Employee benefit plans (Tables)

12 Months Ended

Dec. 31, 2022

Components of Net Periodic Defined Benefit Cost (Income)

	Years ended December 31,
	2020		2021		2022
	(In thousands)
Net periodic pension cost:
Interest cost	$	1,483	$	947	$	1,138
Expected return on plan assets		(1,850)		(1,603)		(1,552)
Plan settlement		—		—		104
Recognized actuarial losses		1,412		1,562		1,664
Total	$	1,045	$	906	$	1,354

Defined Benefit Pension Plans

Expected Benefit Payments

Years ending December 31,	Amount
	(In thousands)
2023	$	3,441
2024		3,368
2025		3,295
2026		3,237
2027		3,164
Next 5 years		14,426

Funded Status of Defined Benefit Plans

	December 31,
	2021		2022
	(In thousands)
Change in projected benefit obligations (PBO):
Benefit obligations at beginning of the year	$	52,873	$	50,367
Interest cost		947		1,138
Plan settlement		—		(188)
Actuarial (gains) losses		295		(10,777)
Change in currency exchange rates		(73)		(965)
Benefits paid		(3,675)		(3,485)
Benefit obligations at end of the year		50,367		36,090
Change in plan assets:
Fair value of plan assets at beginning of the year		50,260		47,940
Actual return on plan assets		226		(10,263)
Employer contributions		1,169		1,228
Change in currency exchange rates		(40)		(1,294)
Benefits paid		(3,675)		(3,485)
Fair value of plan assets at end of year		47,940		34,126
Funded status	$	(2,427)	$	(1,964)
Amounts recognized in the balance sheet:
Noncurrent pension asset	$	1,356	$	1,105
Accrued pension costs:
Current		(61)		(57)
Noncurrent		(3,722)		(3,012)
Total		(2,427)		(1,964)
Accumulated other comprehensive loss -  actuarial losses, net		28,265		27,530
Total	$	25,838	$	25,566
Accumulated benefit obligations (ABO)	$	50,367	$	36,090

Changes in Other Comprehensive Income (Loss)

	Years ended December 31,
	2020		2021		2022
	(In thousands)
Changes in plan assets and benefit obligations recognized in   other comprehensive income:
Net actuarial gain (loss) arising during the year	$	(934)	$	1,618	$	(1,034)
Plan settlement		—		—		104
Amortization of unrecognized net actuarial gain (loss)		1,412		(1,562)		1,664
Total	$	478	$	56	$	734

Information Concerning Defined Benefit Pension Plans (Including Certain Plans for Which ABO Exceeds Fair Value of Plan Assets)

	December 31,
	2021		2022
	(In thousands)
PBO at end of the year:
U.S. plan	$	40,254	$	30,254
U.K. plan		10,113		5,836
Total	$	50,367	$	36,090
Fair value of plan assets at end of the year:
U.S. plan	$	36,471	$	27,185
U.K. plan		11,469		6,941
Total	$	47,940	$	34,126
Plans for which the ABO exceeds plan assets (only our U.S. plan):
PBO	$	40,254	$	30,254
ABO		40,254		30,254
Fair value of plan assets		36,471		27,185

Summary of Assumptions Used to Determine Net Benefit Obligation

	Years ended December 31,
Rate	2020		2021		2022
Discount rate	2.9	%	2.1	%	2.3	%
Long-term rate of return on plan assets	4.2	%	3.3	%	3.3	%

Schedule of composition of our pension plan assets by fair value level

	Fair Value Measurements
			Quoted prices		Significant other		Significant
			in active		observable		unobservable		Assets measured
	Total		markets (Level 1)		inputs (Level 2)		inputs (Level 3)		at NAV
	(In thousands)
December 31, 2021:
U.S.
Equities	$	12,951	$	831	$	—	$	108	$	12,012
Fixed income		21,299		—		—		—		21,299
Cash and other		2,221		1,352		—		—		869
U.K. - Other		11,469		1,324		—		10,145		—
Total	$	47,940	$	3,507	$	—	$	10,253	$	34,180

	Fair Value Measurements
			Quoted prices		Significant other		Significant
			in active		observable		unobservable		Assets measured
	Total		markets (Level 1)		inputs (Level 2)		inputs (Level 3)		at NAV
	(In thousands)
December 31, 2022:
U.S.
Equities	$	8,591	$	694	$	—	$	—	$	7,897
Fixed income		15,954		149		—		—		15,805
Cash and other		2,640		1,903		—		44		693
U.K. - Other		6,941		1,104		—		5,837		—
Total	$	34,126	$	3,850	$	—	$	5,881	$	24,395