“I’ve heard that there are some billionaires that don’t support this plan,” Ms. Warren says in the ad, which proceeds to deride several of the plan’s critics for financial ties to Republicans. “All we’re saying,” she says in conclusion, “is when you make it big, pitch in two cents so everybody else gets a chance to make it.”

Ms. Warren’s campaign worked with Emmanuel Saez and Gabriel Zucman, two economists at the University of California, Berkeley, who support a wealth tax, to estimate how much money it could raise over a decade. But they did not produce what economists call a dynamic analysis, which estimates how the proposal would ripple through the economy and affect growth.

Evaluating a wealth tax in that manner has proved challenging for budget analysts, who are more accustomed to estimating the effects of changes in individual or corporate income tax rates. Thursday’s release is essentially a rough cut of Penn Wharton’s attempt to track the overall economic impact; a fuller version will come in December. For the preliminary analysis, researchers assumed that Mr. Saez and Mr. Zucman’s $3 trillion revenue forecast was correct.

The Penn Wharton Budget Model estimated that wealthy Americans would consume more and save and invest less in order to avoid accumulating wealth that would be subject to the tax. The resulting drop in investment reduces economic growth.

“The wealth tax shrinks the economy because saving is more expensive,” said Richard Prisinzano, Penn Wharton’s director of policy analysis. “The results also suggest that the negative effect of the tax increases as the tax rate increases.”

Mr. Zucman said in an interview that the analysis did not take into account Ms. Warren’s spending plans, which he said would most likely bolster savings, investment and labor-force participation — and, with them, growth.

“If the government collects $3 trillion in wealth tax revenue, and spends $3 trillion on public infrastructure,” he said, “it’s unclear that there should be a reduction” in the amount of overall investment in the economy.