If you’re like me, you’ve cheered the decades-long rise of index funds—investment vehicles that seem (these days) to be a rare case of financial innovation that actually helps regular people. By trying merely to match the market, not beat it—investing passively in stocks that mimic a published market index, like the S&P 500—they’re able to offer both low fees and peace of mind for people not inclined to try to pick which stocks to buy and sell.

Index funds have grown exponentially since John Bogle founded Vanguard in the mid-1970s. The top three families of index funds each manage trillions of dollars, collectively holding 15 to 20 percent of all the stock of major U.S. corporations. Best of all for their investors, index funds have consistently beaten the performance of stock-pickers and actively managed funds, whose higher fees may support the Manhattan lifestyle of many bankers, but turn out not to deliver much to customers.

It’s a feel-good story—a populist victory, as finance goes. Except there’s a problem, or might be. Over the past year or two, a growing chorus of experts has begun to argue that index funds and shareholder diversification are strangling the economy, and need to be stopped. That’s the maximalist claim, anyway, and it is a strain of thinking that is spreading with surprising speed.

Concerns about the potential dangers of shareholder diversification first surfaced back in 1984, not long after index funds themselves did. Julio Rotemberg, then a newly minted economist from Princeton, posited that “firms, acting in the interest of their shareholders,” might “tend to act collusively when their shareholders have diversified portfolios.” The idea, which Rotemberg explored in a working paper, was that if investors own a slice of every firm, they will make more money if firms compete less and collectively raise prices, at the expense of consumers. Knowing this, the firms’ managers will de-emphasize competition and behave more cooperatively with one another. Rotemberg was advised by Larry Summers, then a Harvard economist, and bolstered his argument with 30 pages of mathematical theory. But the argument was counterintuitive and lacked empirical support; his paper sank into obscurity.

Nearly three decades later, José Azar, a young economics consultant who had also gotten his doctorate from Princeton, was having lunch with his colleague Isabel Tecu. Azar’s dissertation had touched on how corporate behavior might change when large investors held highly diversified portfolios. Tecu had worked with airline data, and the two discussed how they might be able to test whether airfares had been influenced by the growth of large shareholders. Azar scoured the literature, uncovering Rotemberg’s paper, and then enlisted an old classmate, Martin Schmalz, to help with the analysis. Schmalz told me he was initially skeptical of Azar’s thesis, saying he found it an “interesting theoretical curiosity, but with no clear evidence in practice.” And so, one of the most controversial studies in modern finance was born.

In April 2014, Azar, Schmalz, and Tecu posted an early draft of a paper titled “Anti-competitive Effects of Common Ownership.” The paper made several astonishing claims. Overall, it said, the high concentration of share ownership had caused serious harm to consumers in the airline industry: Ticket prices were as much as 12 percent higher than they otherwise would have been, because of common ownership of shares. The authors measured how competitive individual routes were, based not only on how often each airline flew a given route—which regulators already examine—but also on the degree to which each airline’s shares were held by common investors. They found that adding common ownership increased the level of concentration on the average route to more than 10 times higher than the levels that regulators presume to be a problem. The paper noted that three mutual-fund families—BlackRock, State Street, and Vanguard—collectively control about 15 percent of the shares of major U.S. airlines, although these funds are by no means the only common owners. At the end of 2016, for instance, Berkshire Hathaway, Warren Buffett’s company, owned 7.8 percent of American Airlines, 8.3 percent of Delta, 7 percent of Southwest, and 9.2 percent of United Continental.

Traditionally, economists have believed that higher prices result from concentration within a consumer market. If one airline has monopoly power over a particular route, the price of a ticket will be high. Likewise, in many cases, prices rise after two airlines merge. For decades, this kind of industry-focused thinking dominated the debate about antitrust enforcement.

The common-ownership argument is different. Instead of looking at the number of companies in a market, it looks at the number of major shareholders those companies have in common. This argument doesn’t obviate the old concerns, but rather adds to them. It suggests an economy in which the incentives for companies to compete and to innovate are smaller than Americans might typically believe, and the opportunities to gouge customers larger. Both market concentration and common ownership have increased in the U.S. over the past two decades, a time that coincides with a slowdown in economic growth. No one would claim this is simple causation—growth results from a complex alchemy of factors. Yet there is no denying that consumers themselves seem unhappy about their treatment by big firms—airlines, banks, insurance companies, cellphone providers, pharmaceutical manufacturers—or that the economy appears sclerotic.

