Inflation is likely getting a temporary boost from the $1.9 trillion coronavirus relief package that the Biden administration ushered in early this year, new Federal Reserve Bank of San Francisco research released on Monday suggested.

The analysis may add fuel to a hot debate in Washington over whether the administration’s policies are contributing to a spike in prices. Critics of the government spending package that was signed into law in March, including former Treasury Secretary Lawrence H. Summers, have said it was poorly targeted and risked overheating the economy. Supporters of the relief program have said it provided critical aid to workers and businesses still struggling through the pandemic.

The new paper comes down somewhere in the middle, finding that the spending had some effect on inflation but suggesting that it is most likely to be temporary. The economists estimated that it would add 0.3 percentage points to the core Personal Consumption Expenditures inflation index in 2021 and “a bit more” than 0.2 percentage points in 2022. Core inflation strips out volatile items like food and fuel.

While those numbers are significant, they are not what most people would consider “overheating” — the Fed aims for 2 percent inflation on average over time, and a few tenths of a percent here or there are not a reason for much alarm.

But the result is only a rough estimate, one the researchers came up with to help inform an continuing political and economic debate.

Both the Trump and Biden administrations signed trillions of dollars in virus relief spending into law. The packages included two bipartisan bills in 2020 that pumped more than $3 trillion into the economy, including direct checks to individuals and generous unemployment benefits. Another $1.9 trillion — called the American Rescue Plan — was passed this year by Democrats after they took control of both Congress and the White House.

“The later timing and large size of the A.R.P. stirred debate about whether it is causing an overheating of the economy and fueling a sustained increase in inflation,” the San Francisco Fed researchers noted.

The economists tried to answer that question by looking at how much spare capacity is in the economy using a labor market measure — the ratio of job openings to unemployment. The logic is that inflation tends to pick up when there is very little labor market slack, because businesses raise wages to attract workers and then raise prices to cover their climbing labor costs.

Government stimulus can push up the number of job openings in the economy as it fuels demand while constraining the number of available workers because it gives would-be employees a financial cushion, allowing them to take their time as they search for a new job.

Based on the package’s size and using historical evidence on how fiscal spending affects the labor market, the researchers found that the American Rescue Plan might raise the vacancy-to-unemployment ratio close to its historical peak in 1968, fueling some inflation — but that the price impact would be small and short-lived.

“This minor impact is attributable to the small effect of slack on inflation and the strong historical stability of longer-run inflation expectations,” the economists wrote.

The researchers assumed that while the labor market is tight, that will not last. And they assumed that businesses and consumers will not come to expect much-higher prices as a result of the short-term inflation burst.

The new analysis is unlikely to be the final word on the matter. Inflation has jumped higher this year — the core P.C.E. measure climbed 3.6 percent in the year through August, and other measures of inflation are even higher. Many economists are concerned that the jump in prices will cause inflation expectations to shift, especially because some measures are already creeping higher.