Unemployment claims jumped in Washington last week, but the state also got some good news: the rapidly recovery economy means employers face smaller-than-expected tax increases to restore the depleted unemployment system.

Washingtonians filed 7,544 new, or “initial,” claims for unemployment insurance benefits last week, a 9.5% increase over the prior week, the state Employment Security Department reported Thursday.

The increase, likely fueled in part by seasonal layoffs at schools, contrasted with new claims nationally, which fell 1.7% to 411,000, the U.S. Labor Department reported Thursday.

But Washington also got a rosier forecast for its unemployment trust fund, which has been heavily depleted by hundreds of thousands of layoffs during the pandemic.

Thanks in part to the faster-than-expected recovery of the state economy — which likely means fewer future layoffs and jobless claims — the trust fund is no longer at risk of insolvency in 2021, a possibility raised in an ESD forecast from November.

The improved outlook, which ESD reported Thursday, means Washington won’t need to borrow federal funds to cover any trust fund shortfall.

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It also means employers, whose taxes largely fund the state unemployment system, will see a roughly 30% smaller increase in taxes between 2021 and 2025 than ESD had forecast in November.

“This latest report is really great news all around,” Cami Feek, ESD commissioner, said in a statement Thursday.

The state paid out an estimated $4.5 billion in benefits in 2020 (compared with around $1 billion in 2019), and expects to pay $1.7 billion in 2021 and $1 billion in 2022, according to Thursday’s report.

In 2020, employers paid around $1.2 billion in unemployment taxes (up from around $1.1 billion in 2019), and can expect to pay $1.3 billion in 2021 and $1.8 billion in 2022.

In November, ESD had projected benefit payments of $5.1 billion for 2020, $3.1 billion for 2021 and $1.6 billion for 2022.

The agency had also forecast employer taxes of $1.9 billion for 2021 and nearly $3 billion in 2022.

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But November’s projections were blunted by the better economic outlook, coupled with tax relief measures by Gov. Jay Inslee and state lawmakers.

Otherwise, the state’s unemployment picture remained largely unchanged from last week.

The number of overall claims — new claims plus ongoing claims that claimants must file each week to receive benefits — dropped 2.3% to 374,810 last week, the ESD reported.

New claims for federal pandemic extended benefits — for workers who have exhausted state unemployment benefits — fell 20% last week compared with the prior week.

The ESD paid benefits on 272,242 individual claims last week, down 5.3% from the prior week. Because individuals can have multiple claims, the number of those claims is often slightly higher than the number of individual claimants.

The ESD also reported some progress in a complicated effort to verify thousands of Washingtonians’ eligibility for unemployment benefits.

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Two weeks ago, the ESD began sending notices to roughly 105,000 current and former claimants asking them to verify eligibility. That’s required by the federal government, which won’t pay federal pandemic benefits to unemployed workers who are eligible instead for regular state unemployment benefits.

About two-thirds of the $19.2 billion in benefits paid to Washingtonians since March 2020 have come from the federal government.

But a similar attempt last fall to verify eligibility went awry when many claimants failed to respond and were hit with demands to repay thousands of dollars in benefits.

This time, ESD officials tried to improve their messaging and gave claimants more time to respond. The agency will also make extra attempts to reach claimants before issuing overpayment notices.

Thus far, around 70% of those receiving verification requests have responded, compared to only around 50% last fall, an agency spokesperson said.