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Wednesday, February 07, 2007

On the value of a 1988 MB560 SL or Why I am a geek

I am trying to figure out what price to ask for my 1988 MB 560SL with 140,000 miles and a distressed interior. How to go about this?

Hedonic models are useful for determining the value of certain product characteristics. To gather a sample of MB 560s, I headed to cars.com and looked up the 1988 560SL's for sale in the United States. I gathered price, color, and mileage, and created a (subjective) measure of overall quality by looking at any pictures provided (arguably not the best measure, see below). This information allows for a (somewhat) naive hedonic regression in which asking price is "explained" by car characteristics - the general quality, the color, and the mileage.

As all the cars are 1988 MB 560SLs, they all have the same options, engine, transmission, etc. The differentiation across vehicles of this age are arguably in the quality of the mechanic that has been working on the vehicle over time. My mechanic is good - others are not so good, but it is difficult to measure that from the information provided on the cars.com website. Therefore, mileage and the general appearance are used to proxy for car quality.

Here's the hedonic model relating asking price to miles, color, and quality (relative to mint):

. reg price red white blue miles good great if year==1988

Source | SS df MS Number of obs = 61
-------------+------------------------------ F( 6, 54) = 11.03
Model | 821863443 6 136977241 Prob > F = 0.0000
Residual | 670443814 54 12415626.2 R-squared = 0.5507
-------------+------------------------------ Adj R-squared = 0.5008
Total | 1.4923e+09 60 24871787.6 Root MSE = 3523.6

------------------------------------------------------------------------------
price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
red | 653.16 1223.711 0.53 0.596 -1800.233 3106.553
white | 1876.029 1130.469 1.66 0.103 -390.4247 4142.482
blue | 3773.104 2180.101 1.73 0.089 -597.7357 8143.944
miles | -.0462573 .0185867 -2.49 0.016 -.0835215 -.0089932
good | -7514.503 2107.488 -3.57 0.001 -11739.76 -3289.244
great | -6351.449 1844.297 -3.44 0.001 -10049.04 -2653.855
_cons | 25290.24 1632.908 15.49 0.000 22016.46 28564.03
------------------------------------------------------------------------------

. lincom _b[_cons]+_b[blue]+140000*_b[miles]+_b[good]

( 1) blue + 140000 miles + good + _cons = 0

------------------------------------------------------------------------------
price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 15072.82 2174.543 6.93 0.000 10713.12 19432.51
------------------------------------------------------------------------------

The 95% confidence interval for the asking price of my MB is from $10, 713 to $19,432. That is a rather large swing, but then again I am only using asking prices not transaction prices. I think the value of my car is closer to the lower end of the 95% confidence interval, but that is me being honest. I could put a sign on my car with an asking price of $15,000 but I don't think it would sell very quickly.

Total time to perform the "analysis":

1. Data gathering: approximately 30 minutes;
2. Regression model: approximately 2 minutes;
3. Blog entry: approximately 6 minutes.

Comments:
What color is it?
 
She's light/sky blue with dark blue interior and dark blue rag-top with 140,000 miles. Rag top needs to be replaced and driver's seat has a rip in it, but mechanically the car is in good condition as I have rebuilt various systems over the years.

I have a windscreen for top-down driving and a garage hoist for the hardtop.
 
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