I don't think I ever used the terms "nanny" and "incentive to be illegal" in the same post or even in the same context.
My belief is that, human nature being what it is, the less scrupulous amoung us value the risks and rewards differently than you or I do (they less fear the consequences of being caught than they value the opportunity to make an additional buck.) The increased incentive to be "off the books" derives from the ability to make an under the table retail transaction at a substantial discount to the customer with both the customer and the provider getting a better deal than executing the same transaction "on the books." That's why folks do it today despite the presence of the all knowing, all seeing, oracle of TaxLand: the IRS.
Today, the nanny is already off the books. That's why Zoe Baird withdrew her name from nomination for Attorney General some years ago. You see, she didn't pay the "nanny tax" for her domestic help ... and SHE was in line to be Attorney General!
Do you really think the illegal Mexican Gardener, working for cash, is going to set himself up with SS system and report their wages? Of course not.
How about the House Painter that says: "I'll tell you what, I'll paint the garage AND the house if you just pay me an additional $550 cash. Otherwise, I have to charge you $650 (because of the Tax) He's otherwise "on the books", but winds up with 10% more in his pocket and a paper trail for a job to keep the auditors at bay. The homeowner saves $100. (Normal, above board price for Garage and House: $650 = $500 cost plus $150 FairTax).
I believe the important aspect of such deals is simple: people will not analyze the risk/reward in any situation based on whether the old tax system would have left them ahead or behind (as you suggest in your example.) People will maximize their immediate opportunity. It there a dose of illegality in it, they'll decide whether they are likely to get caught.
The reason I believe there is more opportunity AND incentive to cheat under the Fair Tax is that people are faced with more consumption options than income options. That, on its face, suggests that there is more opportunity to execute an illegal, tax free transaction under the FairTax.
As for incentive, a retailer could offer up to a 23% discount on an "off the books" transaction to entice a sale, and not loose a dime in income. Like the House Painter, it's quite likely he'll never be caught, especially when the tax-free transaction is buried in a larger above-board transaction.
If you look at the bottom of any post, it will tell you the post that is being referenced. In this case it was your post 423.
"Does anybody really think that those same households that now employ underground nannies, housecleaners and gardeners and don't NOW pay FICA taxes, or withhold income tax from these employees' pay are going to become "in the game" taxable employers and pay the required tax under the FairTax scheme???
I didn't think so."
My post was to show an example of a case where there was sufficient benefit to the nanny to be legal rather than illegal.
My post was not a reference to the "cash economy" that exists amongst contractors such as your painter that are already participating in the system but doing cash work on the side. A similar argument exists, however, in that those people would be cheating themselves of SS credits. So it still decreases the benefit to evasion compared to the current tax system.
These people would not be comparing the current system to the FairTax on a transaction-by-transaction basis. I didn't mean to suggest it. Their decision was simply legal vs. illegal under whichever system exists.
If the "illegal Mexican Gardener" is your point-man for the underground economy, then that is a separate issue. Toss 'em all back over the fence and be done with it ! But as long as he is here, he can't benefit from SS and can't collect the prebate, so he has more incentive to work illegally. Has no choice, in fact. Then it does become up to the employer to reject him.