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By Ben Popken, TODAY contributor

Following President Barack Obama's re-election this week, women's rights and equal pay advocate Lilly Ledbetter told NBC News she was overjoyed. "I no longer have to worry about the Ledbetter Bill being repealed," she said, referring to the Lilly Ledbetter Fair Pay Act, named after her, which increased the timeframe women could sue for pay discrepancies. During the campaign, Republican vice presidential candidate Paul Ryan criticized the bill, saying it "was not an equal pay law" and was instead "about opening up the lawsuits."

So why do women earn less than men? There are many theories out there, but one thing is for sure: The lower your salary when you begin your career, the harder it is to catch up.

That's why the experiment "Do Women Avoid Salary Negotiations?" published in a working paper by the National Bureau of Economic Research is so important for working women. The research found that men were more likely to negotiate their starting salary than women, but — and this is huge — if applicants were told the wage was "negotiable," not only did the gap evaporate, women outpaced men in asking for a heftier paycheck.

Ledbetter said the findings from the study show that "we are still a long way from equal pay and equal benefits."

The percentage varies depending on which study you use, but women as a whole earn at least a quarter less than what men earn (unless they're city-dwelling, under 30, single and childless, in which case they may earn about 8 percent more than their male counterparts.) Meanwhile, wages have been stagnant overall. According to Bureau of Labor and Statistics data, hourly earnings fell 1 cent in October, and worker wages have grown at an anemic 1.6 percent rate, slower than inflation.

In the experiment, researchers placed real advertisements for administrative assistant jobs in nine U.S. cities. Those who replied were randomly chosen to receive one of two responses from the employer.

Both thanked the prospective employee for their interest, apologized if they had any unanswered questions, and told them a little bit more about the job, including the hourly salary. However, one of the replies had the word "negotiable" next to the hourly wage.

When not explicitly told the salary was negotiable, men negotiated for a higher salary 29 percent more frequently than women. When it was clear the salary was negotiable, both sexes negotiated much more, but women actually negotiated 9 percent more frequently than men.

"When the rules of wage determination are concrete, women are more likely to negotiate," study co-author Andreas Leibbrandt of Australia's Monash University told NBC News.

What's up with that?

Victoria Pynchon, co-founder of She Negotiates Sales and Training, a Los Angeles consultancy that coaches women on asking for better pay, says women "are still grateful to be offered a job" and that if they ask for more money, they're worried the job offer will be retracted. Women are taught, says Pynchon, that "if a woman asks for something for herself, she's likely to be punished."

Pynchon offered several tips for women seeking to increase their starting salaries. First, figure out your fair market value, using a salary comparison site like glassdoor.com. Then, "ask for more than you want." This is important because women need to both counter the inevitable haggling, as well as overcome their tendency to undervalue themselves. When psyching yourself up for the salary talk, she says, "tell yourself it's not a game, it's a conversation leading to an agreement."

Above all, experts say, don't get caught in the "good girl" trap, obeying the rules written on the board game box. You'll never win that way. Don't wait to be told you're "allowed" to negotiate your salary. Assume that it is expected and ask for what you're worth. After all, that's what the guy sitting next to you is doing.

"With hard work and perseverance," said Ledbetter, "you can get it."

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