## Tuesday, September 4, 2018

Published September 04, 2018 by with 1 comment

# I Fell Prey To Selection Bias

These things are sneaky and I got caught in one that I feel is worth typing up...

#### My observation

I'm in an area with very high housing inflation (>5%/year for several years straight). Houses sell quickly and above list price. I noticed a larger number of e-mails for listings showing 'price reduced' and long times on the market and concluded that the housing market must be slowing down.

#### What really happened

We were priced out of the market. The listings e-mailed to us are in a certain price and square footage range. Previously, the vast majority of listings in our area were under the price limit. Now, the median price has moved above our price limit so I only see most houses if they happen to have trouble selling and drop in price. I.e., instead of seeing all houses, I'm only seeing the ones that don't sell and are more likely to require the seller to drop the price.

#### Simple Example

For a simplified example with numbers, imagine the following:
• houses list from \$300,000 to \$500,000 and are randomly distributed
• our threshold is \$450,000
• a price drop is \$25,000 and 10% of houses need one
Based on that, if 10,000 houses are listed, we would expect:
• 7500 are seen at list price (10000 * [450k - 300k] / [500k - 300k])
• 750 of those subsequently show a price drop (10% of 7500)
• 250 of the 2500 above \$450k will have a price drop of \$25k (10% of 2500)
• 125 of those will end up below the \$450k threshold (<\$475k - \$25k)
Adding that up...we will see 7500 new listings, and 875 price drops, meaning 875/7500, or ~11.67% of e-mails we get will show price drops.

Now assume housing prices rise but our budget does not...
• houses list from \$400,000 to \$600,000 and are randomly distributed
• our threshold is \$450,000
• a price drop is \$25,000 and 10% of houses need one
Based on that, if 10,000 houses are listed, we would expect:
• 2500 are seen at list price (10000 * [450k - 400k] / [600k - 400k])
• 250 of those subsequently show a price drop (10% of 2500)
• 750 of the 7500 above \$450k will have a price drop of \$25k (10% of 7500)
• 125 of those will end up below the \$450k threshold (<\$475k - \$25k)
Adding that up...we will see 2500 new listings, and 375 price drops, meaning 375/2500, or ~15% of e-mails we get will show price drops. The % of houses showing price reductions based on my e-mail samplings increased by roughly 30% while the actual rate being reduced held steady.

Doing this for a bunch of max house prices gives the following error in the apparent percentage of houses that undergo price reductions in this model:

The percentage actually dropping in price did not change. My sampling of houses did which I misunderstood initially.

#### 1 comment:

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