"[B]oth in the past and today, the evidence is not consistent with the common perception of the “American dream,” whereby immigrants arrived penniless and eventually caught up with US natives. Long-term immigrants in both periods have experienced occupational or earnings growth at around the same pace as natives. As a result, immigrants who held lower-paid occupations than natives upon arrival to the US did not catch up with natives over a single generation. The major difference between the past and present is that, circa 1900, typical long-term immigrants held occupations similar to the native born, even upon first arrival, whereas today the average immigrant earns less than natives upon arrival to the US. Smaller earnings gaps in the past are consistent with the fact that immigrants primarily hailed from European countries that, though poorer than the US, were not as dissimilar in development to the US as are sending countries like Mexico and China today. However, there was a substantial degree of heterogeneity in immigrants' skills and earnings across sending countries, including some immigrant groups that out-earn natives from the outset. We also argue that, when evaluating the pace of immigrant assimilation, methods matter. Studies based on cross-sectional data, which are less well-suited to studying assimilation than are panel data, often provide an overly-optimistic sense of immigrant convergence."