This article is part of a series examining how Mt. Lebanon is likely to be affected by the recent county-wide reassessment. For other articles in the series, see Blog-Lebo’s Reassessment Series. —Tom
In our previous article,
Reality-Checking the Reassessments: Part 2, we compared both old and new assessments to sales prices for homes sold recently in Mt. Lebanon. Our goal was to see whether the new assessments were closer to the market reality than the old. And, on the whole, they were.
But we noticed a concerning trend: Less-expensive properties were more likely to be assessed above their market prices, especially in comparison to more-expensive properties, which were more likely to be assessed below their sales prices. The following plot shows the trend, relating the degree of “over” or “under” assessment to a home’s selling price.
In our sample of recently sold homes in Mt. Lebanon, there is a clear regressive trend to the new assessments. On the x-axis we have the actual sales prices of homes sold in 2010 and 2011. On the y-axis we have the difference between the newly assessed values for those homes and their sales prices. Homes appearing above $0 on the y-axis were assessed at above their sales prices; those appearing below $0 were assessed below their sales prices. As properties become more valuable, they become more likely to be assessed at below-market values.
At a glance, it sure appears that there is some unfairness to these new assessments.
What’s “unfair”?
Before going further, I’m going to be clear about what I mean by
unfair. I’m not interested in discussing, at least for now, whether the
idea of property taxes is fair. Rather, I’m interested in determining whether (or not) the assessments allocate to the owner of each property a slice of the community’s overall property-tax burden that is proportionate to that property’s fair-market value, relative to that of the entire community. For example, if you own property that is truly worth 0.034% of Mt. Lebanon’s total fair-market property value, you ought to pay 0.034% of Mt. Lebanon’s total property taxes. If an assessment scheme causes you pay more, the scheme is unfair to you; if you it causes you to pay less, it’s unfair to everyone else.
By that standard, then, is the new assessment scheme fair? And, in particular, is it fairer than the one it’s supposed to improve upon?
Clumping it
Those are tricky questions. To answer them, we would need to know the true fair-market value of Mt. Lebanon’s properties. And, even with sales data, it’s hard to say what the fair-market value of a home is. If you recently bought a home for $100,000, is that its true fair-market value? Indeed, the sales evidence is
consistent with the hypothesis that the home’s true value is $100,000. But, alas, it’s also consistent with the hypothesis that the true value is really $110,000 (and you’re a shrewd negotiator), and also with the hypothesis it’s really $90,000 (and you’re a sucker). They’re all realistic possibilities. Who’s to say which is true?
We can get around this problem by clumping properties together. If we clump, say, 100 properties together, and they had sales prices totalling $10 million, it’s hard to believe that those properties are truly worth substantially more or substantially less than $10 million. That’s because it’s hard to believe that all 100 of the people who bought those properties are suckers. Or all shrewed negotiators. Or
all anything else. You’ll have some mix of suckers, shrewed negotiators, and every other sort of buyer and seller in the mix. And together their individual preferences tend to “cancel out” one another, and what we’re left with is the market price.
Now we can return to the problem of measuring the fairness (or unfairness) of the new assessment scheme. If the scheme is fair, we should be able to grab the 1000 least-expensive properties in Mt. Lebanon, clump them together, and add up their actual sales prices to arrive at the clump’s fair-market value. And we can do the same for the 1000 next-most-expensive properties. Then we can see whether their respective tax burdens are proportionate to their respective fair-market values. And then we can repeat the process, right up to the 1000 most-expensive properties in town, to calculate fairness across the home-value spectrum.
Running the assessments in reverse
Which brings us to the next problem. We don’t have actual, recent sales prices for all of Mt. Lebanon’s properties. Not every home was put on the market and sold in the last year or so; only some were, and those are the only homes in our data set. And, among those homes, there are some weird transactions like foreclosures and sheriff’s sales, which probably don’t fully reflect market prices. For Mt. Lebanon, we would expect this weirdness to be small, so I’m not going to worry about it further. But we still have to figure out the market prices of homes that haven’t sold recently.
To figure out those prices, we’re going to mine our limited sales data for all it’s worth. Here’s the idea. If we have a clump of homes assessed at about $100,000 each, we’ll comb our sales data for homes similarly assessed at about $100,000 and see how much they sold for on the market. Then we’ll ascribe similar sales prices to the homes in the clump we’re trying to price. While this method would be unreliable for individual homes, we’re working with clumps of a thousand homes, over which we would expect errors to mostly cancel out. Still, there’s a reasonable chance that recently sold homes are somehow different from Mt. Lebanon properties in general, so we ought to take our extrapolations with a grain of salt.
The fairness comparisons
That said, after we divide Mt. Lebanon into clumps, estimate their fair-market values, and then compute their fair-share tax obligations, the results aren’t subtle. The new assessments seem notably more unfair than the old. You’d have to take them with a lot of salt before thinking everything was in fact peachy.
The following plot shows how we predict the new and old assessments to play out in terms of property taxes, distributed across the community’s properties by fair-market value. There’s a lot going on, so take a look, then meet up with me after the plot for some explanation.
(Click for larger version)
Running horizontally we have home prices, starting at a little below $100,000 and ending a little beyond $400,000. This price range covers the bulk of Mt. Lebanon homes. Running vertically we have the degree to which properties are predicted to be overtaxed because of inequities in the assessment scheme.
The lines on the plot trace out what we might call the “tax-fairness curves” of the different assessment schemes. The curve for a perfectly fair scheme would be a flat line at 0%, meaning that, across the pricing spectrum, properties would generally be taxed in equal proportion to their fair-market values. As you can see, however, the curves on the plot are far from flat, and some of them stray into overtaxed-by-10-percent territory.
For now, ignore the dotted lines and focus on the solid lines. The solid red line represents the tax fairness of the old assessment scheme. To my eye it looks pretty reasonable, generally within 2.5% of perfectly fair across the value spectrum, which is better than I would have expected.
Now look at the solid blue line. That’s the new assessment scheme. To use a technical phrase, it’s all over the place. Low-valued properties are getting overtaxed by up to 10%, and higher-valued properties are correspondingly undertaxed. That’s not good.
Now back to those dotted lines. I used two separate statistical models to predict market prices from assessed values. The first is more constrained and therefore “smoother” in its predictions. It’s represented by the solid lines. The other is less constrained and more “wiggly” (another technical term). It’s represented by the dotted lines. So go back and look at those dotted lines. While they look a bit different, their overall pattern is the same as before: the new assessments (blue) are more unfair than the old (red).
Which is pretty much the opposite of what everyone expected of the new assessments.
So it’s not looking good for the new assessments. If they were supposed to fix inequities of the old assessments, they’re not doing a great job at it, at least not for Mt. Lebanon.
As usual, comments are open. This is a complex subject, so feel free to ask questions and share your thoughts. All we ask is that you abide by our real-names policy: When you offer a comment, sign it with your real first and last name. (Otherwise, we won’t be able to post it.)
Blog-Lebo would like to thank the University Center for Social and Urban Research for making available their ever-useful data set of recent Allegheny County residential-property sales, without which this analysis would not have been practical. Any errors in this analysis are Blog-Lebo’s, not theirs.Labels: assessments, blog-lebo-series-reval, property assessment, property taxes, real estate, reassessments
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