You're not wrong, but I think this is just ambiguity of terms. 'Productivity' in wage stagnation discussions is implicitly 'labor productivity', which is techn

You're not wrong, but I think this is just ambiguity of terms. 'Productivity' in wage stagnation discussions is implicitly 'labor productivity', which is technically a "partial productivity" measure judging the amount of output generated by a unit of labor. It's not the same as overall output of value. It also isn't the same as "labor portion" in the equation you sketched, though, because capital expenditures like space or technology that increase worker efficiency still constitute labor productivity gains. (The 'labor portion' there seems closer to what Marxists look at in the labor theory of value - the amount of time and effort expended by labor, isolated from other factors. You're right that that doesn't end up tracking productivity or wages.) The idea that wages trend with labor productivity, then, is that anything increasing labor productivity increases the output value of an hour's work, which ought to increase the amount of money a worker can demand for their time. They won't capture the full rise in value output, because some of it will be consumed by capital expenses promoting that efficiency, but their wages should trend in the same direction. Less hypothetically: let's say Cyberdyne's powered exoskeletons become standard for bricklayers, who can then work 20% faster. Since there are plenty of bricks to lay, buying an extra hour of bricklaying now creates more value, and remains profitable at a higher cost. Bricklayers won't simply collect all the extra output value because the amortized cost of the suits has to be covered, but we'd still expect them to get a raise. And if the new tech increased productivity at a lower capital cost per unit than existing tech, the percentage of output captured by labor could even rise. Now, there can be out increases that don't involve labor productivity, anything from automating away jobs to finding cheap new sources of raw materials. People sometimes confuse the terms and compare GDP or overall productivity to wages, in which case you're right that there's no intrinsic linkage. (Although in the long run, labor's percentage returns tend to outweigh fixed-value changes like trade agreements.) But looking specifically at labor productivity, which should track wages, we still find a close trend seems to abruptly break around 1970.