## Wednesday, March 13, 2013

### Comment on DeLong on Cowan

Click the link if you want to know what I am typing about.

1) We should also consider pulling spending forward. Roads need to be resurfaced sooner or later.  If we do it 5 years sooner we pay the 5 year real interest rate on the cost (which is negative).  The true costs are lanes are blocked by construction sooner and we have to pull the next resurfacing forward 5 years.  The benefit is we get new smooth roads sooner.  Lets ignore the hassle of blocked lanes and any benefit from getting new roads sooner (assume one horse shay depreciation for roads so they are perfect up until the end of their useful life then must be resurfaced to be used at all).  Oh he is also assuming a multiplier of 0 so there is no increase in taxes collected now or any social benefit from lower unemployment now.  We get minus the 5 year rate and pay 5 years rates every 30 years.   A normal 30 years rate means the cost paid in 60 years is worth less than half the cost in 30 years. So say the cost is twice the cost paid in 30 years and discount with the current 30 year rate (-0.65) and hmmm carry the one ... we get total cost equals amount paid to get it done times roughly 5 times the current 5 year rate (-1.39) plus about 1.6 times 5 times the normal 5 year rate (1.52 avg 2003 when FRED starts through 2006) .  If the current real rate were low enough, that would add up to a negative number.

It pains me to actually check the numbers and find out that pointlessly anticipating investments 5 years is currently costly -- costs in 30 years are about like costs now if one is discounting at 0.65% a year.

Note this has nothing to do with dead weight losses from taxes.  The claim is that, for a low enough real interest rate, doing the project 5 years sooner would give a lower debt in 100 years for the same taxes.  It has nothing to do with Keynes.  I am assuming a multiplier of 0.  It has nothing to do with roads being useful.  I am assuming that the new resurfaced road is no better than the one which is within 5 years of the end of its useful life.  This is all 100% about how a low enough real interest rate can make the threshold return on an investment less than zero.

Sad to say I calculated after typing and find that the threshold return is about 1% per year or with Cowan's dead weight losses about 1.2% per year.  That return is the value of having a new smooth road sooner minus the cost of having a lane closed sooner.

The numbers would work better for pulling forward fewer than 5 years.

2) . I think I know why Cowan doesn't believe my argument in point 5. I think it is because he doesn't believe that because we do something which we have to do in 5 years now we will spend less in 5 years.  His world view is that marginal public spending is all due to capture by rent seeking special interests so if we don't have to resurface a road 5 years from now (because we resurfaced it now) we will just spend the same money on something else.

Here we see, as always, that the debate about Keynesian stimulus is always really a debate about public spending in general. Cowan will not accept Krugman's argument that if spending was about right in 2003 then it should be higher now, because he thinks spending was way too high in 2003.  He won't accept my argument that it is better to spend it now than in 5 years, because he thinks that spending if 5 years will have nothing to do with social returns to spending in 5 years.

3) the calculation of how risk averse the Federal Government should be assumes a multiplier of zero.  If unexpected and automatically higher spending or lower tax receipts cause higher GDP (and vice versa) then the correct calculation is different.  I have no doubt at all that the optimal level of Federal risk aversion is negative.  That is for the same expected return it would be socially better for the Federal Government to invest in risky assets whose returns are postively correlated with GDP growth.  Here I am most definitely assuming Ricardian non equivalence.  The general view that automatic stabilizers are a good thing implies the general view that the Federal Government should seak to bear risk (really it is hiding risk not bearing it -- it takes non Ricardian consumers for the trick to work -- but of course it does work).

4) wait with a hurdle rate over 20% how could firms ever possibly decide to invest ? From a survey Larry Summers found out that the median boss uses 30% somehow.  My guess of the way this works is that they when considering an investment of size K they make a stream of profit or loss equal to extra revenues net of other costs minus (r + delta)K using some not totally crazy value for real interest r and depreciation delta (where nominal interest counts as a not totally crazy value for r) and then discount the stream at 30% per year.  This would be pure myopia.  It has nothing to do with restraining cowboy managers.