	Three months ended						Nine months ended
	September 30,						September 30,
	2018			2019			2018			2019
	(In millions)
Expected tax expense, at U.S. federal statutory income tax rate of 21%	$	11.9		$	4.6		$	43.1		$	20.1
Incremental net tax on earnings and losses of non-U.S., U.S. and non-tax group companies		(160.3	)		(2.9	)		(151.3	)		(3.1	)
Non-U.S. tax rates		3.5			1.1			18.4			5.7
Valuation allowance		(2.0	)		1.5			-			5.3
Adjustment to the reserve for uncertain tax positions, net		.3			.5			2.2			1.5
Transition tax		(2.1	)		-			(2.1	)		-
Change in federal tax rate		59.7			-			59.7			-
Change in state tax rate		(3.4	)		-			(3.4	)		-
Canada-Germany APA		-			-			(1.4	)		-
U.S. state income taxes and other, net		1.0			(.1	)		1.6			2.3
Income tax expense (benefit)	$	(91.4	)	$	4.7		$	(33.2	)	$	31.8
Comprehensive provision for income taxes (benefit) allocable to:
Income from continuing operations	$	(91.4	)	$	4.7		$	(33.2	)	$	31.8
Discontinued operations		(.8	)		-			19.0			-
Retained earnings - change in accounting principle		-			-			1.1			-
Additional paid-in capital		-			(.3	)		-			(.3	)
Other comprehensive income (loss):
Currency translation		.7			(2.1	)		(1.2	)		(1.3	)
Pension plans	1.4				1.4			4.4			4.5
OPEB plans		(.1	)		-			(.3	)		(.2	)
Total	$	(90.2	)	$	3.7		$	(10.2	)	$	34.5

The amount shown in the above table of our income tax rate reconciliation for non-U.S. tax rates represents the result determined by multiplying the pre-tax earnings or losses of each of our non-U.S. subsidiaries by the difference between the applicable statutory income tax rate for each non-U.S. jurisdiction and the U.S. federal statutory tax rate of 21%. The amount shown on such table for incremental net tax expense (benefit) on earnings and losses on non-U.S., U.S. and non-tax group companies includes, as applicable, (i) deferred state and foreign income taxes (or deferred income tax benefits) and deferred withholding taxes, as applicable, associated with the current-year change in the aggregate amount of undistributed earnings of all of our non-U.S. subsidiaries, which earnings are not permanently reinvested , (ii) current U.S. income taxes (or current income tax benefit) attributable to current-year income (losses) of one of Kronos’ non-U.S. subsidiaries, which subsidiary is treated as a dual resident for U.S. income tax purposes, (iii) deferred income taxes associated with our direct investment in Kronos and (iv) current and deferred income taxes associated with distributions and earnings from our investments in LandWell and BMI.

We record global intangible low-tax income (GILTI) tax as a current period expense when incurred under the period cost method. We have evaluated the tax impact of GILTI and base erosion anti abuse tax (BEAT) provisions and related U.S. tax credit provisions applicable to tax years beginning in 2018 based on the relevant statutes, including final GILTI and foreign tax credit regulations issued by the IRS in June 2019 which did not materially impact our determinations with respect to such items.

None of our federal U.S. and non-U.S. tax returns are currently under examination. As a result of prior audits in certain jurisdictions, which are now settled, in 2008 Kronos filed Advance Pricing Agreement Requests with the tax authorities in the U.S., Canada and Germany. During the first quarter of 2018, Kronos’ German subsidiary executed and finalized the related Advance Pricing Agreement with the Competent Authority for Germany (the “Canada-Germany APA”) effective for tax years 2005 - 2017. In the first quarter of 2018, we recognized a net $1.4 million non-cash income tax benefit related to an APA tax settlement payment between Kronos’ German and Canadian subsidiaries.

We recognized a non-cash deferred income tax benefit of $3.4 million in the third quarter of 2018 related to a decrease in our effective state income tax rate. This decrease was a direct result of the sale of our interest in the Amalgamated Sugar Company LLC which will reduce the number of state jurisdictions in which we are required to file.

As discussed in the 2018 Annual Report, under GAAP, we were required to revalue our net deferred tax liability associated with our U.S. net deductible temporary differences at December 31, 2017, the period in which the 2017 Tax Act was enacted, based on deferred tax balances as of the enactment date, to reflect the effect of the reduction in the corporate income tax rate. During the third quarter of 2018, in conjunction with finalizing our federal income tax return, we were able to obtain, prepare and analyze the necessary information to complete the accounting under ASC 740 related to the revaluation of our net deferred tax liability associated with our U.S. net taxable temporary differences as of December 31, 2017, which resulted in a measurement period adjustment and recognition of a non-cash deferred income tax expense of $59.7 million, decreasing the provisional amount we recognized at December 31, 2017. Such adjustment is almost entirely attributable to the re-measurement of our deferred income taxes with respect to the excess of the financial reporting carrying amount over the income tax basis of our direct investment in Kronos common stock discussed below.

