At first sight the research reported here is something that only political science researchers should worry about. In trying to explain election results, it is better to use ‘real time’ data rather than ‘revised, final or vintage’ data. But as the authors point out, it has wider implications. Voters do not seem to respond to how the economy actually is (which is best measured by the final revised data), but how it is reported to be. (This does not just matter for elections: here is a discussion of some other research which suggests how the way recessions are reported can influence economic decisions.)
Just one more indication that the media really matters. I would not bother to report such things, if this point was generally accepted as an obvious truth. That it is not, in the UK at least, reflects various different tendencies. Those on the right know that the print media is heavily biased their way, and that this has a big impact on television, so they have an interest in denying that this matters (while funding think tanks whose job is in part to harass the BBC about its alleged left wing bias). Those on the centre left often react negatively to a few of those further left who discount all awkward facts by blaming the media. And the media itself is very reluctant to concede its own power.
As an example, here is Rafael Behr in the Guardian talking disapprovingly about Labour supporters:
“I heard constant complaints about failure to “challenge myths” about the economy, benefits, immigration and other areas where Labour is deemed unfit to govern by the people who choose governments. The voters are wrong, and what is required is a louder exposition of their wrongness.”
What is really revealing about this paragraph is what is not there. We go straight from myths to voters, as if no one else is involved. I doubt very much that many who voice the ‘constant complaints’ Behr is talking about think that voters created and sustained these myths all by themselves.
The discussion of issues involving the economy, the welfare system and immigration among most of the ‘political class’ is often so removed from reality that it deserves the label myth. In the case of the economy, I provided chapter and verse in my ‘mediamacro myth’ series before the election. It was not just the myth that Labour profligacy was responsible for austerity, but also the myth about the ‘strong recovery’ when the recovery was the weakest for at least a century, and that this recovery had 'vindicated' austerity. Given the importance that voters attach to economic credibility, I do not believe I was exaggerating in suggesting that the mediamacro myth was in good part responsible for the Conservatives winning the election.
The media is vital in allowing myths to be sustained or dispelled. That does not mean that the media itself creates myths out of thin air. These myths on the economy were created by the Conservative party and their supporters, and sustained by the media’s reliance on City economists. They get support from half truths: pre-crisis deficits were a little too large, GDP growth rates for the UK did sometimes exceed all other major economies.
Myths on welfare do come from real concerns: there is benefit fraud, and it is deeply resented by most voters. But who can deny that much of the media (including the makers of certain television programmes) have stoked that resentment? When the public think that £24 out of every £100 spent on benefits is claimed fraudulently, compared with official estimates of £0.70 per £100, that means that the public is wrong, and we have a myth. (An excellent source for an objective view of the UK’s welfare system is John Hills’ book, which has myth in its subtitle) As I noted in that post, when people are asked questions where they have much more direct experience, they tend to give (on average of course) much more accurate answers. Its when they source the media that things can go wrong. It is well known that fears about immigration tend to be greatest where there is least immigration.
Of course reluctance to acknowledge myths may not be denial but fatalism. Fatalism in believing that voters will always believe that migrants want to come to the UK because of our generous benefit system because it suits their prejudices. Encouraging those beliefs will be in the interests of what will always be a right wing dominated press. Some argue that myths can only be changed from a position of power. But myths are not the preserve of governments to initiate. According to this, over 60% of Trump supporters think their president is a Muslim who was born overseas. 
Myths need to be confronted, not tolerated. The initial UK media coverage of the European migrant crisis played to a mythical narrative that migrants were a threat to our standard of living and social infrastructure (to quote the UK’s Foreign Secretary!). This reporting was not grounded in facts, as Patrick Kingsley shows. That changed when reporters saw who migrants really were and why they had made the perilous journey north. It changed when Germany started welcoming them rather than trying to build bigger fences. These facts did not fit the mythical narrative.
The UK government was clearly rattled when it realised that many people were not happy with their narrative and policies. Myths can be challenged, but it is not easy. Policy has been changed somewhat, but attempts are also being made to repair the narrative: to take some of those who have made it to the EU will only encourage more (a variant of the previous European policy of reducing the number of rescue boats), and a long term solution is to drop more bombs. Such idiotic claims need to be treated with contempt, before they become a new myth that the opposition feels it is too dangerous to challenge. Challenging these myths does not imply pretending real voter anxieties about migration do not exist, but grounding discussion and policy around the causes of those anxieties rather than the myths they have spawned.
Yes, the non-partisan media needs to recognise the responsibility they have, and use objective measures and academic analysis to judge whether they are meeting that responsibility. But more generally myths are real and have to be confronted. The biggest myth of all is that there are no myths.
 The probability pedants among you who read the link will know that I’m actually making an assumption in writing this!