By Anna Wilde Mathews And Theo Francis 

Amid signs of a tightening labor market, Aetna Inc. plans to boost the incomes of its lowest-paid workers by as much as a third in a bid to draw top prospects and reduce turnover.

The move by the big health insurer highlights larger debates over the pace of the economic recovery and the compensation of people toward the bottom of the wage scale. Around 12% of Aetna's domestic work force will see a raise to a floor of $16 an hour, primarily employees in customer service and billing-related jobs. Aetna, which also said it will cut health-care costs for many of the same employees next year, follows Gap Inc., Starbucks Corp. and others in raising the lower limit on workers' wages.

Aetna Chief Executive Mark T. Bertolini said the company's shift reflects changes in the insurance industry, which is increasingly selling coverage to individuals. "We're preparing our company for a future where we're going to have a much more consumer-oriented business, " he said, and Aetna wants "a better and more informed work force."

Economists and policy makers have been on the lookout for signs of growth in workers' pay, which has lagged behind other markers of improved economic activity, including rising employment and economic output. While many economists say wage inflation remains a remote concern, some point to scattered signs of pressure as an indicator that the recovery may be accelerating and spreading its benefits to a wider group.

"We are getting closer and closer to the inflection point where we will see broad wage pressure," said Torsten Sløk, chief international economist at Deutsche Bank. "We are getting to the stage where companies can no longer find the right workers."

Aetna's decision also comes amid a broader conversation about the incomes of those toward the bottom of the wage scale. State and local governments around the country have moved to raise minimum wages, often generating pushback from business groups. Some companies--mostly in the heavily low-wage retail and restaurant industries--have come under fire from labor groups over their pay. And the Securities and Exchange Commission is crafting a rule requiring publicly traded companies to disclose how much their CEOs make relative to their average worker.

Aetna said it appeared that none of the approximately 5,700 workers set to benefit, who include part-timers, are currently making the minimum wage in their localities. Starting this April, their hourly wage will be raised to $16, an 11% increase on average but an increase of as much as 33% for some workers.

Job ads from Aetna and its competitors, along with wage reports on job-hunting websites, suggest that low-level health-insurer workers in customer-service, billing, claims-processing and similar positions, including both seasoned workers and entry-level employees, are often paid $13 to $15 an hour.

Next year, the company will also let workers with household income below a certain threshold choose health coverage with lower out-of-pocket charges without paying more in monthly premiums, a shift it said could save a worker with a family as much as $4,000 a year. The company said that as many as 7,000 employees may be eligible. Like a growing number of its employer clients, Aetna offers only high-deductible plans to employees.

Mr. Bertolini said Aetna expects to offer a benefits program to employer clients that's similar to the one it's rolling out to its own workers.

The total cost to Aetna for both changes will be $14 million in 2015 and approximately $25.5 million next year, the company said. Aetna has projected operating revenue for 2015 of at least $62 billion, with operating profit of at least $2.4 billion. Overseas Aetna employees won't be affected nor will those working for third-party contractors that provide janitorial, security, cafeteria or other services.

Mr. Bertolini said Aetna hopes to reduce its turnover costs of around $120 million a year and improve the quality of job prospects and the engagement of workers who interact with consumers and health-care providers. He said he isn't certain the changes will pay for themselves in purely financial terms, but the cost is small relative to Aetna's size. "I'm willing to make the investment to see whether or not this happens," he said.

Mr. Bertolini, who said he had recently asked Aetna executives to read economist Thomas Piketty's book on wealth inequality, also framed the move in more idealistic terms: "It's not just about paying people, it's about the whole social compact," Mr. Bertolini said, adding, "Why can't private industry step forward and make the innovative decisions on how to do this?"

Mr. Bertolini said the timing was partly tied to the economic recovery, which, he suggested, will heighten the competition for employees "now that there are more places for them to go."

So far, even as the economy and the labor market have improved, wages have grown slowly. On Friday, the Labor Department said unemployment fell to 5.6% in December from 5.8% in November, and employers added 252,000 jobs, capping the best year of job growth in nearly 15 years. By contrast, average hourly earnings fell slightly--likely reflecting seasonal part-time holiday hiring--bringing 2014's increase to 1.7%.

Still, the agency's employment cost index, which measures total pay and benefit costs for civilian employers, had ticked up in the third quarter to an annual rate of 2.2% from 1.9% a year earlier. And figures for voluntary job departures hit a six-year high in October, suggesting workers are finding it easier to change jobs.

Raj Bal, a former insurance-industry executive who is now a consultant, said he hasn't seen other health insurers make changes like Aetna's. Indeed, many back-office functions involving billing or claims processing have been moved overseas to trim expenses, he said. Efforts to improve service by consumer-facing workers could make sense, he added, if they increase customer retention.

Economists said Mr. Bertolini's bet could pay off. "There's a very strong relationship between wages and turnover," said Lawrence Katz, a Harvard University economist. There is also evidence that workers who are paid more feel better about their jobs, which "seems to translate into better performance," he added. "The question is whether it's enough to pay for the increase in compensation."

More companies are making that bet. Starbucks, which has for years boasted of better-than-average wages and benefits, said this past fall it would roll out pay increases for its 135,000 U.S. baristas and shift supervisors. About half saw the raise in the paychecks they received Friday, and the rest will see it this week.

Early last year, Gap said it would raise the minimum wage it pays U.S. store employees after six months of work to $9 by midyear and to $10 this coming June. The move was expected to raise pay for about 65,000 of the company's 135,000 U.S. employees.

In October, Wal-Mart Stores Inc. said it would ensure it paid all its workers more than the federal minimum wage, without specifying a time frame. Fewer than 6,000 of its 1.3 million U.S. workers were paid the minimum wage at the time. Also last spring, Container Store Inc. started seasonal workers at $13 an hour, and Hobby Lobby Stores Inc. raised its starting part-time wage by 50 cents to $10 an hour.

Write to Anna Wilde Mathews at anna.mathews@wsj.com and Theo Francis at theo.francis@wsj.com

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