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We provide new estimates of migrant flows into and out of America during the Age of Mass Migration at the turn of the twentieth century. Our analysis is based on a novel data set of administrative records covering the universe of 24 million migrants who entered Ellis Island, New York between 1892 and 1924. We use these records to measure inflows into New York, and then scale-up these figures to estimate migrant inflows into America as a whole. Combining these flow estimates with census data on the stock of foreign-born in America in 1900, 1910 and 1920, we conduct a demographic accounting exercise to estimate out-migration rates in aggregate and for each nationality-age-gender cohort. The accounting exercise overturns common wisdom on two fronts. First, we estimate flows into the US to be 20% and 170% higher than stated in official statistics for the 1900-10 and 1910-20 decades, respectively. Second, we estimate the rate of out-migration from the US to be 76% during 1900-10 and close to 100% during 1910-20. These figures are between two and three times larger than official estimates for each decade. That migration was effectively a two-way flow between the US and the sending countries has major implications for understanding the potential selection of immigrants that chose to permanently reside in the US, their impact on Americans in labor markets, and institutional change in America and sending countries.