Podcast: Why Median Home Prices Are Misleading

By Comms Team | 07/06/2021

Tags: Finance | Podcasts | Real-Estate
Categories: Research

"Median is a flawed statistic for measuring the magnitude of price change. It can't be used to develop an average price appreciation."

FAU's Ken H. Johnson and Paul Owers discuss the use of median sales prices in determining housing market trends. Read more at business.fau.edu/buyvsrent.



Episode Transcript

Paul Owers (00:09):

Hi, I'm Paul Owers, the media relations director for the Florida Atlantic University College of Business, and this is Home Pricing Trends featuring Ken H. Johnson. He is a real estate economist and associate dean in FAU's College of Business. Our discussion today focuses on the use of median sales prices in determining housing market trends. For more information about his real estate research visit business.fau.edu/buyvsrent; that's business.fau.edu/buyvsrent. Ken, thank you for joining us. The National Association of Realtors and state and trade groups use median selling prices to determine an increase or decrease in home prices, but you don't think that's a good idea – why?

Ken H. Johnson (01:00):

Sure, Paul - thank you very much. There are two reasons why this is a bad idea. One's a little wonkie and I'll go with it first; the other is much more straightforward and everybody can see it a little bit more easily without much of a math background. But first the wonkie answer - the median is a flawed statistic for measuring the magnitude of price change. It can't be used to develop an average price appreciation for the following reason. It is what's known as an ordinal interval measure. I know all this is wonkie, but because it is that you can't use algebra and come out with anything meaningful, but we insist on using algebra on it to come up with average appreciation. The median sales price is up 22%. That's a mathematical algebraic calculation. It's mathematically impossible to use the median to do that. The numbers are wrong and they tend to be skewed.

Ken H. Johnson (01:53):

Now something the median does do, and it's very accurate on - if the median is going up, it is going up. If the median price of homes are going down, they are going down; the median just can't tell you the magnitude or the degree to which it's going up or going down. So that's the wonkie answer. Number two, there's something called a substitution effect, other people call it a grocery cart example, and this is exactly how I've explained to me years ago when I was in grad school. My stats professor explained that look, imagine a number of people coming into the supermarket, and then they're going to Publix to shop, and every week they go in and shop and you look at and calculate the median. Now here's how you calculate the median - you look at all the grocery carts that were, that were bought;

Ken H. Johnson (02:37):

you look at the price, you arrange them from the smallest to the largest, go halfway through those numbers and that is the median number. There's no algebra, there's no calculation, it's just a process; it's a step process. So imagine people go into the supermarket and shop and then the median number is $100 for a grocery cart. And then we have an endowment come to them, some extra money and they go back and shop the next week and everybody goes to Publix and all of a sudden the median price is $150 on the grocery carts, not $100, keep in mind, this is not an average; two things have gone up. With that extra money, people have bid up the price of what they were buying. They bid up the price of mayonnaise, but they've also gone from Hellman's mayonnaise to the specialty...

Ken H. Johnson (03:25):

mayonnaise. They've also gone from hamburger to steak, from frozen to fresh. So you're getting both the price increase and a substitution effect into what they're buying. So when you look at the median price increase, it's gone from a $100 to $150. Then we very often try to say, well, that's one $150 minus $100 divided by $100, that's a 50% increase in the price of food and the price of groceries. That's not true. There's both the price increase and the substitution effect that's going on. And this is exactly what happens in housing. You buy so much housing and there's so many different amenities associated with the house from amenities, pool, no pool, size, age, square footage, et cetera. So when people have an endowment from either the federal government, or we see, we might see endowments coming from the government, or they've got increases in pay, they've got super low interest rates, and that's a big cost right now. You get super low interest rates, making housing pretty inexpensive for you on an ownership level. So people go out and shop and their median price will go up, but they're getting both the increased price per square foot and the fact that, oh, wow, I'm now buying more amenities than I was before. So you get this skewness if you will in the median price; it's misleading - it can't be used. Number one, it can't be calculated and interpreted, and number two, when we do it, we still have this grocery cart effect.

Paul Owers (05:00):

Ok, what do you think would be a better barometer for determining the change in home prices?

Ken H. Johnson (05:04):

Sure, sure. So a number of things going on out there, and we recognize this problem for years, but some big data problems. One - median is an easy number to calculate. You just line them up from lowest to highest and go halfway through the numbers, right? It's easy to do. But when we were going to calculate a control for all of these, the substitution of facts, and we needed some sort of average, we needed an algebraic calculation - that was not easy to do with the massive amounts of data that we have. But thanks to data management, a lot of dedicated data scientists out there and real estate economists, we've developed a number of what have been called repeat sales indices or most-likely transaction metrics. They're pretty common out there. Now there (are) at least three that I work with regularly - FHFA produces a repeat sales index; Case Shiller has a repeat sales index;

Ken H. Johnson (05:55):

Zillow has what's called a Zillow housing value index. And they'll tell you it's not a repeat sale, but in a way it is because it repeats sales the whole market. All of them are really good at algebra calculations. And you could actually better derive the trend, the average property appreciation, and it's not subject to skewness. So you can look through time and see how much property is actually appreciated. So all this begs the question, why does NAR and their state affiliates and others continually provide us with median? NAR's been heavily deregulated by the Department of Justice for years and they are constantly fearful of antitrust lawsuits being brought against them. And one of the outcomes of this is that they've decentralized their data collection. So they provide MLSs for major and minor markets all over the country, but there's no one central data source. They up-feed it, but it's not quite the same to NAR, to Realtor.com and perhaps others.

Ken H. Johnson (06:54):

And I can tell you by a settlement with the Department of Justice, most of Zillow's data comes from the National Association of Realtors. They are just however, very hesitant because of prior issues they've had with the Department of Justice; rightfully or wrongfully. And they settled; there were no major lawsuits or antitrust; it was simply a settlement with NAR, but they're reluctant to centralize their data, which makes creating a repeat sales index, almost impossible. So their hands are kind of tied - they're, darned if they do, and they're darned if they don't. So you got to cut them a little slack on this. So, and they want to give some numbers, you know, to give an idea; how can you be the National Association of Realtors and not be able to talk about where prices are going? And ironically though, now people like Zillow, like Redfin - I'm sure Redfin has their own some form of an index; I don't go to Redfin that often. I know FHFA has these numbers for over 400 metropolitan markets. These numbers are coming from realtors, but yet it's not easy for them to put together these repeat sales indices where they can easily measure property appreciation. So it's this calamity of convenience, I tend to think, that's really causing a lot of problems, and for NAR, in providing this number, and the fact that they just can't or just won't because of fear getting in trouble with the Department of Justice, again, that they're (NAR) centralizing data.

Paul Owers (08:30):

Thank you, Ken. We appreciate it.