April 6 (Reuters) - Cleveland Federal Reserve President Beth Hammack and Chicago Fed President Austan Goolsbee both see inflation as a far bigger problem than employment, underscoring their support for tighter rather than looser monetary policy as the Iran war puts upward pressure on energy prices and the job market remains stuck in low gear.

The pair were asked at a joint interview by The Indicator from Planet Money podcast to provide their economic assessments using a four-color scheme, from "the house is on fire" red to "everything is looking swell" green.

"At least orange. Orange with a chance of meatballs; it hasn't been great," Goolsbee said of the inflation outlook amid rising gasoline prices. "I was optimistic that we would get back to this path to 2% inflation, but yikes, it's going from orange to red lately --- we had tariffs increasing prices, that was supposed to go away, kind of didn't go away, and now we add another stagflationary shock on top ....it's a troubling moment." 

Hammack, too, is troubled by inflation, which she notes has been running above target for five years and has been "basically moving sideways" for the past two. "It's definitely at the brighter, the more vibrant color orange: I don't know if that's burnt orange, burnt sienna: my Crayola box is a little bit old."

The interview was taped on Wednesday, two days before the Labor Department's March jobs report showed the biggest monthly payrolls gain since Donald Trump began his second presidential term last January. The unemployment rate fell to 4.3%, mainly because large numbers of workers left the labor force.  

"To me, the best indicator is really the unemployment rate," Hammack said, and it is currently right around where she estimates full employment should be. While it is a "fragile type of balance," the outlook for her is yellow to green -- perhaps chartreuse, she said, "or actually it's like the Diet Mountain Dew" favored by one of her fellow Fed policymakers at the rate-setting table.

Meanwhile the financial system -- despite stock market losses since the start of the Iran war -- is "generally green," and the economy, from a financial stability standpoint, is in a good place, Hammack said.

Goolsbee was more cautious on both fronts, giving the labor market a "yellow" rating because of its low-hiring, low-firing state, largely explained in his mind by continued uncertainty.

As for the financial system, he said, he's happy with the payment systems but "a little more anxious" about asset prices. "It does look like there is a lot of frothiness," he said, and it is unclear whether that is productivity-driven or a bubble waiting to pop.

"Maybe that's yellow? You are never going to hear me say the word 'chartreuse,'" he said.