Voucher Math, Part 2

The number crunching done in the last Voucher Math post really helped me see how big of a difference the switch rate can be even with just minor changes. What I was hoping to establish is the need to replace assumptions that have to be made by the LFA with hard data. So far, nobody doubts that this would be helpful, but we do seem to disagree on how much this data is worth, the method used to collect it and the extent to which Utah should be involved in that process. I want to take some time to address some of the other assumptions made by the LFA that have a very heavy impact on the numbers.

The first thing we need to look at is how many non-switchers will be collecting and using a voucher. The LFA seems to make an assumption that every non-switcher will be using a voucher, driving up the costs substantially. This, however, is a worst-case scenario. The figures that I've seen used indicate that about 1/3 of Utah's private schools would not quality for vouchers. Of the remaining 2/3 that qualify, I seem to recall that about half of them would not accept vouchers. This leaves about 1/3 of the schools as voucher-eligible. So how does this impact the dollars and cents?

Simply put, dramatically. We go from losing money each year beginning in Year 7 to a net gain for the state in every year of the program. That's a huge difference to the bottom line and doesn't make out vouchers to be the money-loser that everyone seems to think they are. That makes the break-even point for non-switchers participation about 55% given a switch rate of about 1% of the total population.

The second point we need to address is the LFA's price elasticity arguments. Currently, they list the average private school tuition at around $8,000 per year. The question, however, is what "average" this is. If you recall from last post's brief math lesson, there are three kinds of average we need to look at: arithmetic mean, median and mode. I suspect that this figure is an arithmetic mean which, in the field of statistics, is highly ridiculed as being subject to extremes.

Let's use some examples. If you take 5 schools charging $2,500 per year and 1 school charging $25,000 per year, you get an arithmetic mean of $6,250 per year. This doesn't accurately reflect what the majority of the schools are charging. If we look at the median, that's tagged at $2,500 per year; so is the mode. This more accurately reflects the kinds of pricing you should expect and is not as subject to aberrations at either extreme.

Unfortunately, we don't have the raw pricing data that went into this figure to figure it out for ourselves. I will say, however, that I believe the figure used by supporters of somewhere in the neighborhood of $4,500 to $5,100 per year. What I'd like to know is how such a pricing difference affects the adoption rate. This is why I think the estimated adoption rate is highly underestimated.

The final point has less to do with the money end of things and more to do with who's currently using private schools. We all have this great image in our heads of rich kids wearing school uniforms attending gleaming classrooms. The reality, however, is that about 10% of the private school population are below the poverty line. How much of the general populace in Utah is below the poverty line? About 10%. In other words, poor people are using private schools at the same rate as the rest of us. It stands to reason they'd benefit greatly from those vouchers coming their way, especially when paired up with Children First Utah to make up whatever differences remain.

I firmly believe that we need to collect the data on switch rates. I firmly believe that this program will not be a money sink as the LFA has projected. I firmly believe that the poor will reap more benefit from this than is being said. I'm still voting Yes on Referendum 1 and I would encourage the rest of you to do so as well. 

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5 Responses

  1. Jeremy says:

    Just because I’m curious, not because I doubt you, I’d like to refer to some primary sources supporting your argument that 2/3’s of public schools won’t be participating in the plan. Do you happen to know where I could get this information?

    If you are going to remove such a large portion of the private school student population from the formula you need to also calculate how many of those schools are the cheaper schools you favor in your affordability matrix. If a significant number of the schools that are refusing to accept vouchers are the more expensive schools (and they may very well be) than this helps you even more but I haven’t seen any data that could be used to help us with that math.

    You also need to address one large and difficult to assess piece of cultural data relating to your argument and that is the fact that Utahns are historically averse to using private schools. Even wealthy Utahns for whom price shouldn’t be much of a factor have avoided private schools to the point where barely 4% of Utah’s school age children attend private school. I think that demand isn’t as elastic as you assume. Is the marginal decrease in private school tuition brought by this voucher plan really going to make that big a difference for Utah’s students? I don’t know but I do think it is a factor you need to consider whenever we begin a discussion about demand.

  2. Jeremy says:

    I bet not many public schools will be taking vouchers 🙂

    I meant to say private schools in that first paragraph.

  3. Jesse says:

    Fair enough. My data on the voucher-eligible schools comes from (no groans please) The Sutherland Institutes’s press release on private school tuition. The total number of private schools, if I recall correctly is around 117, but I can’t find the source of that. (I have a bad habit of memorizing data I see but forgetting where I saw it. My grandfather did the same thing.) I swear I saw it in a newspaper article, but it’s like looking for a needle in a haystack, you know?

    Don’t I wish we could get a breakdown of which voucher amounts would be used at which schools? About all I can run on right now is a bunch of arithmetic means which, quite frankly, is maddeningly over-simplistic. I can’t imagine someone hasn’t already done the research (and by someone, I mean legislative staff), so it’d be nice if they’d share. We *did* pay for it, after all. 😉

    I know the culture issue is a big one. I think that’s going to be marginalized over time as we get more and more out-of-staters (like me) moving here and bringing in non-Utah ways of doing things. Traditionally, I think the use of public schools is tied to large family sizes more than anything else. (Yes, I could be talking out my rear from this point forward.) With large families it’s harder to send little Johnny and his 6 siblings to private schools so public schools make more financial sense. Also bear in mind that Utah has, historically, been a farm state with fewer wealthy people. That’s also something that’s been changing with the dramatic growth. In the 14 years I was in Las Vegas, I watched growth change all the rules and assumptions as the city tripled population. I think the same thing’s going to hit us here.

  4. Jesse says:

    I tried to find where I read that half of the eligible schools won’t accept vouchers, but I can’t find that either. The best I *can* find is that Challenger schools and a few unnamed others will not be accepting vouchers even though they will be eligible. Just by taking the ineligible schools off the top, we’re already down to 75% of private school students. (My bad on that number.) Add in a few more private schools and we get pretty darned close to that 55% or lower participation rate by non-switchers to break even with current estimated switch rates.

    If the switcher rate is slightly higher and the non-switcher eligibility a little lower, we end up breaking even rather easily. Of course, we’re still working on assumptions so YMMV.

  5. Daniel says:

    One reason to believe there will be a substantial amount of switcher is because of the benefits other voucher programs have provided for students. I summarized the research findings over at Green Jello. http://pramahaphil.blogspot.com/2007/10/vouchers-humble-pie.html

    Here’s a graph that summarizes the random assignment studies on voucher programs: http://spreadsheets.google.com/pub?key=pcyEJ-sIC0Aid8nYzKPU7Pg

    Also, great points on the benefits of vouchers for the poor.

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