreover, this variable represents damage occurring in the majority of a supply chain for a particular location (for example, Frederick County) each weighted by the amount of the supply chain it represents for that location. The top 20% of the FAF zones is used as this typically accounts for 80% of the supply chain. For the state level models, it is the top 10 supplier locations and for the county analysis it is the top 25 supplier locations. Similar to the local hazard damage variable and count variable, there is a supply chain variable for the total number of hazards. This variable is meant to capture any positive impacts from natural hazards.
This analysis uses value added data from 2001 through 2016; however, data on the supply chain from the Department of Transportation is available from 2012. Therefore, 2012 is used to measure shipments from 2001 through 2012 and an indicator variable is included in the model for these years. That is, the selection of supply chain locations and weighting of the hazard damage in the supply chain do not vary for years 2001 through 2012. This is not likely to cause an issue as shipments change slowly over time; thus, the same or similar supply chain locations would likely have been used with similar levels of shipments used to weight hazard damage. The primary variation is likely to be the hazard damage itself, which is the variable that we are examining.
The models examine GDP at the county and state levels. The regression equation in log terms for the models are represented as:
$$\mathrm{ln}\left({\mathrm{GDP}}_{t,x}\right)=\sum_{m=1}^{n}{\beta }_{m}\mathrm{ln}\left({\mathrm{GDP}}_{t-m,x}\right)+\sum_{m=1}^{n}{\beta }_{m+n}\mathrm{ln}\left({\mathrm{HZRD}}_{\mathrm{DMG},t-m,x}\right)+\sum_{m=1}^{n}{\beta }_{m+2n}\mathrm{ln}\left({\mathrm{HZRD}}_{\mathrm{CNT},t-m,x}\right)+{\mathrm{INTRCT}}_{1}+{\mathrm{INTRCT}}_{2}+\sum_{m=1}^{n}{\beta }_{m+5n}{\mathrm{SUPCHN}}_{t-m,x}+\sum_{m=1}^{n}{\beta }_{m+6n}{\mathrm{HZRD}}_{\mathrm{SC},t-m,x}+\sum_{m=1}^{n}{\beta }_{m+7n}\mathrm{ln}\left({\mathrm{ZERO}}_{\mathrm{DMG},t-m,x}\right)+\sum_{m=1}^{n}{\beta }_{m+8n}\mathrm{ln}\left({\mathrm{ZERO}}_{\mathrm{CNT},t-m,x}\right)+\sum_{p=2}^{4}{\beta }_{p+9n}{Q}_{p}+{\beta }_{4+9n}\mathrm{YR}+{\beta }_{5+9n}{\mathrm{GDPNEG}}_{x}+{\beta }_{6+9n}+\mathcal{E},$$
where
$${\mathrm{INTRCT}}_{1}=\sum_{m=1}^{n}{\beta }_{m+3n}\left[\mathrm{ln}\left({\mathrm{HZRD}}_{\mathrm{DMG},t-m,x}\right)\times \mathrm{ln}\left({\mathrm{GDP}}_{t-m,x}\right)\right],$$
$${\mathrm{INTRCT}}_{2}=\sum_{m=1}^{n}{\beta }_{m+4n}\left[\mathrm{ln}\left({\mathrm{HZRD}}_{\mathrm{CNT},t-m,x}\right)\times \mathrm{ln}\left({\mathrm{GDP}}_{t-m,x}\right)\right],$$
$${\mathrm{SUPCHN}}_{t-m,x}=\sum_{z=1}^{25}\frac{{\mathrm{SC}}_{t-m,\mathrm{Top}-z}}{\sum_{\mathrm{i}=1}^{122}{\mathrm{SC}}_{t-m,i}}{\mathrm{HZRD}}_{\mathrm{DMG},t-m,\mathrm{Top}-z},$$
\({\mathrm{GDP}}_{t,x}\) = GDP for all manufacturing for time \(t\) by geography \(x\), where time is in years for Model 1 and Model 2 or quarters for Model 3. The variable \(x\) is either a county for Model 1 or a state for Model 2 and Model 3;
\(n\) = Number of time units for two years. For annual data, \(n\) equals 2 and for quarterly data, \(n\) equals 8;
\({\mathrm{HZRD}}_{\mathrm{DMG},t-m,x}\) = The total damage in geography \(x\) (county or state) caused by all hazards and perils listed in the SHELDUS database lagged by \(m\) number of time units (years or quarters);
\({\mathrm{HZRD}}_{\mathrm{CNT},t-m,x}\) = The total number of hazards and perils from SHELDUS in geography \(x\) (county or state) listed in the SHELDUS database lagged by \(m\) time units (quarters or years);
\({\mathrm{HZRD}}_{\mathrm{SC},t-m,x}\)= The total number of hazards and perils listed in SHELDUS for all counties in the top 20% of supply chain zones for geography \(x\) (county or state) at time \(t-m\) in years or quarters;
\(\mathrm{YR}\) = Indicator variable for 2011 and earlier where \(\mathrm{ln}\left(\mathrm{YR}\right)\) equals 1 when the observation year is less than 2012;
\({\mathrm{SC}}_{t-m,\mathrm{Top}-z}\) = The value of selected shipments shown in Table
1 supplied to location
x from the
zth largest supplier where
z is between 1 and 25;
\({\mathrm{SC}}_{t-m,i}\) = The value of selected shipment types shown in Table
1 supplied to location
x from location
\(i\) where
\(i\) is 1 through 122 of the FAF regions;
\({\mathrm{ZERO}}_{\mathrm{CNT},t-m,x}\) = Indicator variable for zero hazard incidents locally for time \(t-m\) in county x where \(\mathrm{ln}\left({\mathrm{ZERO}}_{\mathrm{CNT},t-m,x}\right)\) equals 1 when there are zero hazard incidents;
\({\mathrm{ZERO}}_{\mathrm{DMG},t-m,x}\) = Indicator variable for zero hazard damage locally for time \(t-m\) in county x where \(\mathrm{ln}\left({\mathrm{ZERO}}_{\mathrm{DMG},t-m,x}\right)\) equals 1 when there are zero hazard incidents;
\({\mathrm{GDPNEG}}_{x}\) = Indicator for national negative growth in GDP in time period \(x\);
\({Q}_{p}\) = Indicator variables for quarter \(p\), where \(p\) is quarter two, three, or four for quarterly time units. Note that these variables are absent in the annual models;
\(\mathcal{E}\) = Error term;
\({\beta }_{y}\) = Parameter set to be estimated where y is parameter 1 to the total number of parameters.
