Yesterday we had our final session, featuring Tom Brennan's Certainty and Uncertainty in the Taxation of Risky Returns.
Tom's article, still in early draft form, is a contribution to the extensive Domar-Musgrave literature on the treatment of risk in an income or consumption tax. It's well-established in that literature that, with a uniform tax rate (including loss refundability) and complete financial markets, neither an income tax nor a consumption tax affects the after-tax return available to taxpayers on their investment portfolios, except that the income tax hits the entire portfolio at the tax rate times the risk-free rate. That rendering may sound esoteric, but the key point is that taxpayers can undo the tax system's mandatory insurance by suitably adjusting their pre-tax portfolios, again assuming that financial markets are complete.
While the Domar-Musgrave reasoning notoriously requires all sorts of strong assumptions, these help to focus (as I put it at the session) on the "income-ness" of the tax base. In other words, there's no claim that the actual tax system has no effect on risk; rather, its being an income tax has no effect that wouldn't generally be the same (e.g., due to incomplete markets) if it were instead a consumption tax.
One feature of the actual tax system actually having a huge effect on risk-bearing is the lack of full proportionate rates. Rates on positive income are graduated (though for large corporations this is relatively insignificant), and net losses are non-refundable except insofar as one has net income in other years permitting the use of net operating losses (NOLs).
Tom Brennan, who has a math PhD, aims in his paper to give us a new way of looking at the tax rate effect on risk. Taking the simple case of an investment that will either gain $X (taxable at the statutory rate) or lose $Y (assumed to be non-recoverable despite the possibility of other taxable income in the same or a different year), he models nonrefundability as equivalent to a government call option on the value of the asset, based on the statutory rate.
His analysis used investments changing value over time, but I thought it could be made simpler through an example involving an instantaneous coin toss bet. E.g., suppose if it's heads you win $100, tails you lose $100, and the tax rate is 50%.
The standard Domar-Musgrave point (leaving out time and thus income taxation) could be illustrated by noting that, if there's a 50% tax with full loss offsets, all you have to do is double the bet to $200 pre-tax to end up in exactly the same place as if there were no tax.
Tom proposes to look at the case where the gain is still taxable at 50% but the loss is disallowed. Now, to restore after-tax the $200 dispersion in outcomes that you had in the non-tax world (since you'd either gain or lose $100), the amount bet has to be jumped up to $133.33. This will leave you, after-tax, either plus $66.67 or minus $133.33. Only, this is not very satisfying despite restoration of the prior level of dispersion, since the expected after-tax return is now minus 25%. So in fact you'd refuse to bet if you demand at least the 0 expected return that you could have gotten by doing nothing.
Tom notes that one could look at the government's tax claim as akin to its having gotten a free call option permitting it to claim half of the betting outcome. Win and the government takes half of your risky outcome for the strike price of zero; lose and the government lets the option expire as it's out of the money (a negative return being worth less than zero). Under these facts, the government's option was worth ex ante 25% of the amount bet.
Final step in restoring Domar-Musgrave style equivalence, if you happen to have an aesthetic taste for going there, is that, if the government compensated the TP for the value of the option, we'd end up (as in the standard Domar-Musgrave scenario). Specifically, the TP would bet $133.33, the government would hand him $33.33 in cash to make up for the option that it's taken, and the taxpayer would end up after resolution of this bet with either $66.67 or minus $133.33, in either case plus the cash that the government handed him.
The point not being that this is either a policy recommendation or a prediction of any kind; it just closes the circle so we can square our accounts (so to speak). Or, a bit more pertinently, if the government doesn't compensate the TP for the value of the option (and why would it, if it evidently wants to impose the asymmetric tax), the value of the option that's been taken tells us something about the burden being imposed through the asymmetric rates.
All this may sound a bit esoteric, but it was a good last PM session, as we were able to help clarify what the paper says (it's math-heavy and tough reading for lawyers). Question to be answered down the road is how much the model helps us in advancing our understanding of the real world impact of asymmetric rates. While this particular way of parsing them is new, experts have certainly long understood that loss nonrefundability is potentially important to risk-taking, as are graduated marginal rates.
More on this from me in a few days and in a different setting. I will be in Milan, Italy for a couple of days next week, to speak on April 30 at a conference entitled "Tax Policy and the Financial Crisis," to be held at Econpubblica, Universita Bocconi. I'll be on a panel addressing the financial crisis's long-term implications for tax reform, and one of the topics I plan to address is the interplay between loss nonrefundability and excessive risk-taking, AIG-style.