Background

Research Questions

  • How does claims response times vary by socioeconomic characteristics?
  • How does claims payouts vary by socioeconomic characteristics?
  • How do claims without payments differ across neighborhoods?

Data

Claims data comes from FEMA (will update to OpenFEMA claims dataset v2), and goes from 1978 - 2012. Geography of claims data is 2010 Census Tract boundaries. Census data comes from Longitudinal Tract Database (Brown University), which provides interpolated data between historical census results and 2010 census tract boundaries; estimates are based on the documented population and household counts.

Current filters:

  • Loss year: 1990 - 2012
  • Occupancy type: Single-family homes
  • Claim Status: Closed

Total claims records after filtering: 1139833

Model Structure

Base Model:

\(Y\) is the outcome variable, depending on research questions:

  • \(days\) for claims to close processing time
  • \(clmratio\) is the ratio between the claims payment (accounting for deductible) / assessed damage
  • \(CWOP\) for claims closed without payment

\(X\) is independent variable of interest (i.e. measures of income, wealth, race). The rest of the base model variables are claims-level characteristics that account for flood event severity and damage: \(damage\) is the ratio between assessed damage / property value (omitted when either component value is included); \(waterdepth\) is the recorded depth of floodwater; \(duration\) is the length of the flooding event; \(cat\) is the indicator that the claim is associated with a catastrophe. The final covariate is an indicator if the claim was reopened during processing (\(reopen\)).

Model includes State Fixed Effects (\(i\)) + Year Fixed Effects (\(t\)).

\[log(Y) = \beta_{0} + \beta_{1}X + \beta_{2}(damage) + \beta_{3}(waterdepth) + \beta_{4}(duration)_{it} + \beta_{5}(cat) + \beta_{6}(reopen) + StateFE_{t} + YearFE_{i} u_{it}\]

Full Model:

Base Model, plus two additional sets of covariates:

  • \(\theta\) represents a vector of variables that indicate several building-level characteristics from the claims data: whether the building was floodproofed, located in the SFHA, elevated, and age of building.
  • \(\gamma\) represents a vector of other census social variables, like tract poulation.

\[log(Y) = \beta_{0} + \beta_{1}X + \beta_{2}(damage) + \beta_{3}(waterdepth) + \beta_{4}(duration)_{it} + \beta_{4}(cat) + \beta_{6}(reopen) + \theta_{it} + \gamma_{it} + StateFE_{t} + YearFE_{i} u_{it}\]

All independent variables are standardized for easier comparison.

Standard errors are clustered at the state level (see Appendix for base model result comparisons with several SE clustering approaches. ). Some references for SE cluster identification:

Correlation Check of Variables

A check of the correlation across covariates validates our approach to model structure: there is high collinearity between census variables of income, wealth, and race, such that separate models and interaction effects will be necessary. There is low collinearity between our claims variables. Monthly claim volume is correlated with damage, and catastrophe indicator, such that we should consider omitting one or the other. Notably, there is little correlation between the claim-level property value, and tract-level wealth and income variables - including median home value.

Claims Processing Time

Data Distribution
  • Data removed:
    • Negative claim time data - data errors
    • Top 5% of claim times - extreme outliers; possible data errors (5% of data)
    • Records with undefined damage
    • Claims closed without payment

Percent Total claims records after filtering: 71%

Income & Wealth Effect

Using several measures of income (median HH income, poverty, and income buckets), we can see a small but statistically positive relationship between income and claims processing time, meaning that claims from higher-income tracts tend to take longer to resolve. Income Model 1 shows us that with one standard deviation increase in census tract income, there is about a 4% increase in claim processing time. That is consistent with Model 2 results, which show the effect of income on claims time based on income quantiles (compared to reference group of $ 100 - 150,000 med income). The relationship between the amount of households in poverty and claims processing is negative, suggesting a similar relationship.

