Biggest changeFor example, the 2013 column indicates that at December 31, 2023 payments equal to $282.0 million of the currently re-estimated ultimate liability for net losses and loss expenses of $289.3 million had been made. -19- Index Year Ended December 31, (in thousands) 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 Net liability at end of year for unpaid losses and loss expenses $ 265,605 $ 292,301 $ 322,054 $ 347,518 $ 383,401 $ 475,398 $ 506,906 $ 557,189 $ 626,359 $ 669,862 $ 689,143 Net liability re-estimated as of: One year later 280,074 299,501 325,043 354,139 419,032 462,466 493,961 525,981 581,538 653,209 Two years later 281,782 299,919 329,115 375,741 413,535 450,862 479,927 498,724 564,326 Three years later 281,666 304,855 338,118 376,060 404,902 440,168 463,441 490,177 Four years later 284,429 307,840 339,228 372,230 398,560 432,027 459,835 Five years later 285,130 310,354 338,020 370,960 396,695 431,115 Six years later 287,439 310,380 338,200 372,346 396,748 Seven years later 287,063 311,594 339,625 371,859 Eight years later 288,298 313,354 340,191 Nine years later 289,066 313,539 Ten years later 289,278 Cumulative deficiency (excess) 23,673 21,238 18,137 24,341 13,347 (44,283 ) (47,071 ) (67,012 ) (62,033 ) (16,653 ) Cumulative amount of liability paid through: One year later $ 131,766 $ 131,779 $ 149,746 $ 163,005 $ 175,883 $ 195,956 $ 172,497 $ 182,223 $ 218,304 $ 260,739 Two years later 194,169 206,637 228,506 250,678 276,331 275,993 276,069 297,860 346,107 Three years later 233,371 251,654 274,235 306,338 317,447 335,310 343,912 374,043 Four years later 255,451 274,248 300,715 324,628 342,583 371,231 393,068 Five years later 265,841 287,178 309,630 337,946 362,061 394,251 Six years later 272,431 292,327 315,105 349,496 372,584 Seven years later 275,357 295,106 321,777 355,809 Eight years later 277,315 300,306 326,617 Nine years later 279,928 303,708 Ten years later 282,030 Year Ended December 31, (in thousands) 2015 2016 2017 2018 2019 2020 2021 2022 2023 Gross liability at end of year $ 578,205 $ 606,665 $ 676,672 $ 814,665 $ 869,674 $ 962,007 $ 1,077,620 $ 1,121,046 $ 1,126,157 Reinsurance recoverable 256,151 259,147 293,271 339,266 362,768 404,818 451,261 451,184 437,014 Net liability at end of year 322,054 347,518 383,401 475,398 506,906 557,189 626,359 669,862 689,143 Gross re-estimated liability 593,565 626,950 682,354 758,861 797,903 883,492 950,867 1,047,996 Re-estimated recoverable 253,374 255,091 285,606 327,746 338,068 393,315 386,541 394,787 Net re-estimated liability 340,191 371,859 396,748 431,115 459,835 490,177 564,326 653,209 Gross cumulative deficiency (excess) 15,360 20,285 5,682 (55,804 ) (71,771 ) (78,515 ) (126,753 ) (73,050 ) -20- Index Third-Party Reinsurance Our insurance subsidiaries and Donegal Mutual purchase certain third-party reinsurance on a combined basis.
