Perhaps Lawrence's new paper isn't quite as bad as I imagined when I first saw this on twitter, at least with some interesting data, although there isn't much there, as the "analysis" is done by simple plots of aggregate data. My expectations for him were quite low, though, and so I still have plenty of points of contention.
The main issue is that the central argument is against a straw man. He toggles back and forth seamlessly between two related, but different issues with different causes. One is the long-run decline of manufacturing employment as a share of total employment. This long-run decline is, in fact, caused by faster productivity growth so in that he is correct. However, as far as I know, no economists actually dispute this. And when Trump cites China for the declining in US manufacturing, he is talking about the level, not this "as a share of GDP" bullshit. The rather sudden decline in the level of manufacturing employment in the early 2000s is a different issue than the long-run decline in the share. This was caused mostly by trade, and also by slow demand growth (which isn't necessarily unrelated to the trade shock), but it was not caused by productivity growth. At first, it's unclear which of the two Lawrence is talking about, and given that he says many people believe trade is the cause, it makes it sound as though he is talking about the 2nd. However, then he switches back to arguing the first point.
He then plots this figure, which is meant to show that China didn't cause a deviation from the US's long-run trend in its share of US manufacturing employment.
below its long-run trend. The reason is that the long-run trend implies negative employment within several decades (see above), which can't happen, so naturally it must flatten out at some point, precisely like agriculture has done. But, there is no clear counterfactual for what the share of manufacturing employment "should" be. Secondly, the slow growth in overall employment after 2000 was likely caused in part by the swift loss of 3 million manufacturing jobs (see my previous post, and here). Detroit lost many of its tradable sector jobs, but then also lost lots of retail and government jobs as revenues dried up. Its share of manufacturing jobs could also well be on its long-run trend. One could then conclude, erroneously, that the loss of tradable-sector jobs in Detroit is not what caused its decline.
Lawrence says that, even in the period of the China shock, fast productivity growth caused the loss of many more manufacturing jobs than China. But, that's not what I found in my paper. I found instead that productivity growth was normal after 2000, and only a normal number of jobs were lost due to productivity growth after 2000, comparable to any decade before. (Below is the evolution of VA per worker. The growth rate looks pretty constant -- nothing to suggest a very sudden decline in the level of manufacturing employment.)
In addition, productivity for the median manufacturing sector actually declines in the 2000s. This is offset by very fast productivity growth in the top sector, growth which may not have actually happened.
Another hole in the story that after 2000, the main contributor to the decline in manufacturing was fast productivity growth and low demand is that these two factors imply that the US should have had a trade surplus, not a large trade deficit (see the trade balance in blue plotted vs. two measures of real exchange rates, more about the differences between them here). To be sure, I also find slow demand growth after 2000 (particularly for the 2007-2010 period), although, once again, I believe this was caused in part from the collateral damage from trade and the collapse in manufacturing employment.
I was also slightly annoyed that when he cites Autor, Dorn, and Hanson (2013) for 985,000 jobs lost due to China (out of 5 million total) rather than the follow-up paper by Acemoglu, Autor, Dorn, Hanson and Price (2016), which includes a longer time period and arrives at 1.475 million jobs lost due to the China shock and input/output linkages in manufacturing, and 3.1 million jobs overall, but this is a minor quibble. But, even this estimate does not include the exchange rate shock in the early 2000s, or do anything special for China's WTO accession and the MFA agreement in particular, which almost certainly cost the US jobs in the textile sector. Also, it is also computed with quite conservative methodology -- they multiplied their regression coefficients by the R-squared of the regression.
There are also holes in his analysis with the international comparison. Most of the manufacturing jobs lost in Germany after 1990 were in East Germany. Second, the only Asian, or "capital account" country in his basket is Japan, a country that has been stuck in a liquidity trap for a quarter of a century. There's no Korea, Hong Kong, Singapore, Taiwan, or China. He also doesn't look at levels of manufacturing employment.
One particularly egregious error he makes is to show the decline in spending on consumer goods using 2010 as the last year, without realizing that this was the end of the worst recession since the Great Depression! The problem is that consumer durables slump badly in a depression, so his table is mostly picking up cyclical effects. He then remarks, that, surprisingly, as countries are coming out of a recession the share of goods consumption picks up, without any trace of irony.
In any case, the central message of the paper is clear: Robert Lawrence means to let trade off the hook, one way or another. But he builds his case on trickery. And his pro-status quo position is also not likely to be a winning political strategy for the Democrats in the next election -- it's bad economic analysis and bad politics, and, if followed, likely to lead to precisely the outcome Robert Lawrence, and yours truly, want to avoid.