"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...
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?
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.
http://www.slate.com/articles/double_x/doublex/2013/08/gende...
http://www.huffingtonpost.com/christina-hoff-sommers/wage-ga...
The 77 cents on the dollar myth actively shifts attention away from the real issues with gender roles and western culture in favour of a simple outdated narrative that isn't going to help anyone.
It's a useful shibboleth though, the people using it are either well meaning but uninformed or interested more in attention/marketing than actual equality.