Biggest changeFor example, the 2014 column indicates that at December 31, 2024 payments equal to $306.0 million of the currently re-estimated ultimate liability for net losses and loss expenses of $314.5 million had been made. -18- Index Year Ended December 31, (in thousands) 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 Net liability at end of year for unpaid losses and loss expenses $ 292,301 $ 322,054 $ 347,518 $ 383,401 $ 475,398 $ 506,906 $ 557,189 $ 626,359 $ 669,862 $ 689,143 $ 704,364 Net liability re-estimated as of: One year later 299,501 325,043 354,139 419,032 462,466 493,961 525,981 581,538 653,209 674,171 Two years later 299,919 329,115 375,741 413,535 450,862 479,927 498,724 564,326 638,428 Three years later 304,855 338,118 376,060 404,902 440,168 463,441 490,177 550,972 Four years later 307,840 339,228 372,230 398,560 432,027 459,835 480,865 Five years later 310,354 338,020 370,960 396,695 431,115 455,494 Six years later 310,380 338,200 372,346 396,748 429,865 Seven years later 311,594 339,625 371,859 396,167 Eight years later 313,354 340,191 372,477 Nine years later 313,539 340,800 Ten years later 314,490 Cumulative deficiency (excess) 22,189 18,746 24,959 12,766 (45,533 ) (51,412 ) (76,324 ) (75,387 ) (31,434 ) (14,972 ) Cumulative amount of liability paid through: One year later $ 131,779 $ 149,746 $ 163,005 $ 175,883 $ 195,956 $ 172,497 $ 182,223 $ 218,304 $ 260,739 $ 269,701 Two years later 206,637 228,506 250,678 276,331 275,993 276,069 297,860 346,107 405,216 Three years later 251,654 274,235 306,338 317,447 335,310 343,912 374,043 426,648 Four years later 274,248 300,715 324,628 342,583 371,231 393,068 418,283 Five years later 287,178 309,630 337,946 362,061 394,251 414,690 Six years later 292,327 315,105 349,496 372,584 404,251 Seven years later 295,106 321,777 355,809 378,937 Eight years later 300,306 326,617 359,527 Nine years later 303,708 329,651 Ten years later 306,019 Year Ended December 31, (in thousands) 2016 2017 2018 2019 2020 2021 2022 2023 2024 Gross liability at end of year $ 606,665 $ 676,672 $ 814,665 $ 869,674 $ 962,007 $ 1,077,620 $ 1,121,046 $ 1,126,157 $ 1,120,985 Reinsurance recoverable 259,147 293,271 339,266 362,768 404,818 451,261 451,184 437,014 416,621 Net liability at end of year 347,518 383,401 475,398 506,906 557,189 626,359 669,862 689,143 704,364 Gross re-estimated liability 621,200 674,826 751,479 787,575 869,571 938,746 1,011,779 1,072,359 Re-estimated recoverable 248,723 278,659 321,614 332,081 388,706 387,774 373,351 398,188 Net re-estimated liability 372,477 396,167 429,865 455,494 480,865 550,972 638,428 674,171 Gross cumulative deficiency (excess) 14,535 (1,846 ) (63,186 ) (82,099 ) (92,436 ) (138,874 ) (109,267 ) (53,798 ) -19- Index Third-Party Reinsurance Our insurance subsidiaries and Donegal Mutual purchase certain third-party reinsurance on a combined basis.
At December 31, 2023, the Donegal Insurance Group actively wrote business in 23 states (Arizona, Colorado, Delaware, Georgia, Illinois, Indiana, Iowa, Maine, Maryland, Michigan, Nebraska, New Hampshire, New Mexico, North Carolina, Ohio, Pennsylvania, South Carolina, South Dakota, Tennessee, Texas, Utah, Virginia, and Wisconsin).
At December 31, 2024, the Donegal Insurance Group actively wrote business in 21 states (Arizona, Colorado, Delaware, Georgia, Illinois, Indiana, Iowa, Maryland, Michigan, Nebraska, New Mexico, North Carolina, Ohio, Pennsylvania, South Carolina, South Dakota, Tennessee, Texas, Utah, Virginia, and Wisconsin).
