Equalizing quantization error in the wage channel

Bruce points us to research that shows the self-employed consistently under represent wage reporting by 30% relative to the employed. Whys is that?

The employed have a wage channel decomposed in the the firm and the employee. The Self employed have to decompose the wage channel within their business. To make the two channels coherent, the self employed maintain the imprecision within their own businesses, the employed share the imprecision with the employer.

This is the conclusion from channel theory, the short the wage channel manages imprecision in one stage, the long channel splits the imprecision among two stages. In both cases, the amount of imprecision is biologically fixed.

The wage reports are correct, the researchers don't get channel theory.