Azar, Schmalz, and Tecu’s paper went viral among academics, launching a whole new field of inquiry and many heated debates. An array of new research blames common ownership for various ills, including high bank fees and stratospheric CEO pay. At the annual meeting of the American Law and Economics Association, in May, common ownership was the subject of multiple presentations and nonstop chatter. Various remedies have already been proposed, some of which are punitive. One journal article argues that large index funds are violating antitrust law; another recommends a limit on index funds owning stock in more than one company in an industry. No one expects these ideas to lead to political action under the current presidential administration, but they are gaining traction among Democratic lawmakers.

The obvious question, of course, is how, exactly, common ownership would encourage these ills. Would common owners actually pressure company managers to collude and raise prices? Would those managers, facing less investor pressure, simply stop competing so hard with one another, enjoying fat paychecks and allowing prices to float up and cost-saving innovation to wither? And would any of that plausibly happen when index funds own just 15 percent of an industry?

Not surprisingly, the managers of index funds have thrown cold water on these possibilities, and on the empirical research itself. In March, BlackRock published a 24-page missive on common ownership, disputing much of the evidence and many of the claims. The analysis—echoed by other critics, including many academics—finds unconvincing, for instance, the airline paper’s claim that higher fares were “a direct result” of the 2009 merger between BlackRock and Barclays Global Investors (which increased BlackRock’s share of airline stocks by only a few percentage points). I spoke with several senior executives at Vanguard who likewise expressed skepticism. They denied any attempt at collusion, and underlined their hands-off approach to investing: One reason Vanguard is able to charge such low fees is that it doesn’t expend a lot of resources investigating individual companies or meeting with managers. Vanguard does have some actively managed funds and a “stewardship group” that meets with hundreds of companies about corporate governance, but its index-fund managers don’t engage with companies about their businesses. If they did so, they’d have to change their investment guidelines and make thousands of new regulatory filings.

What’s more, these funds have frequently been allies to shareholder activists seeking to improve the efficiency and bottom line of individual companies. BlackRock says it votes with activists more than it votes with managers. And even if index funds could cause airline fares to go up, they might not benefit: Those higher fares would mean higher business-travel costs to many other companies in their portfolios.

No academic has accused shareholders of directly asking corporate managers to raise prices—that would clearly violate antitrust law. Azar emphasized to me that common ownership is less problematic if index funds own only a small share of a company’s stock, or if the company has other very large shareholders who don’t also own shares in the company’s competitors. But the three authors were unwavering about the anticompetitive effects of common ownership generally. A revised draft of the airline paper, published in March, is more circumspect about why common ownership leads to higher consumer prices, but remains firm in the conclusion that it does. So far, some other scholarship has supported that position—but the jury is still out.

Edward Rock, an antitrust expert at NYU School of Law, told me that the debate about common ownership is so intense because the underlying issues are fundamental to American capitalism and the country’s long-standing distrust of concentrated power. “The last time we had this degree of concentrated financial power was in the Morgan days,” Rock noted—as in J. P. Morgan, the man. Still, he cautions against overreacting. Rock and his colleague Daniel Rubinfeld have suggested a less disruptive response than most that have so far been proposed: modest antitrust guidelines that would constrain shareholders when they approach a significant stake—say, 15 percent.

Passive investment has been a boon to the affluent and the upper-middle class, at the expense of a relatively small number of much richer bankers. But only about half of Americans own any stocks at all—the rest are consumers but not investors. And so they bear the weight of any damage caused by higher prices, not just for air travel but potentially for every product and service. (Whether common ownership might influence prices in industries that are not dominated by just a few companies—software, say, or consumer goods—is an open question.) Ultimately, the new theory of common ownership is a theory about inequality: To the extent that passive investing shifts costs to consumers, it makes the rich richer, and the poor poorer.

Sometimes academic fights are so ​​vicious because the stakes are so low. But this battle really matters. Diversification has brought undeniable benefits to large numbers of Americans. If recent scholarship is right, it has brought hidden costs to many more. The difficult question, hotly debated but as yet unanswered, is which effect matters more.