Last week I wrote about falling wages in public sector unions, and suggested that due to the power of public sector unions those wages will just return to trend after the recession is over. I therefore suggested it would be better if public sector unions lost power rather than wages, since you could permanently take power but not above market wages. Via twitter labor economist Mark Price (@price_laborecon) disagreed with my claim that public sector unions have “too much” power.  If they did, he argued, it would show up in compensation data, and the evidence suggests it doesn’t. He linked to three reports (here, here, and here) that show that public sector wages are no higher than, and often lower than private sector wages.

I’ve seen the paper by Bender and Heywood, and the one from CEPR before, and the third one is a paper on public sector premiums from the Economics Policy Institute. The Bender and Heywood paper uses household survey data on income and worker characteristics from the yearly Outgoing Rotation Group in the Current Population Survey (CPS) to estimate whether there is a public sector wage premium after controlling for worker characteristics. I’m going to focus on this paper because it is the strongest and most relevant: the CEPR paper is missing important controls, and the EPI one only applies to New Jersey.

In short, the study finds that controlling for age, education, race, gender, whether they are married, state of residence, and union status, both local and state public sector employees are paid less than private sector employees. The first thing to note is that union status is controlled for, which means that public sector workers are paid less if you ignore the wage premium they get from being in a union. My claim was that public sector unions possessed too much power, so removing a wage premium attributable to union status gives you an answer that is beside the point. My claim isn’t that all public sector workers have too much power, or that public sector unions have too much power relative to private sector unions.

This study in fact supports my argument if you use Dr.Price’s metric. The regression coefficients on page 8 of the report show that the union wage premium is between 15% to 16%, while the public sector wage discount is around 11%, meaning unionized public sector employees are paid 4% to 5% wage premium. Thus the power is showing up in compensation, which is what Dr.Price suggested should be the metric for “too much power”.

There are other interesting issues here as well. I obtained the datasets from here and with the help of Dr. Bender, one of the study’s authors, I was able to recreate the results. One important point is that if you include occupation controls, and include average hours worked and hours worked squared (which you should) the union premium increases and the public sector discount drops, so that the total differential (union + public sector) grows to 18.1% for local and  15.2% for state.

Another important point is that some public sector jobs will obviously pay less than private sector jobs for reasons unrelated to unions or wage setting power. This is particularly true for more high skilled occupations. Public defenders, for instance, are going to get paid less than the average private sector lawyer. I don’t know whether this is due to lower abilities and skills or simply a willingness to accept lower pay because they want to perform a civic duty, but either way it’s pretty unrelated to the issue of public sector union power.

The heterogeneity of these results across different skill levels becomes clearer when we look only at workers with less than a college education (including those who had some college but not complete it). The union wage premium here increases to 22% for both local and state, and the (now statistically insignificant) public sector discounts are 1.2% and 1.3%. Thus lower educated workers earn around 20% more when working for a public sector union than they would if they were non-unionized public or private sector workers.

A final point I’d like to make is that a wage premium is not equal to public sector union power. A powerful union may use all of it’s bargaining power to negotiate for absolute job security, which could then select for a different set of workers with lower unobservable skills. In this case you would observe wages equal to or even below private sector wages despite a clearly powerful union. Some would argue this is exactly what teachers unions do.

[UPDATE: Regression results above slightly corrected]