Thursday, February 18, 2016

Kansas Education Policy: Building a Funding Formula

I haven't posted recently on Kansas Education Policy, mainly because I have been busy with other projects, and just busy generally.  But Education policy was pushed back into my interest this last week with the Kansas Supreme Court's striking down of the way Kansas currently funds its schools. I'll get to statistics in a second, but lets start with some background.  

BACKGROUND

The recent history of education funding in Kansas is a tale of multiple lawsuits, funding formulas, and adequate funding research projects.  The entire background is too much for this blog, however the Wichita Eagle has a great timeline, found here.  Here's the short of very recent history:
In 2015, the Kansas legislature replaced an old "funding formula" with a new block grant system.  The old system used variables describing a school district's attributes (poverty rates, student FTE, transportation needs, special education, etc) and dynamically calculated funding each year.  The new system allocated a certain amount to each district based on legislative allocation.  In essence, the new system created a process that removed a dynamic mathematical equation with a direct political process to fund schools.
A week ago, the Kansas Supreme Court invalidated that block grant formula for reasons you can read about here.  Now the Kansas legislature has to figure out a new way to fund schools (there's another ruling coming later this spring that might actually cost the legislature more money)
That's where we are now, the Kansas Legislature needs to figure out a new way to funds schools.  But I haven't heard too much about how they're going to do it.  I thought-what the hell-why don't I get a head start on them anyways, and help out the government when they're down?

FORMULA OF THESE POSTS

To create a new funding formula, we will need to identify and evaluate factors that should be included.  In essence these will be the factors that cause certain districts to be more costly than others.  Some of those can be evaluated through a statistical process, others are more difficult to analyze, so we may look at them in other ways. Each week, I'll look at a new factor, and see how it plays into the puzzle.  Please feel free to comment on this blog with your ideas of where we might look next.

Quick general methodology: We downloaded twelve years of education data 2004-2015 and cleaned it for missing data and outliers (e.g. districts on military bases).  Then we regressed.

TODAY'S FACTOR: DISTRICT SIZE

One of the primary factors determining how much school districts need to spend is the size of the district.  We're already calculating our output variable as $/FTE, so we're already compensating for the fact that more kids = more total dollars to the district. (Why do Wichita schools gets more total money than Salina schools? More kids.)

But there's still another way that size of the district impacts costs: efficiencies and economies of scale:  Very small school districts operate at higher costs per student due to lack of economies of scale. 

From a methodological standpoint, we can estimate this cost/economy of scale curve by regressing cost per FTE by district size.  Here's what it looks that looks like out of R for the nerds.



A few notes, we're using a log-log equation here, so the coefficients are effective elasticities, relative to the "missing case" which is districts from 0-100 students.  

So what does this interpretation mean to all of the non-nerds: schools of 1700 - 2500 FTE  are 46.5% less costly than the smallest schools (0-100 FTE) due to economies of scale. Here's what the entire cost curve looks like relative to 2015 spending.  (Keep in mind this is a basic model, and we need to add more factors to make accurate predictions for individual school districts.)

Quick note, if I'm in optimization mode here, I would be thinking, hey, let's consolidate some of these smaller school districts and move them further down the cost curve.  That may work for some, but for many districts structural factors will prevent true economies of scale (the additional transportation and still having to run multiple buildings).  Luckily, there are some statistical ways to look at that coming in the next few weeks.


DRAWBACKS AND METHODOLOGICAL ISSUES

We need to address some methodological issues here that we'll deal with down the road two in particular:
  • Size of district varies with a lot of other factors, how are you accounting for those: Answer: we'll get to that in the next few weeks.  There's actually evidence of other things at play in our above regression.  For instance, why do the very largest districts actually cost MORE than mid-sized districts.  The classic story is that these largest districts come in only two forms, both of which are very high cost: affluent suburban (high demands, cost of living for teachers) and high poverty (costs more to get similar results.)  We will evaluate this in the next few weeks.
  • Data is based on a prior deterministic formula! Answer: So one of the drawbacks is that we are measuring outcomes (prior spending) that was mostly determined by a prior funding formula.  That means that our dependent variable (spending per FTE) could be seen as just measuring that prior formula and how do we know that actual the spending that formula created created wasn't artificially inefficient or austere?  This is actually a huge concern with statistically measuring something that was recently a determined formula.  This is a concern we will also be dealing with conceptually next week.

CONCLUSION

  • Over the next few weeks, we will be doing the government's work for them, and identifying the parts of a new funding formula.
  • We can successfully estimate economies of scale, and get an idea of how funding needs to be adjusted for small school districts.
  • There are some methodological issues, including additional exogenous factors and deterministic funding formula, that we will be working on in a future analysis.

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