Monday, March 05, 2012

Are the New Assessments Fair?

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.

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Anonymous Anonymous said...

The outcome of our reassessments as presented here is surprising. So, the question remains regarding our two local taxing authorities. How will the millage be adjusted going forward now that we all know our new assessed values? If there is a downward adjustment initially to offset a potential windfall, what will happen later?

Considering the school district’s current budget deficit (just under $3 Million) in addition to another anticipated $30+ Million debt load for construction expenses that will increase the budget for that additional debt service, and the increasing costs on the municipal side including the costs for some desired enhancements (e.g. $1 Million on fields), what can the residents of our community expect in terms of increasing taxes going forward?

I would like to see our School Board Directors and Commissioners come forward now and provide some tangible financial direction to our residents. In support of the taxpayers, will they now “talk turkey” so residents can plan ahead, leaving out extraneous concepts like $30 Million fundraisers?

-Charlotte Stephenson

March 05, 2012 11:00 AM  
Anonymous Anonymous said...

Hello Tom,

A number of thoughts have crossed my mind about this issue and your analysis, but the only one that I want to express at the moment is my sincere thanks to James Fraasch who voted with courage and conviction to stop this insanity when he served on the Board - just like John Ewing did back in 1994.

-John Kendrick

March 05, 2012 11:19 AM  
Blogger James Fraasch said...


I also calculated a slightly different way for people to understand the data. Not as pretty as a line plot, just straight percentages.

See the data table below:


50-100k $5045933 $8043800 159%
101-200 $62150311 $64487700 104%
201-300 $64547392 $60932000 94%
301-400 $34303320 $30356500 88%
401UP $40993490 $35268900 86%

What this shows is five different ranges of homes that sold in the last two years. Column 1 clumps those sales into the ranges seen. Column 2 adds all the sales for that range together, and column three adds up the total assessed values of all those homes that sold. Column 4 then just looks at the assessed value as a percentage of the sales price.

As you note in your post, in a perfect world you would like to see the assessed value BE the sales price, that is, the assessed value would be 100% of the sales price. However, what you and I are finding in different ways is that is not the case and it appears that the lower the cost of your home, the more likely it is to be over-assessed. Conversely, the higher price the home, the more likely it is to be underassessed. The assessed value for homes in the low range is 159% of their actual sales prices. At the high end, the assessed value of the home is only 86% of the actual sales prices.

Yes Sheriff sales might account for some of the discrepancy if you assume most sheriff sales are happening at the low end. Even if I concede that point (which I don't) that still doesn't explain what happens at the high end. Lot's of sheriff sales at the low end resulting in homes selling for less than assessed value would not result in higher end homes being largely underassessed. The two have nothing to do with one another.

What's also interesting is that in your graph and in my playing around with the data, the breakeven (assessed values=sales prices) seems to be right at the level of the average price home in Mt. Lebanon, $200,000 to $220,000.

So, that's what the data shows for Mt. Lebanon. Now, how do we figure out the why?

I understand there was an article recently which noted that the assessment formula would be shared with the attorney that argued before Judge Wettick.

March 05, 2012 4:33 PM  
Anonymous Anonymous said...

Enough with the analysis - the ship is sinking! What we need are creative approaches to keep the ship afloat and (eventually) moving forward in the right direction.

Taxing the snot out of the properties on the bottom-end won't increase property values and if anything we're risking transforming the community into a slum.

I've offered my thoughts on how we can creatively apply tax policies to build property values. Does anyone else have any thoughts?

How does the community feel about selling naming rights? I am really not for it, but it may be necessary to save the community! My hope is that if we turn to this desperate measure then it should only be used if there is an agreement in place to curtail the out-of-control spending by Miss Piggy School District!

-John Kendrick

March 05, 2012 6:37 PM  
Anonymous Michael Goodin said...

Again, I have to point out that this was a countywide assessment. You cannot pull out the Lebo data and point to a specific Lebo problem. The sky may in fact be falling in the Lebo bubble, but the countywide assessment does not give us any insight into why the sky is falling in Lebo if the sky is not falling throughout the rest of county.

