Thanks to some useful comments to my earlier post, I am following up with several more graphs depicting the relationship between union membership and fiscal outcomes in the states.
First, here is a graph similar to my earlier one, except with FY2011 deficits plotted against the percent of the public-sector workforce that is unionized (data from unionstats, specifically this Excel file—thanks to commenter Jon).
The plot resembles the earlier one, except that the bivariate correlation is larger (0.33) and statistically significant (p=.03). In a bivariate linear regression model, a 5 percentage point increase in public sector union membership is associated with a 1 percentage point increase in the FY2011 deficit as a percent of the budget.
There are three big outliers, obviously: DC, Alaska, and Wyoming. If we include those cases, there is no significant correlation (0.22; p=.11). If we exclude those cases, there is a larger and significant correlation (0.70; p< .001). In a bivariate linear model that excludes these 2 states and DC, a 25 percentage point increase in public sector union membership—roughly the difference between Wisconsin and Idaho—is associated with an addition $1,500 of spending per capita.
Third, following on this post by Chris Edwards at Cato that was suggested by commenter Matt, here is a graph of state and local debt as a percent of gross state product, again plotted against public sector union membership.
This shows the same relationship as did the post at Cato. The bivariate correlation is 0.39 (p=.006). In a bivariate model, a 25 point increase in public sector union membership is associated with a 2.7 percentage point increase in state and local debt relative to gross state product.
Fourth, see this comment by Mark:
I just coded the data “TheRef” posted to distinguish between states with no collective bargaining law and states with some sort of law (0=no law, 1=anything else) and used this to predict the 2011 shortfall as a percentage of budget. I have no idea if this coding is appropriate, but it should provide a rough estimate.
While the relationship was positive (like the r coefficient in the post) it explained less than 2% of the variance (R^2 = .017). This is actually less explained variance than that explained in the above post (.19*.19 = .04), though this could be due entirely to the linear compared to categorical nature of the predictors. Just to note, the unstandardized beta was 3.08.
In sum, I have made the graphs in these two posts—and solicited some feedback—because it seemed valuable to have some data to look at when debating the fiscal impact of unions. But note that my claims in both posts are descriptive (“is associated with”) and not causal. The associations that I document here may not reflect causation and may instead be spurious, given that I have controlled for nothing else. In other words, I agree with how Reihan Salam summarized my first post.
As before, I welcome further suggestions and feedback.