* Retailers post mixed monthly sales in January
* Greenlight Capital sues Apple
* Dow off 0.1 pct, S&P off 0.03 pct, Nasdaq off 0.1 pct
NEW YORK, Feb 7 (Reuters) - U.S. stocks were little changed on Thursday after data showed modest improvement in the labor market and retailers posted mixed monthly sales.
Weekly initial jobless claims dipped last week, with the four-week moving average falling to its lowest level since March 2008, signaling the economy continues to recover slowly.
A separate report said fourth-quarter productivity registered its biggest drop in nearly two years, while unit labor costs jumped 4.5 percent, more than economists expected.
"Claims didn't look too exciting. They are pretty much in line. The bigger surprise was the jump in unit labor costs that was pretty substantial," said Peter Jankovskis, co-chief investment officer at OakBrook Investments LLC in Lisle, Illinois.
"Overall the market took the whole thing in stride."
Recent data has pointed to a slow improvement in the economy, but one without enough strength to cause the Federal Reserve to abandon its easy monetary policy, which has helped the benchmark S&P index to climb 6 percent this year.
"We are probably in a pretty stable policy regime from the Fed standpoint, certainly until midyear, then as we get later in the year if we are seeing the economy picking up, then maybe they start taking their foot off the accelerator a little bit," said Jankovskis.
Several U.S. retailers reported mixed January sales results, as consumers faced a hit to their take-home pay from higher payroll taxes. The S&P retail index gained 0.3 percent.
Macy's Inc rose 1.4 percent to $40.04 after reporting January same store sales rose 11.7 percent.
But Ann Inc dropped 7.9 percent to $30.20 after forecasting fourth-quarter sales below analysts' expectations.
The Dow Jones industrial average dropped 13.90 points, or 0.10 percent, to 13,972.62. The Standard & Poor's 500 Index dropped 0.43 points, or 0.03 percent, to 1,511.69. The Nasdaq Composite Index dropped 3.04 points, or 0.10 percent, to 3,165.43.
Fund manager David Einhorn's Greenlight Capital on Thursday said it has sued Apple Inc and said the company needs to do more to unlock value for shareholders. Apple shares gained 1 percent to $459.27.
Akami Technologies Inc lost 17.8 percent to $34.17 as the worst performer on the S&P 500 after the Internet content delivery company forecast current-quarter revenue below analysts' expectations.
According to Thomson Reuters data through Thursday morning, of 317 companies in the S&P 500 that have reported earnings, 69 percent have exceeded analysts' expectations, above a 62 percent average since 1994 and 65 percent over the past four quarters.
Fourth-quarter earnings for S&P 500 companies rose 5 percent, according to the data, above a 1.9 percent forecast at the start of the earnings season.
The European Central Bank held its main interest rate unchanged at 0.75 percent, as expected.