I am still thinking about Krugman and the Gravelle GeardownDo click the link if you are interested in understanding what I am typing about. Very briefly the question is: what effect would cutting the tax on profits have on the _US capital stock ? The particular issue is what difference does it make that most of US production is production of non traded goods and services. Gravelle claims that this implies a lower long run effect of the tax cut on US capital stock than would occur if all goods and services were traded (or that’s what I think based on Krugman’s explanation).

Here the key words are “long run” and, I think, an important issue is long run mysticism. This post is getting long. I will put the conclusion here. It seems to me that standard assumptions about the long run make even less sense in open than in closed economies and I think that is the key issue here. Macroeconomists have the most consensus and confidence about the long run. The reason is that it is all handled by simple assumptions made for convenience. In particular, it is standard to assume that there is a unique long run steady state determined by tastes and technology. This doesn’t follow from other core assumptions. I think this is a terrible problem, because politicians think it is honorable to focus on the long run and that means they make policy influenced by the assumptions we make for convenience (austerity, the EU stability and growth pact, and European Single Bank single mandate). Over in the USA they talk about the effect of tax cuts assuming the government intertemporal budget constraint will be satisfied with equality — this when commenting on GOP policy proposals which would violate it.

I will hint at a model used (by Krugman say) to assess the effects of a profit tax cut. It starts with two strong assumptions. First prduction is determined by technology and accumulated capital — the model is solved as if there were full employment. This makes (some) sense if one assumes the unemployment rate is detrmined by monetary policy. Second it is assumed that consumption is not affected by interest rates. This assumption is based on the evidence — it is radically different from the standard assumption made in theoretical macroeconomics. Finally Government consumption plus investment is taken as given.

With those thee assumptions, increased investment must correspond to reduced net exports. This matters a lot for short run dynamics. To get higher investment, the USA must run a higher current account deficit. Krugman recently argued that this has implications for exchange rate dynamics which, in turn, imply slow convergence to a new steady stated. But here I will just discuss the long run and assume it is a steady state.

I will now make an invalid argument as to why non-traded goods don’t matter. In the long run, everthing will be in balance, The US after tax return on capital will be equal to the world real interest rate. The current account deficit will be zero. The real exchange rate will be that consistent with current account balance. It doesn’t matter if all or onl ysome goods are traded.

Here the trick is that I assumed that there is a unique steady state even though the model must have a continuum of steady states. I assumed that each countries intertemporal budget constraint (that the present value of it’s foreign debt must go to zero) is satisfied in the simplest way with each country having no foreign debt. Nothing guarantees that. Another steady state is one in which the USA is a net debtor and services the debt with trade surpluses forever.

Here long run mysticism has met representative agent mysticism, but an extreme representative agent assumption which is never made (but which I accidentally implicitly assumed). The assumption is that I can treat all countries as the representative country, so, in the long run, none is in debt to another. This is expecially crazy. It was an honest intellectual mistake I made.

In fact, I’m pretty sure I can guess what would happen if I actually worked through a model. The US cuts corporate taxes, foreigners want to buy US stock. This drives up the dollar and drives down net exports. The workers freed up by the reduced net exports build more capital in the USA until the after tax return drops to the world level. The dollar slowly depreciated until the world reaches a new steady state in which the US has more capital and the same rate of investment so the current account is at the constant level which satisfies national budget constraints. That does not imply zero net exports. The US has accumulated foreign debt while adjusting to the new higher capital stock. This means that the budget constraint implies positive net exports to service that debt. So the dollar will depreciate in the long run. The amount of capital which can flow in is limited by the amount of debt the USA can service. I think Gravelle gets her result, because this limit is binding.

Here my error was assuming that I could model the long run as a unique steady state in which all countries are symmetric — none is a creditor nor a debtor. There is nothing in the model which implies this. It is an insane assumption about the representative country, which has no place in a model in which different countries have different tax policies. TThis is an extreme case of a very common error. Also in a closed economy, it doesn’t really make sense to assume there is a representative agent. The assumption is just one of the many tricks used to get a single steady state when assumptions about tastes and technology are consistent with many different steady states.