## Monday, June 23, 2014

### Growth Modeling: The nonlinear thing

Total factor productivity is the otherwise unexplained productivity left over after all the individual factors (labor, capital, etc.) are taken out.

See? That's why I say TFP seems like an error term, a correction value, an adjustment to make the answer come out right. I never forget, my chemistry teacher in college joked one time that we can "multiply by zero and add the right answer." That's not exactly what TFP is, but it is pretty much how I used it for yesterday's graph.

In Total Factor Productivity (PDF, 5 pages) Diego Comin writes:
Total Factor Productivity (TFP) is the portion of output not explained by the amount of inputs used in production. As such, its level is determined by how efficiently and intensely the inputs are utilized in production.

TFP growth is usually measured by the Solow residual. Let gY denote the growth rate of aggregate output, gK the growth rate of aggregate capital, gL the growth rate of aggregate labor and alpha the capital share. The Solow residual is then defined as gY − α∗gK − (1−α)∗gL.

This is starting to get familiar. The growth of output minus weighted values of the growth of capital and the growth of labor leaves a "residual" because the growth of labor and capital do not fully account for the growth of output. The difference, the discrepancy, is said to be due to changes in the efficiency of labor and capital, and it is called TFP, Total Factor Productivity.

So if I get labor and capital and TFP from FRED, and use an appropriate alpha, I should be able to plot a line very similar to Real GDP. Did it yesterday, in fact.

That's why I dwell on the Solow Growth Model. I think I can use it to create a simulation of the economy in a spreadsheet. That's one of those things I try to do every once in a while, create a spreadsheet where each row represents a year, and the numbers for one year are used to generate the numbers for the next year. Doesn't sound difficult, but I've never got a satisfactory result. Maybe the Solow model will help.

One of the basic ideas I try to convey on this blog is the idea that there is a particular level (or a limited range of levels) of finance that is best for economic growth. Too little finance, and money for economic expansion is unavailable. Too much finance, and the cost of accumulated debt undermines growth. When you hear people talking about the "nonlinear" effects of debt, this is exactly the phenomenon they mean. (You heard it here first.)

But I can't really show what I think happens unless I can simulate a growing economy. I think I can take the Solow growth model and add something to simulate a financial sector and a growing accumulation of debt. So then we can see if accumulating debt has the effects I describe.

And my financial sector will be built on the stable, predictable economy of the Solow model, so that changes arising from the addition of a financial sector will be quite obvious. But don't expect to see it tomorrow.

Meanwhile...