ERRATA To: Recipients of MG-388-RC, Estimating Terrorism Risk, 25 From: RAND Corporation Publications Department Date: December 25 Re: Corrected pages (pp. 23 24, Table 4.1,, Density, Density- Weighted, and Grant Allocations for Urban Areas Receiving UASI Funding in Fiscal Year 24); Corrected page (p. 34, Figure 4.1, City Shares of Total Risk Estimated Using Four Indicators of Risk, Sorted by Aggregated Estimate, with a Vertical Line Indicating Equal Risk Across Cities); Corrected page (p. 43, Figure 5.2, Mean Risk Underestimation as True Risk Deviates from Estimates: Model 1a); Corrected page (p. 45, Figure 5.3, Maximum Risk Underestimation as True Risk Deviates from Estimates: Model 1a); Corrected page (p. 46, Figure 5.4, Mean Risk Underestimation as True Risk Deviates from Estimates: Model 2; and Figure 5.5, Maximum Risk Underestimation as True Risk Deviates from Estimates: Model 2); Corrected pages (pp. 57 6, Figure A.1, Mean Risk Underestimation as True Risk Deviates from Estimates: Model 1b; Figure A.2, Mean Risk Underestimation as True Risk Deviates from Estimates: Model 1c; Figure A.3, Mean Risk Underestimation as True Risk Deviates from Estimates: Model 1d; Figure A.4, Mean Risk Underestimation as True Risk Deviates from Estimates: Model 1e; Figure A.5, Mean Risk Underestimation as True Risk Deviates from Estimates: Model 1f; Figure A.6, Mean Risk Underestimation as True Risk Deviates from Estimates: Model 1g); Corrected pages (pp. 61 62, Table A.1, Shares of 23 DHS UASI and City Risk Shares Estimated Using, Density-Weighted, and Aggregated Estimator Methods) An error resulted in erroneous data in some tables and figures. The following adjustments have been made for precision. All conclusions and calculations that they were based upon remained unchanged. All figures in the Density (per Square Mile) and Density-Weighted columns in Table 4.1 have changed. The figures for St. Louis, MO-IL; San Antonio; San Diego; San Francisco; San Jose; and Seattle-Bellevue-Everett in the FY24 UASI Grant Allocation column in Table 4.1 have changed. The placement of symbols for and Density-Weighted have changed in Figure 4.1 for the following cities: San Francisco ( and Density-Weighted ); Seattle- Bellevue-Everett ( and Density-Weighted ); San Diego (Density-Weighted ); St. Louis, MO-IL (Density-Weighted ); San Antonio (Density-Weighted ); and San Jose (Density-Weighted ).
Two Approaches to Estimating Terrorism Risk in Urban Areas 23 Table 4.1, Density, Density-Weighted, and Grant Allocations for Urban Areas Receiving UASI Funding in Fiscal Year 24 Urban Areas a Density a (per Square Mile) Density- Weighted b FY24 UASI Grant Allocation c ($ million) Albany-Schenectady-Troy 875,583 272 237,926,588 7 Atlanta 4,112,198 672 2,761,386,37 11 Baltimore 2,552,994 979 2,498,144,264 16 Baton Rouge 62,894 38 229,154,762 7 Boston, MA-NH 3,46,829 1,685 5,74,79,241 19 Buffalo-Niagara Falls 1,17,111 747 873,657,856 1 Charlotte-Gastonia- 1,499,293 444 665,682,378 7 Rock Hill, NC-SC Chicago 8,272,768 1,634 13,519,96,414 34 Cincinnati, OH-KY-IN 1,646,395 493 811,141,96 13 Cleveland-Lorain-Elyria 2,25,871 832 1,871,77,337 1 Columbus, OH 1,54,157 49 755,141,752 9 Dallas 3,519,176 569 2,2,93,12 12 Denver 2,19,282 561 1,183,64,989 9 Detroit 4,441,551 1,14 5,62,484,593 14 Fresno 922,516 114 15,84,482 7 Houston 4,177,646 76 2,948,39,4 2 Indianapolis 1,67,486 456 733,47,541 1 Jersey City 68,975 13,44 7,943,237,618 17 Kansas City, MO-KS 1,776,62 329 583,476,273 13 Las Vegas, NV-AZ 1,563,282 4 62,76,79 11 Los Angeles-Long Beach d 9,519,338 2,344 22,314,867,674 4 Louisville, KY-IN 1,25,598 495 57,651,616 9 Memphis, TN-AR-MS 1,135,614 378 428,953,952 1 Miami, FL 2,253,362 1,158 2,69,185,2 19 Milwaukee-Waukesha, WI 1,5,741 1,28 1,542,728,464 1 Minneapolis-St. Paul, 2,968,86 49 1,453,687,745 2 MN-WI e New Haven-Meriden, CT 542,149 1,261 683,67,545 1 New Orleans 1,337,726 394 526,45,217 7
