America’s schools received an unprecedented $190 billion in federal emergency funding during the pandemic. Since then, one big question has loomed over them: Did that historic infusion of federal relief help students make up for the learning they missed?

Two new research studies, conducted separately but both released on Wednesday, offer the first answer to that question: Yes, the money made a meaningful difference. But both studies come with context and caveats that, along with that headline finding, require some unpacking.

How much of a difference did the money make?

$190 billion is an enormous amount of money by any measure. But districts were only required to spend a fraction of the relief on academic recovery, by paying for proven interventions like summer learning and high-quality tutoring. So how much additional student learning did the federal aid actually buy?

Study #1, a collaboration including Tom Kane at Harvard’s Center for Education Policy Research and Sean Reardon at Stanford’s Educational Opportunity Project, estimates that every $1,000 in federal relief spent per student bought the kind of math test score gains that come with 3% of a school year, or about six school days of learning. That’s during the 2022-23 academic year.

Improvements in reading scores were smaller: roughly three school days of progress per $1,000 in federal relief spending per student.

The federal relief “was worth the investment,” Reardon tells NPR. “It led to significant improvements in children’s academic performance… It wasn’t enough money, or enough recovery, to get students all the way back to where they were in 2019, but it did make a significant difference.”

Study #2, co-authored by researcher Dan Goldhaber at the University of Washington and American Institutes for Research, offers a similar estimate of math gains. The increase in reading scores, according to Goldhaber, appeared comparable to those math gains, though he says they’re less precise and a little less certain.

“It did have an impact,” Goldhaber tells NPR, an impact that’s “in line with estimates from prior research about how much money moves the needle of student achievement.”

Who benefited the most?

The federal recovery dollars came in three waves, known as ESSER (Elementary and Secondary School Emergency Relief Fund) I, II and III. The first two waves were relatively small, roughly $68 billion, compared to the $122 billion of ESSER III.

The windfall was distributed to schools based largely on need – specifically, based on the proportion of students living in or near poverty. The assumption being: Districts with higher rates of student poverty would need more help recovering. COVID hit high-poverty communities harder, with higher rates of infection, death, unemployment and remote schooling than in many affluent communities.

“These and other factors likely caused greater learning loss during the pandemic and dampened academic recovery,” Goldhaber writes in Study #2, pointing out that, “the Detroit, MI public school district received about $25,800 per pupil across all waves of ESSER… [while] Grosse Pointe, MI (a nearby suburb) only received about $860 per pupil.”

Here’s where the story of these federal dollars gets complicated, because the learning they appear to have bought wasn’t experienced evenly, according to Goldhaber.

In Study #2, he and co-author Grace Falken, found larger academic benefits from federal spending in districts serving low shares of Black and Hispanic students. Though he tells NPR, these patterns “do not necessarily imply that ESSER’s impacts vary because of student demographics. Rather, the results could reflect other district characteristics that happen to correlate with the student populations the districts serve.”

Reardon and Kane did not find statistically significant evidence of this kind of variation.

Goldhaber and Falken also found that towns saw more math gains than cities, while rural areas led the way in reading growth. Interestingly, suburban districts generally experienced “smaller, insignificant impacts” from the federal spending in both subjects.

But did the money help enough?

If your standard for “enough” is a full recovery for all students from the learning they missed during the pandemic, then no, the money did not remedy the full problem.

But the researchers behind both studies say that’s an unrealistic and unreasonable yardstick. After all, Congress only required that districts spend at least 20% of ESSER III funds on learning recovery. The rest of the relief came with relatively few strings attached.

Instead, the researchers say, the money’s effectiveness should be judged by a more realistic standard, based on what previous research has shown money can and cannot buy.

Harvard’s Tom Kane, of Study #1, points out that their results do line up with pre-pandemic research on the impact of school spending, and suggest a clear, long-term return on investment.

“These academic gains will translate into improvements in earnings and other outcomes that will last a lifetime,” Kane tells NPR.

For example, the academic gains associated with every $1,000 in per student spending would be worth $1,238 in future earnings, Kane estimates. Increased academic achievement also comes with valuable social returns, he says, including lower rates of arrest and teen motherhood.

What’s more, Reardon tells NPR, because these federal dollars disproportionately went to lower-income districts, “not only do we find that the federal investment raised test scores, but we also find that it reduced educational inequality.”

But the work’s not over.

In Study #2, Goldhaber and Falken write, “to recover from these remaining losses, our estimates suggest schools would need between $9,000 and $13,000 in additional funds per pupil, assuming the return on those funds is similar to what we estimated for ESSER III.”

They also warn that middle-income districts could continue to struggle – because they experienced academic losses but got less federal aid.

In a presidential election year, it’s unlikely Congress will agree to send schools more money. And Goldhaber worries, as ESSER funds begin to expire this year, districts will have to cut staff.

“Some districts, particularly high poverty, high minority districts, are going to lose so much money that I think teacher layoffs are inevitable,” Goldhaber tells NPR. “So I’m worried that the funding cliff – there’s a downside that we’re not thinking hard enough about.”

The good news, says Kane, is that ESSER was a massive, “brute force” effort, and a far smaller, state-driven effort could still make a big difference, so long as it’s hyper-focused on academic interventions.

Kane says, “It falls to states to complete the recovery.”