How much would German stimulus raise the steady-state return on private capital?

I have been following a bunch of Twitter discussions around this topic, but I would like a firm estimate — if only your guesstimate — how much more German spending on infrastructure would boost general rates of return.  One side question is whether such a policy might drag Germany out of its current negative yield equilibrium.

There is (I think) general agreement on a few magnitudes, noting that the moving averages may be more relevant than last year’s numbers:

Government consumption in Germany is modestly below 20% of gdp.

Total government spending in Germany is modestly below 50% of gdp.

Germany could and should spend another 1% or 2% more of gdp boosting its infrastructure.

The current German unemployment rate is about 3%.

Germany runs large trade surpluses, relative to gdp, so the aggregate demand shortfall there cannot be biting too hard.

It would be good for the Eurozone as a whole if the ECB were to adopt a more expansionary monetary policy, at least under some conditions (so no need to reiterate that in the comments).

OK, so here is the thought experiment. Let’s say Germany spends 2% of gdp more a year on roads, better internet speed, upgrading airports — whatever is best.  And they do this each year for “as long as it takes.”

As we approach the new steady-state, how much higher is the private return on capital?  (And what is then the implied rate of return on fiscal policy?)

Note that the higher taxes, even if you postpone them through debt, will involve some deadweight loss and output restrictions sooner or later.

And what is the chance that brings Germany out of negative yield territory on its government securities?

Inquiring minds wish to know.

Addendum: Keep in mind that most government projects these days are not direct output, rather they are inputs toward selling or producing further private sector outputs.  So you build a better road so more people can get to the store, and the journey of the supply trucks is easier too.  That means when the private sector activity shows constant returns to scale, while the greater output will be desirable, the private rate of return on those activities won’t be going up at all, not in the steady state.  So a big chunk of the government spending, while it may boost consumer surplus, won’t increase rates of return period.

According to this study (its p.8 source is official but I cannot verify “according to the author’s calculations”) the rate of return on private capital in Germany in 2013 was slightly below four percent.  But say you have a capital share of output at about fifty percent and a four percent yield on that.  Capital then is giving you an extra 2% a year of gdp, it would seem.  Say that by spending 2% of gdp on infrastructure you could double the rate of return on all that capital (which seems implausible to me I might add).  You are then spending about 2% of gdp a year to get…about 2% of gdp a year.  I am sure those are not the correct, exact numbers but…what is the better non-question-begging way to think about the problem?

Your best bet of course is to invoke project durability.  Say you spend 2% of gdp for seven years (Germany isn’t so quick at building things), and you get infrastructure that lasts say twenty years before needing another upgrade.  Years 8-20 it is pure bonanza (except the higher taxes may be kicking in then).  That is indeed why I think the spending is a good idea.  But that is hardly “stimulus.”  It is much closer to “we forgo valuable output for a bunch of years and much later people are better off with better roads and yes long-run growth is important.”

Of course that explains why the current government is less than enthusiastic to do this “stimulus.”  The Merkel government isn’t stupid, it simply has a limited time horizon, and it doesn’t assume that demand-side economics is a free lunch at three percent unemployment.

And by the way, that spending is not, over any time horizon, likely to actually double the private rate of return on capital.

Along the way, how are the negative yields supposed to disappear?  In year eight, when the net benefits finally kick in?  Reflected in the term structure now, for the arrival of year eight?  (Really?)  In the meantime, the German economy is modestly poorer.

If you disagree, please show your work.  No moralizing about austerity or surplus countries, please.  Show your work.


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