## Sunday, June 22, 2014

### Growth Modeling: I chickened out

I found a PDF titled Creating a Macroeconomic Model Using Real Economic Data, only five pages (plus a page of questions I didn't look at).

The file is SolowProjectNotes.pdf, and (backtracking the URL) it comes from Professor Rodney Smith of the Department of Applied Economics at the University of Minnesota. From his home page, click Teaching to get a list of Professor Smith's handouts and notes on his Solow Project and other stuff.

The SolowProjectNotes PDF is great! Smith takes you step-by-step and explains everything along the way. I spent most of Saturday going through the PDF, gathering data and entering calculations in a spreadsheet. It's one of those things where you have to put a lot of hours into it before you can make a graph to see if you're anywhere near right. I have patience for that kind of work, but it was most of Saturday.

I was almost ready to make a graph in the spreadsheet, and I chickened out. My brain got full, I couldn't do any more, I didn't have any time to check my work, it was just too much. So I stopped work on that project.

But you know what? I learned some stuff along the way. Here's the first formula Smith presents:

Here's what I understand (I hope I got it right):

"Y" is real output, or real GDP. The little "t" means "for the year we're figuring numbers for" or something like that.

"B" is a constant that scales the right side of the equation to equal the left side.

"K" is capital (and K-sub-t is the amount of capital in the year we're figuring). The K-sub-t is raised to the power of alpha, I think that little fish-looking thing is alpha. I'll get back to alpha in a minute.

// EDIT 28 SEPT 2014: WELL, THE NEXT PARAGRAPH IS WRONG. "A" IS LABOR PRODUCTIVITY, NOT TOTAL FACTOR PRODUCTIVITY. I'M NOT SURE WHAT THOSE THINGS ARE YET. BUT I THINK THEY'RE NOT THE SAME.

"A" is Total Factor Labor Productivity, and "L" is labor, or the number of people in the workforce. A-sub-t is multiplied by L-sub-t, and the result is raised to (one minus alpha).

// EDIT 28 SEPT CONTINUED: I'M NOT CHANGING THIS PART. I DID USE TFP FOR A TO PRODUCE THE GRAPH BELOW AND IT SEEMED TO WORK PRETTY WELL. SO MAYBE tfp AND LABOR PRODUCTIVITY ARE SIMILAR??

You can use "gross fixed capital formation" or "gross domestic fixed investment" or something similar for K, and "Total Factor Productivity" for A, and "Civilian Labor Force" for L, and you've got most of the numbers to fill in the equation.

The "alpha" we can use the value Professor Smith gives, 0.371 for the U.S. Then, one minus alpha is 0.629; Smith gives that number also. So now we've got everything for  the right side of the equation, everything except B.

I took FRED's Real GDP and put it on a graph. Then I took investment and factor productivity and labor numbers from FRED and arranged them according to the equation. I plugged in Professor Smith's values for alpha and one minus alpha. And I set B equal to one.

I graphed the thing, then fiddled with the value of B until the calculated line got close to the Real GDP line. Came up with B = 1.25. Here's the graph:

 Graph #1: Real GDP (blue) and a Solow Simulation (red)
Nice.

I don't know how they figure Total Factor Productivity. Maybe it's an error term. Maybe there's a discrepancy in the calculation and they use TFP to reduce or eliminate the discrepancy. In that case what I'm doing here would be circular and silly. But even if that's true, I know more now than I did before.

All in all, pretty neat.

The Arthurian said...

The "alpha" number, and one minus alpha...

The "one" stands for 100% of income. The numbers refer to shares of income. By Smith's figures, 37.1% of income accrues to owners of capital, and the other 62.9% is paid to labor.

shtove said...

I have no idea what you're talking about.

Where is this blog going?

And why aren't you full of pompous conclusions?

I visit everday for your scepticism.

The Arthurian said...

Where else would you find "alpha" described as a fish-looking thing?

Hi, Shtove. I have an advantage over most people, who always think they are right. I always fear I'm wrong (and I'm often right about that) so I have no need for most of my conclusions.

I don't know where I'm going, either. I investigate. I did notice that on the 20th I warned about assumptions, and the next day I sort of brought shame on the Solow growth model. And then today I'm admiring it and trying to understand it and make a copy of it for myself. That even struck me as odd.

Tomorrow I'm saying I think I can use it to create a simulation of the economy in a spreadsheet. I need that.

The Arthurian said...

Switched to Labor Productivity and messed with the constants. New graph:

https://fred.stlouisfed.org/graph/?g=cpbW

What I really want is to add finance to the Solow model.