The savviest boards looking for a new CEO should consider adding a step to the screening process — and send someone to the parking ramp to note the candidate’s car.

If it’s a BMW 650i convertible, keep looking.

Yes, it may just be a car, but it turns out that a CEO with a fondness for luxuries like a $100,000 convertible isn’t as likely to run a tight ship as a more cautious spender. Appoint a spender, and the risk of some inventive accounting just went up.

That’s the conclusion of a team of researchers that includes accounting professor Aiyesha Dey of the Carlson School of Management at the University of Minnesota, in a paper to be published soon in the Journal of Financial Economics.

This project was shaped in part by the corporate board experience of Dey’s research colleague, Abbie Smith of the University of Chicago’s Booth School of Business. Smith had just helped pick a new CEO with a strikingly conservative personal lifestyle.

“The prior guy was this loose, let’s not bother with the cost-cutting, let’s just go ahead with the acquisitions type,” Dey said. “The new CEO was literally, in his personal life, a coupon cutter. He was a CEO but he would save coupons and be very careful about where he spends, and he brought that style into the management of the firm’s resources.”

From this observation the team thought it was worth looking into how personal spending by the top executive can affect the quality of a company’s financial statements.

So who is a spendthrift? It’s a CEO who spent more than twice the typical home price in neighborhoods near headquarters plus any vacation properties that cost more than twice the average home price in that metropolitan area. He or she also owns a boat longer than 25 feet and a car that cost more than $75,000.

Dey said they considered carefully what might indicate CEO frugality, not professor frugality. To spend $75,000 on a car eliminates not just Fords or Buicks but the entire Volvo range. Even in BMWs you can spend far less than what a 6-series convertible costs.

But a car that starts at $82,900 (and with a few common-sense options quickly gets to $110,000) isn’t frugal even for a CEO.

Lots of chief executives drive expensive cars and live in baronial houses, but there are enough who do not to draw some conclusions.

The most stunning is that the probability of a serious financial reporting error is 41 percent lower in firms run by a frugal CEO. The probability of reporting errors decreases over the tenure of a frugal CEO while it increases significantly over the tenure of a non-frugal CEO.

They also looked into the chief financial officer role. It looks like in situations where the boss owns a big boat and lives in a big house, the CFO is likely to have that kind of lifestyle, as well. Hiring a CFO who also likes to spend freely is part of the cultural change the researchers write about that takes place after a big spender takes over as CEO.

They also see other changes, including an increase in executives’ equity-based compensation and a decrease in some of the measures of board monitoring. For example, big-spending CEOs are more likely to have social ties with the board.

The research team did not confine itself to looking just at personal spending, either — they also looked for CEOs who previously had a legal problem, even things like speeding violations. What they assumed they’d find, they did: A top executive with a legal record meant higher incidence of fraud in the financial statements than at companies led by CEOs with spotless records.

The good news is that the “un-frugal” CEOs were just sloppier and greedier, not more likely to be personally engaged in fraud. Yet the research suggested that the likelihood of fraud occurring increased while they were the boss, as the company’s culture changed.

Looking to further explore this rich vein of research, Dey and her colleagues have already mostly finished a similar project that looked at insider trading. In this work, she said, it was easy enough to see an entire organization flip from frugal to non-frugal as the CEO changed, and others in the organization became more likely to exploit opportunities to trade on inside information.

The virtues of frugality have been taught in American business since Philadelphia printing entrepreneur Benjamin Franklin wrote about them well over 200 years ago, but Dey and her colleagues don’t say to pick only frugal CEOs. As she put it, “maybe these lavish or un-frugal executives have other qualities that make them desirable.”

There are executives, and I have worked with some, who view big spenders as attractive candidates for leadership jobs.

A flashy lifestyle shows that someone is “hungry,” that they will be “aggressive” in pursuing financial goals, or that there’s a need for “risk takers” when the company has had its fill of risk avoiders.

But here’s some sensible advice for corporate directors: Put a big spender in charge, and you should plan to spend a lot more time just watching.