## November 08, 2006

### Mortgage rates and new home sales

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.

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Posted by James Hamilton at November 8, 2006 05:25 AM

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Drive housing demand equations by mortgage rates and you can drive yourself into an odd corner. While there is no doubt that mortgage rates matter,they matter more sometimes and less other times. If the mortgage rate was decomposed into an after tax rate scaled by an expectation of house inflation and put into an equation that included a measure for income and employment, I wonder how it would turn out. Sometimes it could even be more interesting to see how the coefficients change as you shift the time period used for the regression. That could be an interesting graph against the business cycle, etc. Anyway, just a thought.

Posted by: steve blitz at November 8, 2006 08:11 AM

Makes sense, Professor. Very useful for policymakers.

Will you stand pat on your one factor model, now, or will you move to a multifactor model for home sales?

It appears that prices are moving down here in So Cal, and what interests me is trying to predict when prices will reach their trough (ideal buying opportunity) (in the last downturn, sales for resale homes troughed in Feb. '95 and prices troughed later, in Dec. '95.).

I analyzed monthly San Diego resale home sales and prices over '88-'97 (spanning the last San Diego downturn), and arrived at the following factors as predictors of trough home price: notices of default 30 and 36 months prior, employment 12 months prior, and resale home sales 3 months prior.

I tried Fed Funds and 30 year mortgage rates and lags of such as predictors of sales, and found that Fed Funds was a useful predictor in the run up in prices, but was not useful in the run down in prices.

I look forward to extensions of your work, Professor, to see if you find interest rates as sufficient, or only one of many factors, for predicting sales.

Posted by: jg at November 8, 2006 08:31 AM

Steve and JG,

Note the model includes GDP as one of the predictors. I looked for a role for inflation, which I agree should matter, but it did not enter statistically significantly. I also looked for, and failed to find, an interaction between the mortgage effects and seasonals.
In any statistical model, there is a tradeoff between trying to include all the relevant details and being able to get a good estimate of what you're interested in. In my experience, you're often better off trying to be as parsimonious with parameters as you can, particularly if, as here, what you really want to know is the average effect and time delay for mortgage rates. That's not to say that other variables such as defaults might not be important as well. It depends on the question you're trying to answer. The question I'm trying to answer here is, how long does it take before monetary policy starts to affect home sales?

Posted by: JDH at November 8, 2006 09:19 AM

Steve, excellent point!
Also,
Given the increase in housing prices and the increase in Average Loan Balance, Housing should be more sensitive to interest rates. However, borrowers no longer fit the agency conforming standards, and majority of the mortgage activity in recent year has been on the non-agency side. Therefore, the mortgage rates observed via Fannie and Freddie (which cover conforming loans) are no longer a good estimator of housing response to interest rates. It maybe good for some regions, but definitely not California and the other frothy regions which are the most rates sensitive regions and cover the majority of the mortgage volume…Any thoughts?

Posted by: Zar at November 8, 2006 09:49 AM

Jim,

Minor technical point that does not alter that the main story line, but have you tested for superiority of Weibull over some alternatives such as Poisson?

Posted by: Barkley Rosser at November 9, 2006 11:17 AM

Barkley, I found the Weibull worked a little better than the Gamma, did not compare with Poisson. Another advantage of the Weibull is easy calculation of the implied hazard rate and common use for waiting-time distributions.

Posted by: JDH at November 9, 2006 11:25 AM

The inventory of unsold homes is a somewhat deceptive figure. The basic nature of inventory is that those assets where the buyer's perception meets or exceeds the seller's demands always sell first, with the result that the majority of inventory is always weighted to properties where the asking price exceeds the buyer's assignment of value. In a slowing market, the inventory becomes even more weighted by overpriced properties.

In some instances, the listings are simply potential sellers that are looking for a Cinderella price, but are not in any hurry to sell. Other sellers may be forced to set a price that will cover debt that exceeds value. In the latter instance, the foreclosure process will clean up some of the inventory.

In our developmental planning a year ago, we were most concerned that mortgage base rates might climb to 8%. With apparent stability near 6%, we do not expect the cost factor to have a very great impact on sales. We perceive that the factor that has the greatest current impact is the expectation of future appreciation. Through 2003-04 we encountered many folks that thought that real estate would appreciate at 20% a year to infinity and beyond. With the reality of minimal inflation being impressed upon both buyers and lenders, real estate will have to return to a more rational balance between demand and supply. Demand for real estate is a local matter based upon either employment or retirement draw. Those communities that attracting new populations should see a reasonable recovery unless we have a significant slow down in the economy. Markets that did not have this natural growth in demand generally did not have the high levels of appreciation over the last five years.

Bill

Posted by: Bill Ellis at November 9, 2006 04:55 PM

Bill, thanks and

Shouldn't cancelations also be taken into consideration in re. unsold inventory? In a recent study adjusting for this, Credit Suisse found that months of supply is noticeably higher than official data indicates.

Posted by: juan at November 9, 2006 10:25 PM

The months of supply number is at best only a period to period comparison. I believe the general basis is the units listed in multiple listing services divided by the sales of pre-existing homes. That would miss for sale by owner, and from market to market the ratio of pre-existing versus new construction can be dramatically different.

In the end, all real estate is local. Interest rates are national (or international.) Thus, me thinks that interest rates can impact a local market, but months of supply across a broad swath of territory is pretty meaningless.

Bill

Posted by: Bill Ellis at November 10, 2006 02:28 PM

I was puzzled at the strange lag in interest rate changes until I looked at people.

There are a couple of things that we need to take into account. First there are a few weeks between the time that people start looking for a home to the time that the actually fund a mortgage, that seems to account for the 10 weeks as these people would be waiting a bit to see what will happen with rates and then plunge anyway.

The next people issue is that when interest rates go up there are a few people that get scared out of the market that were originally looking and these people will have left the market and will not fund at all. These people are lost to the market until rates drop into their range again.

Posted by: Home Seller Tips at November 14, 2006 07:28 PM