WASHINGTON — The government shutdown is delaying another major economic report, leaving policymakers at the Federal Reserve with a cloudier picture even as the economy enters a challenging phase of stubbornly persistent inflation and a sharp slowdown in hiring.

The Labor Department’s monthly inflation data was scheduled for release Wednesday, but late last week was postponed until Oct. 24. The department is recalling some employees to assemble the data, which was collected before the shutdown began. The figures are needed for the government to calculate the annual cost of living adjustment for tens of millions of recipients of benefit programs such as Social Security.

The shutdown could make things worse for agencies like the Fed if it continues, because government agencies cannot collec

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