Does mismeasured inflation overturn a relative stagnation thesis?

In the comments, Slocum writes:

My skepticism is not that the nominal household income or GDP number are wrong, but that the inflation-adjusted numbers are wildly off because they fail to capture the innovations and transformational improvements in goods and services. Consider music. The music industry, measured in sales, is shrinking. 25 years ago as a college student, I bought a lot LPs and CDs (probably a few hundred $$ a year). Now I spend very little. Am I worse off as a music listener now? Obviously not — I am immensely better off. But judging by the gross dollar volume of the music business, you would reach exactly the wrong conclusion about 'stagnation'.

The fundamental fact is that U.S. real median income has risen at a lower rate since 1973, not that progress has been absent.  One might think that the CPI is skewed and there are reasonable arguments to be made in this direction.  But the CPI will be most skewed to underappreciate progress when truly new goods and services are being introduced into the marketplace or spreading to new regions.  And that is (roughly) the 1870-1950 period, more than any other time.  In other words, if you account for CPI bias, the slowdown in median income growth — the difference — is probably larger than the numbers make it appear, even though in absolute terms both growth rates will be higher than measured. 

When some people hear the relative stagnation thesis, their minds shoot to various bogeymen: Paul Ehrlich, ridiculous 1907 proposals to close the patent office, predictions of mass starvation, and so on.  The simplest version of the point is that technological progress is not uniform, and that is borne out by thousands of years of human history.  This isn't Lake Wobegon, so some periods have to have lower than average growth in living standards than other periods.  One of those periods happens to be now, since 1973, give or take.  And from that flows many propositions of importance, for politics too.

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