Saturday, February 25, 2012

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.)

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Anonymous John David Kendrick said...

Hello Tom,

Looking at the scatterplot there is an interaction present.

My question to you (and it is a question to you) is what other factor is influencing home sale prices above $275,000?

February 25, 2012 5:36 PM  
Anonymous John David Kendrick said...


The data is also appears to be heteroscedastic.

As I said, I want to hear what you think.

February 25, 2012 6:09 PM  
Blogger Tom Moertel said...

JDK, I don't see a clear interaction, but it wouldn't shock me if there was one in there. It's pretty clear from that plot, however, that there's some nolinearity present and that less-expensive homes tend to be overassessed, and more-expensive homes underassessed. Most of the points in the upper half of the plot (representing >= $250K in sales price) fall into the left triangle above the diagonal (= underassessed). (But this plot makes the regressive nature easier to see.)

If you have any hypotheses about the interaction you see, I'd love to hear them.


P.S. Just saw your other comment. Yes, of course, the assessments are heteroscedastic. (Wouldn't you expect more expensive homes to have larger assessment variability?)

February 25, 2012 6:28 PM  
Anonymous John David Kendrick said...

So, let's assume for the moment that above $275,000 there is some type of change in consumer behavior. Perhaps housing affordability on the high end of the market has changed because of "something".

Do you think that it is possible that the higher end of the market is falling in value becasue of "some reason"?

Do you have any thoughts on what the reason might be?

February 25, 2012 6:43 PM  
Anonymous Michael Goodin said...

I don't think that the graph says the higher end of the market is falling (for properties over $275K). If anything, it says that people are willing to overpay for higher end properties.

Also, we need to be cautious about ripping this data out of its original context. The reassessment was countywide. It would be a mistake to cull the Lebo data out of the larger county context and then try to infer a cause that is Lebo specific. From what I have read, the knock on the reassessment has been that higher value properties have had smaller percentage increases in the reassessed value than lower value properties.

If it true that the issue of higher value properties being under-assessed when compared to recent sale prices is a countywide problem, we cannot infer anything about Mt. Lebanon specifically other than it follows the county pattern. It is not some internal Lebo problem that is causing the disparity in sale price to assessment value.

Before JDK questions my motives, I am woefully out of my league because I write the above having taken only one course in public finance and four courses in statistics thirty years ago. So what do I know?

February 25, 2012 7:33 PM  
Blogger Tom Moertel said...

JDK, I see what you're getting at. And, yes, I tend to agree that the high-school project (and other largely unsustainable spending by the school district) is probably having some influence on the desirability of more-expensive properties. (Really, folks, I am not a defender of that project's many excesses and, way before now, predicted it would not be good for high-end Mt. Lebanon properties.)

But I don't think these data make a convincing case that we're seeing – or not seeing – an erosion of high-end property values. We don't yet have a good understanding of how the assessments relate to actual sales, let alone the counterfactual sales that would have existed had the school district spent the community's resources more wisely. And we would need a good understanding of both relationships to make such a case from these data.


February 25, 2012 7:42 PM  
Blogger C. Briem said...

Most plots in absolute prices like that will have some heteroscedasticity with an apparent increase in variance with value. It you were modeling the price data you would actually model ln(price) which would likely take away the heteroscedasticity. I think Tom is just laying out what it looks like to start out. I'm sure folks don't want to be looking at plots of ln($'s) here.

The underassessment by a few % is likely an artifact of the recent sales being a bit dated by just a year or two. There has been real estate price appreciation in the local market in recent years and from what I've seen relatively more appreciation in higher valued homes. So comparing a transaction value even in 2010 ought to be a few percentage below what the current assessed value is.

February 25, 2012 8:52 PM  
Anonymous John David Kendrick said...

How recent are the sales relative to the re-assessed values? Tom's approach has been to model based on an inherent assumption that this is cross sectional data.

Tom, do you feel comfortable with that assumption in the current economic cycle?

