Thursday, October 9, 2008

A New Version of the Profitable Government Enterprise Myth

Greg Mankiw's Blog: How to Recapitalize the Financial System proposes to have the Treasury co-invest in banks with private investors. This is a (significantly) watered down version of the profitable government enterprise myth, and thereby dilutes -- but does not eliminate -- the fundamental problems with government enterprises. Government enterprises LOSE MONEY unless they enjoy a legal monopoly, and even in the latter case a government profit is no guarantee. Are you familiar with Amtrak? The U.S. Post Office?

Even if these problems were sufficiently diluted, Professor Mankiw's version does not eliminate the deadweight cost of taxes because the Treasury funds are collected from involuntary taxpayers by the IRS. The widely-accepted principle of deadweight costs says that a dollar in the public treasury costs the economy more (probably about twice, although we can debate the magnitude) than a dollar in a private treasury. Quite simply, the fact that private investors cannot find their own partners proves that the taxpayer would not, under Professor Mankiw's plan, be a voluntary co-investor. A taxpayer's only choice to reduce his or her participation in the government enterprise is to further shift away from taxable activities.

This point can also be seen by a couple of examples (these examples have been improved, thanks to comments from Professor Mankiw). Suppose that the Treasury borrows to make its co-investment. In one state of the world, the investment returns exactly enough to repay the Treasury borrowing -- no problem. In another state of the world, the investment loses, say, $x (relative to borrowing cost) -- a shortfall that has to be made up by the taxpayer. Because taxpayers don't like to pay taxes, the taxpayer has to be harmed $2x in order to get $x in the Treasury to make up the shortfall. In the third state of the world, the Treasury makes a profit of, say $x (again, relative to borrowing cost).

Example 1. Taxpayers are not full owners of windfalls. Suppose for a moment that the $x profit (if it occurs) were paid to taxpayers in a lump sum fashion. Even in this lucky case, the taxpayer has been forced to take a gamble with possible outcomes +$x, 0, and -$2x, whereas the private co-investor's gamble was +$x, 0, and -$x.

Now back to the assumption of lump sum subsidy. In reality, a profit of $x for the Treasury will be the subject of political competition between groups wanting more than their share of the $x. So, even when the rosy scenario plays out, the $x profit benefits the taxpayer far less than $x.

Example 2. Even if taxpayers were full owners, deadweight costs are convex. You might say that taxpayers own as much of Treasury windfalls as they own of the shortfalls -- that is, the $x windfall would be to cut taxes, which would save the taxpayers $2x. So Professor Mankiw's plan gives taxpayers a gamble with outcomes -$2x, 0, and +$2x? A problem with this argument is that, aside from the fact that the taxpayer's risk is twice his private co-investor's, deadweight costs are convex, so that taxpayers are more risk averse in their role as taxpayers than they are in their roles as investors [I wrote about this in my senior thesis at Harvard; Professor Hehning Bohn has published some articles on this too]. That is, the deadweight costs suffered from a tax hike are more than the deadweight costs saved from a tax cut.

Assuming that deadweights costs are convex and, absent the plan, would be about equal to Treasury revenue, the contribution of Professor Mankiw's plan to expected deadweight costs depends on (i) the degree to which Treasury portfolio shocks can be smoothed over time, and (ii) the coefficient of variation of the portfolio of financial companies to be purchased by the Treasury. For (i), the opportunity for intertemporal tax smoothing can be pretty powerful -- a $700 billion gamble looks pretty small compared to the present discounted value of taxes. In other words, a $700 billion gamble is more like a $50 billion gamble on an annual basis. So the $700 billion adds about $50 billion * (coef of var)^2 to the expected deadweight costs of taxes.

For (ii), I looked today at options traded on XLF (the financial component of the S&P 500) for expiration in January 2010, which suggest that the coefficient of variation of the XLF is 0.6 over that horizon. [This is likely an under-estimate of volatility of any portfolio to be formed by the Treasury, because (a) troubled banks are probably more volatile, (b) the Treasury horizon is more than 15 months, and (c) in any case the Treasury will not own the entire XLF. I admit that January 2010 options are not the most liquid.]

So that comes to at least $18 billion worth of deadweight costs imposed on taxpayers.

In summary, Professor Mankiw's plan has three kinds of social costs: (1) the costs of underperforming government enterprises (mitigated, but not absent, because his plan co-invests with private parties), (2) the costs of uncertain incidence of the tax hikes and cuts that would result from good and bad performance of the government investment, respectively, (Example 1 above) and (3) the convexity of the costs of tax collection (Example 2 above). All of these costs can be avoided if the market alone decides whether and how much banks should be recapitalized. Taxpayers should be allowed to make their own investment decisions, and do not need to be herded by the Treasury.

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