The Case-Shiller index for December came out today (Feb 24,2009). Prices are still plunging of course. Although they are still falling, we can at least ask if the rate of decline is starting to stabilize. House prices are not like stocks. They don't move stochastically. The price changes are correlated. So the rate of change in price declines (the second derivative) will improve before the rate itself (the first derivative). Lets see if there is any evidence of this. The plot below shows the month-to-month rate of decline, annualized. I have done a seasonal correction and fit a 7th order polynomial to the data which is shown in red.

Looking at the red line, it appears that the annualized rate of price decline is about 20% and it at a maximum (that is most negative). There is some hint that we may be near the maximum rate of decline. The rate of decline will probably start to decrease slowly over 2009 but it will probably take a couple of years to get back to zero (price stability).

This of course is simply fitting the data and extrapolating and is not using any information about the economy, historic relationships of say price to rent, inventory levels etc. Still, I think it is useful since historically these house price bubbles have followed similar patterns. They always decline back to the mean, in real terms.

## Tuesday, February 24, 2009

## Saturday, January 3, 2009

### Extrapolation and prediction

In this post, I will try to estimate the future direction of the Case-Shiller home price index to see when the bottom occurs and to determine what the total decline will be. The plots below show the results of this. In the top plot, we have plotted the real Case-Shiller 10-city index, that is corrected for inflation. The 20-city would perhaps be more representative of the nation but only the 10-city index has the full history back to 1987 so we use that. The natural assumption would be to assume that the REAL index falls back to the previous trough which occurred about 1997 and that the fall will take about as much time as it took to build up. History shows that house price bubbles generally fall fairly symmetrically so this is probably a fairly good estimator for the future direction of the real index over the next few years until the next trough. It took about 9 years to go from trough to peak and will probably take about 9 years to go from peak to trough.

I have fit the peak profile to a particular analytic form and use this to extrapolated the curve forward. This curve (in green) reaches the previous trough value in 2015.

Now we can use this to make predictions for the nominal index which is what most people care about. All we have to do is pick a future inflation rate. I have chosen 2.0%. Small changes from this do not make a big difference in the results. However actual deflation or high inflation rates obviously would change them substantially.

This is shown in the second plot. The red line shows the CPI; the actual CPI in the past and my 2.0% extrapolation. I have defined it to be 100 at year 2000 just like the index to put them on the same plot. The green curve shows my extrapolated model including inflation. The next trough in the nominal index occurs about 2013. The fall from the peak value is about 47%.

I have applied the same modeling to the individual cities in the Case Shiller index. Here are the results below.

I have fit the peak profile to a particular analytic form and use this to extrapolated the curve forward. This curve (in green) reaches the previous trough value in 2015.

Now we can use this to make predictions for the nominal index which is what most people care about. All we have to do is pick a future inflation rate. I have chosen 2.0%. Small changes from this do not make a big difference in the results. However actual deflation or high inflation rates obviously would change them substantially.

This is shown in the second plot. The red line shows the CPI; the actual CPI in the past and my 2.0% extrapolation. I have defined it to be 100 at year 2000 just like the index to put them on the same plot. The green curve shows my extrapolated model including inflation. The next trough in the nominal index occurs about 2013. The fall from the peak value is about 47%.

I have applied the same modeling to the individual cities in the Case Shiller index. Here are the results below.

City | Trough year | Decline from peak |
---|---|---|

Phoenix | 2011.7 | 51% |

Los Angeles | 2013.5 | 59% |

San Diego | 2013.5 | 56% |

San Francisco | 2013.0 | 53% |

Washington DC | 2013.4 | 46% |

Miami | 2012.3 | 53% |

Tampa | 2012.1 | 45% |

Chicago | 2011.7 | 26% |

Boston | 2015.0 | 40% |

Las Vegas | 2010.7 | 44% |

New York City | 2015.0 | 43% |

San Francisco | 2013.0 | 53% |

10 city composite | 2013.2 | 47% |

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