More details, please—in what sectors do you think shadowstats is incorrect?
All of them. If you take shadow stats #s from 1980 and grow them today, prices would have to be more than double that they are now for them to be accurate. Seriously, run them in excel. Then compare the price of say milk or a 2000 sq ft home in 1980 and do the same today - they are far, far closer to CPIs #s.