Commenter John Handley points out (correctly) that Paul Romer is talking about real output, while in my previous post, I talk about the price level. The problematic extrapolation from RGDP growth rates doesn't really depend on using real output or the price level (specifically, the physical analogy I wrote down); I was attempting to connect the result to a previous result about the price revolution of the 1500s (or so).

So I went back and re-worked the result in terms of real output (

*R*) with real growth rate*ρ*(i.e.*R ~ exp ρ t*). I also made use of some stuff from the section on the AD-AS model in the paper. Using the market (information equilibrium relationship)*P : N ⇄ M*we can show*k M ≤ R ≡ N/P*

And the picture we produce is very similar to the price level one and has the same interpretation -- simply extrapolating back with constant real growth rate

*ρ*doesn't capture the fact that there probably wasn't a monetary economy in the past:
What's also interesting is if we assume information equilibrium and use the "money mediated AD-AS model" from the paper, i.e.

*N ⇄ M*

*⇄ S*

we can show that, if

*k ≡ kn/ks*where*kn*is the IT index of the market*N ⇄ S*and*ks*is the IT index of the market*M ⇄ S*, we have the information equilibrium relationship*R ⇄ S*with IT index*ks*. That means*R ~ exp ρ t ~ exp ks σ t*

where σ is the growth rate of aggregate supply. Therefore

*ρ = ks σ*. The real rate of growth*ρ*is only proportional to the rate of growth σ of aggregate supply widgets. See the derivation in the postscript below.
We don't know if

*ks*is changing or even what its value is (except that it is of order*kn*in order for*k ~ 1*empirically). It could be greater than one or less than one. Therefore so-called real output doesn't necessarily represent real widgets, but rather some conversion of physical widget units to money units. We have*R ≡ N/P = N/(dN/dM)*so the units of real output are the units of*M*(i.e. dollars).
An argument about real growth isn't an argument about physical widgets, so saying 2% real growth extrapolated backwards to the year 1000 is a small number doesn't tell you anything about the number of physical widgets. If

*ks*> 1, then*σ*< 2% and the number of physical widgets in the year 1000 could be much greater than would be surmised from a tiny value for*R*.
Of course, this is a model dependent result. And that is the point -- Romer's argument that real growth has been accelerating is also model dependent.

...

PS Here are more details of the derivation (in long hand):

"if k ≡ kn/ks where kn is the IT index of the market N ⇄ S and ks is the IT index of the market N ⇄ S"

ReplyDeleteBoth kn and ks are the IT index of the same market?

O/T, you might like this Jason: I "earned" a "touche" from Sumner:

http://www.themoneyillusion.com/?p=30920#comment-403899

(I couldn't have done it w/o reading this blog)

Fixed.

DeleteAnd nice one!

Yes, excellent jab, Tom! :)

Delete"In a sense, there is disagreement between humanities and social science/economics over what constitutes fact."

ReplyDeleteTo which I say, Elvis is really dead. ;)