February 25, 2012 11:14 PM  
Anonymous Anonymous said...


Do you or any of the readers know the actual reason(s)why the reassessments do not include a manner like the current assessments ?

Bill Lewis

February 25, 2012 11:29 PM  
Anonymous john David Kendrick said...

I was intrigued by the re-assessment of (I think it was the) Rite Aid on Castle Shannon Blvd. The new assessed value declined by $2,500,000 for this new site - and the Co website said that there were not any comparables so a cost method was used.

The simple fact is that a home is worth what someone is willing to pay for it. The valuation studies that he european banks use is a distinct contrast to our home appraisal method; and then outside of banking we have various methods employed by our tax offices either at a state or local level (depending on where you live); commercial real estate, which was also reassessed by the County is viewed from an income valuation, replacement cost, and a new construction cost so that three point estimates can provide a framework to give insights into the value of a property.

But all of these are only opinions - just like Tom's model, the professor's interpretations, or any analysis that I might or might not be inclined to perform on this PANEL data... ;)

Several matters concern me with this discussion: (1) I believe that our Board recently made some very bad decisions to proceed with expenditures that our community can not afford; (2) I also feel that, having seen the Supt's Communicator list, this medium is being used to sugar coat these very bad decisions, when the reality is that the greatest burden of paying for the bad choices that the Board made will be borne by many people in the community who are the least able to pay; (3) I believe that the recent budget gap is only the beginning and that the District will ultimately need to increase the millage rate and perhaps apply for an exemption in the short term to finance the bad decisions that they made; (4) I believe that a three tier progressive tax structure with the tiers set at 5%, 10%, and 15% would generate more revenue and be more equitable - and it isn't a legal issue, professor - just my opinion (5) I feel that a study like this takes a significant investment of time and money, and while I applaud Tom's interest in statistical methods, all practitioners need to be careful and thoughtful concerning the models that they construct.

As George Box, once said, "All models are wrong, some models are useful." I would caution the readers on this thread about drawing any definitive conclusions from this model concerning the accuracy of the reassessment.

It would be interesting to perform an AOV on the appraisal approach - how accurately was the data itself collected? Has anyone ever though about that? Is there an interaction between the appraiser and the object being measured? Maybe the employee just didn't feel like walking up to every home; or maybe that person couldn't get access - so they "estimated" what they thought was there... who would know? Has anyone investigated this in the past?

What would be really nice to see, is what I have asked the District for for over a decade, and that is an econometric study that will support their claim that we need to invest in our school district in order to protect and enhance our property values. I've never seen a study in Mt Lebanon that addresses this question. It may have made selling the new school building a lot easier if a credible investigation could have been referenced.

Unfortunately, we're in it now - and moving forward. I truly think that this story is not going to have a happy ending, but only time will tell.

That's what's on my mind.

Tom, it's all yours now - carry on.

February 26, 2012 10:34 AM  
Blogger Tom Moertel said...

Good grief, JDK. I don’t know where to begin. First, you seem to think we’re having a conversation about something we’re not. Second, you seem to think I said a lot of things I didn’t actually say. Third, if you think I’m “sugar coating” anything, then present your evidence: Lay out the claims I made (and not imaginary claims I didn’t make) and demonstrate what makes those claims false. Fourth, if you think I’m wrongly “drawing any definitive conclusions” from “this model” (a plot, for crying out loud!), then present your evidence: Lay out the claims I made (again, warning on imaginary claims) and demonstrate what makes those claims false or, in this case, unsupported.

I’m perfectly willing to believe I’ve made mistakes, John. But I’m not willing to move toward that conclusion just because you have vague feelings about statistical methods or believe I’ve been corrupted by the Superintendent’s Sooper-Secret Communicator Cult.


February 26, 2012 11:53 AM  
Anonymous Anonymous said...

Whoops ! My prior comment was not at all clear. Sorry about that. It was late and I was tired.

