Tim Taylor has a nice piece  about the recent arguments over what the top tax rate could be to maximise revenue: where the peak of the Laffer Curve is that is. Various of the usual types have been jumping up and down in excitement at a paper that shows that it could be 76%. It isn't, it's 54%, that's the total tax rate including VAT, NI and income tax and, in what is really the great switch in the paper, that takes no account whatsoever of the changes in long term incentives, it looks only at the short term. Scott Sumner  is incandescent about the paper, a point which Taylor addresses.
It is also fair to note that political beliefs probably play a role in these differences. Greg Mankiw is a Republican-leaning economist: he was chair of the Council of Economic Advisers in the George W. Bush administration and has been an adviser to Mitt Romney. On the other side, Peter Diamond is a Democratic-leaning economist: Barack Obama attempted to appoint him to the Federal Reserve Board of Governors, and when he was blocked by Republican senators, his name was rumored as a possibility for Obama's Council of Economic Advisers. To be clear, I'm not suggesting that either author would consciously shade his analysis to fit pre-existing political beliefs. But I do believe that when working through a complex model with a number of discretionary choices, we all have a tendency to come out with what seems a "reasonable" answer--which often happens to be not too far from our preexisting beliefs.
Sumner does indeed assume that: but I think that the causation goes entirely the other way around. It isn't that our pre-extant political beliefs make us pick the numbers which lead us to our desired solution. It's that our beliefs about what are the appropriate numbers help to determine our political beliefs.
In this example the numbers chosen by Diamond and Saetz do lead to what we might call a left wing solution. Much higher taxes on the rich. The sort of numbers that Sumner or I would put into the same equation would lead to a much more "right wing" solution, a lower peak for the Laffer Curve. The numbers we're talking about are things like the effect of higher taxes on the propensity to work and so on.
But I don't think that Sumner and I would put in lower numbers in order to get a lower Laffer peak: just as I don't think that our two lefty economists would do the opposite (I can think of plenty of people who would but not these two of this stature). Rather, I think that it's our prejudices about what these elasticities are which lead to our having right or left views on tax rates. Perhaps prejudices is too strong there: our inclinations as to what the numbers are given our own view of the world.
As an example, my marginal income comes from freelance writing. There are enough outlets that I can, if I need a bit more money, just write for more hours. Not go off to the pub, sit at the keyboard instead of taking the bike out for a spin. I know what my reaction to 70% tax rates would be: I'd shoot off on the bicycle and over the Portuguese hills and have a few pints when I came back. My output would decline and decline quite substantially. So I'm prepared to believe, primed to believe, that work effort is quite elastic as compared to tax rates. Other people might have very different ideas about life and the work life balance: no harm in that. They might be more swayed by prestige for example, or have always worked in jobs where income doesn't vary much with effort or hours (like a university professor for example). Thus, from their own experience, their own internal values, they're predisposed to believe that work effort, hours, have a low elasticity with respect to tax rates. Because people are more motivated by things other than post-tax income.
Of course, where we're trying to see what the effect on the entire economy is we're supposed to be inputting the numbers that apply to everyone else, not what apply to us alone. But where there is judgment, where there are choices as to what number to use, I really do think that it's our own opinions, our own experiences, of what these numbers are that then feeds through into our having right wing or left wing results.
I've rather over-egged this argument in order to get the point over. But I do think it to be true that it isn't that we choose economic models, or numbers to put into them, because we want to reach a conclusion that accords with our political ideals. Rather, our political ideals grow out of what we think those numbers are before we start to run them through the models. And I think this goes far beyond simple economic models as well. I, to use my favourite subject as an example once again, absolutely despise having to fill out paperwork. It is, I am certain, because of my hatred for having to do so that I am so vociferously opposed to a governance system that insists on people filling out paperwork all the time. I'm sure you can think of other examples of the same point: our own character, our own wants and desires, do get projected onto the world around us.
All of which is grist to the mill of the classically liberal world view of course. Those who wish to may, whatever consenting adults voluntarily choose to do. But the impositions upon such in what they must do or may not do have to be incredibly limited, for what must and may not be done is being determined by those internal prejudices of those doing the deciding rather than the free will of the participants.