## Wednesday, February 1, 2017

### Regression model on small-firm insurance offer rates

Employer-Sponsored Insurance at Small Firms in Blue and Red States

Question:  How did the role of employer-sponsored insurance at small firms differ in blue states versus red states in 2013 (the year prior to the enactment of state exchanges) and 2015 (the year after enactment of state exchanges?)   How did the change in reliance on employer-sponsored insurance differ for blue and red states over this time period?

Data:   The information on the share of employees at firms with fewer than 10 employees with offers of employer-sponsored health insurance by state was obtained from the MEPS-IC database.   Here is a link to this data.

The blue versus red distinction variable was based on the results of the 2012 election.  I am a politics junkie so I know that by heart.

I am putting data for some of my statistics problems at my statistical resources blog.   Go here for this data.

Methodology:   I consider this question with three simple regression models.   The dependent variable in the three models are --  (1) share of small-firm employees with ESI offers in 2013,  (2) share of small-firm employees with ESI offers in 2015, and (3) the difference in share of small firm employees with ESI offers (2015-2013).

The explanatory variable in all three regressions was a dummy variable set to 1 if the state was blue and set to 0 if the state to red.

The intercept term of this model is our estimate of the average of the dependent variable in red states.

The sum of the intercept and the blue dummy coefficient is our estimate of the dependent variable in blue states.

The estimate of the blue dummy coefficient is the difference in the dependent variable for red and blue states.

The Regression Coefficients:

The regression coefficients for the three models are presented in the table below.

 Impact of Blue Versus Red Political Status On Percent of Firms With ESI Offers % employees at small  firms with ESI offers in 2013 Variable Coefficient t-statistic p-value Blue2012 0.098 3.86 0 _cons 0.304 17.06 0 % employees at small  firms with  ESI offers in 2015 Variable Coefficient t-statistic p-value Blue2012 0.090 3.1 0.003 _cons 0.260 12.83 0 Change in % of employees at small firms  with ESI offers Variable Coefficient t-statistic p-value Blue2012 -0.009 -0.46 0.648 _cons -0.044 -3.36 0.002

Discussion of Results:

The difference in percent of employees at firms with fewer than 10 employees who have ESI offers was significantly higher in blue states than red states in both 2013 and in 2015.   The point estimate of the difference in this percentage was 9.8 percentage points in 2013 and 9.0 percentage points in 2015.

The difference (2015-2013) in percent of employees with ESI offers is negative.  The point estimate is -0.044 for red states and -0.035 for blue states.

Discussion of Political Implications:

The ACA state exchanges created an alternative for small-firm employer-based insurance.   The regression results presented here suggest that the new state exchanges are more important for employees in red states than blue states because small firms in blue states are more likely to provide offers of health insurance.

Other Statistical Issues:

It would be interesting to run these regressions on the blue classification from the 2016 election.   The regressions could be estimated with the log of the odds as the dependent variable.   A broader ranged of cross-state health insurance regressions should be considered.

Concluding Remark:

The results presented here pertain to only one health insurance statistics.   I strongly suspect that red-state are more dependent on state exchanges in many other dimensions.

To paraphrase Alanis Morisette, “Isn’t it ironic that red-states will probably lose much more from repeal of ACA than blue states.”

Authors Note:  People interested in the ACA debate should consider some of my posts at my health insurance blog.  Here is a post on a plan that could improve upon the current ACA.