More on Beveridge Curve: Disequilibrium and Oversupply in the Housing Market

Earlier I posted on some research that I was working on about a Beveridge curve in the housing market (the work that motivates the name of this blog). The working paper version of the paper is now finished and available for downloading.

The main results of the paper:

• The Beveridge Curve represents a long-run supply condition
• Short run deviations represent periods of disequilibrium, either over or under supply
• Using a years of oversupply metric, the observation of 2007-2008 was an all-time high of 0.995 years of oversupply, more than three times the previous peak of 0.285 in 1973-1974.

Results regarding the differences between the owner-occupied and rental markets:

• Generally, oversupply is a phenomena in the rental market
• Oversupply in the rental market is twice as volatile as in the owner-occupied market
• Oversupply first shows up in the rental market

Last, I find that

• Oversupply in the owner-occupied market is related to house prices, reinforcing the idea that short run deviations in house prices from fundamentals (such as bubbles) can lead to periods of oversupply

Below, I give a summary of these results, except for the last bullet on house prices which I leave to another post.

The primary change from the earlier results is that instead of doing the fairly ad-hoc HP filter, I have gone ahead and estimated the model using biannual data. In my opinion this gives a better estimation. In addition to the new estimation I have also found some interesting results relating oversupply of houses to house prices. I will go over those results in my next entry, for now I give an overview of my previous results under the new estimation.

The main idea of the Beveridge curve is that it represents the long-run equilibrium in the housing market. The Beveridge curve has its origins in labour economics, where Lord Beveridge found a negative relationship between the unemployment rate and the amount of job vacancies. For an example, see Rob Shimer's website. In the housing market I have found a negative relationship between the rate of household formation and the residential vacancy rate. I deem this negative relationship the Beveridge curve in the housing market. The Beveridge curve relationship exists in the owner-occupied market, the rental market, and the overall market irrsepective of ownership. Figure 4 from the paper, shown here below, shows the relationship for the overall house market. There is a clear and statistically significant negative relationship and the R-squared from a linear regression is 0.626.

As I stated, the curve represents a long-run relationship, so that short-run deviations (two to four years) represent periods of disequilibrium in the housing market, these are periods of under or over supply, see figure 7 below.
The next figure shows the estimated time-series of oversupply for the total housing market irrespective of home-ownership. The metric of oversupply is in a % of the total housing stock. Here we clearly see three periods of oversupply since the start of the data in 1968: (1) the 1974 crisis; (2) the mid to late 1980s housing boom; and (3) the current crisis. The oversupply in the current crisis is similar in magnitude to the 1974 crisis, with both having an oversupply of just under 1% of the total housing stock.
However, the rate of household formation is much lower now, so that it may take much longer to work off the oversupply. The next figure plots the estimate of oversupply in years of oversupply. This is the oversupply in years of household formation. For instance, if the rate of household formation was 1% and the oversupply of the housing stock was 1%, then it would take one year of no housing production for the oversupply to disappear. Using this metric, the amount of oversupply is staggering, being about one year of supply in 2007-2008 compared to under 0.3 years in the 1974 crisis.

One point that I cannot stress enough is that what we are currently facing is a huge oversupply of housing, irrespective of whether it is rental or owner-occupied housing. As I stated in the earlier post there is actually more oversupply in the rental market. To see this, below is figure 12 from the paper. The metric is years of oversupply in terms of the total rate of household formation, so that we are comparing apples to apples. There are several striking features in this figure:

• Generally, oversupply is a phenomena in the rental market
• Oversupply in the rental market is twice as volatile as in the owner-occupied market
• Oversupply first shows up in the rental market

These results suggest that the rental market is sponge the soaks up oversupply in periods of overall oversupply, and then lets it out once housing becomes relatively scarce. This suggests that research on the housing market, especially empirical, needs to include data from the rental market when doing structural work.

