How much would expanding Medicaid help in states that haven’t accepted the expansion?

Perhaps the single biggest story about the implementation of the Affordable Care Act has been the battle in states deciding whether to accept the Medicaid Expansion. The expansion is perhaps the single most important tool in the ACA’s coverage expansion tool kit. It takes 50 state-based single payer systems and drastically expands eligibility for them, which is the single largest progressive victory in politics since the Great Society. Other important Medicaid reforms drastically streamline the application procedures and eliminated asset tests to draw out formerly eligible people who might have gotten tangled up in the system or not bothered applying because the state made you apply in person on Tuesday between the hours of 2:30 p.m. and 3:04 p.m.

However, the expansion is not some magical talisman that instantly enrolls all eligible individuals. Some people will remain ignorant of the program despite the best outreach efforts, while other will not enroll for any variety of reasons. And more to the point, 24 states hadn’t fully taken advantage of the Medicaid expansion by the beginning of 2015. Pennsylvania, Indiana, Montana and Alaska have all signed on this year, leaving 20 holdouts (half of whom were in the former Confederacy – but I digress).

The cool thing that we have some real data of how ACA has actually performed on the ground over the last two years, we make some interesting dynamic projections of what would have happened had some states accepted the Medicaid, instead of simply discussing the number of people who would be eligible for help under the expansion.

I mean, heck, this Charles Gaba fellow has been counting the people who actually signed up for coverage for two years, I might as well take one shot at figuring out who would have signed up if they could have. 

To accomplish that, follow me below the fold, where I build a simple interactive regression model to project the reduction in the uninsured population in states that haven’t expanded Medicaid. Don’t worry; I’ll label the scary part where I work through the model so you can skip the simple summary where I discuss the results in plain English (but you really should read the model section, it’s rather of important and it makes fun of Bobby Jindal).  

Detailed Explanation of the Model

This model differs from my last simple two-variable regression model using Gallup data because I’m using a different dependent variable: the reduction of the uninsured rate in percentage points, which I simply think is a bit more intuitive to understand for the question at hand. (e.g. Massachusetts had 4.9 percent of its population uninsured in 2013 before the ACA kicked in and had 3.0 percent uninsured in the first half of 2015, for a reduction of 1.9 percentage points, which would be the MA case’s value in the dependent variable column. The big issue with that, methodologically speaking, is because some states start with much higher percentages of uninsured population they have the potential for much greater reductions.  That’s something we have to control for, or we might get skewed results that may even suggest that expanding Medicaid may very well increase the uninsured rate.

But how do we do that? We build an interactive model. We start with the same two independent variables in the other model: whether or not the state expanded Medicaid by 2015 (0 if it didn’t expand and 1 if it did); and what type of exchange the state had (0 for Federal, 1 for a partnership and 2 for a full state-based exchange).  From there, we add two more variables. The first one is the initial level of the state’s uninsured rate, which is straightforward. The second variable is the product of the Medicaid expansion variable and the initial insured rate variable. This fourth variable is what makes the model interactive: the total effect that accepting the Medicaid expansion will have is dependent on how large the initial uninsured rate is.

We get a model that looks like this:

Reduction in Uninsured Rate= (m1)(Expansion) +(m2)(State Exchange) +(m3)(Original Uninsured Rate) + (m4)(Expansion)(Original Uninsured Rate) + Constant 

It’s still pretty similar to that basic y=mx+b model you saw in your first-year algebra course, except 1. It have more variables and 2. Two of those variables get multiplied together (it also should have an error term, but don’t worry about that for now).

Note that the interactivity also makes it a bit more complicated to calculate the effect size of a given variable. To calculate the predicted effect of the Medicaid expansion in a given state, we can’t simply multiply the coefficient on the “Expansion” variable by the value of the Expansion variable, we have add that product to the value of the Original Uninsured Rate variable and its coefficient AND the interactive term.  Mathematically:

Reduction in Uninsured Rate due to Medicaid Expansion = m1(Expansion) +(m3)(Original Uninsured Rate) + (m4)(Expansion)(Original Uninsured Rate).

OK, let’s estimate the regression with our ever handy  Stata software:

Table 1: Influence of Medicaid Expansion on Percentage Point Decline in the Uninsured Rate
Variable Name	Coefficient
Medicaid Expansion:	-.447
State-based Exchange	.354
Initial 2013 Uninsured Rate	.298
Interaction (Expansion x Initial Uninsured Rate)	.198
Constant	-.543
N= 50
Adjusted R-squared =.4422

Before we get into what the coefficients mean, note that this simple model predicts about 44 percent of the total variation in our data. Also, again I don’t report standard errors because this is the universe of states, not a subsample. These effects are the “real” effects (baring omitted variable bias etc.)

At a glance it looks like accepting the Medicaid expansion actually increases the uninsured rate, I mean look at that negative coefficient! (which would equate to a negative decrease (increase) in the percent uninsured).  But it doesn’t –the other variables will interact to end up giving it a positive effect.  Let’s take an example and go through the math (no, not that math).

