Tax Policy Colloquium, week 3: Jake Brooks' "Taxation, Risk and Portfolio Choice: The Treatment of Returns to Risk Under a Normative Income Tax"

Yesterday we discussed Jake Brooks' above-titled article on income and consumption taxation (available here).  It's situated in a literature that is very familiar to tax academics, but much less so, unfortunately, to students who are new to the field.  This is the Domar-Musgrave literature concerning whether an income tax, and/or a consumption tax, can in theory tax risky returns.

The standard models that are used always involve a risky asset (e.g., one that might with equal probability reap a 30% profit or a 10% loss) plus a risk-free asset with a very low but certain return.  One might start with the portfolio allocation that the taxpayer would prefer in a no-tax world, then we impose the tax, which lowers the after-tax gain and loss from the risky asset, in effect providing insurance against the variance that the taxpayer evidently didn't want.  One can then demonstrate, that if the taxpayer responds by holding more of the risky asset and less of the risk-free asset (and, if necessary, borrowing at the risk-free rate in order to hold more of the risky asset, she can wholly undue the insurance effect.  Under the consumption tax, she can get back to exactly where she was before.  Same story under the income tax, except that her after-tax return is reduced, even after the portfolio shift, by the product of the risk-free rate and the income tax rate on the entire portfolio (even if the taxpayer ends up holding no risk-free assets).

Moral of the story in the standard account: neither tax affects risky returns, and the only difference between the two is that the income tax reaches the risk-free rate of return.  So that is the fundamental difference between the two systems.

Obviously, this is a very abstract and simplified presentation (and I haven't even actually presented it here), with lots of underlying assumptions.  Among other things, one assumes that the tax (either one) has a flat rate and allows full loss offsets (that is, net losses are refundable at the tax rate).  The reason for that assumption, which obviously doesn't hold for real world income tax systems, is that one is trying to look at what the choice of tax base does, not at what the actual system does in light of its various features (such as rate structure and treatment of net losses) that are distinct from the tax base choice as such.

I think that almost all of the underlying issues can be demonstrated much more simply.  Suppose you and I had wanted to bet $1 million on the Super Bowl.  But then it turns out that gains are taxed, and losses are refunded at a 50 percent rate.  (Forget about the rule in the actual Code that gambling losses are disallowed, reflected that they are viewed as a cost of consumption - the Super Bowl bet is a stand-in for a business venture, although in this example it's a financial instrument with counter-parties, rather than a one-party bet against Nature.)  The obvious thing for us to do, given that we apparently want to bet $1 million after-tax, is to cancel out the seemingly mandatory insurance by betting $2 million, rather than $1 million.

Under either  an income tax or a consumption tax with a 50 percent rate, we end up in exactly the same place, i.e., with $1 million in after-tax stakes.  Question that I'll hold off on for a moment: Is there anything wrong with that?  But to complete the picture about income taxes versus consumption taxes, suppose that bettors need collateral to secure their potential obligations, and that the income tax, but not the consumption tax, places a very low fee on the amount of the collateral.  (Which, by the way, would not increase under the revised bet if capital markets were functioning well - and there is no point to speculating about the hyper-counterfactual question of how well they actually would function in this fictional world.)

Jake's paper reflects the view that it's unfortunate if taxpayers can negate the mandatory insurance by scaling up the bet.  This would be a difficult view to defend if we think purely in terms of consumer sovereignty - that is, by supposing that the two individuals know what is best for themselves and that there are no externalities.  However, one can imagine lots of reasons why we might not want to let them fully scale up the bet, if there indeed was any way we could prevent it (which of course appears implausible under the terms of the hypothetical, but can't as easily be ruled out for more complicated real-world circumstances that we actually care about).

For example, suppose the bettors misunderstand the risks they face, or are systematically over-confident.  Or suppose that some people usually win the bets and others usually lose, due to "ability" differences that we can't otherwise observe.  Or suppose losers will end up on the dole.  Or suppose that the bets create a socially costly diversion of effort from genuinely productive activity to unproductive "arm's races" between bettors to outsmart each other.  (This relates to a real-world story about the stock market, in which investors have a strong incentive to try to trade based on new information one second before everyone else learns it.)

For any of those reasons, we might be glad if the tax system was able to prevent the bettors from wholly undoing the otherwise mandatory insurance that it provides.  (It is a tradeoff, however, if there is also deadweight loss from limiting the bettors' ability to do what they want.)  And again, in the real world circumstances that are actually relevant - including, for example, graduated rates, loss limits, and incomplete financial markets - retaining an after-tax impact may actually be feasible.

OK, so much for the basic story.  What about income tax versus consumption tax?  The paper argues that the former has better chances than the latter of limiting scale-up to reverse out the insurance feature of both taxes.  I tend to disagree.  Stated in terms of my little story with the Super Bowl bet, the paper makes two arguments.  First, the income effect of the tax on the collateral will make the bettors more risk-averse.  As they are poorer, they no longer want to bet as much as $1 million after-tax.  The paper also calls this voluntary reduction in the size of the bet a "tax."    However, I wouldn't call it a tax, as there's no burden from adjusting one's behavior to do what one wants given one's circumstances.  I also question treating the shift from a consumption tax to an income tax world as having income effects, since one might expect them to be budget-equivalent.  The paper offers some responses to this view, and readers are invited to judge for themselves.

Second, the paper argues that investor departures from full rationality in the standard neoclassical sense may lead to incomplete cancellation of the insurance under an income tax, but not (at least to the same degree) under a consumption tax.  Thus, in terms of my example, suppose that the bettors really hates losing more than $1 million from a given "transaction" before-tax, even though after-tax should be all that matters.  Then in both scenarios they might be reluctant to scale up fully.  But suppose further that, in thinking about the "transaction" to which they apply this pre-tax loss aversion, they score the income tax's collateral fee as a part of the overall return.  Then they will scale up a bit less under the income tax than under the consumption tax.

Obviously, my little hypothetical will not help us to think about whether, in the analogous real world situations that the paper actually has in mind (where the tax on the risk-free return from the entire portfolio is playing this role), this is an important and realistic element indicating that the income tax and consumption tax, in their real world versions with all the departures from the hypothetical's assumptions, will actually play out differently.  I am skeptical, but again you can read the paper if you want a contrary view.