Biggest changeFor example, the 2012 column indicates that at December 31, 2022 payments equal to $268.4 million of the currently re-estimated ultimate liability for net losses and loss expenses of $275.6 million had been made. -18- Index Year Ended December 31, (in thousands) 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 Net liability at end of year for unpaid losses and loss expenses $ 250,936 $ 265,605 $ 292,301 $ 322,054 $ 347,518 $ 383,401 $ 475,398 $ 506,906 $ 557,189 $ 626,359 $ 669,862 Net liability re- estimated as of: One year later 261,294 280,074 299,501 325,043 354,139 419,032 462,466 493,961 525,981 581,538 Two years later 268,877 281,782 299,919 329,115 375,741 413,535 450,862 479,927 498,724 Three years later 270,473 281,666 304,855 338,118 376,060 404,902 440,168 463,441 Four years later 270,794 284,429 307,840 339,228 372,230 398,560 432,027 Five years later 271,954 285,130 310,354 338,020 370,960 396,695 Six years later 272,553 287,439 310,380 338,200 372,346 Seven years later 274,111 287,063 311,594 339,625 Eight years later 274,472 288,298 313,354 Nine years later 275,385 289,066 Ten years later 275,638 Cumulative deficiency (excess) 24,702 23,461 21,053 17,571 24,828 13,294 (43,371 ) (43,465 ) (58,465 ) (44,821 ) Cumulative amount of liability paid through: One year later $ 126,677 $ 131,766 $ 131,779 $ 149,746 $ 163,005 $ 175,883 $ 195,956 $ 172,497 $ 182,223 $ 218,304 Two years later 191,208 194,169 206,637 228,506 250,678 276,331 275,993 276,069 297,860 Three years later 225,956 233,371 251,654 274,235 306,338 317,447 335,310 343,912 Four years later 245,094 255,451 274,248 300,715 324,628 342,583 371,231 Five years later 254,502 265,841 287,178 309,630 337,946 362,061 Six years later 259,437 272,431 292,327 315,105 349,496 Seven years later 263,386 275,357 295,106 321,777 Eight years later 265,026 277,315 300,306 Nine years later 266,433 279,928 Ten years later 268,446 Year Ended December 31, (in thousands) 2014 2015 2016 2017 2018 2019 2020 2021 2022 Gross liability at end of year $ 538,258 $ 578,205 $ 606,665 $ 676,672 $ 814,665 $ 869,674 $ 962,007 $ 1,077,620 $ 1,121,046 Reinsurance recoverable 245,957 256,151 259,147 293,271 339,266 362,768 404,818 451,261 451,184 Net liability at end of year 292,301 322,054 347,518 383,401 475,398 506,906 557,189 626,359 669,862 Gross re-estimated liability 564,561 594,072 628,241 679,800 755,701 792,676 872,833 933,712 Re-estimated recoverable 251,207 254,447 255,895 283,105 323,674 329,235 374,109 352,174 Net re-estimated liability 313,354 339,625 372,346 396,695 432,027 463,441 498,724 581,538 Gross cumulative deficiency (excess) 26,303 15,867 21,576 3,128 (58,964 ) (76,998 ) (89,174 ) (143,908 ) -19- Index Third-Party Reinsurance Our insurance subsidiaries and Donegal Mutual purchase certain third-party reinsurance on a combined basis.
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.
At December 31, 2022, the Donegal Insurance Group actively wrote business in 24 states (Alabama, 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, Vermont, Virginia, and Wisconsin).
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).
The following table sets forth the investment results of our insurance subsidiaries for the years ended December 31, 2022, 2021 and 2020: Year Ended December 31, (dollars in thousands) 2022 2021 2020 Invested assets (1) $ 1,290,752 $ 1,249,024 $ 1,165,878 Investment income (2) 34,016 31,126 29,504 Average yield 2.6 % 2.5 % 2.5 % Average tax-equivalent yield 2.7 2.6 2.7 (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, 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.