This mostly data and accompanying analysis. If you are a casual reader, I apologize for complete lack of background or any real readability. It may be of use to people who are already familiar with the issue. I asked the question "What is the effect of having right-to-work laws on a 'meaningful measure' of income?" First, a look at those states with right-to-work laws as of 2015:
| Blue: No RTW; Red: RTW |
The first question unanswered is what would constitute a "meaningful measure". I began with by-state median income. I chose median instead of mean because median is a far more robust estimator of the central tendency than is mean. Unfortunately, my limited access to data (American FactFinder) meant that I could only get state median incomes for "households" or "families". Since many households are non-family households, I chose median by household. I also downloaded average sizes of household by state. I then obtained the "Implicit Regional Price Deflator" (by state), or IRPD, from the BEA. This combines differences in cost of living by state with inflation per year. It can be used to give a state-adjusted, real-dollar estimate of income. This was only available for the years 2008-2015, which limited my analysis to those years. I finally downloaded total civilian full-time employed and total military employed, both by state. I divided this by the total population of a state for a year. I did not restrict this to "workforce", since children have to be supported, too, even if they are not in the workforce. Each state's status as right-to-work or not was coded as an ordinal variable by year. The basic data set is available for you to check, yourself
| Factor | Estimate | CI | |
|---|---|---|---|
| Right to Work† | -0.1504 | +0.1052/-0.0570 | * |
| Year | -0.0088 | +0.0047/-0.0096 | * |
| Right to Work × Year | 0.0002 | +0.0166/-0.0103 | |
| * Factor is significant at p ≤ 0.05 by nonparametric bootstrap. | |||
| † Estimate corresponds to state having right-to-work law. | |||
From these numbers, I created my "metric": (((Median Income)/(IRPD/100))/Average Household Size)*(Employment Percent). I call it "Effective Income per Person". I modeled this Metric using generalized linear mixed models. State was the grouping factor for random effects. Sums contrasts were used. The fixed portion was "Metric ~ RTW + Year + RTW*Year". For calculation purposes, year was divided by the standard deviation of all years in the data set. Different error structures were compared by second-order Akaike Information Criterion (AICc). The compared models used Gaussian, gamma, and inverse Gaussian distributions, with identity, inverse, and log link functions. Of these, many did not converge. Of those that converged, the lowest AICc belonged to the model with a gamma distribution and log link. The next-nearest model had a gamma distribution and identity link. Δ AICc was greater than 6.9, indicating very strong evidence to favor the first model over all other models that converged. The model was evaluated by stratified non-parametric bootstrap, "state" as the stratifying feature.
Since this had a log link, the estimate for "Right to Work" means that, on average, a right-to-work state could be expected to have a 15% lower effective income per person. I bootstrapped the estimated average effective income for RTW and non-RTW states for each year and subtracted the RTW average from the non-RTW average. Adjusted for multiple comparisons, the 95% confidence intervals show that the difference was significant for all years examined, as the chart shows. In addition, overall effective income per person dropped by roughly 1% every six months, regardless of right-to-work status. There was no significant interaction between right-to-work and year, meaning the difference due to right-to-work remained constant.
I glossed over using a mixed (or multilevel) model to reach my results. I chose such a model for two reasons. First, this was repeat measures data. The same states were "measured" each year. That means we can presume that the data within each state will be correlated to data for other years from the same state. Second, as has been noted in other analyses of RTW laws, individual state effects may play large roles that could mask overall RTW effects. The mixed model allows one to account for both within-state correlations and individual state effects. What it does not let us do, with the data on hand, is actually identify those individual state effects. That is, we can estimate how large the effects are but not what they are. It's like measuring a hole without knowing what actually made it. You don't need to know how a hole was made to measure how wide and deep it is. I will present those "random effects" in a later post.
An alternate model
After getting snark from someone who believes that a "differences in differences" model magically establishes "causation" better than does a mixed-level glm (Free clue: Neither type of model actually establishes causation.), I ran the magical DID on my data. My results:
| Factor | Estimate | CI | |
|---|---|---|---|
| Right to Work† | -0.956.61 | +412.31/-399.59 | * |
| Year | -148.08 | +349.18/-402.62 | * |
| DID | -63.48 | +589.13/-611.93 | |
| * Factor is significant at p ≤ 0.05 by nonparametric bootstrap. | |||
| † Estimate corresponds to state having right-to-work law. | |||
Now, what does this mean? It will make more sense if you understand that "DID" is actually the same thing as interaction between Right-to-Work and year. The only difference is that "Year" has been coded as a 0/1 variable instead of specific years. The cutoff was 2012, which was the only year in which some states swapped from not having RTW to having RTW. While the values of the coefficients are different, the result is the same. DID analysis indicates that, overall, non-RTW states had a higher per-person adjusted income and that imposing RTW did not significantly alter this.
So, what does that mean? It means that, using this metric, there is no net benefit to most people in a state from imposing RTW over not having it. Now, if one believes "the more regulation the better", then one would say "Okay, so impose RTW everywhere, since it doesn't make a difference." However, if one believes that more laws are not good in and of themselves, and that government interference in business practices (interfering in permitted terms of contracts is government interference) should only be done if there is a compelling benefit, then RTW fails to actually grant sufficient benefit.