What I meant to really say was (1) the four 2013 reassessment "comparables" (one is shown twice) for our property are entirely different properties than the five existing 2012 assessment "comparables"; and, (2)in the case of both 2012 & 2013 "comparables", all had/have lower assessed values than ours; and, (3) in the case of the five 2012 "comparables", the 2013 reassessed values in one decreased 14% for 2013, values in two increased about 26%, one 14% and the last by 2% v. an increase in ours of 7%.

In no case can I visually see any changes in the exteriors of any of the properties. Has your property been treated similarly ? Does this make any particular sense ? Does this perhaps suggest that the 2012 "comparables" are not all really valid ? If so, does this bring into question that 2013 "comparables " are any more valid ?

Recent sales comparables are needed for 2013 "comparables" are all seemingly intentionally *underassessed* examples in that the actual recent sales prices are higher than the reassessed values, and are of course not useful for an appeal. Toms mapping in this post, however, provides an excellent tool to quickly ID possible *overassessed* properties where the recent sales prices are below the reassessed values and therefore potentially useful for appeals. Without Tom's map, it would take the average person hours and hours of frustrating searching.

The County will not consider or entertain any of the threads on this post dealing with sophisticated and very learned statistical and financial theory & facts...they'll only deal with their data, however flawed, in appeals...unless you want to risk a lot of money in appraisals and still have to deal with a formal appeal that would likely end up with you and your lawyer before their Board of Viewers in their courtroom setting.

Thank you Tom for your extremely valuable service to the community !

Bill Lewis

February 26, 2012 12:15 PM  
Blogger James Fraasch said...


Taking a slightly longer look at the map, it looks like a greater percentage of the homes at the lower end of the spectrum are over assessed when compared to recent sales price (they are to the right and below the line) while homes at the higher end of the sales range are more likely to be to the left of the line or slightly underassessed.

This is very similar to the trend I picked out from the earlier map where it seemed that middle of the road homes seemed to be getting higher increases in asessments (based on the color of their heat map) than areas in Mt Lebanon that most would see as more pricey.

Is this a conclusion that others can draw from the data as well? And if so, why is this happening? Someone had mentioned that the SD and Muni had earlier appealed a number of higher priced properties to correct for an under assessment. If so, how many were "corrected". If this number is significant, that could explain much of what I see here.


February 26, 2012 7:52 PM  
Blogger Tom Moertel said...

James, you're spot on. As I mentioned earlier, there is a clear regressive bias to the new assessments, most easily seen on this comparison plot, which takes the "error" between assessed value and actual sales price and compares it to sales price. You can see that, as sales price goes up, properties are more likely be underassessed. Likewise, less-expensive properties are more likely to be overassessed. Under $150 thousand, it looks like the majority have been assessed at more than their sales prices.


February 26, 2012 8:06 PM  
Anonymous Anonymous said...


Not that many years ago the Muni, with SD concurrence and participation I believe, decided to appeal the assessments of any - not necessarily just higher-end - residential property that had a recent selling price 15% or more above its assessed value or its preceeding purchase price, I can't recall which for sure. The Muni hired an attorney who specialized in this kind of process for a fee cost of something like $150 or so per property. The number of properties appealed exceeded 650 as I seem to recall, and the reported appeal success rate for the Muni was something like 98%...I'm going by vague memory on this because neither I nor any of my friends were appealed, so I was not paying close attention. A small number of, but certainly not all, taxing bodies in the County pursued appeals in a similar manner.

As I further recall, the appeals were eventually scrubbed by the County, either by edict from the CEO & County Council or by court order...something to do with it being spot assessing and/or a countywide reassessment was coming.

I mention this at the risk of presenting some incorrect information or details; however, this might be enough to motivate someone to research the matter further and present the entire, factual story. I think it important to do so because there could conceivably be a repeat performance by some taxing bodies now that we have a fresh countywide court ordered reassessment. And there are a large number of what appear to be now 2013 underassessed properties of all types and classifications.

