Premiums for employer-provided health insurance increased by relatively modest amounts for the second year in a row, according to a new survey, further evidence that once-fierce health care inflation might be abating.
 
The average annual premium for a family is now $16,351, up 4 percent from last year, according to the results of the survey released on Tuesday by the Kaiser Family Foundation. Of that amount, workers paid an average of $4,565. Premiums for individual policies purchased through an employer rose nearly 5 percent, to $5,884 annually, from $5,615 in 2012. The average contribution from the worker is $999.
 
The 4 percent increase for a family is relatively tame, at least by historical standards for health care. But it is still a far bigger increase than for wages, which grew 1.8 percent over the last year, the foundation said.
 
“We are in a prolonged period of moderation in premiums, which should create some breathing room for the private sector to try to reduce costs without cutting back benefits for workers,” Drew Altman, president of the nonprofit foundation, said in a statement.
 
The increase this year is roughly the same as the increase in 2012 over 2011, and much smaller than the 9 percent increase in 2011. Still, since 1999, insurance premiums have nearly tripled, while wages have increased by only 50 percent and consumer prices by 40 percent, the foundation said.
 
One reason for the recent moderation was clearly the recession, which caused some people to forgo visits to doctors and certain treatments and procedures. Even insured people face deductibles and co-payments they might wish to avoid paying at a time of tight household budgets.
 
There is debate about whether changes related to the new health care law, the Affordable Care Act, might be having an effect even though it is not yet fully implemented. The debate about health care has at least focused more attention on the importance of controlling medical costs, including by reducing the number of unnecessary procedures.
 
One way increases in premiums have been kept in check has been to add or increase out-of-pocket costs like deductibles and co-payments.
 
The survey found that 78 percent of covered workers have a general deductible, up from 72 percent in 2012. About 38 percent of workers covered by employer plans now face a deductible of at least $1,000. At firms with fewer than 200 workers, 58 percent of covered workers have a deductible that large, with 31 percent having a deductible of at least $2,000, up from 12 percent in 2008.
 
About 57 percent of all companies are offering health benefits this year compared with 61 percent last year, a difference that was not statistically significant, the survey found. That is down from the levels of around 67 percent about a decade ago.
 
About 93 percent of companies with 50 or more workers offer health benefits, according to the survey. All companies of that size will have to offer health benefits or face a fine under the Affordable Care Act. That mandate, however, will not take effect until 2015.
 
Among small firms, with three to nine workers, 45 percent offered some benefits compared with 50 percent in 2012, a decline that was not statistically significant. A decade ago, more than 55 percent of such small employers offered health benefits.
 
The survey found that only 36 percent of covered workers, down from 48 percent last year, are now in health plans that are grandfathered in under the Affordable Care Act and therefore exempt from certain provisions, like the requirement to provide preventive services without any out-of-pocket costs.
 
The annual survey, which received responses from more than 2,000 companies, was conducted jointly by the Kaiser Family Foundation and the Health Research and Educational Trust, which is affiliated with the American Hospital Association. A discussion of the results was also published on Tuesday in the journal Health Affairs.