What's the starting time for that series? Early 1900s (say WW1), or back in the 1800s?
I've got an alternate explanation for the grandparent: the economy is undergoing a phase change from an industrial economy to an information economy, which will bring with it different assumptions about what an economy is. A future historian looking back on us from a century later will see steady growth in whatever metric they measure the economy in (likely volume of data produced) since about the 1970s. The fact that large sectors of the economy have shown negative productivity growth will drop out of the history books, because neither these non-software industries nor productivity as a concept will seem important to this historian.
I'm basing this on a thought experiment: what does the last major phase change in the economy (from largely subsistence-based agriculture to industrialization) look like now, and how do the metrics by which we judge it differ. The concept of productivity is basically nonsensical in a pre-industrial agricultural society - crop yields, of course, depend upon the wind, rain, and weather, and why would we expect them to increase in any non-random fashion? But real agricultural wages (likely a good proxy for productivity) skyrocketed between 1790 and 1810, and then declined by 20% [1, p 20] between then and 1850. To a farmer (that's most of society back then), their plight wouldn't look all that different from today's factory workers: the generation that came of age in 1850 did significantly worse than that of 1810. There was a bit of a bump when mechanized agriculture and meatpacking came out in the early 1900s, but this trend largely continued into the 1930s, at which point we basically stopped talking about small family farmers and got agribusiness instead.
But do we consider the 1800s a time of low productivity? No. We associate them now with the first and second industrial revolutions, which dramatically changed society and hugely increased productivity. "Industry" initially meant "the textile industry", because that was the first area that mass-production techniques were applied to. Over time these techniques spread until they took over the whole economy, at which point we could start measuring the economy by metrics like "productivity" that assume that innovation and capital can allow an individual worker to produce more than they could before. Former metrics like crop yields become an afterthought: as long as they're "enough", who cares?
If you start the clock at 1910 or even at 1870, you're looking only at the portion of history where the industrial economy is the economy. To get a better analogy to current conditions, you have to go back, before the Civil War, when the nascent industrial revolution is causing the collapse of plantations, slavery, seamstresses, tailors, whalers, and small farmers.
[1] http://old.econ.ucdavis.edu/faculty/gclark/papers/farm_wages...