NEW YORK — As the American economy slowed to a crawl and stockholders watched their money evaporate, chief executive officers’ pay still chugged to yet more dizzying heights last year, an Associated Press analysis shows.

The AP review of compensation for the heads of companies in the Standard &Poor’s 500 index finds the median pay package added up to nearly $8.4 million. That’s a comfortable gain of about $280,000 from 2006.

The 3 1/2; percent pay increase for chief executives came even as the landscape for both workers and shareholders darkened considerably and the economy was choked by a housing market in free fall, layoffs and soaring prices for fuel and food.

At the top of the AP list: John Thain, who took the reins of Merrill Lynch on Dec. 1, 2007. His $83 million pay package was supercharged by a signing bonus and other enticements that lured him from the New York Stock Exchange to lead the investment bank as it was suffering its worst-ever losses.

Collectively, the 10 best-paid chief executives made more than half a billion dollars last year. Yet half the members of this stratospheric club were leading companies whose profits shrank dramatically.

The AP examination of chief executive pay in 2007 mined data from the 410 companies in the S&P 500 that filed compensation disclosures with federal regulators in the first six months of this year.

The AP’s formula, based on data from the past two years, adds up salary, perks, bonuses, above-market interest on pay set aside for later, and company estimates for the value of stock options and stock awards on the day they were granted last year.

That provides a clearer picture than pay totals required by the Securities and Exchange Commission, compensation experts say, because the SEC totals include expenses companies book during the year for previously granted stock compensation and retirement benefits.

The value of stock and options given to chief executives may turn out to be significantly higher or lower if they are ultimately cashed out, but the numbers in the AP formula do reflect the board of directors’ estimate of the likely eventual payout.

The median salary figure of about $8.4 million means half the chief executives in the AP analysis made more than that and half made less.

There were some signs companies were pulling back on pay at the top: Out of the 316 companies in the AP survey that had the same chief executive two years running, about two-fifths lowered the total pay package for their chief executives. However, the primary culprit for some was falling stock prices that cut into the value of the shares included in pay packages.

In many more cases, overall pay ballooned.

Rick Wagoner, chief executive of General Motors Corp., announced earlier this month the company had to close four plants that make trucks and SUVs because of lagging demand as fuel prices soar. That followed the posting of a $39 billion loss in 2007, a year when its stock price fell by about 19 percent, without adjusting for dividends.

And Wagoner? His pay rose 64 percent, to $15.7 million.

Last year was rocky for the economy and the stock market, making it a useful test of a concept called pay for performance — a term companies use to sell shareholders on the idea chief executives are being paid based on how well the company does.

According to this concept, trotted out frequently by the compensation committees of corporate boards in their proxy statements, a big chunk of chief executive pay is considered “at risk,” meaning it could disappear if chief executives don’t meet established metrics.

But the AP analysis found that chief executive pay rose and fell regardless of the direction of a company’s stock price or profits.

Take KB Home, battered by the subprime lending crisis and the weak housing market. According to the Los Angeles-based homebuilder’s proxy statement, chief executive Jeffrey Mezger is entitled to a cash bonus based on a percentage of KB’s profit.

The problem was there was no profit. KB Home lost almost $930 million in 2007 and its stock lost 60 percent of its value. But Mezger still made $24.4 million, as valued by the AP, including a $6 million cash bonus.

He pocketed that bonus because he exceeded certain objectives the board had set out for him. Among them were improving performance on a customer satisfaction survey and developing senior leadership in his first year as chief executive.

“Compensation has become a shell game,” said Richard Ferlauto, director of pension and benefits policy for the American Federation of State, County and Municipal Employees, a Washington labor group representing government workers.

“So they take away the bonus,” he said, “but then they still come up with ways to make sure the executive gets a big payout.”

Pay packages were somewhat smaller in the financial industry last year — banks, investment firms, mortgage companies, insurers and other institutions, all were roiled by the subprime lending disaster.

For companies in the financial sector that had the same chief executive two years in a row, median pay dropped 4¼ percent to $8.7 million in 2007. But that was still a smaller decline than the 6 percent drop in earnings and 15 percent slump in stock prices before dividend adjustments, according to Standard &Poor’s Capital IQ data service.

In some cases, companies appeared at first glance to have kept their promise to base pay on performance — only to have a different picture emerge on closer inspection.

For example, Washington Mutual Inc.’s stock took a nosedive last year — almost 70 percent — because of fallout from the housing and mortgage crises. The Seattle-based banking and mortgage lender lost $1.87 billion in the fourth quarter alone, and $67 million for the year.

WaMu’s board decided not to give chief executive Kerry Killinger a bonus for 2007. But board members also eliminated real-estate foreclosures and mortgage defaults as factors in whether to award him a bonus this year. After a shareholder revolt, the board decided to revise the formula, though it has not yet announced what metrics will be used.

Profit at insurer XL Capital fell more than 80 percent last year, and its stock price slumped about 30 percent. But Chief Executive Brian O’Hara made $7.5 million, a raise of 23 percent.

In its proxy statement, the company called its profits “unsatisfactory” but said operating earnings, which exclude certain factors, were better than planned.

O’Hara, who plans to retire later this year, was also given 62,500 shares of restricted stock and 250,000 stock options, which were not included in the calculation of his total compensation. The company said that was to “reflect the importance of Mr. O’Hara’s role in the CEO succession process.”

“The cracks in the idea of pay for performance really start to show when performance falters but pay still rises,” said Paul Hodgson, senior research associate at The Corporate Library, an independent corporate governance research firm. “It’s always a win-win scenario for executives.”