GEOFF BENNETT: As we just reported, inflation in the U.S.

picked up last month.

The Labor Department's report was delayed over a week due to the government shutdown.

And the White House said today there will likely be no inflation report next month.

The shutdown has also halted the release of monthly jobs numbers.

But even before the shutdown, experts were sounding the alarm about risks to government data.

That's after President Trump fired the head of the Bureau of Labor Statistics, angry about the employment numbers.

Our William Brangham has this report with lessons from nations where trust in government data was lost.

WILLIAM BRANGHAM: It's October 2009.

The streets of Athens are buzzing after Greece's parliamentary election.

The opposition PASOK Party had won a landslide.

A new prime minister took office.

And George Papaconstantinou became the new minister of finance.

GEORGE PAPACONSTANTINOU, Former Greek Finance Minister: When you are asked to serve, you serve.

WILLIAM BRANGHAM: But Papaconstantinou had little idea of the mess he was inheriting.

GEORGE PAPACONSTANTINOU: It was clear that Greece was, let's say, living beyond its means.

The government thought that, rather than dealing with the runaway fiscal deficit, it would be best to not exactly portray the situation as it was and to send to our European partners data which showed the deficit significantly lower.

WILLIAM BRANGHAM: The year before, at the end of 2008, the previous administration had projected its budget deficit would be around 2 percent of the nation's GDP.

After Papaconstantinou's party took office, the government revealed what had been hidden.

The deficit was actually 12 percent and later revised up to 15, more than five times the limit set by the European Union.

GEORGE PAPACONSTANTINOU: Suddenly, you have a big problem, and you have to explain to Greek citizens that you need to deal with this problem.

And dealing with a runaway deficit means some degree of austerity, means reducing expenditures, increasing taxes.

WILLIAM BRANGHAM: The government implemented sharp spending cuts and needed a massive bailout from the E.U.

Greeks took to the streets in the thousands.

Multiple people died during violent riots and clashes with police.

Ultimately, Greece suffered enormously, losing about a quarter of its GDP, while unemployment eclipsed 25 percent.

It would take years for the country to recover.

GEORGE PAPACONSTANTINOU: Trust is lost almost overnight, and it takes years to bring it back, because you are basically telling the world that you will manipulate the data for political means.

It is the country as a whole that gets a bad name.

And very quickly, the shortest joke around European capital was Greek statistics.

WILLIAM BRANGHAM: Before Greece's crisis, Argentina experienced its own number-fudging scandal.

Around 2006, Argentinean policies had resulted in high government spending.

The country's economy ran hot, inflation rose, and price controls didn't work.

So Argentina's president turned his attention to the national statistics agency, eventually firing a key official.

Argentinean-born Alberto Cavallo teaches at the Harvard Business School.

ALBERTO CAVALLO, Professor of Business Administration, Harvard Business School: At the time, it was not obvious that there was going to be manipulation, because the president said, we just don't think the data is being constructed correctly, and we're going to improve the methods, we're going to put people in place who will do this better.

WILLIAM BRANGHAM: At first, the government stopped publishing certain numbers.

Then, when numbers did come out, they appeared detached from reality.

So, Cavallo, who was a Ph.D.

Student in the U.S.

at the time, started doing some digging.

ALBERTO CAVALLO: I decided I would try to collect data online from the largest supermarkets in the country, and I pretty soon realized that the numbers I was getting were two or three times higher than the official numbers for inflation.

WILLIAM BRANGHAM: As the real data became clearer, both regular Argentineans and global investors lost trust in the country's economic numbers.

ALBERTO CAVALLO: It became very hard for the government to finance itself.

And they started relying more on printing money, which led to even more inflation.

WILLIAM BRANGHAM: This summer, after President Trump fired the director of the Bureau of Labor Statistics, the BLS, saying he was unhappy with the agency's job reports, Cavallo saw some parallels to Argentina, but also some key differences.

ALBERTO CAVALLO: There's no evidence yet of any manipulation of the data in the U.S., so I'm hopeful this will not happen.

I honestly think it would be much harder to do here in the U.S.

There are a lot more checks and balances.

The BLS is considered one of the best statistical agencies in the world.

They have a lot of staff, highly qualified staff still that would probably raise flags.

WILLIAM BRANGHAM: Here's what Cavallo says would be a real warning sign, if the government stops putting out data sets altogether, or if the numbers don't roughly match private sector estimates.

Researchers like Amy O'Hara are watching closely for those signals.

O'Hara was a senior official at the U.S.

Census Bureau and is now an expert on public data at Georgetown University.

AMY O'HARA, Georgetown University: Right now, you can think of it as a numbers factory and the raw materials come in and these indicators come out.

The absence of that would be, I fear, one of two things.

One, no numbers come out, and that would be devastating because we would lose the signal to understand what's going on in the country.

And the other thing I would fear is that you don't have the factory running and you have the equivalent of a writers room.

You have people that just make up the numbers and then tell people that this is what happened.

WILLIAM BRANGHAM: O'Hara acknowledges that the government's data collection and its dissemination can always be improved.

AMY O'HARA: I think that we do have something of an opportunity here to say, OK, well, if we're worried about these numbers, great, put more money into improving the measures without scapegoating any individuals.

WILLIAM BRANGHAM: O'Hara too hopes the U.S.

doesn't follow the paths of Greece or Argentina.

But she fears some of the trust in America's statistical agencies, which have collected data for over a century, may already be shaken.

For the "PBS News Hour," I'm William Brangham.