This is the third of three posts based on my new research paper titled Daily Monetary Policy Shocks and the Delayed Response of New Home Sales, in which I describe the delays between Fed policy actions and what happens in the housing market.
My research on the consequences of mortgage rates for housing begins with a simple baseline model for predicting the logarithm of the seasonally unadjusted level of new home sales. Important factors included in this model are the month of the year, a time trend, the previous quarter’s GDP growth, and the level of sales over each of the previous 5 months. I then looked at how you would adjust the forecast based on this model in response to how mortgage rates may have changed each week for the last 30 weeks. The estimated coefficients on previous changes in the mortgage rate along with 95% confidence intervals are plotted below as a function of how many weeks in time you are looking back.
These coefficients imply a response of new home sales to mortgage rates that is quite sustained and spread out over a long period of time. About three-quarters of the t-statistics for changes that occurred between 1 and 5 months earlier are below -1 with eight below -2. As I noted in my previous post on this paper, the change in the mortgage rate itself does not have much correlation from one week to the next, meaning that these individual regression coefficients are roughly independent of each other. Hence, the broad block of estimated negative effects is extremely statistically significant; (try flipping a coin 20 times and see if you come up with 19 heads).
These estimates imply that some of the home sales for a given month depend on mortgage rate changes that occurred during the previous month, while sales of other homes within that same month appear to be responding to mortgage rates up to five months earlier. Presumably that phenomenon reflects some fundamental disparities across different home buyers, with some people taking considerably more time to locate and purchase a home than others. If one uses a Weibull probability distribution to describe differences across households in search times, one accepts the hypothesis that the pattern of coefficients in the graph above could be explained by such a distribution, with an implied average search time of 14.4 weeks. That turns out to be remarkably similar to the average time lag of 14.7 weeks which the National Association of Realtors 2005 Profile of Home Buyers and Sellers reported elapsed between the time households started looking for a home and the time at which they signed a contract to purchase a home.
Using these estimated Weibull weights, I then calculated the expected implications over time of a 10-basis-point increase in the 30-year fixed mortgage rate. The graph below shows the percentage by which new home sales would be expected to deviate from their usual trend the indicated number of weeks after the change. Because of the long cumulative lag as well as the feedback effect on subsequent home sales, the biggest effect on home sales is not observed until 16 weeks after the interest rate goes up.
In my previous post I described a framework for interpreting how changes in Fed policy feed into this process, presenting evidence that the mortgage rate on any given day already incorporates a rational anticipation of what the Fed is going to do next, with any new information about where the Fed is headed showing up virtually immediately in the current mortgage rate. This implies that the time path of the response of housing to an unanticipated change in Fed policy has exactly the same shape as the graph above. Using the numerical estimates described in my previous post, the above graph could equally well have been labeled as the effect of a 20-basis-point increase in the level of the near-horizon term structure of fed funds rates, or of a 7-basis-point increase in its slope. Again I found confirmation of these predictions in the estimated direct relation between changes in fed funds futures prices and subsequent changes in the number of homes sold.
I also noted in my previous post that the fact that the Fed has stopped raising the fed funds rate was a factor in bringing mortgage rates down since this summer. But because mortgage rates had previously been rising up through the beginning of July, the lags in the process mean that one would expect to see home sales falling relative to the usual seasonal pattern in August and September, even though the mortgage rate by then was coming down. Given the rate hikes in the spring and early summer and the long lags in the process, I calculate that recent changes in the mortgage borrowing rate have on balance been a factor causing home sales to be lower than they otherwise would have been up through the middle of October. It is only within the last few weeks that one would expect to see home sales stop falling as a result of the policy change that first began to be recognized this summer.
It was partly because of this calculation that I have been more open than many other analysts to the possibility that the most recent data might be suggesting that the bottom for home sales may indeed have already been reached. However, even if sales now stabilize, the inventory of unsold homes will continue to put downward pressure on house prices and employment, either of which could easily become a new factor in the unfolding story. But what we can say is that one very important fundamental has now turned from negative to positive.