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Income taxes
 9 Months Ended
Sep. 30, 2024
Income taxes [Abstract]  
Income taxes
8. Income taxes

We recorded an income tax benefit in the third quarter of 2024 of $148 thousand at an effective tax rate of (21.2%) compared to an income tax expense in the third quarter of 2023 of $169 thousand at an effective tax rate of 15.7%.  For the nine months ended September 30, 2024, we recorded income tax benefit of $511 thousand at an effective tax rate of (21.1%), compared to an income tax expense for the nine months ended September 30, 2023 of $1.2 million at an effective tax rate of 19.8%.
We are subject to U.S. federal income tax, as well as income tax in certain U.S. state and foreign jurisdictions.  We have substantially concluded all U.S. federal, state and local income tax, and foreign tax regulatory examination matters through 2020.  However, our federal tax returns for the years 2021 through 2023 remain open to examination. Various U.S. state and foreign tax jurisdiction tax years remain open to examination as well, but we believe that any additional assessment would be immaterial to the Condensed Consolidated Financial Statements.  The Company maintains a valuation allowance against certain deferred tax assets where realization is not certain.