The announcements of the results of the Florida race while the Panhandle still had the polls open were designed to affect the results. This was because the panhandle is in the Central time zone, while the main part of Florida is in the Eastern time zone. The exit poll announcements were designed to cause Bush voters in the Panhandle to give up and not vote.
Similarly, the results in the Eastern states when Jimmy Carter lost to Ronald Reagan were announced before the polls closed in the Western states. This caused Mr. Carter to concede by 5 PM Pacific time and the polls were still open on the west coast.
In the latest election (Trump vs. Clinton) some states were declared for Clinton that went to Trump in order to affect voting in the later time zones. However, we cannot verify if this had an effect or if it caused Trump voters to show up.
A study in France Exit Polls, Turnout, and Bandwagon Voting:
Evidence from a Natural Experiment showed
We estimate that knowing the exit poll information decreases voter
turnout by about 12 percentage points. Our study is the first clean
empirical design outside of the laboratory to demonstrate the effect
of such knowledge on voter turnout. Furthermore, we find that exit
poll information significantly increases bandwagon voting; that is,
voters who choose to turn out are more likely to vote for the expected