It’s always problematic when a president takes credit for an improving economy, just as it is when he’s blamed for things going bad. A leader can only do so much, for better or worse, and there are two sides to every economy. But after an election in which Obama largely held off on chest-beating, he claimed credit in bold terms for what is going right.

Also in his speech, Obama skimmed over the cost to taxpayers of free community college tuition and invited closer scrutiny with his claims about US support for Syrian moderates and about his record of public-lands preservation.

A look at some of his claims, and the facts and the political climate behind them, as well as a glance at the Republican response:

Obama: “At this moment — with a growing economy, shrinking deficits, bustling industry and booming energy production — we have risen from recession freer to write our own future than any other nation on Earth.”

The facts: By many measures, the economy is still recovering from the deep scars left by the Great Recession.

Job growth has been healthy, but fueled in part by lower-paying jobs in areas such as retail and restaurants, which have replaced many higher-paying positions in manufacturing and construction. Part-time jobs also remain elevated: There are still 1.7 million fewer workers with full-time jobs than when the recession began in December 2007.

And the faster hiring hasn’t pushed up wages much. They have been growing at a tepid pace of about 2 percent a year since the recession ended 5½ years ago. That’s barely ahead of inflation and below the annual pace of about 3.5 to 4 percent that is typical of a fully healthy economy.

That has left the income of the typical household below its pre-recession level. Inflation-adjusted median household income reached $53,880 in November 2014, according to an analysis of government data by Sentier Research. That is about 4 percent higher than when it bottomed out in 2011. But it is still 4.5 percent lower than the $56,447 median income in December 2007, the month the recession began.

Booming energy production is indeed a reality, but that’s a phenomenon many years in the making, with the development of cost-effective extraction from fracking and other means playing into the rise of the US as an energy production giant.

Obama: “I am sending this Congress a bold new plan to lower the cost of community college — to zero.”

The facts: Zero for qualifying students; an estimated $60 billion over 10 years to the Treasury.

Obama confronts a Republican-controlled Congress that can be expected to be wary of a new program costing that much. Moreover, the proposal requires states to contribute about a quarter of the money, and getting them to go along is bound to be tough. Many states refused to expand Medicaid under the health care law, for example, even though Washington is picking up the entire cost in the first years.

On the other hand, community college is an issue close to home for state government, perhaps more appealing than partnering with Washington on the health law, so the idea could have a fighting chance if it can get through Congress. Educators are divided on its merits, with some worrying that aid for a community college education could divert students and scholarships away from four-year schools.

Obama: “We’ve set aside more public lands and waters than any administration in history.”

The facts: Waters is the key word here. Before expanding the Pacific Remote Islands National Monument last year from almost 87,000 square miles to more than 490,000 square miles, Obama had protected far fewer acres than his four predecessors, including President George W. Bush.

Expansion of the massive Pacific islands monument puts Obama on top. It’s nearly all water, however, and the move has limited practical implications. While it bans commercial fishing, deep-sea mining and other extraction of underwater resources, little fishing or drilling occur in the mid-ocean region now.

Obama: “Thanks to a growing economy, the recovery is touching more and more lives. Wages are finally starting to rise again. We know that more small-business owners plan to raise their employees’ pay than at any time since 2007.”

The facts: A survey of small businesses by the National Federation of Independent Business does show that a rising proportion plans to raise wages. But plans to raise pay aren’t the same as actually raising them.

Average hourly earnings rose just 1.7 percent in December from 12 months earlier, according to the Labor Department. That’s about half the rate that is typical of a healthy economy and actually lower than the previous month. Economists generally expect wage gains to accelerate this year, as unemployment continues to fall and businesses are forced to offer higher pay to attract workers. But there is scant evidence that it is happening yet.

Obama: “In Iraq and Syria, American leadership — including our military power — is stopping ISIL’s advance. Instead of getting dragged into another ground war in the Middle East, we are leading a broad coalition, including Arab nations, to degrade and ultimately destroy this terrorist group. We’re also supporting a moderate opposition in Syria that can help us in this effort.”

The facts: The US also has been slow to set up long-promised training for the moderate Syrian opposition, and has yet to begin the actual vetting of the rebels. Also, despite persistent pleas from the rebels, the US hasn’t sent the more lethal weapons they want. US officials have expressed concerns that the weapons could end up in the hands of insurgents.

Military leaders, however, agree that coalition airstrikes and the military effort in Syria and Iraq have stopped the momentum of the Islamic State group, or ISIL, made it hard for the insurgents to communicate and travel, and hurt their oil revenues.

Sen. Joni Ernst: The freshman from Iowa listed Obama’s health care law among his “failed policies” and added, “We see the hurt caused by canceled health care plans and higher monthly insurance bills.”

The facts: The jury is still out on the law Republicans call “ObamaCare.”

The number of uninsured people is down by at least 10 million. A large ongoing Gallup survey documented a steady drop in the nation’s uninsured rate since the law’s big coverage expansion began last year.

The law’s record on affordability is mixed. The share of Americans forgoing needed medical care because of cost is down significantly, according to a Commonwealth Fund survey, and fewer are struggling to pay medical bills. Yet many insured people with modest incomes still have problems with high out-of-pocket costs.

As for harm caused by lost insurance, many in Ernst’s party are intent on repealing the law, which would probably mean even more lost coverage, because many of the estimated 10 million uninsured people who have gained coverage through the Affordable Care Act would no longer be able to afford their premiums.