Which leads me to another issue. And that is for local taxing bodies to reconsider, clarify, formalize or maybe do away with what I think is now a flawed and perhaps legally questionable practice. And that is the unwritten, very long standing and so-called "gentlemens agreement" that the Muni would pursue residential property appeals and the SD would do the non-residential or commercial property appeals. This needs to be an early subject for the joint, public meetings of Muni & SD officials. As I recall, this "agreement" was not in play or adhered to those several years ago when the SD took it upon themselves to pursue a number of residential property I recall.

Again, research and disclosure of all of the actual and relevant facts would likely be helpful.

Bill Lewis

February 26, 2012 9:12 PM  
Blogger James Fraasch said...


You are right on the money.

I did some digging and found an article in Mt. Lebanon magazine but I can't figure the date.

The number was 15% so if a house sold for more than 15% of the assessed value, it was likely that Mt Lebanon would appeal. This article says that there were 214 appeals but it also says the SD millage was 20.76 which would place this article in May 2002 (there is no date on it) but the filename is 7547.cover.may.

I wonder if there is a recent update to those numbers.

As an aside, I came across a link to Bloglebo that had some of this same assessment discussion back in 2007:

One more link (just saw this farther down the search results) is the money shot from Bill:

At the time of this article in April 2005 there had already been over 600 appeals on the part of the school district which resulted in a significant amount of new revenue to the budget.

So, back to my previous comment, the next thing to figure out is if 600+ properties is enough to suggest that the reason the results appears as they do is that many of the higher end properties had already had their assessments challened by the school district in the past and, therefore, had less of an upward adjustment to make this time around.

I have to assume that besides the 15% factor, the district also had some floor below which they would not go. For instance, would it make sense for them to spend the money to appeal a $100,000 assessment on a house that sold for $120,000? For that $20,000 difference it would be a revenue difference to the school district of only $400 per year at 20 mills (2002 levels). However, for a $300,000 home that is the same 20%off, that revenue difference would be $1,200 @ the same 20 mill rate.

I think the puzzle may be starting to come together...tell me if you think I am on the wrong track.


PS, is it just me or are these "prove you're not a robot" code words getting harder and harder to figure out?

February 26, 2012 10:47 PM  
Anonymous David Brown said...

What Bill and James are onto is interesting, but not necessarily nefarious. If the goal is to be fairer by having fewer outliers, and assuming that extremely over-assessed property owners are motivated to appeal their own cases, who else is there but the government to appeal the extreme under-assessments? And, to the extent that property owners are successful, the government is almost forced to try and win an equal number of cases just to remain revenue neutral.

February 27, 2012 3:00 AM  
Blogger James Fraasch said...


You are exactly right. I don't think either of us is saying it is nefarious. We are more or less reverse engineering the reassessments.

One of my conclusions at the moment (subject to change if given more or different evidence) is that the reassessments appear to put a bigger burden on middle to lower priced homes only because many of the higher priced homes had already had their assessments successfully appealed upwards by the school district.

I don't think that conclusion, however, can explain very well the divergence between recent sales price and recent assessed value (or at least I haven't figured out how to make that connection yet). I mean, if a house was assessed in 2011 and the house was purchased in 2011, shouldn't the assessed value BE the purchase price?

February 27, 2012 8:13 AM  
Anonymous Anonymous said...


You're on the right track. And David, you're really not correct in my opinion, which I'll cover in awhile.

James, many will not recal that there were County reassessments in 1993, 1998, 2002 and 2005 prior to the now 2013. The 1993 County reassessment resulted in a overall Lebo increase of 17%....this was prior to and the likely reason for eventual "anti-windfall" legislation. The Muni *returned* most of the increase voluntarily, through millage reduction, while the SD retained most of it...surprised ? The 2005 reassessment is unique in that (1) it was never *certified* and was cancelled by the then CEO & County Council because it was a political landmine. My property assessment would have increased by 30% over the 2002 assessment had the 2005 reassessment gone into effect. I had not changed or made any improvements to the property in the 3 years since 2002. CEO Fitz tried to cancel the 2013 reassessment also in purely political grandstanding, but he knew he would fail under present court-ordered circumstances; and (2) I believe the 2005 debacle paved the legal road to what was supposed to be a 2008/9 reassessment that legal wrangling and County foot-draging postponed to now 2013.

