I strongly disagree with Mankiw’s take here on the PPP. I have pored over all of the available evidence on the PPP. The two best existing studies unquestionably underestimate the impact of the PPP, likely substantially. The reasons are over the fold.

http://gregmankiw.blogspot.com/2020/08/the-high-cost-of-ppp-jobs.html
Chetty et al. and Autor et al. both identify the effect of the PPP by comparing firms above and below 500 employees—i.e., PPP eligibility. Two problems. 1) Smaller firms were likely harder hit. 2) Large firms that didn’t get the PPP instead got the employee retention credit.
Both of these mean the two studies underestimate the impact of the PPP. Moreover, Chetty et al, which find no employment impact, use a highly unrepresentative sample (and no SEs!). Autor et al use ADP payroll data on 20+ million workers and find 2.3m jobs saved in the short run.
But these studies only measure the contemporaneous impact of the PPP on jobs. They don’t tell you how many jobs will be saved in the medium term due to fewer firm closures. Or the stimulatory benefit to jobs in the broader economy (PPP was 2.5% of annual GDP paid out in 1 qtr).
They also don’t tell you the value of the firm-specific human capital and job matches preserved by having the PPP incentivize businesses to hold onto those 2.3 million workers. This will have positive effects on economic activity and jobs in the long term.
Moreover, as always, it’s wrong to measure the “cost” of jobs saved in terms of its fiscal cost, as that is mostly a transfer. Instead, you want to measure the deadweight loss generated by the $500bn of revenue the PPP absorbed, an order of magnitude less than its fiscal cost.
But even if we want to look at the fiscal cost, we should also consider that the 2.3 million jobs contemporaneously saved by the PPP prevented those people from entering the UI system, which would have cost the the budget at least $2bn per week.
In short, it is too early to do a proper cost-benefit analysis of the PPP. And it is particularly unwise given that the costs have already been borne but many (most?) of the benefits are still to accrue. If anything, I’m amazed that the calculation comes out so well this soon.
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