This stylized fact seems relatively true: the most recent estimates suggest that U.S. corporations are holding over $2 trillion in "profits" overseas; these profits, if repatriated, would be subject to a tax equal to the difference between the U.S. corporate rate (35%) and whatever was paid initially to the foreign country [omitting some details]. Members of Congress would love to see this cash brought home, even if the benefits only accrue to shareholders and executives, as the recent literature has suggested. (Of course, the profits need not actually be "held" overseas; we just mean that some controlled foreign corporation has yet to pay its U.S. parent corporation a big fat dividend of those profits.)

With this in mind, I went looking for a simple model of business investment taking account the basic features of how the U.S. taxes foreign profits of U.S. corporations, and I couldn't find one --- if you know of one, send it my way! (I did seem to recall seeing something of this sort in this textbook back when I worked for Bob Pozen.)

So, I wrote down as simple a model as I could imagine. There are two periods. In the initial period, corporations are endowed with domestic capital K

_{D0}and foreign capital K

_{F0}. In this initial period, the corporation chooses its dividends D

_{0}and tomorrow's allocation of capital (K

_{D1}and K

_{F1}). If repatriations (K

_{F0}-K

_{F1}) are positive, then the corporation owes a repatriation tax τ

^{R}applied to that amount (that's saying that

*all*of the K

_{F0}represents "profits" held overseas). In the second period, the corporation uses its capital (and no other factor) to produce at home and abroad. Let Q

_{D}(.) and Q

_{F}(.) denote the net-of-depreciation production function; consider these as having already subtracted out current corporate income taxes. The corporation then distributes all of its earnings and assets as a dividend D

_{1}, after paying any applicable repatriation tax, again at rate τ

^{R}. The objective function is just D

_{0}+βD

_{1}, where β=1/(1+ρ).

The solution to this model is quite simple. K

_{D1}is always pinned down by the condition that ρ=Q

_{D}'(K

_{D1}). This is just saying that large U.S. firms have essentially an infinite supply of financing available at a constant rate.

More interestingly, the repatriation decision is governed entirely by the initial stock of foreign capital, K

_{F0}. First, if the marginal product of foreign capital evaluated at the level of

*initial*foreign capital--- that is, Q

_{F}'(K

_{F0})---is smaller than ρ, the firm will adjust its foreign capital downward by repatriating until the marginal product is equal to ρ. Second, if this quantity is larger than ρ/(1-τ

^{R}), then the firm will adjust its foreign capital upward by

*expatriating*until the marginal product equals ρ/(1-τ

^{R}). Third, if Q

_{F}'(K

_{F0}) is between ρ and ρ/(1-τ

^{R}), the firm will stand pat.

Let me restate the first result in a different way: So long as Q

_{F}'(K

_{F0}) is less than ρ, the firm repatriates. Furthermore, it is easy to see that, in this case, the repatriation decision is completely unaffected by the presence of the repatriation tax! Suppose a firm repatriates an extra dollar. It gets an extra 1-τ

^{R}in domestic capital, which will create (1-τ

^{R})(1+Q

_{D}'(K

_{D1})) in output tomorrow. It loses (1+Q

_{F}'(K

_{F1})) in foreign output tomorrow, which will be worth (1-τ

^{R})(1+Q

_{F}'(K

_{F1})) after repatriation tax. The first order condition (assuming positive repatriation) calls for these to be equalized --- which causes the repatriation tax to cancel! I should stress that this is not a new result; I'm pretty sure I saw a similar result in the textbook I linked above.

There is an analogy to be made here to the equivalence of IRA and Roth IRA, with constant tax rates. With a repatriation tax, keeping foreign capital foreign represents "pre-tax dollars" being invested in an IRA (where the tax in question is the repatriation tax). Repatriating foreign capital is like using after-tax dollars to fund a Roth IRA. At the same rate of return, the two choices are identical.

Thus, in this toy model, the effect of the repatriation tax is solely to reduce

*expatriation*, not to reduce repatriation. (When a corporation is considering expatriating capital, it is comparing the domestic return to the foreign return, net of the repatriation tax to be paid in the next period on the foreign profits. In this context, the repatriation tax tilts the playing field in favor of domestic capital.)

So, there's obviously something else going on that must explain the $2 trillion in overseas profits, basically sitting idle. The most likely answer is that firms do not expect τ

^{R}to remain constant between now and tomorrow. They probably anticipate some probability of a repatriation tax holiday; because everything is linear, this is equivalent to a certain partial reduction in tomorrow's τ

^{R}.

To explore this, I parameterized my model with a Cobb-Douglas production function that is identical at home and abroad, but with a higher (current) tax rate in the U.S. In the baseline, I specified τ

^{R}such that the repatriation tax would represent the difference between foreign tax liability and domestic tax liability. I found that even a small chance of tax holiday tomorrow causes the phenomenon of "holding profits overseas" despite better returns available in the U.S. In particular, I set ρ=0.1; a 15% chance of a repatriation tax holiday takes the foreign return threshold down from 0.1 (the repatriation tax-free benchmark) to 0.063. In other words, my toy firms are willing to forego a 50%+ increase in marginal product in order to gamble that they will be able to repatriate their profits tax-free tomorrow.

Put in this light, we can see how truly terrible the 2004 repatriation tax holiday was. Perhaps more concerning, all the current foreign tax reform proposals involve some sort of "transition relief" to existing foreign profits. Even if these reforms are sensible when viewed as a package, the continuing

*discussion*of these plans is making the distortions to capital allocation worse. This is truly a "s--- or get off the pot" moment for Congress.

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