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Income taxes - Component of Income Taxes (Detail) - USD ($)
$ in Thousands
3 Months Ended
Mar. 31, 2024
Mar. 31, 2023
Income taxes    
Expected tax expense (benefit), at U.S. federal statutory income tax rate of 21% $ 1,744 $ (949)
Rate differences on equity in earnings (losses) of Kronos, net of dividends (782) 2,305
U.S. state income taxes and other, net 26 65
Income tax expense (benefit) $ 988 $ 1,421