Assessment update: County’s own analysis shows a regressive bias in Mt. Lebanon

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

Via Chris Briem’s blog, I learned that the county hired an independent team to review the recent assessment process. That team’s report is offered as Exhibit 4 of a recent court filing, part of the ongoing court case at the center of the controversy.

The findings of the independent review support Blog-Lebo’s conclusion from March that the new assessments for Mt. Lebanon are unfairly biased toward overtaxing owners of low-end properties and undertaxing owners of high-end properties. In particular, the report gives the independent reviewers’ estimate of the coefficient of price-related bias for Mt. Lebanon as about −7.5% (see page 19 of the report; look for the PRB-coefficient value for school district 26, Mt. Lebanon).

The PRB coefficient is a crude measure of bias, but it’s telling. What that −7.5% means is that, when you examine residences of increasing value in Mt. Lebanon, as their market value doubles, the corresponding assessed value tends to get a 7.5% discount. For example, if residences worth $150,000 tend to be assessed at a full 100 cents on the dollar with respect to market value, residences worth $300,000 will tend to be assessed at only 92.5 cents on the dollar, and residences worth $600,000 will tend to be assessed at only 85 cents on the dollar.

As a result of this “regressive” bias, owners of low-end properties effectively wind up paying some of the property taxes for high-end properties.

How could this happen? The report suggests some answers.

According to the report (page 9), each residence was valued by (1) selecting similar, recently sold residences as comparables, (2) taking a weighted average of the comparables’ sale prices, and (3) adjusting that average based on how the comparables differed from the residence being valued, with this adjustment being done using a statistical predictive model. I have some concerns about this process, as applied to Mt. Lebanon.

One concern is that the model predicts property values based on their characteristics – bedrooms, bathrooms, fireplaces, living area, and so forth. But these characteristics tend to be underreported because many homeowners fail to fully declare them on property questionnaires for fear that, if they declare them, they’ll get overtaxed because everybody else is failing to declare them, for similar fears. The problem, then, is that if you do declare them, you’ll probably end up being assessed for them more than once – once through the comparables, and once again through the adjustment on top of the comparables, which assumes that the comparables’ sale prices don’t already account for these characteristics.

Another concern is that the predictive model ignores multiplicative effects. From page 7 of the report: “All models are additive, meaning that the contribution of the various terms in the model are added (rather than multiplied or some combination of additive and multiplicative adjustments).” What this means – oversimplifying a bit – is that when the model is trying to predict the value of a residence, if the model learns that the residence has, say, 3 bathrooms instead of 2, it will always add some constant third-bathroom increment to its current prediction, say $15,000 (I’m just making that figure up, by the way).

A better predictive model might add a varying third-bathroom increment based on what else it knows about the residence. It might adjust that increment upward (say, to $30,000) for high-end mansions and downward (say, to $7,500) for low-end ranch houses. Because that adjustment does not occur when the county’s model makes its predictions, however, the model ends up predicting too low for mansions and too high for ranch houses. That’s not a problem if your community is all mansions or all ranch houses, but if your community is like Mt. Lebanon and has properties all over the pricing spectrum, it is.

The report reveals a lot more about the assessments, too, and not just for Mt. Lebanon. I encourage you to read it for yourself, especially if you have an appeal hearing coming up.

Let me know if you find anything else interesting.

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.

Reality-Checking the Reassessments: Part 2

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, we compared the new assessments to recent residential property sales in Mt. Lebanon to see if we could learn whether they fairly represented actual market prices. Taken as a whole, they seemed reasonable (“not horrible” was the technical term I used), but for many individual properties, they seemed far from reality. Also, it seemed that less-expensive properties tended to be overassessed and more-expensive properties underassessed. So there seems to be some cause for grumbling.

Now we perform a second reality-check: Do the new assessments do better than the old assessments? (Recall that the motivation for the new assessments was to remedy the inequities of the old assessments.) To help answer this question, we return to our data set of recent Mt. Lebanon residential property sales (courtesy UCSUR) and compare recent sales to the new assessments. But this time, we also compare them to the old assessments, to see whether new or old are closer to the actual market.

The easiest way to see how new compares to old is, well, to see how they compare. So here’s another statistical plot, much like the plot from our previous article, but this time with two dots for each home sold in Mt. Lebanon in 2010 or 2011. Take a look and then I’ll explain more below.

(Click image for a printable high-resolution version in PDF format.)

