However, ever since I put that model together I asked myself: does it have to be capital? What else could Z be in the model:

*CPI : NGDP ⇄ L*

*X : NGDP ⇄ Z*

Here's the graph of nominal capital alongside nominal wages (times a normalization factor):

They have about the same shape -- maybe that would work just as well for

*Z*? Or maybe some measure of money? It turns out those choices don't work. The problem is that they have too much of the business cycle in them making nominal growth fluctuate too much and inflation jump around.
It also looks like NGDP, but

*Z*= NGDP is problematic for obvious reasons. It's also not smooth enough.
Note that it's not just the annual data smoothing out the results -- annual data doesn't smooth out wages or money enough to work. Nominal capital is smoother than wages or money.

So what else could it be? Here's the FRED series (real capital multiplied by price level of capital). Is there anything that is comparable?

" Or maybe some measure of money? "

ReplyDeleteCumulated gross saving would probably give a similar - and perhaps comparably smooth - curve. FRED doesn't have it , but you could download the flow data ( gsave/quarterly or A929RC1A027NBEA/annual ) and sum it up in a spreadsheet.

Marko

Thank you very much! It does appear to be smooth enough and have the right curvature ... so it is possible it will work just as well.

DeleteOne thing is that if you use S = I, then savings gives roughly the same result as investment, which while not exactly the same thing as capital, is in the same ball park.

Yes , the S=I relationship was what made me think of it when you suggested you might like to look at a "measure of money".

DeleteCumulated gross savings will total up to a somewhat larger sum than nominal capital , since it also includes consumed capital/depreciation. On the other hand , cumulated gross savings misses debt-funded capital accumulation.

My sense is that we probably overstate consumed capital in the U.S. , as nominal market asset values of various types tend to hold up pretty well over time ( with some exceptions , of course , like when you drive your new car off the showroom floor ). For the most part , capital consumption is an estimated , rather than a measured , metric , so who knows what the "right" value is.

Marko