We recognize deferred income taxes with respect to the excess of the financial reporting carrying amount over the income tax basis of our direct investment in Kronos common stock because the exemption under GAAP to avoid such recognition of deferred income taxes is not available to us. At December 31, 2018, we had recognized a deferred income tax liability with respect to our direct investment in Kronos of $40.7 million. There is a maximum amount (or cap) of such deferred income taxes we are required to recognize with respect to our direct investment in Kronos. The maximum amount of such deferred income tax liability we would be required to have recognized (the cap) is $155.4 million. During the first nine months of 2019, we recognized a non-cash deferred income tax expense with respect to our direct investment in Kronos of $3.3 million for the increase in the deferred income taxes required to be recognized with respect to the excess of the financial reporting carrying amount over the income tax basis of our direct investment in Kronos common stock, to the extent such increase related to our equity in Kronos’ net income during such period. We recognized a similar non-cash deferred income tax expense of $19.2 million in the first nine months of 2018. A portion of the net change with respect to the excess of the financial reporting carrying amount over the income tax basis of our direct investment in Kronos common stock during such periods related to our equity in Kronos’ other comprehensive income (loss) items, and the amounts shown in the table above for income tax expense (benefit) allocated to other comprehensive income (loss) items includes amounts related to our equity in Kronos’ other comprehensive income (loss) items. Due to uncertainties and complexities of the 2017 Tax Act, we were still evaluating the impact of the one-time deemed repatriation of the post-1986 undistributed earnings of our non-U.S. subsidiaries up through December 31, 2017 as it relates to the income tax basis of our direct investment in Kronos at December 31, 2017. During the third quarter of 2018, in conjunction with finalizing our federal income tax return and based on additional information that became available (including proposed regulations issued by the IRS in August 2018 with respect to the Transition Tax), we recognized an adjustment, which is treated as a measurement period adjustment, to the deferred income taxes we recognized at December 31, 2017 associated with our direct investment in Kronos common stock (before revaluation of our deferred tax liability related to the decrease in the corporate income tax rate). Such adjustment resulted in an investment basis adjustment under the income tax regulations which increased the income tax basis of our direct investment in Kronos attributable to the income recognition related to the deemed repatriation of the post-1986 undistributed earnings of our non-U.S. subsidiaries in 2017. Such adjustment resulted in a non-cash deferred tax measurement period adjustment decreasing the deferred income taxes we recognize with respect to the excess of the financial reporting carrying amount over the income tax basis of our direct investment in Kronos common stock. Including the impact of the non-cash deferred tax revaluation adjustment discussed above, we recognized a net non-cash deferred income tax benefit of $113 million in the third quarter of 2018 related to the incremental tax on Kronos. Excluding the impact of such adjustment, our effective income tax rate from continuing operations in the third quarter and nine months ended September 30, 2018 was 38% and 38.9%, respectively.

The 2017 Tax Act amended the rules limiting the deduction for business interest expense beginning in 2018. The limitation applies to all taxpayers, and our annual deduction for business interest expense is limited to the sum of our business interest income and 30% of our adjusted taxable income as defined under the 2017 Tax Act. Any business interest expense not allowed as a deduction as a result of the limitation may be carried forward indefinitely and is treated as interest paid in the carryforward year subject to the respective year’s limitation. We determined that our interest expense for 2018 and 2019 was limited under these provisions. The limitation in 2018 resulted in part because of the loss we recognized on the sale of WCS for income tax purposes and the limitation in 2019 is primarily attributable to lower earnings. We have concluded that we are required to recognize a non-cash deferred income tax asset valuation allowance under the more-likely-than-not recognition criteria with respect to the portion of our deferred tax asset attributable to the nondeductible amount of business interest expense carryforward. Consequently, our provision for income taxes includes a non-cash deferred income tax expense of $3.0 million in the first nine months of 2018 and $6.7 million in the first nine months of 2019 (including $1.4 million recognized as a component of our incremental tax benefit related to Kronos’ dual-resident subsidiary) for the amount of such deferred income tax asset that we have determined does not meet the more-likely-than-not recognition criteria. In accordance with the ASC 740 guidance regarding intra-period allocation of income taxes, the full amount of such non-cash deferred income tax expense in 2018 is classified as part of the income taxes associated with the pre-tax gain we recognized for financial reporting purposes on the sale of WCS which is classified as part of discontinued operations as discussed in Note 3.

We believe we have adequate accruals for additional taxes and related interest expense which could ultimately result from tax examinations. We believe the ultimate disposition of tax examinations should not have a material adverse effect on our consolidated financial position, results of operations or liquidity. We currently estimate that our unrecognized tax benefits will decrease by approximately $3.7 million during the next twelve months primarily due to certain adjustments to our prior year returns and the expiration of certain statutes of limitations.