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With a one, two and three year time lag, all give us significant results at the 90% level. Only year two gives us significant results at the 95% level. Year 1 and Year 3 are very close to the threshold of being significant at the 95% level.



<table id="wp-table-reloaded-id-11-no-1" class="wp-table-reloaded wp-table-reloaded-id-11"><tbody><tr class="row-1 odd"><td class="column-1">Years</td><td class="column-2">Housing Lag</td><td class="column-3">Coefficient</td><td class="column-4">Intercept</td><td class="column-5">R^2 (% Explained)</td><td class="column-6">Significant at 95%</td><td class="column-7">Significant at 90%</td>
</tr><tr class="row-2 even"><td class="column-1">1972–2006</td><td class="column-2">No Lag</td><td class="column-3">-0.022</td><td class="column-4">0.018</td><td class="column-5">0.002 (0.2%)</td><td class="column-6">No</td><td class="column-7">No</td>
</tr><tr class="row-3 odd"><td class="column-1">1972–2005</td><td class="column-2">1 year</td><td class="column-3">-0.149</td><td class="column-4">0.018</td><td class="column-5">0.109 (10.9%)</td><td class="column-6">No</td><td class="column-7">Yes</td>
</tr><tr class="row-4 even"><td class="column-1">1972–2004</td><td class="column-2">2 years</td><td class="column-3">-0.182</td><td class="column-4">0.018</td><td class="column-5">0.174 (17.4%)</td><td class="column-6">Yes</td><td class="column-7">Yes</td>
</tr><tr class="row-5 odd"><td class="column-1">1972–2003</td><td class="column-2">3 years</td><td class="column-3">-0.142</td><td class="column-4">0.021</td><td class="column-5">0.103 (10.3%)</td><td class="column-6">No</td><td class="column-7">Yes</td>
</tr></tbody></table>

Regression Analysis


The coefficient is the calculation that would be used to forecast housing price changes based solely upon interest rates. For example, using a housing lag of 2 years (1 ½ years ), if today there were a 100% increase in mortgage rates (5% to 10%), we would expect a housing drop of 16.6% (-.182+.018) in year 2. The R-squared is the percentage of the change that is explained by the mortgage rate change. If R-squared were 1.00, then 100% of the changes to the housing prices are explained by changes in the mortgage rate. A figure of .174 means that less than 20% of the changes of the housing prices are explained by the changes in the mortgage rate. In other words, there is a lot of other factors which combined are even more relevant than just the mortgage rate.


Why is R-squared so low?


The previous graph shows that when there are large changes to the mortgage rate, the relevance is much greater than the R-squared we calculated. Mortgage rates being stable allows other issues dominate. If there were a large scale increase in inflation (say from 1% today to 6% three years from now), that would increase the nominal mortgage rate from about 5% today to 10% credit spreads being equal. The R-squared, or significance would likely shoot way up.


How do we use these numbers?


With an R-squared of .174, less than 20% of the change is explained by the mortgage rate. Consequently, I would not use the coefficients and intercept to forecast when there are small changes in the mortgage rates as other factors would dominate. What I am most concerned about is a large scale increases in inflation and how this would affect real housing prices. In the case of large scale increases, forecasting using the coefficients would be acceptable as the mortgage rate would dominate.


Adding the effect from multiple years


While using the data with a 2 year lag is the only dataset that is relevant at the 95%, years 1, 2 and 3 are relevant at the 90% level. The coefficients and r-squared values suggest that changes to housing prices come slowly over time as a bell curve with the majority of the changes coming in year 2, but significant changes also occur in years 1 and 3.


One way to capture the effect of multiple years would be to simply add the coefficients from years 1, 2 and 3, in which case we would get a coefficient of -0.473. However, given that there are different R-squared and different levels of significance, it would be a challenge to know the level of confidence we would have in our forecasting. Also, I would not be comfortable using data that did not have a higher significance level.


The more proper way to capture multiple years would be to take the product of the changes over three years. If we regress that dataset against the changes in the mortgage rate we get a dataset which captures the effect of a change in the interest rate on multiple years.



<table id="wp-table-reloaded-id-12-no-1" class="wp-table-reloaded wp-table-reloaded-id-12"><tbody><tr class="row-1 odd"><td class="column-1">Years</td><td class="column-2">Combined Years</td><td class="column-3">Coefficient</td><td class="column-4">Intercept</td><td class="column-5">R^2 (% Explained)</td><td class="column-6">Significant at 95%</td><td class="column-7">Significant at 90%</td>
</tr><tr class="row-2 even"><td class="column-1">1972–2003</td><td class="column-2">2 years </td><td class="column-3">-0.268</td><td class="column-4">0.023</td><td class="column-5">0.155 (15.5%)</td><td class="column-6">Yes</td><td class="column-7">Yes</td>
</tr><tr class="row-3 odd"><td class="column-1">1972–2003</td><td class="column-2">3 year</td><td class="column-3">-0.339</td><td class="column-4">0.038</td><td class="column-5">0.133 (13.3%)</td><td class="column-6">Yes</td><td class="column-7">Yes</td>
</tr></tbody></table>


Scatterplot of 3-year combined real housing increase against change in the mortgage rate




Current Interest Rate Volatility


But how do we know where the interest rate will be in the future? We can estimate the volatility of the mortgage rate by looking at the history of the30-year treasury yields pSubprimemortgagemorgage Zh TW Tag Ideal Subprime Mortgage Mortgage Correlation of mortgage rates with real housing prices: How increasing inflation could affect housing prices | Facebookq z Forex cSubprimemortgagemorgage Zh TW Tag Ideal Subprime Mortgage Mortgage Correlation of mortgage rates with real housing prices: How increasing inflation could affect housing prices | Facebookt v v Subprime Mortgage Mortgage High Subprime Mortgage Mortgage