Distressed Sales and House Prices

In my last entry I argued that a shock was causing existing home sales to rise relative to new home sales, and that this same shock was causing house prices to fall more than would be suggested by the level of existing home sales. This `shock' is more than likely a supply side shock: quantity up, prices down, Econ 101 at work. A question is how much of this is being driven by distressed sales where the house is being sold because the current owner has stopped paying the mortgage.

Andrew Leventis, a researcher at the Federal Housing Finance Agency has attemped to answer this question is a recent working paper: "The Impact of Distressed Sales on Repeat-Transactions House Price Indexes".

In the paper, Leventis uses transactions data from California and breaks down transactions into distressed and non-distressed. A transaction is distressed if a Notice of Default was filed on the property up to a year before the transaction occurred and no other transactions occurred for the same property between the transaction and the Notice of Default. He performs the analysis for two different groupings of data. The first grouping he calls `Enterprise' data, and this consists of the transactions that would be included for calculating the FHFA House Price Index (HPI). The second grouping is `Recorder' data, which consists of the data that would be used to calculate the Case-Shiller index. His figure one shows that the share of distressed sales has increased from less than 5% before the fourth quarter of 2006, and has been rising steadily ever since, now over 45% for the first quarter of 2009. The rise in distressed sales is very similar to the gap that has appeared between new and existing home sales.

The main question of the paper is "How much are these distressed sales driving down house prices?" To paraphrase Leventis, we can breakdown the effect of distressed sales on house prices into two categories:

1. Direct Effect: distressed houses sell at a discount, therefore, as the share of distressed sales in the sample increases, then the reported house price index will fall.
2. Indirect Effects: the more distressed sales there are, the harder it is for a non-distressed seller to sell a house, lowering the prices for all houses.

In his paper, Leventis can only get at the direct effect. His figure 4 shows the discount for distressed sales. We can see that before 2006, that distressed sales sold at about a 4% discount. At the peak of the bubble in 2006, the discount almost went completely away--it didn't matter if a seller was distressed, seemed that buyers were willing to buy everything and anything in sight. However, after 2006, the discount gets significant, approaching almost 20% for the `Enterprise' data, and 15% for the `Recorder' data (there is an interesting divergence between the two types of data in the last couple of quarters).
Therefore, by the end of 2008, distressed sales were selling at a 20% discount and made up roughly 45% of sales. Relative to the peak in the housing bubble in 2006 (when the discount was essentially zero), if this sales pattern would maintain itself for a year, it would imply that the house price index is being pushed down an extra 9% due to the direct effect from distressed sales. However, the total effect so far has been smaller. His figure 2 shows the effect of the distressed sales on year-over-year price growth for the `Enterprise' data. The figure contains two plots: one showing price growth for the entire sample, another with the distressed sales removed. The effects are fairly small. The cumulative effect of the distressed sales is estimated to drive down prices an extra 5.3% from the peak, for a fall of 41.3% relative to only 36.0% when the distressed sales are excluded. The effect on the `Recorder' data is smaller, implying an extra house price fall of 1.9% from 44.8% to 46.7% (see his figure 3, not shown here).

To summarize, the divergence between new and existing homes seems related to the surge in distressed sales. The work by Leventis suggests that the direct effect of the distressed sales on the reported house price indexes is most likely small relative to the total decline we've seen in house prices. What we do not know is whether the distressed sales are directly responsible for the fall in house prices and the increase in existing sales relative to new sales, or if the distressed sales are simply the result of the large supply of housing, which is then responsible for distressed sales, housing price falls, and an increase in existing relative to new sales. My viewpoint is that we are just seeing the effects of supply at work.

House Prices and New versus Existing Homes Sales

This week we have received the May data on existing home sales (from the National Association of Realtors) and new home sales (from Census). Existing home sales have been flat or rising a bit for 2009. Such stabilization in the market for existing homes has been a sign to many observers that we may be reaching the bottom in house prices. However, at the same time new home sales have continued to fall relative to their 2008 levels. As people have noted (see CalculatedRisk), there is now a gap between new home sales and existing home sales that did not exist before 2006. As I show here, whatever is driving a gap between new and existing homes sales is also driving a gap between the relationship of existing home sales and real house price growth. The evidence suggests that a supply side shock is driving up existing homes sales relative to new home sales and at the same time driving down prices, just as standard econ 101 predicts. Furthermore, price growth is related to new home sales, not existing home sales. The punchline: if we are seeking stability in house prices we should look at new home sales, not existing sales.




