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Economists and policy makers have been ratcheting up their forecasts for how the U.S. economy will perform this year. But if the vaccination campaign now under way succeeds in stamping out America’s Covid-19 crisis, those forecasts could still be too low.

In the beginning of January, economists surveyed by IHS Markit said on average that they expected that real, or inflation-adjusted, gross domestic product would be 4% higher in the fourth quarter than it was in the same period of last year. One $1.9 trillion economic relief package and more than 100 million Covid-19 vaccination dose administrations later, that forecast has risen to 6.3%. Similarly, Federal Reserve policy makers now project GDP will grow 6.5% over the same period, which compares with a projection of 4.2% back in December.

If those forecasts come true, 2021 will mark the year of the fastest growth the economy has experienced, on a fourth-quarter-to-fourth-quarter basis, since 1983. Considering how much money there is to put to work, it is easy to imagine GDP growing even more quickly.

The $1.9 trillion in additional relief Congress passed earlier this month amounts to 8% of GDP, and although not all of it will make its way into the economy this year, plenty of it will. Similarly, the combination of last year’s government relief and people’s reduced spending during the pandemic substantially raised the amount of money Americans have on hand, with Fed figures showing that at the end of last year, U.S. households had $2.8 trillion more in savings, checking and money-market accounts than at the end of 2019. That comes to about 13% of GDP. Not all of that will be spent as the economy opens, but it seems likely that at least some of it will be pouring into the economy.

One reason forecasts aren’t higher may be that the most optimistic scenario, in which vaccinations continue apace and the Covid-19 crisis lessens, is no sure thing. Variants of the novel coronavirus might prove less resistant to current vaccines than is hoped. The vaccine rollout might hit an unexpected speed bump, such as a high number of people who opt against vaccination. Or people could be slow to lower their guards even when the Covid-19 threat has passed.

Moreover, the Covid-19 crisis is a global phenomenon, and with few exceptions the vaccine rollouts in other countries aren’t nearly as far along as in the U.S., if they have started at all. That includes major destinations for U.S. exports, such as the eurozone, Canada and Mexico. So layering a bit of caution into a bullish forecast makes some sense.

There also is a question of just how quickly U.S. households could step up their spending even if the Covid-19 all-clear signal sounds. The downturn that the pandemic set off hit services spending categories, such as restaurant meals and movie tickets, much harder than goods, such as washing machines. But any rebound in services could face some limits—people might well eat out more than they did before the pandemic, for example, but there are only so many seats at the restaurant. The effect might be to push some spending into next year, in which case forecasts that 2022 fourth-quarter GDP will be about 3% above the year-earlier level could be too low.

Still, when the economy grows quickly, forecasters have a tendency to set their sights too low. In the four years spanning 1996 to 1999, for example, economists surveyed by the Philadelphia Fed in the first quarter of each of those years said that GDP in the fourth quarter would be up by 2% to 2.5% from a year earlier. But when those fourth-quarter GDP reports came out they were consistently higher by a significant degree. Revised Commerce Department figures now show the economy was then growing in excess of 4% each year.

If things go well in the months ahead, they could go really well.

The IRS sent roughly 90 million stimulus checks to Americans in March. WSJ’s chief economics commentator Greg Ip explains why stimulus checks alone are unlikely to spur inflation. Photo Illustration: Carlos Waters

Write to Justin Lahart at justin.lahart@wsj.com

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