A number of economists have attempted to use monetary data to develop an estimate of tax noncompliance. All are based on the assumption that 'excess' demand for cash occurs because persons desire to hide income-generating transactions on which no payment of taxes is made. This measurement method has serious shortcomings because (1) there is no independent means to verify the assumed connection between changes in monetary relationships and income underreporting; (2) there are a large number of other plausible factors that could explain changes in the monetary relationships used; and (3) monetary-based indexes of noncompliance are highly unstable. In using a measure of tax violations based on the difference or residual left when two sets of income data are compared, the data are translated into a common definition of income and adjusted for income received by persons falling below Federal income-tax filing requirements; the difference between these two aggregate totals should, to the extent the original two series are accurate, measure the amount of income improperly omitted from tax returns because of underreporting or failure to file. Although the use of this residual method in examining income data from 1945 to 1947 results in estimates of decreasing levels of tax noncompliance, the sensitivity of the residual method to errors in estimating personal income mitigates against drawing any firm conclusions. Graphic and tabular data are provided, along with 57 references and 15 notes.