The Solow Model and the Low-Wage Class: Labor Day Edition (Very Wonkish)

One of the great pleasures I have in Sociology (and more specifically, in Political Economy) is tying the economics models to real life social facts on the ground. There are a lot of crappy models, most of them micro; such as the income substitution effect of labor model. Surprisingly, most of the macroeconomic models (specifically, Keynesian) paint a more accurate picture of what people (and labor) go through in their daily lives. However, Dr. Paul Krugman’s post on CBO Methodology reminds me to sometimes look at neo-classical models that may also apply to everyday life; specifically, the Solow Growth Model.

Basically, for my purposes in the Sociology of labor, and forgetting about Keynes for a brief moment, the Solow Growth Model says that there’s a point where wages mean nothing in the growth of capital. This is interesting, because my own modeling on rent seeking in labor also says that once a wage is constrained, hours doesn’t matter in the growth of wage income. The difference in my model is that units of time are factored into an earnings calculus. The Solow model doesn’t do that (for a myriad of good reasons).

Here’s a picture of how it works, followed by an explanation.

solow model

Output is a factor of productivity of workers. Capital is a factor of wages. As you can see, “potential” output can always be maximized in a wage constraint; meaning that there is always a way to bleed your workers dry for less cost. The equilibrium is the relationship of K to Y.

So does the Solow model fit social facts for every day life on the ground for people? In a retail, low-wage economy, there’s only one way to measure “productive output”, and that’s by “Sales”.

Untitled

(Data Source: Federal Reserve Bank St. Louis)

Essentially, everything correlates EXCEPT what matters in the model; capital wages, and output (sales). The Solow model is premised on the idea that capital is spent on wages, and output correlates to capital. It’s therefore reasonable to assume that, as capital increases from increased profit, so should wage earnings – at least according to the model (up to a certain point). That’s not happening. Wage and hours have no correlation as well as wage earnings and sales. Here’s the correlation matrix:

Wage Earnings
Hours Worked
Real GDP
Retail Sales
Wage Earnings
1.0000
-0.0737
0.5990
0.0471
Hours Worked
-0.0737
1.0000
0.6722
0.8944
Real GDP
0.5990
0.6722
1.0000
0.8070
Retail Sales
0.0471
0.8944
0.8070
1.0000

The Solow Model was created just after World War II as a long-run macro theory based on manufacturing. To be fair, I’m testing it in a retail-based economy, and straddling the fence on the macro thing. So the Solow Model is a bit off on describing social facts. But all is not lost; it does indeed describe (very well, I might add) a social problem in constrained wages. What problems? That would take a thesis; but if you look closely at the matrix, and then the model, it’s easy to see.

The great thing about testing theory is that it’s supposed to be able to withstand the test of time, as well as tests from outliers like me. While not accurate in describing social facts in every day life, the Solow Model does give some direction is where to look for social problems in labor markets. For that, it was indeed useful to look at.

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One Response to The Solow Model and the Low-Wage Class: Labor Day Edition (Very Wonkish)

  1. Pingback: Measuring Seven Cents | The Conscience of a Progressive

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