You are correct that the current unemployment spike started from a lower rate than in 1981, but not as much as you might think. Unemployment cracked 4% on the downside momentarily at the end of the Clinton administration. Under Bush unemployment was never great.
Yes, the absolute unemployment trough at the start of the current move was about 4.5%--the lowest point of the Bush era. The Bush presidency averaged 5-6% unemployment so I don't know that it was a period of "very l0ow" unemployment.
Also, rate of change does matter in terms of effect. Measured from the previous unemployment trough today's move is smaller than 1981. Measured from the previous unemployment peak today's move is much larger than 1981.
2001-2009 is famous for creating almost no jobs. As you'll recall, we talked about this throughout the Bush presidency. The only reason unemployment briefly reached 4.5% under Bush was the climax of the housing bubble. That rate was achieved despite a famously horrible job creation record.
The 21st century economy wasn't creating many jobs at its best. It is less able to handle this than the world of 1981 was, and the median duration of unemployment tells the tale:
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Today is worse than 1981 all around.
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"But wasn’t the unemployment rate higher in the past? Well, in 1982, although not in the 1970s, it was briefly a bit higher than the peak this cycle:
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But back then the “full employment” level of unemployment was higher, so the increase wasn’t as large; more important, most of the unemployment was short-term, nothing like the deeply corrosive long-term unemployment we’re facing now:
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