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WORKERS' COMPENSATION AND PNEUMOCONIOSIS | 6 Months Ended
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Jun. 30, 2023
WORKERS' COMPENSATION AND PNEUMOCONIOSIS |
WORKERS' COMPENSATION AND PNEUMOCONIOSIS | 13.WORKERS' COMPENSATION AND PNEUMOCONIOSIS ​ The changes in the workers' compensation liability, including current and long-term liability balances, for each of the periods presented were as follows: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | Three Months Ended | ​ | Six Months Ended |
​ | ​ | June 30, | ​ | June 30, | ​
​ | ​ | 2023 |  | 2022 |  | 2023 |  | 2022 | ​
​ | ​ | (in thousands) | ​
Beginning balance | ​ | $ | 50,017 | ​ | $ | 53,206 | ​ | $ | 49,452 | ​ | $ | 53,448 | ​
Changes in accruals | ​ |  | 2,196 | ​ |  | 2,271 | ​ |  | 6,070 | ​ |  | 4,546 | ​
Payments | ​ |  | (2,646) | ​ |  | (3,278) | ​ |  | (6,505) | ​ |  | (6,082) | ​
Interest accretion | ​ |  | 551 | ​ |  | 287 | ​ |  | 1,101 | ​ |  | 574 | ​
Valuation loss (gain) (1) | ​ |  | 990 | ​ |  | (5,265) | ​ |  | 990 | ​ |  | (5,265) | ​
Ending balance | ​ | $ | 51,108 | ​ | $ | 47,221 | ​ | $ | 51,108 | ​ | $ | 47,221 | ​
(1) | Our estimate of the liability for the present value of current workers′ compensation benefits is based on our actuarial calculations. Our actuarial calculations are based on a blend of actuarial projection methods and numerous assumptions including claims development patterns, mortality, medical costs and interest rates. The valuation loss in 2023 is due to adverse claims development. The valuation gain in 2022 is due to an increase in the discount rate from 2.41% on December 31, 2021 to 4.22% on June 30, 2022.
​ We limit our exposure to traumatic injury claims by purchasing a high deductible insurance policy that starts paying benefits after deductibles for a claim have been met. The deductible level may vary by claim year. Our workers' compensation liability above is presented on a gross basis and does not include our expected receivables on our insurance policy. Our receivables for traumatic injury claims under this policy as of June 30, 2023 are $4.1 million and are included in Other long-term assets on our condensed consolidated balance sheet. ​ Certain of our mine operating entities are liable under state statutes and the Federal Coal Mine Health and Safety Act of 1969, as amended, to pay pneumoconiosis, or black lung, benefits to eligible employees and former employees and their dependents. Components of the net periodic benefit cost for each of the periods presented are as follows: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | Three Months Ended | ​ | Six Months Ended | ​
​ | ​ | June 30, | ​ | June 30, | ​
​ | ​ | 2023 |  | 2022 |  | 2023 |  | 2022 |
​ | ​ | (in thousands) | ​
Service cost | ​ | $ | 675 | ​ | $ | 954 | ​ | $ | 1,344 | ​ | $ | 1,901 |
Interest cost (1) | ​ |  | 1,238 | ​ |  | 749 | ​ |  | 2,476 | ​ |  | 1,496 | ​
Net amortization (1) | ​ |  | 346 | ​ |  | 259 | ​ |  | 691 | ​ |  | 519 | ​
Net periodic benefit cost | ​ | $ | 2,259 | ​ | $ | 1,962 | ​ | $ | 4,511 | ​ | $ | 3,916 | ​
(1) | Interest cost and net amortization are included in the Other income (expense) line item within our condensed consolidated statements of income.

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