Louisiana, governed by Bobby Jindal -- possibly the dumbest man ever to win a Rhodes Scholarship -- has refused to take the Medicaid expansion. Between 2013 and 2015, the state has seen its uninsured rate decline from 21.7 percent to 16.3 percent (a 5.4 point decline), despite its best efforts to fight the socialist menace of Obamacare. But if Zombie Karl Marx had staged a coup and forced the state to accept Communis -er, I mean the Medicaid expansion, what would have happened? Well, we can estimate it in our model:

Reduction in Uninsured Rate= -.447(Expansion) +(.354)(State Exchange) +(.298)(Original Uninsured Rate) + (.198)(Expansion)(Original Uninsured Rate) + -.543

Where:

Mediciad Expansion =1 (we’re accepting it)

State Exchange =0 (Louisiana defaulted to the Federal Exchange)

Original Uninsured Rate= 21.7

OK campers, Plug and chug!

= -.447(1) + .354(0) + .298(21.7) + .198(1)( 21.7) + -.543

=-.447+ 0 +6.47+4.3 + 0.543

= 9.6 (more or less after rounding)

So instead of declining by 5.4 points, to 16.3 percent it would have declined by 9.6 points to 12.1 percent.  That works out to about 194,000 more people with health insurance.

Clearly a certain Cajun state governor didn’t do his maths homework at Oxford.

One final thought: Notice how much easier computationally the equation is to estimate when Medicaid isn’t expanded: two terms become zero, leaving us with a reduction in the percentage of uninsured of about 30 percent less of the original uninsured rate less one half a percentage point (The estimated reduction for Louisiana without Medicaid Expansion was 5.8 percentage points, very close to the actual rate of 5.4, which indicates our model is working fairly well.)

Again, there are several sources of error here. One potential problem is leaving out variables that are predicting systemic bias in the uninsured rate. One possibility that jumps to my head is the percentage of the state’s population that are undocumented immigrants, who are generally not eligible for subsidies or Medicaid. I feel a bit more comfortable with this as states with (Arizona, New Mexico, California) as well as without (Texas, Florida) have large populations of undocumented residents. However, if the average between the two sets of states is different, these measures will be skewed. Also, remember the Gallup data is based on samples from each of the states, and states with small samples – especially in 2015, which only takes up the first six months of the year, have a larger margin of error, which could skew these results a bit as well.

Plain English Summary of Results

Based on the simple interactive model, using the state’s decision to expand Medicaid, decision to implement a state-based exchange and the state initial uninsured rate as variables, I was able to calculate the following potential additional reductions in the uninsured rate for each state in Table 2 below. The first column shows the state’s uninsured rate at the end of 2013, the second shows where it was in July 2015. The third column is the projected uninsured rate in July 2015 if the state had accepted Medicaid. The fourth column shows the improvement between columns two and three. And the fifth give our estimate of the number of additional people who would have been insured had the state not been governed by vandals.

Table 2 State	Uninsured % 12/2013	Uninsured % 7/2015	Projected Uninsured 7/2015 % with Medicaid Expansion	Difference	Total increase in projected number insured
WY	16.6	18.2	9.4	8.8	51,274
TX	27.0	20.8	14.6	6.2	1,639,788
OK	21.4	17.7	11.8	5.9	227,184
ID	19.9	16.2	11.7	4.5	72,546
VA	13.3	12.5	7.7	4.8	396,499
LA	21.7	16.3	12.1	4.2	194,270
UT	15.6	13.2	8.9	4.3	124,737
KS	12.5	11.3	7.3	4.0	115,758
GA	21.4	15.3	11.8	3.5	349,726
NC	20.4	14.7	11.3	3.4	334,834
TN	16.8	12.9	9.5	3.4	220,863
FL	22.1	15.2	12.1	3.1	606,139
MT	20.7	14.4	11.4	3.0	30,455
MO	15.2	11.4	8.7	2.7	163,193
IN	15.3	11.1	8.7	2.4	157,702
SC	18.7	12.6	10.4	2.2	105,046
AL	17.7	12	9.9	2.1	101,508
MS	22.4	14.2	12.3	1.9	56,833
NE	14.5	10	8.3	1.7	31,765
PA	11.0	7.7	6.5	1.2	153,286
ME	16.1	9.4	9.1	0.3	3,985
AK	18.9	10.3	10.5	-0.2	-1,470
SD	14.0	7.2	8.1	-0.9	-7,604
Total:					5,128,316

Don’t worry too much about those numbers for Alaska and South Dakota – the Medicaid Expansion would decrease the rate of uninsured there, but they have already over performed according to the model, so the estimates look negative.

Bottom line is the estimate of the number of people who would get insurance through Medicaid in the right hand column: 5.13 million. 30 percent of those would be in Texas, which had the distinction of being governed during 2013 and 2014 by a man who literally could not count to three.  Molly Ivins save us all.

Medicaid Expansion; it's still worth fighting for.