Because there may be a difference between the impact of income and wealth, we look separately at factors that indicate household wealth. While we do not have perfect census measures of wealth, property ownership, educational attainment, and property value (as assessed by insurer at the property level, and in Census at tract level) may be a sufficient proxy for wealth and class separate from income (see Chetty et al 2019 as examples indicators of wealth within ACS data). Here we see a negligible effect of homeownership and property value on claims processing time. Educational attainment (measured by the percent of population with a college degree) has a statistically significant positive relationship with claims processing time.

Race Effects

There is high correlation between median income and percent owners, population by race, and education levels of tract data, so they are not used as covariates together in models. Instead, we estimate separate models looking at the effect of race, interacted with income categories, to understand how the claims processing time differs for tracts with different demographics. Here, we see that overall, tracts with higher percentage of white population is associated with longer claims processing time, and tracts with higher percentage Black population are associated with shorter claims processing time; there is no statistically significant effect of the percentage of hispanic population.

However, that effect varies by income. In tracts at the lowest income brackets, tracts with a higher percentage of Black population are actually associated with longer claims process times. Compared to other low-income census tracts, 1 standard deviation increase in the percent of black population in tract is associated with > 10% increase in estimated claims processing time.

Control Variables

Claims Payment

Data Distribution
  • Data removed:
    • Records with undefined damage
    • Claims closed without payment

Percent Total claims records after filtering: 74%

Claims payment measured as the percent of recorded damage actually paid by insurer: the ratio of total payment (including deductible) / assessed damage.

Income & Wealth Effects

We see little statistically significant relationship between several measures of income and claims payment (relative to damage). Notably, tracts with higher college educated populations are associated with higher claims payment.

Race Effects

Generally, the racial demographics of the census tract are not associated with claims amount. The exception here are tracts with higher Black population: those tracts experienced statistically significant lower claims payment ratios. That effect does seem to vary by income bracket, as tracts with high Black population have relatively higher claims amount ratios compared to that baseline mean.

Control Variables

Claims Closed without Payment

Many claims in the insurance claims record (~ 23%) are closed without payment. Here, we consider any claims that are either labeled as “CWOP” in claims status, or labeled as “closed” but resulting in $0 claim payment, and the assessed value of damage exceeds the deductible.

Income & Wealth Effect

There appears to be no effect of income on the likelihood of a claim being closed without payment. Indicators of wealth show a similar story: homeownership and education are not strongly correlated, but college education rates in a census tract is associated with a higher likelihood of a claim being closed without payment.

Race Effects

There does not appear to be any statistically significant relationship between race and income of a tract, and the likelihood of a claim being closed without payment.

Controls

## Fixed Effects
### State and Year on Median Income
# Further Analysis
* Incident-specific dynamics (i.e. Hurricane) * County fixed effects? * Other dependent variables to test: + Usage or denials of ICC

Appendix

Model Selection

Claims Time Model

Outcome variable is time between claim submitted and claim closed, measured in days. Because it is count data (integer, non-negative, with long tails) it would typically be a Poisson distribution. However, the assumption for Poisson distribution that the mean = variance is clearly not true for this data (see Table 1 below), suggesting overdispersion of the data.

Table 1: Distribution of Claims Processing Time Dataset (filtered)
mean median min max variance
62 49 0 296 2865

A quick test on the basic model, Poisson, shows high overdispersion (well above the threshold of 1).

## 
##  Overdispersion test
## 
## data:  tm_p
## z = 402.63, p-value < 2.2e-16
## alternative hypothesis: true dispersion is greater than 1
## sample estimates:
## dispersion 
##    46.4318

Applying a negative binomial regression model (which does not assume mean and variance are equal) is a common model for such real-world count data. Comparison of model fit of basic model structure through AIC (lower relative value suggests better fit) indicates that Negative Binomial model is best structure. Note: models tested is basic model structure without Fixed Effects; fixed effects will not impact AIC.

