It is always interesting to see how real wages evolve, as they allow to understand how much a worker can buy from his income. Usually, this is done by dividing the nominal wage by a price index, usually the commodities said worker would typically buy. The results may vary considerably, as a different price index is needed for different workers, and the basket of goods may also vary over time. The latter is particularly important when the sample period is long. It also depends whether you look a hourly, weekly or annual income, and how benefits are included.
John Pencavel reviews a centuries old literature on the topic that came to the conclusion that except for some periods on stagnation, real wages generally were upward bound. He then comes up with his own indexing procedure, and finds that real wages in the US manufacturing sector have declined by 40% since 1960. Wow, this seems to be a real big result, and this requires understanding how this was computed. Indeed, Pencavel does not measure the real wage in the conventional way, but rather the ratio of what workers get to what they could get if the firm made no profit. This does not necessarily mean that the buying power of the worker has decreased by 40%. but rather that a smaller share of firm income goes to labor. With the increased mechanization of manufacturing, this evolution should not surprise many people. But this is not necessarily a 40% fall in real wages as advertised in the paper's abstract.