Wednesday, August 17, 2011

Even in principle, figuring out a fair tax system is hard

How does one set up a system such that everyone pays their fair share of taxes?  Let us suppose that a "fair" tax is one where everyone gives up the same share of utility to pay for public goods.  One could formulate this such that

U(X(L)-L-t)/U(X(L)-L) = K

The idea is that the fraction of utility one keeps after taxes is the same for everyone.  X is consumption; the amount one gets to consume is a function of effort, L.  To make things easy, we will assume people consumer their incomes, so that income and consumption are the same. Assume that utility function has the shape U' > 0 and U" < 0.  K is dependent on how much society wishes to spend on public goods.

Just this simple formulation presents three problems.  First, the fair rate of progressivity will be a function of the magnitude of U".  For instance, if we assume log utility, U' = 1/(X-L) = U" = -1/(X-L)^2.  This means U" gets very small very rapidly, which also means that the need to increase marginal tax rates in income to maintain the above definition of fairness gets quite small.  We do know that taking money away from people at or below subsistence levels of income will lead to substantial diminution of utility, but beyond that point it is hard to say how sharply progressive taxes need to be in order to be fair.

Second, the correspondence between consumption and effort is not one-to-one.  If the correlation between consumption and effort is less than one--and I will go out on a limb and say that it certainly is--taxing income actually only approximates taxing utility.  The lower the correlation, the worse the approximation.

Finally, defining effort is a problem.  As Matthew Yglesias notes, NYU professors make a lot less money than Wall Street bankers, but their life might well be better.  Perhaps I am wrong, but it seems to me that the -L in a steel worker, coal miner, or line worker is a lot bigger than mine, and so looking at income alone is adequate for approximating utility.

So what to do?  Here is why, despite my liberal leanings, I find a flat tax with a large exemption and a large earned income tax credit appealing.  The rate would have to be sufficient to raise revenue, and would apply  equally to all type of income.  Deductions would be limited.  Such a set up would assure that Warren Buffett would pay no less a share of his income than anyone else.  Bob Hall proposed a similar plan 15 years ago.  I would dress it up with the earned income tax credit.  


Acad Ronin said...

I can live with that, including capital gains as income, once they are indexed for inflation. Much of the gain on houses has been purely nominal and taxing real gains would permit bringing housing gains (and losses) back into the tax system. I have no problem with getting rid of the interest deduction on mortgages (esp. since I just paid off mine), and the deductions for state and local taxes, debt payments and the like. I suspect that the state and local taxes exemption pushes people towards cities and away from rural areas. Now, how do you feel about ending the exemption for medical insurance? I am for ending it, subject to a per capita deduction that could be part of everyone's basic deduction. Also, how about ending the double taxation of dividends? Might help create pressure on firms to return retained earnings to stockholders.

Sullmeister said...

How did we get from (X-L) to an *income* tax? High-income people who go to work every day in a old Camry carrying a tuna salad sandwich, and save the rest, will have low values of (X-L). I think the logic of the post argues for a mildly progressive consumption tax with refundable personal and earned income credits.

devin said...

A flat tax is a political impossibility unless you're willing to also eliminate deductions for businesses (i.e. go to a gross receipts tax on businesses). Otherwise, you're setting up a system in which businesses get to deduct everything while real, flesh and blood human beings deduct nothing. I can't imagine more than a tiny portion of the population would stand for such a system.

Oh wait, we just passed a cuts-only approach to deficit reduction even though over 70% of the population opposes that approach, and the Supreme Court decided corporations deserve greater free speech rights than human beings (something I'm sure another 70%+ of the population opposes). I guess what the majority wants is secondary to what the powerful want. [channeling Gilda Radner...] Never mind...

Acad Ronin said...

The biggest argument in favor of the corporate income tax is that we don't know which flesh and blood people pay it. We know the corporation signs the tax check, just as I sign, with power of attorney) the checks to the IRS for my father (who is senile), drawing on his savings. The fact that I sign the checks doesn't mean that I pay the tax. As Arthur Okun apparently once said, "If we put a tax on cows, some people will think cows pay the tax." If there were no corporate income tax, wages would be higher, prices would be lower, and there would be a one-time jump in the price of shares, which would benefit my defined contribution pension fund. (Also many accountants and lawyers would be out of job.) However, we don't know how much benefit would flow to each of the three stakeholder communities - employees, customers and owners. Best guess is that customers and employees would benefit most, but we don't know and they don't know, so they don't lobby for the tax's abolition.

himaginary said...

Very interesting post.

"We do know that taking money away from people at or below subsistence levels of income will lead to substantial diminution of utility, but beyond that point it is hard to say how sharply progressive taxes need to be in order to be fair."

I think you can get the approximate answer as for log utility.
In that case, the numerator of the left-hand side of the formula can be transformed as:
log(X(L)-L-t) = log(1-t/(X(L)-L)) + log(X(L)-L)
which can be approximated as:
-t/(X(L)-L) + log(X(L)-L)
Therefore, t = (1-K)(X(L)-L)log(X(L)-L)

LVTfan said...

Why wouldn't we simply follow Henry George's wise recommendation on how and where to collect public revenue? Nothing else I've seen makes as much sense.

Efficient, just, administrable, and meeting all the criteria for a good source of public revenue.

Natural public revenue.