Ask any CEO what’s keeping them up at night these days, and the answer 99 times out of 100 is: finding good workers.

“We are trying so hard every day to find people to come to work in our operations,’’ co-owner Seana Gaherin of Dunn-Gaherin’s restaurant in Newton, said in a recent Newton-Needham Regional Chamber video promoting a housing campaign to draw more workers in the area.

The monthly employment report released Friday appears to offer no relief for Gaherin or other employers scrambling to fill jobs as the economy continues to expand. The unemployment rate fell to 3.6 percent in April, the lowest since December 1969, while nonfarm payrolls grew at a stronger-than-expected pace.

“The strength of an already-strong labor market may even be accelerating,’’ said Tony Bedikian, head of the global markets team at Citizens Bank.

But the data from the Bureau of Labor Statistics — which is culled from separate surveys of households and employers — is a bit more complicated than the headlines suggest. And it has important implications for the Federal Reserve as it seeks the right level for interest rates to keep business humming without sparking inflation, and for the 2020 presidential election, in which President Trump hopes to run on a record of rising employment and stock prices.

While the job market remains undeniably strong, there are caveats.

The reason the unemployment rate declined, from 3.8 percent in March, was mainly because 490,000 people left the job market. Baby boomers retiring? That’s part of the answer. But other workers with out-of-date skills may be giving up the job search.

The labor force participation rate fell to 62.8 percent in April from 63 percent the prior month, meaning a smaller percentage of the population is working. The number of people working part time even though they want to be full time was unchanged at 7.3 percent.

“There were dark clouds in the jobs report,’’ noted Daniel S. Kern, chief investment officer at TFC Financial Management in Boston. “Workers leaving the workforce is not a bullish indicator.’’

April marked the 103rd straight month of rising payrolls, a remarkable run that dates to October 2010. Employers created 263,000 jobs last month — exceeding analysts’ forecasts of 190,000 — and routine revisions added a net 16,000 jobs to the tallies for March and April.

Still, the average monthly payroll gain of 203,000 this year is down from all of last year, and only about what it has been since October 2010.

Average hourly earnings rose 3.2 percent from a year ago for the second straight month. However, with unemployment so low and the economy expanding at a decent pace, wage growth should be stronger.

Manufacturers added 4,000 jobs in April — the third straight month of minimal change. That could be a problem for Trump, who draws support from factory workers. According to BLS, in the 12 months prior to February, manufacturing added an average of 22,000 jobs a month.

Investors cheered the jobs report. The Dow Jones industrial average rose 197 points, or 0.75 percent, after two days of declines. Its closing price of 26,504 is just 1.2 percent off the record set in October.

“We can all agree that AMERICA is now #1. We are the ENVY of the WORLD — and the best is yet to come!’’ Trump tweeted after the report was released.

But the president persists in berating the Federal Reserve for not cutting interest rates, which the central bank would normally do only if the economy were in danger of contracting.

The latest jobs data lends support to the Fed’s decision Wednesday to leave rates unchanged amid good growth and tame inflation.

“We do think that our policy stance is appropriate right now,’’ Fed chairman Jerome Powell said on Wednesday, referring to officials’ wait-and-see approach. “We don’t see a strong case for moving in either direction.’’

Kern, of TFC management,agrees. “There is no urgency for the Fed to raise rates, nor is there a need for the Fed to ‘rescue’ the economy by cutting rates,’’ he said.

At this point, Trump’s reelection campaign faces a lot of negatives, but the economy isn’t one of them. He wants a rate cut as an insurance policy against any slowdown that might arise in the run-up to voting day.

The Democrats seeking their party’s nomination will no doubt hammer Trump on growing income inequality, but that’s a tough message to sell when unemployment is the lowest since the year Neil Armstrong walked on the moon.

You can reach me at larry.edelman@globe.com and follow me on Twitter @GlobeNewsEd.