Of the hypothetical $127 billion in increased economic output that IER ties to scrapping restrictions, the group attributes more than half of the supposed gains, or $68 billion, to "spillover" effects into other industries. IER says, for example, that increased drilling in offshore fields "might lead to more automobile purchases that would increase economic activity in Michigan."
Similarly, most of the 552,000 jobs hypothetically gained would not be directly related to the oil and gas sector. IER believes 75 percent of the employment gains would be in high-wage, high-skill employment like health care, education, professional fields and the arts.
Maniloff's research into the economic effects of increased drilling show a substantial boost in employment and wages in the boomtowns where drilling takes place, and finds that most statistically significant labor gains outside the energy industry are in the construction and retail sectors.
Though Maniloff acknowledges energy executives and investment bankers typically have more cash to spread around during boom times, he said it is too difficult to draw a straight line between increased activity in the oil patch and an improvement in complex urban economies.
Maniloff also noted little impact on the transportation sector, which led him to believe that many of the truckers who haul water to fracking sites came from beyond the regions where drilling occurred. That reflects one of Kinnaman's findings from his study of shale gas production in Pennsylvania: Not all the windfalls remain in the regions that must deal with the pollution, noise and potential health impacts that are part and parcel of industrial activity.
Mason, the IER study author, acknowledged to CNBC that he did not attempt to quantify the environmental costs of more drilling and mining, but he noted that he also left out a potential economic benefit: Oil, gas and coal production inevitably leads to environmental damage, which requires the services of remediation companies.
"I know it's a perverse argument, but it is there," he said of the economic benefits that can come from environmental damage. "As economists, we're caught. ... This is not about what should be, but about what is."
Democratic presidential nominee Hillary Clinton has vowed to ramp up clean energy while reducing America's dependence on fossil fuels. Meanwhile, Trump has vowed to throw out President Barack Obama's hard-won Paris climate change deal.
— CNBC's Jacob Pramuk contributed to this report.