Here’s what’s going on. For every home sold in Mt. Lebanon, there are two dots, one red and one blue, connected by a horizontal gray line. The vertical position of that line gives the home’s actual sales price. The horizontal positions of the dots give the old and new assessed values of the same home. The red dot represents the old assessment; the blue, the new assessment. You can think of a house’s assessed value as having “traveled” along the horizontal line from the red dot (old) to the blue dot (new). The question, then, is whether they traveled toward (or away from) fair-market prices.

To help answer that question, we have added a 45-degree reference line to show where the assessed values would line up if they perfectly reflected market prices, as estimated by our recent sales data. To the extent that a home is underassessed, it will appear to the left of this line; to the extent it is overassessed, to the right. The actual market is a bit of a moving target, so we won’t worry too much about assessments near the reference line, just those far from it.

So what can we see? First, the blue dots are almost always to the right of the red dots. That means that most of the homes had their assessments increase. And that’s what we would expect, given that property values have generally increased since the old assessments took place. So far, so good.

Second, the blue dots are closer to the 45-degree reference line than the red dots. That means the new assessments are closer to actual market prices than the old. In other words, the new assessments seem to be closer to reality than the old assessments. That’s a clear improvement.

Okay. So the new assessments are truer.

But are they fairer? We’ll look into that question next time.

Until then, comments are open. Let us know your thoughts.

Reality-Checking the Reassessments

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, Making Sense of the New Assessments: Winners and Losers, we looked at the reassessment’s likely effects on your property taxes. In this article, we look at the assessment, itself, and ask whether it’s likely to do what it’s supposed to do – make all property owners pay a fair share of property taxes based on the actual market values of their properties.

To help answer that question, let’s look at the selling prices of Mt. Lebanon residential properties on the market in 2010 and 2011 and compare them to the newly assessed values of the same properties. Selling prices make a good reality check because they define the market. Sellers aren’t willing to sell for less than they think the market will bear, and buyers aren’t willing to pay more than they think they must. If the new assessments reflect the market reality, they should be similar to their respective sales prices.

Using a data set of recent Allegheny County residential-property sales provided by the Pittsburgh Neighborhood and Community Information System at the University Center for Social and Urban Research, we identified 1,184 Mt. Lebanon residences sold in 2010 and 2011 for between $50 thousand and $500 thousand (our Mt. Lebanon–specific data set). We then merged that sales data with our previous data on property reassessments and compared the sales prices to the corresponding newly reassessed property values.

Overall, the homes in the data set sold for an average of 4% above their newly assessed values, which supports the notion that the new assessments are generally close to actual market prices and therefore not horrible. For individual properties, however, some of the new assessments are hard to fathom.

Here is a plot showing how each home’s sales price compares to its newly assessed value. Each point on the plot represents a home that was sold in Mt. Lebanon in 2010 or 2011. Its horizontal position gives its new assessment value, and its vertical position gives its actual sales price. If the two are the same – and they ought to be close if the reassessment is working properly – the point ought to fall on the gray reference line running across the plot at 45 degrees. To the extent a point misses the line, its corresponding assessment can be said to be “over” or “under” its market price. Points to the left of the 45-degree line represent underassessment; to the right, overassessment.

As you can see, most of the points are reasonably close to the reference line. But many aren’t.

Those far-away points represent properties that sold for considerably higher or lower than their supposedly true-to-the-market assessed values. Those are the properties we ought to start asking questions about. Likewise, some of the owners of those properties have a good reason to appeal their new assessments. Conversely, some of those properties seem to be way underassessed. The local taxing bodies might want to look more carefully at those deeply discounted assessments.

To see if there are any geographic patterns in the under/overassessments, let’s put all 1,184 of those properties on a map.

The Blog-Lebo Reassessment Reality-Check Map



Blues represent assessments below sales price; red, above sales price.
Click on properties to see their details.
(Full Screen)

Overall, things look pretty evenly distributed. But, if you look more closely, you can see some small patterns in certain areas. For example, on the north side of Scrubgrass Road, nearly ten recently sold properties were assessed at considerably higher than their sales prices, but their neighbors on the south side of the street had relatively gentle assessments. Anybody know what might be going on there?

Take a look at the map and let me know what you find. As usual, discuss it in the comments section. Let me know if you see anything interesting or want Blog-Lebo to take a look at something else about the reassessments.

Blog-Lebo would like to thank reader Lisa Brown for suggesting that we compare the assessments to recent sales. (Got an idea for an interesting analysis? Let us know in the comments.)

Making Sense of the New Assessments: Winners and Losers (Updated 2)

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

Update 2012-02-22 00:10: I’ve updated the map to show some properties that were previously not showing up.

