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Revenues Revenue
6 Months Ended
Jun. 30, 2020
Revenue from Contract with Customer [Abstract]  
Revenue from Contract with Customer [Text Block] Revenues
For the three months ended June 30, 2020 and 2019, we recognized revenues of $217.9 million and $220.8 million, respectively. Of the $217.9 million recognized in the second quarter of 2020, we recognized revenues of $5.6 million from obligations satisfied, or partially satisfied, in prior periods, of which $4.0 million was primarily due to the release of allowances on unbilled services as a result of securing contract amendments and $1.6 million was due to changes in the estimates of our variable consideration under performance-based billing arrangements. Of the $220.8 million recognized in the second quarter of 2019, we recognized revenues of $3.6 million from obligations satisfied, or partially satisfied, in prior periods, primarily due to the release of allowances on unbilled services due to securing contract amendments. During the second quarter of 2019, we recognized a $0.3 million decrease to revenues due to changes in the estimates of our variable consideration under performance-based billing arrangements.
For the six months ended June 30, 2020 and 2019, we recognized revenues of $440.5 million and $425.2 million, respectively. Of the $440.5 million recognized in the first six months of 2020, we recognized revenues of $10.0 million from obligations satisfied, or partially satisfied, in prior periods, of which $6.2 million was due to changes in the estimates of our variable consideration under performance-based billing arrangements and $3.8 million was primarily due to the release of allowances on unbilled services as a result of securing contract amendments. Of the $425.2 million recognized in the first six months of 2019, we recognized revenues of $2.1 million from obligations satisfied, or partially satisfied, in prior periods, primarily due to the release of allowances on unbilled services due to securing contract amendments. During the first six months of 2019, we recognized a $1.5 million decrease to revenues due to changes in the estimates of our variable consideration under performance-based billing arrangements.
As of June 30, 2020, we had $76.4 million of remaining performance obligations under engagements with original expected durations greater than one year. These remaining performance obligations exclude obligations under contracts with an original expected duration of one year or less, variable consideration which has been excluded from the total transaction price due to the constraint, and performance obligations under time-and-expense engagements which are recognized in the amount invoiced. Of the $76.4 million of performance obligations, we expect to recognize approximately $30.1 million as revenue in 2020, $29.7 million in 2021, and the remaining $16.6 million thereafter. Actual revenue recognition could differ from these amounts as a result of changes in the estimated timing of work to be performed, adjustments to estimated variable consideration in performance-based arrangements, or other factors.
Contract Assets and Liabilities
The payment terms and conditions in our customer contracts vary. Differences between the timing of billings and the recognition of revenue are recognized as either unbilled services or deferred revenues in the consolidated balance sheets.
Unbilled services include revenues recognized for services performed but not yet billed to clients. Services performed that we are not yet entitled to bill because certain events, such as the completion of the measurement period or client approval in performance-based engagements, must occur are recorded as contract assets and included within unbilled services, net. The contract asset balance as of June 30, 2020 and December 31, 2019 was $12.7 million and $12.6 million, respectively. The $0.1 million increase primarily reflects timing differences between the completion of our performance obligations and the amounts billed or billable to clients in accordance with their contractual billing terms.
Client prepayments and retainers are classified as deferred revenues and recognized over future periods in accordance with the applicable engagement agreement and our revenue recognition policy. Our deferred revenues balance as of June 30, 2020 and December 31, 2019, was $35.0 million and $28.4 million, respectively. The $6.6 million increase primarily reflects timing differences between client payments in accordance with their contract terms and the completion of our performance obligations. For the three and six months ended June 30, 2020, $6.8 million and $21.3 million, respectively, of revenues recognized were included in the deferred revenue balance as of December 31, 2019.