> Productivity has a precise economic definition - ratio of output to inputs - and correlates highly to standard of living. We don’t fully understand how and why technology advances, but we measure increased technology through a variable called the solow residual.

What happens when you can't measure the outputs? What's the total value added by the financial sector? Or the legal sector for that matter? If I invent an inexpensive cure for a disease that renders expensive medicines obsolete, has productivity gone up or down?

Regarding the Solow residual, you certainly can put income on one side of a regression, and estimates of labour and capital on the other side, and set them equal using a residual term. I don't think you can convincingly argue to anyone besides an undergrad economist that the residual represents technology though. Don't think too hard about what the units of that residual are...