# Abstract

In Economics, we have a lot of statistical tools and theory that we can use to examine prices, probability, trends, and whatnot. I decided to use econometric methods to measure the price of a single house in terms of *expected value* rather than *market price*. To do this, I wrote a computer program to dig through over a million sales transactions in King County, Wa. to create a set of comparable houses, which I then averaged as quarterly averages, and ran an ARMA(1,1) white-corrected least squares log-linear regression against. I then used that regression and several auxiliary regressions to find the expected value, and used the expected value and the regressors to determine what the best course of action is for a house — buy, sell, trade-up, or hold.

# Background

Wit the recent economic crash, I wanted to know what to do about my house. Did I buy too high? How much? Are prices now “normal” or falling further? Is there any way to explain the fall, and can I predict the future? Should I Sell? Trade? Do nothing? Since I have training in econometrics and statistics, I decided to use my quantitative skills to find out.

# Methods

I went to the King county assessor’s website and downloaded all house sales transactions from 1981 through April, 2010. I then wrote a computer program to select sale records for houses located in the Juanita area of Bothell/Kirkland with sizes between 0 and 1575 square feet. The query I used against the data was something like:

Select Year, Quarter, AVG(SalePrice), AVG(SquareFootage)

From HousePrices

where Area = 083 and SquareFootage < 1575

Group by Year, Quarter

Order by Year, Quarter

Note — this is not the exact query, but pretty close. The actual query joins a few tables, as info about the house is in a different table than info about the sale, as is info about the location. Email me for the actual query — it’s much too long and hard to read.

I then got some additional data on employment, unemployment, and labor market size for King county from the bureau of labor statistics, and imported the results into EViews, and ran a regresion in log scale. The final equation I used was:

Log(HousePrice) = C + Time + SquareFootage + Log(Unemployment) + AR(1) + MA(1), with white standard correction. This regression gave me an R-squared of .96, and a standard error of regression of .07 — an excellent fit! I’ve left off intermediate equations, and an intermediate sample where I allowed house sizes to vary only from 0 to 1200 Square feet. I’ve also omitted “what if” equations and the like, but may discuss them in the results.

# Findings

With the regressions in hand, I discovered a few interesting things:

1. This house appreciates around 6% per annum. I didn’t realize that house price appreciation could be modeled as a simple yield function, and I didn’t realize that the return was 6%. This makes housing a good/bad/ugly investment depending on factors like cost of capital, opportunity costs, etc… Using your house as an investment vehicle would require more research than most of us normally do when we buy one.

2. Check out the figure 1 graph! This is an intermediate regression graph for houses between 0 and 1200 square feet in the same area. The red line is the quarterly average sale price, the green line a time regression, all in log linear scale. The blue line is the “residual” the difference between the two lines. For this house, prices have been this low and lower before. Prices were worse in 1984 and 1987! Right now, prices are only a little worse than 1989.

3. From the main regression in Figure 2, house prices are super dependent on unemployment. I knew this, but I didn’t realize the effect was so strong! The elasticity is -.27 for a single quarter…

4, Another intermediate regression that I did showed that unemployment effects last a long time in the housing market — at least 3 quarters.

5. Check out Figure 2! This is the average price vs regression with unemployment taken into account. Jingle mail is stupid for small houses in Juanita. It might be a good idea in other places, but the regressions show that even the “worst off” buyer — the person who bought at the very, very top, will have recovered his expected value loss by 2011. All he has to do is wait out the recession, and about a year to 18 months after unemployment has returned to normal, his house price should also revert to normal. Unemployment does a great job explaining the current fall in house prices, though not perfect. There’s some other force in the system that I can’t find — a certain, “pervasive doom” if you will. It’s affecting house prices down a bit right now, but it’s luckily a small force right now…

6. This house is very underpriced right now. The regressions show the market price is at least 15% under the expected value. The bubble years show at least a 15% rise above the expected value. In short, during the boom years, prices for this house were way above their expected values. Today, prices are way below. Anyone buying a small house in Bothell now can expect to make windfall profits when the economy recovers.

7. These results don’t really hold outside of small houses in Bothell. See my caveats later in this post for more.

**More specific answers**

I really wanted to know — did I overpay? Yes, but not terribly so — about 10%.

Since prices are currently falling, did they fall back to expectations? No — they overshot, and are now below expected values. Market prices often deviate from expected values. Two things happen in that case — expected values adjust to market prices, or market prices adjust to expected values. I’m asserting that houses revert to expected values — but this assertion is often wrong. The regressions show that this assertion as been right since 1981 in this area. Of course, the people of Detroit probably thought the same thing…

Should I trade up now? Yes, another auxiliary regression shows that I would lose money selling this house, but make money buying a bigger house. I’d still net lose on the deal. Under normal conditions — that is, without this recession — I’d normally have to pay more to trade up. I’d lose less money by buying now vs waiting. though either way, I’d lose some money. The gap between the two decisions is small — small enough that waiting is also an option.

# Caveats

This is a linear regression, not a panel of data or better method. This is also a mixed supply-demand equation. Both of these methods are controversial, to say the least. I believe they’ll work — but for very short periods of time. They’re really more useful for measuring what has happened than in predicting what will happen. But that doesn’t stop me from using them as a crystal ball….

Also — I sampled houses in a very small region of king County, and in a very small size band. If you own a house larger than 1304 square feet, in an area not within a 5 minute drive of exit 22 of the 405 freeway, or bordering a special terrain feature( golf course, river, etc…), then this regression’s results aren’t for you. To put it into perspective — I did another sampling of larger houses, and got ***very*** different results — the market for housing is very fragmented, house ages count, house types count, what’s located near them counts, etc… I wanted to see the effects of time and unemployment on a single house, not predict the housing market as a whole. My methods are optimized for that purpose.

# Do it for you?

Want me to do this type of analysis for you? contact me and I can do this for you.

[…] it gives me regression diagnostic data that tells me if the regression is any good. You can see my previous post to see the results for my home. Leave a […]

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