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Fmr Bush advisor: With jobs, 'things are not terrible, but they're not great'

Wage growth typically indicates the final stages of a recovery, but if this is the peak of labor growth, former Bush advisor Ed Lazear worries it will not be felt among the U.S. population as much as it should be.

"If we look at the economy, it basically looks like we've peaked out and we've peaked out at a low level," the former chairman of the Council of Economic Advisers under President George W. Bush told CNBC.

And, with the employment rate "stuck" and lower job number increases relative to 2015, Lazear told "Squawk on the Street" that while "things are not terrible, they're not great."

Lazear noted the inconsistency in the year 2015 between the numbers — a pretty good year, by his standards — and how they affected the U.S. population, which he contended still felt like it lacked buying power.

"Primarily what's going on is we have more people working … but the point is we're working harder and we're not making a whole lot more," Lazear said.

Moving forward, Lazear would like to see a more significant increase in productivity, which jumped in October but remained flat year over year.

"To my mind, the only way to get [more sustained productivity growth] going is to see higher investment, to create a climate where businesses want to get capital expenditures growing again," the former chairman said.

"Without that, we're not going to see productivity growth; without productivity growth, we're not going to see wage growth," he added.

Former Labor Secretary under President George W. Bush Elaine Chao saw a different solution.

Appearing in a separate interview on "Squawk on the Street," Chao said one of the major hindrances to economic growth is regulation.

"There is a dampening effect on job creation with overly intrusive and burdensome regulations," Chao said, adding that 66 percent of net new jobs created come from small businesses, which are often hit hardest by regulatory measures.

Chao found the most disappointing aspects of October's report to be the participation rate, which she said suggests a lot of discouraged workers still looking to enter the workforce, and stagnating GDP growth.

"We are still not seeing the robust, vibrant job creation rate that we would hope after … nearly eight years," she said, noting that generally, recovery occurs much faster.

Although Chao said she will be supporting Donald Trump for president in the 2016 election, she did stray from the candidate's hard-hitting views on trade.

"I think trade overall, fair and free trade, creates more jobs within the United States that are related to exports and imports and I'm for anything that creates new jobs," the former labor secretary said.