Christopher D. Johnston and Andrew Ballard have a new paper on this neglected topic, the abstract is this:
Given an increasing presence in the public sphere, what role do economic experts play in shaping public opinion on economic issues? In this paper, we examine the responsiveness of American public opinion on five economic policy issues to real information regarding the distribution of opinion on these issues among economists. We also examine the extent and role of trust in economists within the public. On average, we find meaningful changes in public opinion in the direction of expert consensus when citizens are given explicit information about expert opinion. However, we also find heterogeneity in citizen responsiveness across issues, such that aggregate opinion change is smaller on symbolic policy issues relative to technical ones. Further, on symbolic (but not technical) issues we find that citizens use judgments of the trustworthiness of economic experts in a motivated fashion, as a means of reinforcing prior opinions.
That is a little bloodless and the paper is also poorly written and organized but nonetheless it is important work. Here is one very interesting bit:
…strongly left-leaning citizens are about 12 percentage points more trusting of economists than strongly right-leaning citizens.
This part of (sort of) encouraging:
…all three groups of respondents show greater trust than predicted after exposure to consensus information. This pattern is consistent with the notion that exposure to highly technical, means-oriented issues makes one’s lack of knowledge salient, and perhaps engenders greater respect for experts…
The full paper is here, I would say start reading on p.16 and return to the beginning later on if you wish.