34 Estimating Terrorism Risk Figure 4.1 City Shares of Total Risk Estimated Using Four Indicators of Risk, Sorted by Aggregated Estimate, with a Vertical Line Indicating Equal Risk Across Cities New York NY Chicago IL Washington DC-MD-VA-WV San Francisco CA Los Angeles-Long Beach CA Boston MA-NH Philadelphia PA-NJ Houston TX Newark NJ Seattle-Bellevue-Everett WA Orange County CA Jersey City Detroit MI Dallas TX Orlando FL Atlanta GA Oakland CA San Diego CA Phoenix, Mesa AZ St. Louis MO-IL Cincinnati OH-KY-IN Baltimore MD Indianapolis IN New Haven-Meriden CT Fresno CA Columbus OH New Orleans LA Sacramento CA Buffalo-Niagara Falls NY Denver CO Albany-Schenectady-Troy NY Memphis TN-AR-MS Cleveland-Lorain-Elyria OH Las Vegas NV-AZ Richmond-Petersburg VA San Antonio TX Baton Rouge LA Charlotte -Gastonia-Rock Hill NC-SC Milwaukee-Waukesha WI Tampa-St. Petersburg-Clearwater FL Portland-Vancouver OR-WA Louisville KY-IN Miami FL San Jose CA Kansas City MO-KS Minneapolis-St Paul MN-WI Pittsburgh PA Urban Areas Aggregated Estimate Density Weighted FY24 Allocation Equal Allocation.1.1.1.1.1.1 City Risk-Share (%).1.1 1 RAND MG388-4.1
Evaluating the Performance of Different Estimates of Terrorism Risk 43 loss across terrorism risk outlooks. As such, these models use all or a superset of the RMS model estimates of risk as the basis for simulating true risk (three types of consequences in each of three terrorism risk outlooks). Since the aggregated estimator was developed to minimize using the RMS model, it might be expected to outperform the other estimators. Nevertheless, we include measurements of the performance of the aggregated estimator in the first series of models, because it provides information on how well an optimized risk-share estimator could perform, which aids in the interpretation of the performance of the other risk-share estimators. Figure 5.2 presents the mean performance for the three risk-share estimators and the random estimator when true risk is assumed to vary around all nine RMS estimates of city terrorism risk (Model 1a). As expected, the random estimator is associated with the greatest and the aggregated estimator is associated with the lowest. Figure 5.2 Mean Risk Underestimation as True Risk Deviates from Estimates: Model 1a 4 3 2 1 RAND MG388-5.2 2 4 Factor (k) by which true risk may differ from RMS estimates of risk combining all threat outlooks and all consequences 6 8 1
Evaluating the Performance of Different Estimates of Terrorism Risk 45 Figure 5.3 Maximum Risk Underestimation as True Risk Deviates from Estimates: Model 1a Sum of squared 8 6 4 2 RAND MG388-5.3 2 4 Factor (k) by which true risk may differ from RMS estimates of risk combining all threat outlooks and all consequences 6 8 1 In Model 2, simulated true risk is based on density-weighted population, rather than RMS estimates of risk. As seen in Figure 5.4, this change has the effect of making the density-weighted population estimator the optimal choice, at least when true risk is assumed to differ from density-weighted populations by no more than a factor of five. Interestingly, however, the aggregated estimator exhibits a comparable mean to the density-weighted population estimator for higher levels of k. As in the first series of models, the population estimator produces s closer to the random estimator than to either the density-weighted population estimator or the aggregated estimator. Figure 5.5 presents the worst-case performances for Model 2. Here the aggregated estimator clearly exhibits higher underestimation error than the density-weighted population estimator, but otherwise the relative performance of the estimators is similar to what has been observed in all earlier models.
