To whom should economists offer advice? Traditionally, the answer has been: politicians.But I'm not sure this should be so.
This isn't just because economists can't foresee the future and so a lot of advice on monetary and fiscal policy is pointless.It's because policy is shaped not by what is the right thing to do, but by what politicians can sell to inattentive and sub-rational voters. Whatever else informs immigration policy, for example, it is not economic research.
Of course, economists do sometimes influence policy for the better - auction theory being a good example - but this happens only when economic ideas don't rub too harshly against prejudice and vested interest. Otherwise giving policy advice is, to paraphrase Robert Heinlein, like teaching a pig to sing: it wastes your time and it annoys the pig.
I suspect that, insofar as economic ideas do influence policy, it is often through the lengthy and subtle process of changing the intellectual climate - as free-marketeers did in the 60s and 70s - rather than through advice leading directly to policy.
This, though, doesn't mean economists shouldn't or can't give advice. We can - to "ordinary" people*. It's often said that "max U" economics is at least as much a normative theory as a positive one. Which suggests that there is a role for economists in helping people make everyday decisions. This role is enhanced by the fact that a lot of the best recent research in economics has been in precisely how individuals' decisions often do fall short of rational maximization. It's rather sad that many economists' reaction to the cognitive biases research programme has been: how can we use this to give policy advice (eg nudge)? when it could equally be: we can use this to help people improve their everyday decision-making.
Granted, most of the financial advice you'll ever need would fit on an index card. But, hey, repetition is the mother of learning. And the need for impartial advice is perhaps exacerbated by the fact that a lot of the advice proferred by the financial "services" industry is self-serving crap.
In truth, I'm talking my book here. A fair chunk of my day job is being like an agony aunt; I'm more like Marje Proops or Abby van Buren than Stephanie Flanders. If economists want to become like dentists - as Keynes hoped - they should deal less with politicians and more with real people, both in advising them and learning from them.
* I hate the phrase "ordinary people"; most of our rulers - in politics and business - are far more ordinary than "ordinary people." I wish I could think of an alternative.