The view that the latest employment news is good rests on the observation that the rate of decline in payroll jobs has slowed. I would not put much confidence in this data.
Consider the following counterpoints:
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Payroll numbers are notroiously unreliable until final revisions are completed (monthly revisions occur for 2 months after the initial report, and an annual revision is done that corrects data stretching back multiple years).
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The payroll data includes an unknown number of "phantom jobs" due to double-counting workers who change jobs during the month (my research here; BLS confirmation here). Since the rate of turnover tends to slow during the early phase of a downturn, and rise again during a recovery, it seems likely that the highest declines in January and February were exaggerations.
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Aggregate Hours data show no deceleration, as noted by Jeff Frankel (HT Paul Krugman).
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The Unemployment rate data show no deceleration. This is especially relevant because these data are almost never revised (I think we can call it "tweaked"). Consider the chart above, which contrast the change rate in unemployment compared to the the payroll jobs (in percent terms).
The chart above shows way too many upticks in the unemployment rate for me to start looking for green shoots. The monthly correlation between these two series is -0.57 which would probably be higher if not for the constant U rate fluctuation between -0.1 and 0.0 in growth periods. The 6-month moving averages of the series have a correlation of -0.87. So in the chart above, knowing only one series gets revised and the other does not, what should we expect? It's too early for me to say conclusively, but my guess is that the payroll numbers are likely to be revised downward and/or continue in deep negative territory.
One other depressing observation: There have been 39 instances since January 1948 when the change in the unemployment rate was 0.4 or more. How many have occurred in this recent recession? Nine. That includes six of the last six months.

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