OLS Poisson Negative Binomial
asinh(days) days days
Constant 4 . 206*** 4 . 125*** 4 . 121***
(0 . 002) (0 . 000) (0 . 001)
Median Income (thousands) 0 . 109*** 0 . 050*** 0 . 059***
(0 . 002) (0 . 000) (0 . 001)
Depth of Water 0 . 154*** 0 . 042*** 0 . 041***
(0 . 002) (0 . 000) (0 . 001)
Damage as Percent of Prop Value 0 . 031*** 0 . 018*** 0 . 071***
(0 . 002) (0 . 000) (0 . 001)
Monthly Claims in Tract 0 . 142*** 0 . 099*** 0 . 101***
(0 . 002) (0 . 000) (0 . 001)
AIC 2865728 . 295 36774751 . 064 7964668 . 071
p 0 . 000 0 . 000 0 . 000
N 776096 776096 776096

Significance: *** = p < 0.001; ** = p < 0.01; * = p < 0.05

Standard Error Clustering

Model Results: Summary Tables

Claims Processing Time

Income Effects on Claims Processing

Outcome: Claims Processing Time
IM 1 IM 1 (full) IM 2 IM 2 (full) IM 3 IM 3 (full)
Med Income ($thous) 0.036*** 0.039***
Income: <35 -0.112*** -0.124***
Income: 35-50 -0.095*** -0.102***
Income: 50-75 -0.048** -0.055***
Income: 75-100 -0.025 -0.027+
Income: >150 0.071* 0.074**
Pct Poverty -0.024*** -0.026***
Flood depth 0.056*** 0.056*** 0.056*** 0.056*** 0.056*** 0.056***
Damage 0.043 0.044 0.043 0.044 0.042 0.042
Flood duration 0.026*** 0.026*** 0.026*** 0.026*** 0.026*** 0.026***
Reopened 0.740*** 0.742*** 0.740*** 0.742*** 0.741*** 0.743***
Catastrophe 0.093*** 0.089*** 0.093*** 0.088*** 0.094*** 0.089***
SFHA zone 0.023 0.022 0.021
Elevated 0.058** 0.058** 0.057**
Floodproofed -0.195*** -0.192** -0.195***
Population -0.021*** -0.022*** -0.020***
R2 0.011 0.011 0.011 0.011 0.011 0.011
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001

Wealth Effects on Claims Processing

Outcome: Claims Processing Time
WM 1 WM 1 (full) WM 2 WM 2 (full) WM 3 WM 3 (full)
Property value 0.001 0.001
Homeowners 0.008** 0.007**
College Educated 0.039*** 0.040***
Flood depth 0.058*** 0.058*** 0.058*** 0.058*** 0.058*** 0.059***
Flood duration 0.026*** 0.026*** 0.026*** 0.026*** 0.027*** 0.026***
Reopened 0.746*** 0.748*** 0.746*** 0.748*** 0.745*** 0.747***
Catastrophe 0.111*** 0.107*** 0.111*** 0.107*** 0.106*** 0.102***
SFHA zone 0.025 0.025 0.028+
Elevated 0.051** 0.051** 0.053**
Floodproofed -0.217*** -0.214*** -0.240***
Population -0.019*** -0.020*** -0.017***
R2 0.011 0.011 0.011 0.011 0.011 0.011
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001

Race & Income Effects on Claims Processing

Outcome: Claims Processing Time
R&IM 1 R&IM 1 (full) R&IM 2 R&IM 2 (full) R&IM 3 R&IM 3 (full)
Percent white 0.028*** 0.052*
Percent black -0.024*** -0.122***
Percent hispanic -0.014*** 0.014
Race*Income: <35 -0.044+ 0.116** -0.016
Race*Income: 35-50 -0.032 0.098** -0.010
Race*Income: 50-75 -0.016 0.094** -0.037
Race*Income: 75-100 0.005 0.052+ -0.048
Race*Income: >150 0.046 -0.138** 0.062+
Flood depth 0.055*** 0.056*** 0.055*** 0.056*** 0.056*** 0.057***
Damage 0.041 0.041 0.042 0.043 0.040 0.040
Flood duration 0.025*** 0.025*** 0.025*** 0.025*** 0.025*** 0.025***
Reopened 0.741*** 0.743*** 0.741*** 0.742*** 0.741*** 0.743***
Catastrophe 0.099*** 0.095*** 0.097*** 0.092*** 0.099*** 0.095***
SFHA zone 0.024 0.023 0.022
Elevated 0.048* 0.052* 0.052*
Floodproofed -0.215*** -0.201*** -0.207***
Population -0.016*** -0.018*** -0.018***
R2 0.011 0.011 0.011 0.011 0.011 0.011
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001

