Statistics on Under-the-table work: Are they out there?

Factual Questions
1

I’m having a devilishly hard time doing a simple Internet search; either my Google-fu is pitifully weak or this information just isn’t available online:

I’m living in France, and writing a paper on undeclared work in France and in the U.S., specifically in the restaurant/bar/hotel industry. I’m trying to find some estimations of the number/percentage of undeclared workers, broken down by industry. For France, these numbers are marvellously easy to find, the Délégation Interministérielle à la Lutte contre le Travail Illégal publishes a report with it all broken down in great detail.

I’ve been tearing my hair out trying to find similar info. for the United States, at the national level.

I’ve tried searching the websites of the Internal Revenue Service , US Department of Labor Bureau of Labor Statistics , and the Government Accountability Office , without success. In addition, I have tried Google searching a variety of terms, “undeclared work”, “under the table work”, “employer fraud,”…and coming up empty.

Are these statistics simply not out there? Am I using the wrong search terms? Or, maybe, must I search state-by-state?

I don’t post here very often, but I know of no other Internet forum with such a wide range of expertise, so I throw this out there hoping someone can tell me what I am doing wrong.

Mille mercis!

2

Add this to your search list , delinquent dads, deadbead dads.

Dont know enough about the states but up here in Canada , one of the things that the government does is to garnish wages for child support. That leads to some people having to find work in the underground economy.

Declan