David, if you really peel the factual onion, the entire 20-year history of County reassessments that I am only just somewhat familiar with is repleat with political nefariousness from bow to stern, port to starboard. Add to that the tactics used by the local taxing bodies in appeals and you have to sit back and really wonder.

For instance, if the local's feel it warranted and want to appeal, (a) why limit the appeals to only what they determine to be grossly underassessed residential properties...why not all so-called underassessed properties for *fair and equal treatment under the law*; and, (b) on what factual basis did the local bodies determine that the properties were underassessed...they were assuming, to their advantage, that the County assessments were 100% correct...they did not have the properties formally appraised before instituting appeals; and, (c) why were only residential properties appealed and not the multitude of non-res or commercial property painly obvious underassessments; and, (d) further to the issue of fairness and equal treatment, why did the local bodies not also appeal the grossly overassessed residential properties in behalf of those largely owners of the modest homes that are even today believed to be overassessed and at risk ? ? ?

I could go on and on David, but I won't...I'm reaching a keystroke limit I'm sure.

Bill Lewis

February 27, 2012 9:18 AM  
Blogger Tom Moertel said...

Just a reminder: If you want us to publish your comment, you must sign it with your full name. (For more on our comments policy, click on the "Post a Comment" link and read the text above the comment box.)

If you tried to offer a comment recently but it didn't show up, it's probably because you forgot to sign it with your name. Try again and remember to include you full name at the closing of your comment.

February 27, 2012 10:47 AM  
Blogger Sarah said...

Forgive my ignorance of comparative statistics, but could you please explain what "dB" means with respect to the relative intensity of over or under-assessments? Is it similar to standard deviation or some other measure against the mean reassessment?

sarah olbrich

February 27, 2012 10:50 AM  
Blogger Tom Moertel said...

Again, dear readers, please don't forget to sign your name when you offer a comment. If you forget, we won't be able to post your comment.

I mention this because I just had to reject a thoughtful comment because it wasn't signed.

February 27, 2012 11:51 AM  
Blogger Tom Moertel said...

Sarah, I'm using a logarithmic scale – measured in decibels – to make the relative magnitude of overassessments and underassessments comparable across different home prices.

On the map, I want to make clear – visually – that assessment errors of –50% and +100% represent the same relative error: being off by a factor of 2. Therefore, I use a logarithmic scale to represent the intensity of reassessments relative to actual sales, and then I project that scale onto a linear color gradient running from blue to red. Since I have the choice of the logarithmic base, and since constant factors wash out in the color mapping when I calibrate the endpoints, I chose decibels because they are more convenient to interpret. For example, being off by a factor of 2 is a 3-dB error:

10 * log10( 2/1 ) = 3.01 dB
10 * log10( 1/2 ) = –3.01 dB

That was a long and tedious answer, but it boils down to me wanting to make sure that when you looked at the map your eyes would be telling you the truth about how far (or close) the new assessments were to the mark.


P.S. That was a great question.

February 27, 2012 11:54 AM  
Anonymous Anonymous said...


I just wanted to thank you for all of your hard work on what seems to be a labor of civic love. Statistics were never my forte but I find your analysis very interesting and informative.

Dave Brumfield

February 28, 2012 8:41 AM  
Anonymous Marcy McCool said...

As one of the homeowners on the north side of Scrubgrass, I cannot figure out what is going on. I was just appraised a few months ago for a refi and the reassessment is $45k over that amount. There are larger homes with larger lots in Virginia Manor that were reassessed for amounts less than ours. It doesn't make any sense at all.

Thanks for all of the information you've put together!

Marcy McCool

March 15, 2012 4:46 PM  

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