Update 2012-02-24 19:50: Map change: I was getting feedback that the colors were too subtle and that patterns in the more moderate property-tax changes, which affect the majority of residents, were hard to see. To make these patterns more visible, I’ve revised the color gradient to focus on the range –50% (blue) through +50% (red). If you’ve looked at the map before, the colors should now seem more vivid.

Now that the new property assessments for Mt. Lebanon are out, everyone is wondering what they mean. To help make sense of it all, I’m planning on doing a few articles on the subject.

First off: How do the assessments affect your taxes and, under the new assessments, who wins and loses?

Here’s my understanding of how it works. The county and municipal governments and, to a larger extent, the school district all collect taxes based on the value of your property. The more valuable your property, the more you pay. (They also collect taxes based on how much you earn, but those taxes aren’t affected by the reassessment; I won't talk about them further.)

What determines how valuable your property is? The official county assessment. In theory, this assessment is supposed to reflect reality, but, in practice, assessments tend to get out of alignment with actual market prices. When they get too far out of alignment, people start complaining, and eventually there’s a big reassessment in which everybody’s property is supposed to be reassessed using the same standard.

One of those big reassessments just happened for Allegheny County, and yesterday the County released the results of those assessments for Mt. Lebanon.

I was able to analyze some of the new assessment data, and here’s what I’ve got so far. Understand, however, that I’m simplifying some of the calculations and making some educated guesses here; reality may differ from my predictions. For example, I’m sure there are some properties that get special tax incentives, but I’m not accounting for them. I trust that you have the good sense to take what I’m about to show you with a grain of salt.

With that out of the way, let’s get to the fun stuff.

First, for most property owners (82%) the reassessment won’t change their property taxes by more than 25%. About half of property owners will have their taxes increase; about half, decrease.

About 12% of property owners, under the new assessment, will have their property taxes go up by more than 25%. These are the people who “lose” under the new assessment. Only about 6% will “win” and have their taxes go down by 25% or more.

Perhaps the best way to understand the reassessment is to see its effects on a map. I was able to combine assessment data with GIS data to make a map of how things are likely to play out here in Mt. Lebanon. (I’d like to thank Commissioner Kelly Fraasch, the Mt. Lebanon GIS department, and researcher Christopher Briem for their generous help in getting the data I needed. I’d also like to thank James Fraasch and Bill Lewis for their feedback on earlier drafts of this map that led to substantial improvements. All errors in the map, of course, are mine alone. And if you find any, please let me know.)

The Blog-Lebo map of winners and losers in the reassessment game


Hotter colors represent property-tax increases; cooler colors, decreases.
Click on properties to see their details.
(Full Screen)

In that map, hotter colors (oranges and reds) represent tax increases; cooler colors (purples and blues) represent tax decreases. There’s also a lot of gray, representing taxes that didn’t change much. You can also click on properties to see their details and get links to the county assessment web site to do deeper research.

Take a look at your home (or business) and see how the assessment is likely to affect you. Note that if your home’s assessment went up, your taxes could go up or down. It all depends on how much your assessment went up compared to the community, as a whole. The community-wide total increased by about a third, so unless your assessment went up by a third or more, your taxes will actually decrease. In the map, I’ve done the calculations for you: just click on your property and look for the line that reads “Estimated Property Tax Increase.”

There are a lot of interesting patterns in that map. What stands out to you? If you see anything you want to discuss, post a comment below.

As for me, I plan to look into the data further and post more about it soon. If you see anything you want me to look into, or can spot a problem with the map, please let me know in a comment.

New Court-Ordered Assessments for Mt. Lebanon are now online

The county has just posted to its web site the new, court-ordered assessments for Mt. Lebanon. You can search for your new assessment here: Court Ordered Reassessment Values.

Please remember that these assessments won't take effect until the 2013 tax year, at the earliest.

Also, don't freak out if your assessment is higher. Most properties will have their assessed values go up. What matters is how much yours goes up compared the community as a whole.

I hope to do a deeper analysis shortly, when I can get some more data, and then I’ll post more on how the new assessments are likely to affect Mt. Lebanon – and you. Stay tuned.

Galleria Agrees To Assessment Increase, Lowers Millage Increase for 2008-2009 Budget

An agreement with the Galleria shopping mall on an assessment increase will allow the Mt. Lebanon school board to lower its projected millage increase in the 2008-09 budget from .59 mills to .25 mills.

The change in assessment covers two prior years and the coming year and resulted in about $700,000 in additional revenue for the district, said Finance Director Jan Klein.

The budget will be presented for a final vote by the board on Monday. If adopted, it will mean a tax hike of about $56 on a home assessed at $225,000.

Link: www.post-gazette.com/pg/08136/881805-55.stm