What do Silver (538) and Gelman models tell us about the impact on vote share of the Russian hacking of Democrats and the FBI intervention in the US election? If we took the prediction at the time and then extrapolate to get the counterfactual, what was the impact?
IMPORTANT NOTE: The question as asked seems to conflate two absolutely unrelated things: (1) "hacks" (which refers to someone hacking into DNC and Podesta's emails that were released to WikiLeaks) and (2) Comey's letter regarding Clinton's email server investigation; which had absolutely nothing to do with "hacks" and was all about Hillary Clinton's violating rules as SecState.
I'll answer both items separately, as 538 addressed them separately (duh).
1. Wikileaks emails (allegedly hacked by Russians from DNC and Podesta).
TL;DR: 538 sees no meaningful direct evidence that WikiLeaks affected the race. There's circumstantial evidence it had some impact but they can't measure that at all.
538 They were VERY VERY careful and explicit on the podcast to state that (paraphrasing from my listening) "When we say hacking, there was no accusation that election itself was hacked in any way; the only possible hacking we are aware of was the method by which WikiLeaks obtained the Clinton related emails"
538 sees no meaningful direct evidence that WikiLeaks affected the race. There's circumstantial evidence it had some impact but they can't measure that at all. That doesn't constitute proof of lack of impact, merely lack of any evidence of impact that can be measured by them (and the implication was that, due to slow speed of Wikileaks releases and lack of any dramatic info in the emails; any impact is pretty much impossible to measure).
The precise word 538 used was "drip drip drip".
From Harry Enten's "How Much Did Wikileaks Hurt Hillary Clinton?":
The drip, drip, drip of the hacked emails — published weekly during October — makes it all but impossible to measure their effect precisely. So much else happened during the final weeks of the campaign — the “Access Hollywood” tape, the Comey letter, the debates, etc. But we can say two things: (i) Americans were interested in the Wikileaks releases, and (ii) the timeline of Clinton’s fall in the polls roughly matches the emails’ publishing schedule.
Now, Clinton’s drop in the polls doesn’t line up perfectly with the surge in Wikileaks interest. When Wikileaks had its highest search day in early October, Clinton’s poll numbers were rising. They continued to go up for another two weeks, even as Wikileaks was releasing emails. That is, there isn’t one pivotal “aha!” point which shows that Wikileaks caused Clinton’s numbers to drop.
There just isn’t a clean-cut story in the data. For instance, you might have expected a decline in the percentage of Americans who trusted Clinton after Wikileaks began its releases. As Politico’s Ken Vogel pointed out in mid-October, both Trump campaign officials and even progressives said the Wikileaks emails revealed that Clinton would be “compromised” if she became president. But the percentage of Americans who found Clinton to be honest or trustworthy stayed at around 30 percent in polling throughout October and into November.
The evidence that Wikileaks had an impact, therefore, is circumstantial.
... Of course, one thing didn’t sink Clinton. The evidence suggests Wikileaks is among the factors that might have contributed to her loss, but we really can’t say much more than that.
TL;DR: Nate Silver things it meaningfully affected the voting, although on the podcast there was no consensus that it was the direct cause of election loss for Clinton (as opposed to one contributing factor).
They suspect that Comey letter had some effect (they can't prove causality, but the timing fits down to 2-week period and there's a pretty big move of 3 points).
There's a compilation of Nate Silver's views in "Nate Silver: Clinton Would’ve ‘Almost Certainly’ Become President If Not for Comey’s Letter" article, quoting his tweets and 538 tables.
November 6, 2016 blog entry by Nate Silver himself "How Much Did Comey Hurt Clinton’s Chances?" has details:
When FBI Director James Comey told Congress on Oct. 28 that he was reviewing additional emails pertinent to the case of Hillary Clinton’s email server, Clinton had an 81 percent chance of winning the election according to our polls-only forecast. Today, her chances are 65 percent according to the same forecast. The change corresponds with Clinton’s drop in the national popular-vote lead: from a 5.7-percentage-point lead in our estimate on Oct. 28 to a 2.9-point lead now — so a swing of about 3 points against her.
However they never found any polling that would support actual attribution (as in, "did hearing about Comey letter affect your vote" type poll); and they openly admit it's impossible to know how much of the 3 point drop is attributable to Comey letter, how much to normal race tightening, and how much to other causes.
A relevant quote seems Dan Hopkins' 538 Voters Really Did Switch To Trump At The Last Minute, based on their panel interviews:
As to what moved these Americans in the final weeks of the campaign, the panel has little to say. The timing of James Comey’s letter to Congress — released on Friday, Oct. 28 — makes it one potential explanation. When making sense of campaigns, people often search for overarching narratives, and Comey’s letter provides a ready-made story.
- 538 December podcasts (especially December 12th 2016 "Politics Podcast: Russian Interference")