No "construction" will be needed, boys. This is a racist and sexist nation. That's not even a question just, how bad is it at the moment and is it getting better or worse?
Of course construction is needed. You have to carefully avoid accounting for anything beyond the chosen categories because the pay differential tends to disappear (unless you work for either Obama or Hillary, who pay women less).
Black man versus white man? Man versus woman? The difference in pay will be there nearly without question, even when accounting for all other factors. This isn't a new thing, it's been that way for ages. Being dishonest about it helps you not at all.
I always paid my workers the same pay for the job they were doing no matter their race or sex.
When I was running a motel the desk clerk were paid the same except for the lead where she got one dollar more a hour. Maintenance worker got paid more because of the work they would do, and the House Keeper was paid less than the Maintenance worker but more than the Desk clerk, and leads made more than those under them.
I had two leads that were female and one that was male and they were all Hispanic and the only other white beside me worked in the maintenance department under a Hispanic lead.
Had my desk lead or house keeping lead moved into the maintenance lead position they would have been paid the same pay as the lead was being paid for that position and not less because of the work that was involved.
I am not saying that discrimination does not happen but not all whites subscribe to the train of thought you are suggesting, and many will be fair if left alone, and not pushed by the government.
I know you will mock and disagree as you usually do so have at it but the reality is I will pay someone according to the job they are doing and their race and sex does not enter the discussion...