The Leprechaun Long Run

by
Robert Waldmann
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The more people think about the Republican proposal to cut corporate taxes the worse it looks. Most people dismiss the argument that the benefits will trickle down to workers. Supporters’ argument is that reduced taxes on profits will cause increased investment which causes higher production and wages. There are strong arguments that the tax cut won’t cause firms to invest more. But aside from that, increased investment wouln’t cause (all) of the promised increase in wages. In this post, I will, for the sake of argument, make many assumptions favorable to advocates of the tax cut.

As often, I am following Paul Krugman and thinking of tax incidence in an open economy. Among others including Jared Bernstein, he argues that advocates of the tax cut have neglected their assumption that the increased investment will require foreign funds & that foreigners don’t invest in the US as a charity and expect to be repaid. This means that, in the short run, advocates argue that foreigners will buy US assets (the US will have a capital account surplus) which means that the US will have an even larger current account deficit. The plan is to cause high trade deficits in the short run.

Krugman has a post on the dynamics of convergence which he correctly notes is insanely wonkish. I will write only about the long run — the new steady state. So the math will be relatively simple. But mostly he writes comprehensible about Leprechaun economics, which is what he names it, because the number one example of trying to grow by cutting corporate taxes is Ireland. The basic point is embarrassingly simple, since foreigners require a return on their investment, attracting it does not cause national income to increase as much as gross national product. With foreign direct investment, more would be produced in the US but a lot of the revenue would belong to the foreigners. He has written four posts on the topic (the first four hits in this search)

Another interest of his the Gravelle Geardown which discusses how Jennifer Gravelle explains why the effect of a corporate tax cut on wages would be lower than some have argued. The point of this post (if any) is that the two issues are linked — the effect on wages is reduced by the fact that the country which attracts foreign investment will have to pay foreigners returns on that investment in the new steady state. I tried to begin to argue this here (reading I see I didn’t get very far).

Some assumptions
1a) The economy is not in a liquidity trap so unemployment (and spare capacity) are at the levels targetting by the Federal Reserve Board. In practice this is like assuming that there is full employment. This means that additional investment has to crowd out something: consumption, government consumption and investment, or net exports.

1b) Consumption is not measurably affected by interest rates. This corresponds to the evidence. This is the reason supply siders have had to appeal to the open economy and foreign investment.

1c) we are talking about tax cuts without government spending cuts.

This implies that the increased investment corresponds to reduced net exports — to a larger trade deficit.

2a) firms invest until the marginal product of capital is equal to the return demanded by investors, so that return is critically important (in the real world interest rates have small effects on investment by firms & mainly affect residential investment).

2b) the production function is smooth and allows substitution of capital and labor. In fact I assume a Cobb-Douglas production function. This means that the concept of “spare capacity” doesn’t apply to the model (and vice versa the model doesn’t apply to the real world).

These are key (implausible) assumptions made by advocates for the tax cut.

3a) Capital and labor are paid their marginal products. This means that the wage measured as a quantity of domestically produced goods depends on the capital labor ratio.

3a) foreigners demand a fixed after tax real return on their investments r* which is not affected by the policy. This is the assumption that the US economy is small. Again a concession for the sake of argument to tax cut advocates.

4) for both US consumption and US investment domestically produced and imported goods are not perfect substitutes. Instead they appear in a utility function (for consumption) or what is called an aggregator for investment. I did algebra (which I won’t inflict on anyone) assuming both have the form (foreign goods)^beta(domestic goods)^(1-beta). I assumed this so the share of spending on foreign goods is fixed. This means that the ratio of quantities demanded is the inverse of the ratio of relative prices. This is, honestly, just a convenient assumption which simplifies algebra. It means that there is a valid price index — utility is the same if dollar spent divided by the price index is fixed, capital is the same if dollar investment divided by the price index is the same and production is the same if capital and labor are the same. The price index is (price of foreign goods)^beta(price of domestic goods)^(1-beta) [oh how convenient]

5) someting similar is happening outside the USA (over here) so the share of foreign spending on US exports is constant. Also, the US is small, so total foreign spending is constant. This means that the value (in terms of foreign goods) of US exports is fixed.

OK that’s about it. I might use some horrible notation. I will use e to refer to the real exchange rate, the price in US goods of a unit of foreign made goods. This means that an increase in e is a real depreciation of the dollar. I will set current e to 1, so e will always refer to the depreciation casused by the policy. I will also set the price of US made goods to 1. This means that the price index is e^beta.

OK the story.
As the economy converges to the new steady stat, the US will run trade deficits summing to the increase in US located capital due to the tax cut. This means that the US will have to run a trade surplus to pay the returns on to the foreigners. This means that, in the long run, the policy will cause a real depreciation of the dollar. e will rise.

This has two important effects. First workers are less well off for a given capital labor ratio. The capitol labor ratio determines the wage measured as an amount of domestic goods. The price index relevant for workers as consumers is e^beta times the price of domestic goods. The real depreciation makes workers poorer.

Second the product of capital is also an amount of domestically produced goods. But the cost of a unit of capital is also e^beta>1. This means that, for a given capital labor ratio, the rate of return is lower. So this means that the real depreciation implies a lower capital labor ratio is required to pay the foreigners their required rate of return.

Given the assumption of the same shares beta and 1-beta is spent on domestic and foreign goods both for consumption and investmnet, the two effects have the same magnitude for small changes in K. Both hurt US workers.

To solve for the depreciation required to finance the returns on the additional capital, I have to make some assumption about exports. I think assumption 5) makes sense. It implies that the share of foreign spending on US goods is constant, so the amount of goods exported is proportional to e (I almost wrote exports measured in units of domestically produced goods, but hey the exports *are* domestically produced goods).

This makes the closed form solution pretty simple (although not simple enough to type in plain ascii). Indeed the effect on wages of a cut in the tax on profits is reduced.

This Gravelle gear ratio is a bigger deal if a large share of spending is on imported goods (high beta) and if the share of capital is large. I’m pretty sure the closed form solution and those two statement depend a lot on Cobb-Douglas assumptions made for convnenience.