Pareto's Limits: Improving Inequality Estimates in America, 1917 to 1965

American income inequality, generally estimated with tax data, in the 20th century is widely recognized to have followed a U-curve, though debates persist over the extent of this curve, specifically regarding how high the peaks are and how deep the trough is. These debates focus on assumptions about defining income and handling deductions. However, the choice of interpolation methods for using tax authorities' tabular data to estimate the income of the richest centiles -- especially when no micro-files are available -- has not been discussed. This is crucial because tabular data were consistently used from 1917 to 1965. In this paper, we show that there is an alternative to the standard method of Pareto Interpolation (PI). We demonstrate that this alternative -- Maximum Entropy (ME) -- provides more accurate results and leads to significant revisions in the shape of the U-curve of income inequality.