Claims Payment Amount

Income Effects on Claims Amount

Outcome: Claims+Deductible Payment Ratio (payment / assessed damage)
IM 1 IM 1 (full) IM 2 IM 2 (full) IM 3 IM 3 (full)
Med Income ($thous) 0.246 0.240
Income: <35 -1.108 -1.065
Income: 35-50 -1.327* -1.274+
Income: 50-75 -1.020+ -1.005+
Income: 75-100 -1.160+ -1.148+
Income: >150 -1.732 -1.694
Pct Poverty -0.147 -0.131
Flood depth -0.282*** -0.291*** -0.284*** -0.292*** -0.281*** -0.289***
Flood duration -0.055+ -0.063+ -0.056* -0.064* -0.054+ -0.062*
Reopened -0.128 -0.144 -0.124 -0.135 -0.118 -0.133
Catastrophe 0.198 0.169 0.194 0.166 0.222 0.197
SFHA zone 0.597* 0.586* 0.588*
Elevated -0.796*** -0.798*** -0.817***
Floodproofed -2.484*** -2.339*** -2.444***
Population -0.106 -0.092 -0.101
R2 0.087 0.096 0.093 0.102 0.083 0.092
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001

Wealth Effects on Claims Amount

Outcome: Claims Payment Ratio (payment / assessed damage)
WM 1 WM 1 (full) WM 2 WM 2 (full) WM 3 WM 3 (full)
Property value -0.045** -0.047**
Homeowners -0.062 -0.070
College Educated 0.372** 0.375**
Flood depth -0.282*** -0.290*** -0.281*** -0.289*** -0.286*** -0.294***
Flood duration -0.056+ -0.063* -0.055+ -0.061+ -0.050+ -0.055+
Reopened -0.113 -0.126 -0.111 -0.122 -0.155 -0.166
Catastrophe 0.244+ 0.217 0.240+ 0.214 0.183 0.153
SFHA zone 0.590* 0.594* 0.615*
Elevated -0.837*** -0.836*** -0.808***
Floodproofed -2.421*** -2.416*** -2.549***
Population -0.103 -0.102 -0.067
R2 0.082 0.091 0.082 0.091 0.095 0.104
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001

Race Effects (w/ Income Interaction) on Claims Amount

Outcome: Claims Payment Ratio (payment / assessed damage)
R&IM 1 R&IM 1 (full) R&IM 2 R&IM 2 (full) R&IM 3 R&IM 3 (full)
Percent white -0.059 1.396
Percent black 0.150+ -2.543*
Percent hispanic -0.214* 0.327
Race*Income: <35 -1.735 2.893** -0.650
Race*Income: 35-50 -1.711 2.898** -0.509+
Race*Income: 50-75 -0.711 1.685 -0.804*
Race*Income: 75-100 -1.203 2.069* -0.629***
Race*Income: >150 -0.619 3.209+ -1.237***
Flood depth -0.281*** -0.289*** -0.282*** -0.291*** -0.281*** -0.293***
Flood duration -0.055+ -0.060* -0.055+ -0.060+ -0.056* -0.064*
Reopened -0.110 -0.131 -0.109 -0.141 -0.115 -0.131
Catastrophe 0.235+ 0.213 0.237 0.150 0.280+ 0.242
SFHA zone 0.612* 0.588* 0.616*
Elevated -0.875*** -0.824*** -0.883***
Floodproofed -2.525*** -2.481*** -2.526***
Population -0.074 -0.077 -0.071
R2 0.082 0.108 0.084 0.116 0.084 0.098
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001