To further substantiate the results, an alternative model set was created that removes the hazard damage variables (\({\mathrm{HZRD}}_{\mathrm{DMG},t-m,x}\) and \({\mathrm{SUPCHN}}_{t-m,x}\)) that were not statistically significant. The associated count variables (\({\mathrm{HZRD}}_{\mathrm{CNT},t-m,x}\)) and zero hazard indicators (\({\mathrm{ZERO}}_{\mathrm{CNT},t-m,x}\)) were also removed.
Multiple versions of the Breusch–Pagan and Cook–Weisberg test for heteroskedasticity (Stata
2013a) indicated the presence of heteroskedasticity. This issue was addressed using a fixed-effects model using a GLS estimator (producing a matrix-weighted average of the between and within results) (Stata
2013b), which has been shown to provide robust estimates for data with this issue (Hoechle
2007).
4.2 Simulation
Using the regression model and results, a simulation was conducted to estimate the total negative effect that hazards occurring locally and in the supply chain have on manufacturing value added, similar to that conducted in Thomas and Helgeson (
2021). We focus on the negative effects, as we are interested in measuring the losses that occur prior to recovery and excluding those establishments that might benefit from a hazard such as when purchases increase to replace or repair damage. Some establishments might benefit from a hazard; however, that is little consolation for those who are negatively affected. We ran a simulation predicting hazard damage over the study period using the estimated parameters. The estimate of manufacturing value added was then compared to two simulations where: (1) no damage occurred locally; and (2) no damage occurred in the supply chain. Zero damage locally was estimated by setting hazard damage (
\({\mathrm{HZRD}}_{\mathrm{DMG},t-m,x}\)) equals to 1 and the indicator variable for zero damage (
\({\mathrm{ZERO}}_{\mathrm{DMG},t-m,x}\)) set so that
\(\mathrm{ln}\left({\mathrm{ZERO}}_{\mathrm{DMG},t-m,x}\right)\) equals 1. This was calculated only for those hazard damage variables that were statistically significant. The percent change in manufacturing value added was calculated as:
$${\mathrm{PC}}_{\mathrm{LOC}}=\frac{\sum_{x=1}^{n}\left({\mathrm{DEP}}_{\mathrm{LOC},\mathrm{DMG},x}-{\mathrm{DEP}}_{\mathrm{LOC},\mathrm{NO}-\mathrm{DMG},x}\right)}{\sum_{x=1}^{n}{\mathrm{DEP}}_{\mathrm{LOC},\mathrm{NO}-\mathrm{DMG},x}}\times 100,$$
where
\({\mathrm{PC}}_{\mathrm{LOC}}\) = Percent change in manufacturing value added resulting from no hazard damage locally;
\({\mathrm{DEP}}_{\mathrm{LOC},\mathrm{DMG},x}\) = Estimate of manufacturing value added in location x estimated with local hazard damage;
\({\mathrm{DEP}}_{\mathrm{LOC},\mathrm{NO}-\mathrm{DMG},x}\) = Estimate of manufacturing value added in county x estimated with no local hazard damage.
A similar examination was made with and without damage in the supply chain, where manufacturing value added is estimated with
\({\mathrm{SUPCHN}}_{z}\) equaling 1 or USD 1 in damage. The percent change was then calculated:
$${\mathrm{PC}}_{\mathrm{SUPCHN}}=\frac{\sum_{x=1}^{n}\left({\mathrm{DEP}}_{\mathrm{SUPCHN},\mathrm{DMG},x}-{\mathrm{DEP}}_{\mathrm{SUPCHN},\mathrm{NO}-\mathrm{DMG},x}\right)}{\sum_{x=1}^{n}{\mathrm{DEP}}_{\mathrm{SUPCHN},\mathrm{NO}-\mathrm{DMG},x}}\times 100,$$
where
\({\mathrm{PC}}_{\mathrm{SUPCHN}}\) = Percent change in manufacturing value added due to hazard damage in the supply chain;
\({\mathrm{DEP}}_{\mathrm{SUPCHN},\mathrm{DMG},x}\) = Estimate of manufacturing value added in county x estimated with hazard damage in the supply chain;
\({\mathrm{DEP}}_{\mathrm{SUPCHN},\mathrm{NO}-\mathrm{DMG},x}\) = Estimate of manufacturing value added in county x estimated with no hazard damage in the supply chain.
The 95% confidence interval for each estimated percent change was calculated using a bootstrapping procedure. This is done by estimating the impact for a random selection of observations. For this study, the process was iterated 5000 times to generate statistically significant results.