This article[1] links to various sources which cite different values. Of those, this report[2] (research funded by US Department of Labour) states in it's summary (page 35);
"Specifically, variables have been developed to represent career interruption among workers with specific gender, age, and number of children. Statistical analysis that includes those variables has produced results that collectively account for between 65.1 and 76.4 of a raw gender wage gap of 20.4 percent, and thereby leave an adjusted wage gap that is between 4.8 and 7.1 percent."
My personal opinion is that there may be a slight gap, research that conservatively accounts for factors rather than assuming the difference is 100% gender-pay do tend to put it below 10%, however there just isn't enough hard evidence to account for all the variables which may cause such a gap, so finding an accurate value isn't possible. Each side of the debate will always find the most attractive figures to support their agenda, as can be seen by people quoting 20%+ raw wage gap analysis that doesn't account for difference in time worked etc, and others misreading statistics to say that it's lower than reported.
4.8 to 7.1% is quite a bit more significant than your initial claim of 2 to 3%
edit - also, how do you claim to have any kind of confidence in the accuracy of your own estimate, while simultaneously arguing that reaching any sort of accurate value is impossible?
It was someone else who made that initial claim of 2%, however if you read the full summary of my second link, they admit to only accounting for factors they were able to measure. So additional factors they didn't account for, may have influence towards the divide (other than gender-pay), and may account for any number that could further reduce that 4.8-7.1%. I'm not saying it is as low as 2-3%, but its certainly possible.
It was someone else who made that initial claim of 2%
Sorry, complete failure to pay attention on my part.
Though as to your other point, unmeasured factors could push the figure either way, so if you allow the error bars to go as low as 2% purely on a hunch, then you should also consider that it could be up to 9.9%, if trying to work out any sort of reasonable policy.
"Specifically, variables have been developed to represent career interruption among workers with specific gender, age, and number of children. Statistical analysis that includes those variables has produced results that collectively account for between 65.1 and 76.4 of a raw gender wage gap of 20.4 percent, and thereby leave an adjusted wage gap that is between 4.8 and 7.1 percent."
My personal opinion is that there may be a slight gap, research that conservatively accounts for factors rather than assuming the difference is 100% gender-pay do tend to put it below 10%, however there just isn't enough hard evidence to account for all the variables which may cause such a gap, so finding an accurate value isn't possible. Each side of the debate will always find the most attractive figures to support their agenda, as can be seen by people quoting 20%+ raw wage gap analysis that doesn't account for difference in time worked etc, and others misreading statistics to say that it's lower than reported.
-------------------------- [1] http://www.huffingtonpost.com/christina-hoff-sommers/wage-ga...
[2] http://www.consad.com/content/reports/Gender%20Wage%20Gap%20...