Composition Effects for Appraisers

Economist Timothy Taylor posted a discussion about hourly wages recently that had a section that sounded very familiar. Here’s the quote that caught my eye:

“You will sometimes hear statistics people talk about a ‘composition effect,’ which just means that if you are comparing a group over time, you need to beware of the possibility that  the composition of the group is changing.” Why would a residential real estate appraiser care about composition effects?

Much of my time as a residential appraiser is spent determining trends in real estate markets. Every day I create charts like the one below to describe the markets in my reports.

Simple linear regression trendline showing an increasing submarket

These trendlines assume that the group of homes sold do not differ significantly over time. In most cases, this assumption is reasonable. Sometimes this assumption is false.

For example, the global pandemic has affected buyer tastes. My friend Ryan Lundquist wrote about this recently. After six months of being cooped up from the Covid-19 pandemic, buyers want a larger home. Here’s his chart showing the trends in the Sacramento region:

Change in Home Size during the Covid-19 Pandemic in the Sacramento Region from Ryan Lundquist

The average size of a home sold in the Sacramento region has increased 100 sf over the past six months. House size is the primary driver for value, so if all other factors are the same, the average price for that market will increase.

BUT IT’S AN ARTIFICIAL GAIN BECAUSE ANY GIVEN HOME OF THE SAME SIZE WOULD SELL FOR THE SAME PRICE!

Similarly, if homes decrease in size over time with no other changes, that would cause the average price to decline with no impact on individual house prices.

Here’s what I do to have a better understanding of market trends:

  1. I trend sale price of homes sold over time,
  2. I trend price per square foot of homes sold over time, and
  3. I trend home gross living area over time.

Why trend price per square foot? This trick takes into account some variation in size and in conforming areas, can increase the reliability of the trend analysis. However, significant changes in size will influence the PSF trendline.

I see this frequently in Winters, California. Winters is a relatively small city of about 10,000 people located on the western edge of the Sacramento Valley not far from Davis. Below are the three graphs for Winters sales from 1/1/18 to 10/1/19 (all data from Metrolist MLS).

Sale Price trendline showing an increasing market

Prices are clearly increasing in the top graph.

PSF Trendline is stable

Prices are essentially stable when trending price per square foot for the same sales. Why?

Here’s the third chart showing size of homes over time:

GLA trended over time

The size of a home sold in Winters during this time period increased almost 1 sf per day.

Because of the math,

an increase in the average size of homes sold will push down the price per square foot trendline but will push up the sale price trendline, and

a decrease in the average size of homes sold will push up the price per square foot trendline but will push down the sale price trendline.

Here are some other examples that may cause a market to appear to change over time without a real change in market conditions:

  • Average lot size changes, especially for small acreage residential properties
  • Average age of homes changes, especially when new construction ramps up or ramps down
  • Better quality homes come to market
  • An outlier, such as a tear down or the biggest home in the county, pulls the trendline out of true
  • A small, heterogeneous market susceptible to change from the latest sale

A good habit is to take a look at your data. Do you see changes in your data or is it relatively similar over time?

When I do run into composition effects, such as sale price going up and price per square foot going down, I graph both together on the same graph and explain why there is a difference. I then reconcile.

“The sale price trendline is increasing while the sale price per square foot trendline is decreasing. The average size of homes have increased during this time period, skewing the sale price trendline up and the price per square foot trendline down.  I conclude that this market has been relatively stable during this time.”

Hope this adds to your understanding of residential real estate markets.

p.s. This website has instructions on how to show two time series on the same graph like the example above.

13 thoughts on “Composition Effects for Appraisers

  1. Jamie Andrew Owen

    Joe, great article! There are a lot of things that can skew our trends in one direction or another. This is a fantastic article explaining how the size of homes can do so. I have saved this one for my own personal reference. Thanks for putting together this great article my friend!

    Reply
  2. Shannon Slater

    Great post! It is very important for us to do this type of analysis to truly have a good picture of what the market is doing. I like your approach of running the three charts of price trends, the price per square foot trends, and living area trends. Well explained. Thank you!

    Reply
    1. josephlynchadmin Post author

      Thanks Shannon. I’m interested to hear if you see compositional effects in your market since it’s so much bigger than my region.

      Reply
    1. josephlynchadmin Post author

      Great to hear from you Norm. Was just thinking about you. Are you a member of the Massachusetts appraiser association? My group has questions about the web platform they use.

      Reply
      1. Norman Anderson

        Hi Joe,
        If you are referring to the Massachusetts Board of Real Estate Appraisers (MBREA), then yes I am. Stephen Sousa is the Executive Vice President and is the man in charge. He is very helpful and can be reached at Staff@MBREA.org.

        Reply
  3. Ryan Lundquist

    Nice job Joe. I appreciate you thinking through the numbers like this. We always have to consider why the stats are moving the way they are. It’s easy to get a false reading of the market if we’re not careful. Thanks for the shoutout too. I appreciate that.

    Reply
    1. josephlynchadmin Post author

      Thanks. I’ve had this post in mind for quite some time and your analysis was a prompt to start it

      Reply
  4. Michael V. Sanders, MAI, SRA

    An important concept when doing time series modeling, and thank you for increasing awareness of it. I’ve noted this particularly in growing markets when doing long-term trending, as new homes make up a larger share of the total market, something you mentioned in your blog.

    However, I would caution about drawing strong inferences from relatively small and apparently not very homogenous data sets. Looking at the data in the abstract (without any trendlines), it almost looks random, i.e., no apparent trend. While you show the equation on your graphs, you don’t show the coefficient of determination (r2), so it is impossible to know how well the line actually fits the data; my guess is that r2 for any of these would be pretty low.

    One other point worth mentioning as well, is that linear does not always best fit a set of time series data. Polynomial equations are often better representations of what is happening, and Excel can generate these up to the 6th order. A good way to see if a curvelinear trendline is a better fit is to try it, and see if r2 improves significantly. Polynomial trendlines also do a decent job of identifying peaks/valleys and direction changes in the market.

    Reply
    1. josephlynchadmin Post author

      Hi Michael,

      Thanks for your comments. I’ll leave it to George Dell to discuss the relevance of r squared for appraisal work. Good point regarding polynomials fitting better than linear trendlines.

      Reply
    2. Ed Bedinotti

      Mike,

      In regards to r2 and coefficient of determination, r2 is only relevant for inferential statistics, or in comparing the 3rd order polynomial to the linear line. r2 will increase as the order of the polynomial increases as well.

      Reply

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