NB I do not believe the sky is falling in Mt. Lebanon.

Michael Goodin

March 06, 2012 7:34 AM  
Blogger Tom Moertel said...


Even thought the reassessment was countywide, its effects on each taxing body are separate. So we can indeed look at the assessment and sales data for all of Mt. Lebanon to make reasonable statistical inferences about Mt. Lebanon. These inferences do not necessarily hold for the entire county, of course, but they do for the municipality and school district, which account for 85% of property taxes in Mt. Lebanon.

Nevertheless, our data are observational in nature, not experimental, so I would caution readers against using them to make causal inferences (at least not without reliable, supplemental causal knowledge, which I doubt any of us has). While these data allow us to say something about the new assessments and their relationship to recent home-sales prices, they do not give us a reliable basis for claiming that one thing or another caused what we’re seeing. To make such claims, we would need some understanding of how these data would have appeared, had that one thing or another not happened. And, as far as I know, we don’t.

But it’s going too far to claim that “the countywide assessment does not give us any insight into why [X is true] in Lebo if [X is not true] throughout the rest of county.” Such differences are what natural experiments are made of. And they are one way of inferring something about what might have been here under different circumstances.


March 06, 2012 10:33 AM  
Blogger Paul Z. Graf said...

I believe the PG had touched on this trend towards lower assessments for those with expensive properties as well, especially in the East neighborhoods I believe. Also I remember readings that IAAO standards allowed for this kind of approach an an acceptable assessment methodology. It would be interesting to know what the IAAO standards say exactly. The only reason I can think of to justify this trend is that owners of expensive properties with assessments close to their actual value tend to challenge the assessments more often and the local school district and municipalities are not equipped financially or otherwise to defend such an onslaught. In terms of the cost/benefit of fighting the assessment, the taxing authorities may know that the cost is too high for many owners of less expensive properties.

Dave Tkacik

March 08, 2012 10:31 PM  
Blogger Daniel Seigel said...

The discrepancy for over taxing on the lower priced homes is fairly easy to explain. Using data for houses sold with a Realtor, in Mt. Lebanon over the past 2 years, about 20% of homes sold for under $150,000 were "distressed" homes. That is to say homes that were either forclosures, estates, or in rough shape. If the homes in that 20% sold for 30% or 40% below the true market value after repairs are made, it would be the reason for 6%-8% "over taxation" using the models in this analysis. For homes sold above $150,000 in the past two years, distressed homes account for only about 4% of those sold which would only cause about 1% to 1.5% discrepancy.

For higher priced homes the errors are somewhat harder to explain, though would imagine that most of it has to due with the rise in land vs. building value and the scale of the numbers when that happens. While I haven't analyzed the actual numbers, it certainly seems to me that the land values jumped by a much higher percentage than building values. If that is indeed the case, its reasonable to expect that a large jump in land value lends itself to greater errors for over taxation on lower priced homes and lower taxes on higher priced homes.

As an example, if a property has a land value of $50,000 and that number is high by say 20%, the land is overvalued by $10,000. If the building is valued at $75,000 but is undervalued by 10% or $7,500, the entire property is still over valued by $2,500 or 2%. If you take another home that has the same $50,000 land value that is also overvalued by 20% and it has a building that is valued at $250,000 and it also is undervalued by 10% or $25,000, you now have a property valuation that is undervalued by $15,000 or 5%.

I realize that all these numbers don't help the folks that have over valued homes, but perhaps it helps explain why the statistics used in this post came out the way they did.

March 19, 2012 7:09 PM  
Blogger Tom Moertel said...

Daniel, thanks for your informative comment.

Here’s the question I have about the distressed-home hypothesis: If that’s our hypothesis, shouldn’t we predict that the old assessments, when compared to that same set of semi-distressed sales data, will prove even more unfair than the new? After all, if we hypothesize that the unfairness we see is an artifact of recent distress having skewed our sales data, how could the old assessment anticipate this skewing better than the new?

And yet it seems to have done just that.

So what explains why the old assessments appear to be more equitable than the new?


March 19, 2012 9:29 PM  

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