#### Income inequality and union membership

I put this together by taking both values for each year and treating them as x/y pairs. If 18% of the workforce was in a union in 1987 and 38% of the total income went to the top 10% in 1987, you get an x/y pair of 18%/38%.

You can see a clear trend. Income inequality is lower when union membership is higher. If you're curious, the r^2 values there are 0.78 for the top 10% and 0.68 for the top 1% plots (assuming linear which isn't exact but is close enough here).

This includes roughly a century of data. A lot changes in the economy over a time scale that large, so what happens if we restrict it to just 50 years? Here you go:

The trend is actually clearer. Same basic thing, less noise, and r^2 values of 0.90 and 0.86 for the 10% and 1% plots respectively.

The trend is actually clearer. Same basic thing, less noise, and r^2 values of 0.90 and 0.86 for the 10% and 1% plots respectively.

Another way of looking at this is to plot both vs time. Here is the top 10% income share and union membership % plotted vs year:

That one looks like union membership changes before income inequality does which is what you'd expect if income inequality is partially dependent on union membership. As a test, here is the same full history plot, except now the x in each x/y pair is union membership in a given year, and the y is income inequality 4 years later:

Much tighter. The r^2 values are 0.90 and 0.80 for the 10% and 1% plots respectively. What if we then take this relationship, and try to predict income share using union membership as the only input? We get the following:

Pretty good match, and this is particularly nice in that I assumed a simple linear model even though it's not perfectly linear in the plots above and there's no reason to think that this is the only variable explaining it.

That one looks like union membership changes before income inequality does which is what you'd expect if income inequality is partially dependent on union membership. As a test, here is the same full history plot, except now the x in each x/y pair is union membership in a given year, and the y is income inequality 4 years later:

Much tighter. The r^2 values are 0.90 and 0.80 for the 10% and 1% plots respectively. What if we then take this relationship, and try to predict income share using union membership as the only input? We get the following:

Pretty good match, and this is particularly nice in that I assumed a simple linear model even though it's not perfectly linear in the plots above and there's no reason to think that this is the only variable explaining it.

#### Does high union membership hurt economic growth?

An immediate question is...do the unions just eat economic growth so that inequality is lowered simply by making the rich poor without making anyone else richer? I don't know of a great test for that, but as a simple sanity check, I plotted annual GDP growth vs union membership:

There is a very tiny upward trend here (i.e., higher union membership = more growth) but the correlation is tiny (r^2 = 0.02) so it's basically no relationship. Does adding the 4-year lag here change anything?

Nope. r^2 = 0.00. There doesn't seem to be a relationship between these two variables.

There is a very tiny upward trend here (i.e., higher union membership = more growth) but the correlation is tiny (r^2 = 0.02) so it's basically no relationship. Does adding the 4-year lag here change anything?

Nope. r^2 = 0.00. There doesn't seem to be a relationship between these two variables.

#### Conclusions

Correlation does not equal causation and this isn't a thorough analysis. For example, it could be that the same voters that want union protections also want more progressive taxes, so the correlation here is just a reflection of both metrics being driven by the same types of voters. There are many possible explanations other than the obvious 'unions limit income inequality' one. Trying to draw some ideas from just these data though:

- income inequality is higher when union membership is lower
- the reductions in income inequality from increased union membership are great under 15% union membership and seem to start plateauing at ~20% union membership
- increased union membership does not seem to be related to annual GDP growth

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