THE NUMBER OF INMATES in the state’s prisons and jails is going down, but the cost of operating those facilities is going up, largely because correctional institutions are adding more employees and paying their existing workers more, according to a study by MassINC.

The study found that the average daily inmate population of state and county correctional facilities dropped 12 percent between fiscal 2011 and fiscal 2016, falling from 23,850 to 20,691. Yet despite fewer inmates to oversee, the budget for prisons and jails has increased by 18 percent, or $181 million, over the same time period. (Strangely, the budget allocations for corrections don’t correlate exactly with expenditure records, which show an increase in actual spending of $167 million.)

The budget for the state Department of Correction increased by $62 million, or 12 percent, over the six-year period. The budget for the state-funded county sheriff departments rose $119 million, or 24 percent. The $619 million budgeted for sheriffs and the $594 million budgeted for the Department of Correction add up to $1.2 billion, which is slightly more than what the state appropriates for higher education.

The report by MassINC, which is the publisher of CommonWealth, said 84 percent of the spending increase for corrections went to employee payroll. At county sheriff departments, annual salaries for full-time staff over the six-year period rose 17 percent to $63,586. At the state Department of Correction, the average annual salary for full-time staff rose 22 percent to $76,037.

One of the most interesting anomalies in the data was the fact that the payroll at sheriff departments actually increased over the six-year period even as the number of inmates in custody dropped. The number of employees in just security and supervisory roles grew 9 percent to 4,866, which means the sheriff facilities employed one worker to watch every 2.1 inmates.

Overall, the study indicated the total employee count at sheriff departments increased by 5 percent to 7,961, even as the number of inmates fell 16 percent to 10,363. At Department of Correction facilities, by contrast, the employee headcount fell 4 percent to 5,508 as the number of inmates dropped 8 percent to 10,598.

Michael Widmer, the former president of the Massachusetts Taxpayers Foundation who co-authored the report with MassINC research director Ben Forman, said he was surprised that spending was going up as inmate populations were declining. But he said he was astounded that the employee-per-inmate ratio at county facilities was 1:2.

“It’s a staggering number. At least at the Department of Correction, the head count was going down,” he said.

Pressed on what he thinks is happening with hiring at correctional facilities, he said the numbers make  no sense on the surface. “It’s a huge question what’s going on,” he said. “But it’s likely there’s some padding of the payroll.”