????A CEO who accepts an annual salary of $1 sends a powerful message -- namely, that he or she is a team player who wants to make a sacrifice for the good of the company. True, the executive is probably receiving generous stock options on the side, but those payments depend on the corporation's success. The buck-a-year salary is a grand gesture, intended to broadcast the CEO's confidence in the future of the business.

????It may also be a smokescreen. A recent study by Professors Gilberto Loureiro, Anil K. Makhija, and Dan Zhang says that, in many cases, $1 paydays are nothing more than public relations ploys: "We find evidence consistent with the view that $1 CEO salaries are a ruse hiding the rent-seeking pursuits of CEOs adopting these pay schemes," they wrote. "Thus, rather than being the sacrificial acts they are projected to be, our findings suggest that adoptions of $1 CEO salaries are opportunistic behavior of the wealthier, more overconfident, influential CEOs."

????The $1 salary was pioneered by former Chrysler head Lee Iacocca, who slashed his pay in the late 1970s while the struggling car company lobbied the government for help. Other CEOs followed suit: Nelson Peltz of Wendy's/Arby's Group (WEN), Sumner Redstone of CBS (CBS), and a flurry of tech executives including Apple's (AAPL) Steve Jobs, Oracle's (ORCL) Larry Ellison, and Cisco's (CSCO) John Chambers.

????The idea has gained even more traction in recent years, with corporate leaders like Google's (GOOG) Eric Schmidt and Whole Foods' (WFM) John Mackey embracing it. During the financial crisis, the CEOs of automakers GM (GM), Chrysler, and Ford (F) all pledged to pay themselves a dollar. So did Citigroup (C) chief Vikram Pandit, who received a single greenback in 2009 and 2010 (his asceticism was short-lived: the bank recently awarded Pandit with a multi-year pay package worth more than $20 million.

????It's no secret that these self-abnegating chieftains often make up what they lose in salary by loading up on stock options. Loureiro and his co-authors looked at the total compensation for the fifty CEOs of publicly listed companies who made $1 or less between 1992 and 2005 and found that, when equity-based pay was included, they made just as much as their peers did. The $1 CEOs gave up a median of $610,000 in annual wages, but they gained more than $2 million in incremental options awards.

????Stock compensation can be a good thing. When CEOs forgo a large salary or bonus in exchange for equity, they align their wealth with the company's success, which should motivate them to pursue growth. According to the study, this "alignment hypothesis" is the most frequently cited rationale for the $1 salary. But it isn't supported by the facts. The authors found that the companies that cut CEO pay didn't have a demonstrable need to align executive performance with results. They also didn't have significant growth opportunities or a history of rewarding leaders with options.

????The alignment hypothesis is further undermined by the high rate of turnover amongst $1 CEOs. Once the salary plan was discontinued, only 48% of the CEOs who accepted the cut stayed in their positions. Between 1993 and 2001, total turnover amongst the CEOs of publicly traded companies was just 9%.

????The study's authors argue that the stunt salary is better explained by the "managerial power hypothesis," which posits that $1 CEOs are pursuing their own interests. The businesses that instituted $1 salaries, they wrote, had weaker corporate governance. Only 34% had independent compensation committees, compared to an average of 67%. Power at the $1 companies was concentrated at the top; their CEOs had an average ownership stake of 10% (vs. their peers' 3.2%). Outside institutions owned just 53% of the companies (vs. 61%).

????One dollar CEOs are wealthy and confident, even more so than the average executive. This further corroborates the managerial power hypothesis, the study says, because rich and brash leaders are more likely to pursue their own agendas. A whopping 30% of $1 CEOs were on the Forbes 400 list of the richest Americans, compared to an average of less than 5% among CEOs in general. They were twice as likely to be described in news reports as "optimistic" or "confident."

????Confidence alone isn't cause for concern. But the study also found that $1 CEOs frequently had issues that made them vulnerable to public outrage, like pending government inquiries, corporate underperformance, and personal dilemmas. Of the 50 CEOs who accepted a $1 salary, 25 had explicit public relations risks. That could be a coincidence -- but the authors doubt it: "It is not surprising that this group has chosen to adopt $1 salaries as camouflage for their benefits."

????If that seems cynical, consider this: In the first year after companies announced $1 CEO salaries, they achieved returns on assets that were comparable to their peers; after that, their returns deteriorated. One-dollar companies significantly underperformed their peers in the stock market after three years.

????The authors' findings are damning -- but they may not be completely conclusive, according to another recent study. This one, authored by Sophia J.W. Hamm, Michael J. Jung, and Clare Wang, looked at the different CEOs taking $1 salaries and found vast disparities within the group.

????While the executives who received higher total paydays were likely to underperform going forward, they wrote, those who actually did receive lower pay packages were likely to achieve improved stock returns and performance. In the end, the $1 salary was irrelevant; what mattered was the bottom line.

????Editor's note: A previous version of this story erroneously stated that Ford Motor Co. received a federal bailout. This has been corrected.