This view has won support from some people who might be expected to see executive power in more expansive terms. Earlier this year, Jeffrey Immelt, the beleaguered successor to Jack Welch as CEO of General Electric, rather defensively told a gathering sponsored by the Financial Times that in the 1990s, “anyone could have run GE and done well.” Warming to his theme, he added, “Not only could anyone have run GE in the 1990s, [a] dog could have run GE. A German shepherd could have run GE.” Welch, to his credit, more or less agreed with this assessment. “It was an easier time to be a CEO in the 1990s,” he told the FT. “The wind was on our backs.” As they say on Wall Street, never confuse brains with a bull market.

One problem with the idea of the transformative CEO, able to reshape corporate culture or inspire workers to new heights, some scholars argue, is that people simply don’t feel allegiance to large entities like corporations, no matter who’s at the helm. Their loyalties are far more localized. Like infantrymen, their sense of belonging extends to their own platoon but no farther. And in these postmodern times, employees are mostly scornful of any grandiose rhetoric about higher purposes and the nobility of their cause. From this perspective, the CEO’s power to affect performance, while strong within the immediate team of top executives, rapidly diminishes as it extends beyond that team.

J. Richard Hackman, a psychologist at Harvard, has done extensive work on leadership within small teams, and he has found that leaders do exert measurable influence on their team’s success or failure. In his 2002 book, Leading Teams: Setting the Stage for Great Performances, he argues that small groups perform best when they operate collaboratively, and not merely as drones subordinated to a leader. The team leader’s job is to establish the conditions that enable team members to collaborate competently; the leader needs to spell out exactly where teams should end up, but not dictate the step-by-step process of getting there. Leaders who act boldly and intelligently can make significant differences in teams’ effectiveness—but no matter how the leaders act, teams become less effective as they grow in size. Ideal team size, Hackman says, is about six people; performance problems increase exponentially as team size increases beyond that, and the impact of leadership becomes quickly diffused.

The highly localized nature of loyalty, some scholars argue, means that the real power to influence corporate performance resides not with the CEO but with middle management. In the recently published The Truth About Middle Managers, Paul Osterman, a professor at MIT’s Sloan School of Management, contends that middle managers are neither “victims,” robbed of the ability to act independently by some faceless bureaucracy, nor “villains” like Dilbert’s Bozo-haired boss, too clueless to do anything but gum up the works. In Osterman’s view, the middle manager is the secret hero in the large corporation’s rise to social and economic dominance. That rise “depended on middle managers,” he says, “because you just couldn’t achieve the scale that we have without people doing the kind of planning work that they do.” As “craft workers,” middle managers value their task, sense its importance to the larger cause, and feel great loyalty to the people they work with. But their loyalty to the corporation is fraying, largely because they see top management hogging all the rewards and glory. “There’s more cynicism” in the middle-management ranks now, Osterman says. “There’s less willingness to go the extra mile.”

Perhaps to ask whether the CEO really matters is to ask the wrong question. Three Harvard professors—Noam Wasserman, Bharat Anand, and Nitin Nohria—say in a recent paper that the right question is, When does leadership matter? Using advanced statistical techniques that go by a wonderfully CSI-style name, “variance decomposition analysis,” the authors examine 531 companies in 42 industries and isolate leadership effects from other determinants of corporate performance. They conclude that leadership matters sometimes. It doesn’t make much difference at electrical-utility companies, which are so constrained by government regulations and the cost of fuel that there’s very little room for the CEO to exercise any discretion. The professors used the term “Titular Figureheads” for such CEOs. In addition to utilities, you’ll find them in stable, old-line industries—paper mills, meat wholesalers—where the pace of change is slow.