The following table sets forth the investment results of our insurance subsidiaries for the years ended December 31, 2023, 2022 and 2021: Year Ended December 31, (dollars in thousands) 2023 2022 2021 Invested assets (1) $ 1,315,855 $ 1,290,752 $ 1,249,024 Investment income (2) 40,853 34,016 31,126 Average yield 3.1 % 2.6 % 2.5 % Average tax-equivalent yield 3.2 2.7 2.6 (1) Average of the aggregate invested amounts at the beginning and end of the period.
The following table sets forth the investment results of our insurance subsidiaries for the years ended December 31, 2024, 2023 and 2022: Year Ended December 31, (dollars in thousands) 2024 2023 2022 Invested assets (1) $ 1,356,013 $ 1,315,855 $ 1,290,752 Investment income (2) 44,918 40,853 34,016 Average yield 3.3 % 3.1 % 2.6 % Average tax-equivalent yield 3.4 3.2 2.7 (1) Average of the aggregate invested amounts at the beginning and end of the period.
These differences amounted to $32.4 million, $28.7 million and $23.5 million at December 31, 2023, 2022 and 2021, respectively. -18- Index The following table sets forth a reconciliation of the beginning and ending GAAP net liability of our insurance subsidiaries for unpaid losses and loss expenses for the periods indicated: Year Ended December 31, (in thousands) 2023 2022 2021 Gross liability for unpaid losses and loss expenses at beginning of year $ 1,121,046 $ 1,077,620 $ 962,007 Less reinsurance recoverable 451,184 451,261 404,818 Cumulative effect of adoption of updated accounting guidance for credit losses at January 1 1,132 — — Net liability for unpaid losses and loss expenses at beginning of year 670,994 626,359 557,189 Provision for net losses and loss expenses for claims incurred in the current year 625,831 608,900 551,918 Change in provision for estimated net losses and loss expenses for claims incurred in prior years (16,653 ) (44,821 ) (31,208 ) Total incurred 609,178 564,079 520,710 Net losses and loss expense payments for claims incurred during: The current year 330,290 302,272 269,317 Prior years 260,739 218,304 182,223 Total paid 591,029 520,576 451,540 Net liability for unpaid losses and loss expenses at end of year 689,143 669,862 626,359 Plus reinsurance recoverable 437,014 451,184 451,261 Gross liability for unpaid losses and loss expenses at end of year $ 1,126,157 $ 1,121,046 $ 1,077,620 The following table sets forth the development of the liability for net unpaid losses and loss expenses of our insurance subsidiaries from 2013 to 2023.
These differences amounted to $36.0 million, $32.4 million and $28.7 million at December 31, 2024, 2023 and 2022, respectively. -17- Index The following table sets forth a reconciliation of the beginning and ending GAAP net liability of our insurance subsidiaries for unpaid losses and loss expenses for the periods indicated: Year Ended December 31, (in thousands) 2024 2023 2022 Gross liability for unpaid losses and loss expenses at beginning of year $ 1,126,157 $ 1,121,046 $ 1,077,620 Less reinsurance recoverable 437,014 451,184 451,261 Cumulative effect of adoption of updated accounting guidance for credit losses at January 1 — 1,132 — Net liability for unpaid losses and loss expenses at beginning of year 689,143 670,994 626,359 Provision for net losses and loss expenses for claims incurred in the current year 619,090 625,831 608,900 Change in provision for estimated net losses and loss expenses for claims incurred in prior years (14,972 ) (16,653 ) (44,821 ) Total incurred 604,118 609,178 564,079 Net losses and loss expense payments for claims incurred during: The current year 319,196 330,290 302,272 Prior years 269,701 260,739 218,304 Total paid 588,897 591,029 520,576 Net liability for unpaid losses and loss expenses at end of year 704,364 689,143 669,862 Plus reinsurance recoverable 416,621 437,014 451,184 Gross liability for unpaid losses and loss expenses at end of year $ 1,120,985 $ 1,126,157 $ 1,121,046 The following table sets forth the development of the liability for net unpaid losses and loss expenses of our insurance subsidiaries from 2014 to 2024.