Claims Closed without Payment

Income Effects on Claims Closed without Payment

Outcome: Closed Without Payment
IM 1 IM 1 (full) IM 2 IM 2 (full) IM 3 IM 3 (full)
Med Income ($thous) 0.001 0.000
Income: <35 -0.005 -0.002
Income: 35-50 0.003 0.004
Income: 50-75 0.004 0.003
Income: 75-100 0.004 0.003
Income: >150 0.002 0.004
Pct Poverty -0.001 0.000
Flood depth 0.004 0.004+ 0.004 0.004+ 0.004 0.004+
Damage -0.270*** -0.270*** -0.270*** -0.270*** -0.270*** -0.270***
Flood duration -0.002*** -0.002*** -0.002*** -0.002*** -0.002*** -0.002***
Reopened -0.014* -0.013* -0.014* -0.013* -0.014* -0.013*
Catastrophe -0.028*** -0.030*** -0.029*** -0.030*** -0.029*** -0.030***
SFHA zone 0.013 0.013 0.013
Elevated 0.000 0.000 0.000
Floodproofed -0.082*** -0.082*** -0.082***
Population -0.001 -0.001 -0.001
R2 0.175 0.177 0.176 0.177 0.175 0.177
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001

Wealth Effects on Claims Closed without Payment

Outcome: Closed without Payment
WM 1 WM 1 (full) WM 2 WM 2 (full) WM 3 WM 3 (full)
Property value -0.011*** -0.011***
Homeowners 0.003 -0.001
College Educated 0.018*** 0.018***
Flood depth -0.004 -0.003 -0.004 -0.003 -0.004 -0.003
Flood duration -0.006*** -0.004*** -0.006*** -0.004*** -0.005*** -0.004***
Reopened -0.139*** -0.135*** -0.138*** -0.134*** -0.139*** -0.135***
Catastrophe -0.109*** -0.105*** -0.109*** -0.106*** -0.111*** -0.107***
SFHA zone -0.043** -0.043** -0.041**
Elevated -0.017+ -0.017+ -0.016+
Floodproofed -0.078 -0.078 -0.087+
Population 0.002 0.002 0.003
R2 0.049 0.056 0.049 0.055 0.050 0.057
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001

Race Effects (w/ Income Interaction) on Claims Closed without Payment

Outcome: Closed without Payment
R&IM 1 R&IM 1 (full) R&IM 2 R&IM 2 (full) R&IM 3 R&IM 3 (full)
Percent white -0.013 -0.013
Percent black 0.017 0.016
Percent hispanic 0.005 0.005
Race*Income: <35 0.011 0.009 -0.016 -0.014 -0.002 -0.002
Race*Income: 35-50 0.009 0.008 -0.013 -0.012 -0.003 -0.003
Race*Income: 50-75 0.007 0.007 -0.009 -0.009 -0.004 -0.005
Race*Income: 75-100 0.010 0.010 -0.007 -0.006 -0.007 -0.008
Race*Income: >150 0.009 0.012 -0.008 -0.012 -0.011 -0.013+
Flood depth 0.004 0.005+ 0.004 0.004+ 0.004 0.004+
Damage -0.270*** -0.270*** -0.271*** -0.271*** -0.270*** -0.270***
Flood duration -0.002*** -0.002*** -0.002*** -0.002*** -0.002*** -0.002***
Reopened -0.014* -0.013* -0.014* -0.013* -0.014* -0.013*
Catastrophe -0.028*** -0.030*** -0.028*** -0.030*** -0.028*** -0.030***
SFHA zone 0.013 0.013 0.013
Elevated 0.001 0.000 0.000
Floodproofed -0.081*** -0.081*** -0.083***
Population -0.001 -0.001 -0.001
R2 0.176 0.177 0.176 0.177 0.175 0.177
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001