46 Estimating Terrorism Risk Figure 5.4 Mean Risk Underestimation as True Risk Deviates from Estimates: Model 2.5.4.3.2.1 RAND MG388-5.4 2 4 Factor (k) by which true risk may differ from risk estimated using density-weighted population 6 8 1 Figure 5.5 Maximum Risk Underestimation as True Risk Deviates from Estimates: Model 2 1. Sum of squared.8.6.4.2 RAND MG388-5.5 2 4 Factor (k) by which true risk may differ from risk estimated using density-weighted population 6 8 1
APPENDIX Supporting Figures and Table Figure A.1 Mean Risk Underestimation as True Risk Deviates from Estimates: Model 1b 1.5 1..5 RAND MG388-A.1 2 4 Factor (k) by which true risk may differ from RMS estimates of risk combining the RMS Standard threat outlook and all consequences 6 8 1 57
58 Estimating Terrorism Risk Figure A.2 Mean Risk Underestimation as True Risk Deviates from Estimates: Model 1c 1.5 1..5 RAND MG388-A.2 2 4 Factor (k) by which true risk may differ from RMS estimates of risk combining the RMS Enhanced threat outlook and all consequences 6 8 1 Figure A.3 Mean Risk Underestimation as True Risk Deviates from Estimates: Model 1d 1.5 1..5 RAND MG388-A.3 2 4 Factor (k) by which true risk may differ from RMS estimates of risk combining the RMS Reduced threat outlook and all consequences 6 8 1
Supporting Figures and Table 59 Figure A.4 Mean Risk Underestimation as True Risk Deviates from Estimates: Model 1e 1.5 1..5 RAND MG388-A.4 2 4 Factor (k) by which true risk may differ from RMS estimates of risk combining all threat outlooks and fatalities as consequences 6 8 1 Figure A.5 Mean Risk Underestimation as True Risk Deviates from Estimates: Model 1f 1.5 1..5 RAND MG388-A.5 2 4 Factor (k) by which true risk may differ from RMS estimates of risk combining all threat outlooks and injuries as consequences 6 8 1
6 Estimating Terrorism Risk Figure A.6 Mean Risk Underestimation as True Risk Deviates from Estimates: Model 1g 1.5 1..5 RAND MG388-A.6 2 4 Factor (k) by which true risk may differ from RMS estimates of risk combining all threat outlooks and property losses as consequences 6 8 1
Supporting Figures and Table 61 Table A.1 Shares of 23 DHS UASI and City Risk Shares Estimated Using, Density-Weighted, and Aggregated Estimator Methods Risk-Share Estimator Metro Area DHS Allocation Dens.-Wt. Pop. Aggregated Albany-Schenectady-Troy, NY.12.71.12 1.8E-6 Atlanta, GA.159.335.138 6.55E-5 Baltimore, MD.236.28.124 1.69E-6 Baton Rouge, LA.17.49.11 6.15E-7 Boston, MA-NH.283.278.286 2.22E-2 Buffalo-Niagara Falls.15.95.44 1.15E-6 Charlotte-Gastonia-Rock.11.122.33 5.71E-7 Hill, NC-SC Chicago, IL.56.675.673 1.1E-1 Cincinnati, OH-KY-IN.189.134.4 1.82E-6 Cleveland-Lorain-Elyria,.155.184.93 9.44E-7 OH Columbus, OH.129.126.38 1.25E-6 Dallas, TX.181.287.1 3.12E-4 Denver, CO.128.172.59 1.1E-6 Detroit, MI.24.362.252 1.4E-3 Fresno, CA.15.75.5 1.33E-6 Houston, TX.296.341.147 1.52E-2 Indianapolis, IN.151.131.37 1.52E-6 Jersey City, NJ.254.5.396 1.23E-3 Kansas City, MO-KS.197.145.29 2.53E-7 Las Vegas, NV-AZ.156.128.3 8.95E-7 Los Angeles-Long Beach.599.777.1111 3.73E-2 Louisville, KY-IN.133.84.25 4.52E-7 Memphis, TN-AR-MS.149.93.21 1.8E-6 Miami, FL.284.184.13 3.95E-7 Milwaukee-Waukesha, WI.151.122.77 5.23E-7
62 Estimating Terrorism Risk Table A.1 continued Risk-Share Estimator Metro Area DHS Allocation Dens.-Wt. Pop. Aggregated Minneapolis-St. Paul, MN-WI.298.242.72 8.98E-8 New Haven-Meriden, CT.143.44.34 1.39E-6 New Orleans, LA.16.19.26 1.19E-6 New York, NY.696.76.3785 6.72E-1 Newark, NJ.223.166.13 6.36E-3 Oakland, CA.116.195.196 7.79E-6 Orange County, CA.472.232.511 2.66E-3 Orlando, FL.13.134.39 3.6E-4 Philadelphia, PA-NJ.342.416.336 1.53E-2 Phoenix-Mesa, AZ.181.265.36 2.27E-6 Pittsburgh, PA.178.192.6 7.87E-8 Portland-Vancouver, OR-.121.156.36 4.55E-7 WA Richmond-Petersburg,.97.81.17 8.61E-7 VA Sacramento, CA.119.133.32 1.18E-6 St. Louis, MO-IL.16.212.53 1.84E-6 San Antonio, TX.94.13.38 6.77E-7 San Diego, CA.155.23.94 2.52E-6 San Francisco, CA.392.141.147 4.78E-2 San Jose, CA.148.137.19 2.67E-7 Seattle-Bellevue-Everett.245.197.66 5.93E-3 Tampa-St. Petersburg-.137.195.112 4.62E-7 Clearwater, FL Washington, DC-MD-VA- WV.434.42.185 6.23E-2