(12)	Goodwill and other intangible assets

Reconciliations of the changes in the carrying value of goodwill during 2018 and 2017 follows (in millions).

 

		December 31,
		2018				2017
Balance at beginning of year		$	81,258			$	79,486
Acquisitions of businesses			376				1,545
Other, including foreign currency translation			(609	)			227
Balance at end of year		$	81,025			$	81,258

Our other intangible assets and related accumulated amortization are summarized as follows (in millions).

 

		December 31, 2018								December 31, 2017
		Gross carrying amount				Accumulated amortization				Gross carrying amount				Accumulated amortization
Insurance and other		$	40,493			$	8,994			$	40,225			$	7,707
Railroad, utilities and energy			1,011				362				988				324
		$	41,504			$	9,356			$	41,213			$	8,031
Trademarks and trade names		$	5,368			$	750			$	5,381			$	692
Patents and technology			4,446				2,790				4,341				2,493
Customer relationships			28,375				4,573				28,322				3,722
Other			3,315				1,243				3,169				1,124
		$	41,504			$	9,356			$	41,213			$	8,031

Intangible asset amortization expense was $1,393 million in 2018, $1,469 million in 2017 and $1,490 million in 2016. Estimated amortization expense over the next five years is as follows (in millions): 2019 – $1,318; 2020 – $1,224; 2021 – $1,136; 2022 – $1,063 and 2023 – $1,018. Intangible assets with indefinite lives as of December 31, 2018 and 2017 were $18.9 billion and primarily related to certain customer relationships and trademarks and trade names.