Figure 1 plots annual single family existing homes sales and single family new homes sales as a percentage of the total housing stock (the total housing stock is taken from Census). We see that new home sales average about 1% of the total housing stock, while existing home sales average roughly 4%. To get a feel for how the two series move together, figure 2 plots the percentage deviation for each series from its mean from 1975-2008. We see clearly that from 1975 to 2006 (the solid lines) that new home sales and existing homes sales move around together, with a correlation of 0.944 over the the time period up to 2006. However, as shown by the dashed lines, a gap has developed post 2006, resulting in the correlation for the sample from 1975-2008 falling to 0.876. There seems to be some type of a shock that is driving existing homes sale up relative to new homes sales.


Turning to prices, figure 3 graphs expected annual real house price growth next to existing homes sales. Expected real house price growth is the FHFA (formerly OFHEO) house price index, made real by the rate of expected inflation from the Philly Fed survey of forecasters. The existing sales series is the same as in figure 2. Once again, we can see clearly that from 1975 to 2006 both series move around together, with a correlation of 0.921. However, post 2006, a gap develops just like the gap between new home sales and existing home sales. Using the whole sample up to 2008 the correlation falls to 0.812.


Both of the gaps suggest a shock hitting the housing market. To put it more clearly, figure 4 plots both a `price shock' and and `existing sales shock'. The price shock is the shock to price growth that is not explained by existing sales in figure 3. (This is actually the error term from a linear regression of price growth on existing homes sales relative to the housing stock). The existing sales shock is the shock to existing homes relative to new home sales, the difference in figure 2. (the existing sales shock has been normalized to be on the same graph as the price shock). From 1975 to 2006 these two shocks are essentially unrelated. However, in 2007 and 2008 both shocks are sizeable, moving in opposite directions. What we have is a classic supply side shock: quantities rising and prices falling. The glut of vacant houses on the market are doing what they do: drive down prices, and drive up sales.


The implication is that the supply shock is breaking down the standard relationship between sales and price growth. Existing home sales is not the place to be looking for stability in house prices. Instead, figure 5 plots new home sales relative to house price growth. Here we can see that new home sales are related to house price growth, and this relationship has maintained itself through the crisis. The correlation from 1975-2006 is 0.881, while for the whole sample from 1975 to 2008 it is 0.899. Therefore, if we are looking for price stability, we should look to new home sales, not existing home sales. The supply side shock that is hurting prices and raising existing home sales causes new home sales to fall. To stress the point a bit more, the stability in the housing market that we want for economic recovery is stable prices and new home construction. Stable prices are associated with new home sales not existing home sales. The current stability in existing home sales is most likely just the effects of a supply side shock that is driving down both prices and new home sales. In my next entry I will use search theory to guide us in understanding this behavior in the housing market.

Housing Market Recovery: Shadow Inventory?

We all want to know when the housing market will recover. A recent piece by David Leonhardt in the NY Times suggests that the housing market still has not reached bottom. Central to clearing the housing market is eliminating the oversupply of homes (see my earlier entry). There are several measures of oversupply: the National Association of Realtors provides a monthly measure of homes for sale; the Census Bureau provides a monthly measure of new homes for sale; and the Census Bureau also provides us with a quarterly measure of vacant homes for sale.

All of these measures rely upon the owner of the property putting the housing unit up for sale. As Calculated Risk has been saying (here, here, and here) there is most likely a large shadow inventory of sellers keeping their homes off the market. A recent piece in the San Franciso Chronicle (article here, Calc Risk Blog here) suggests that banks are also keeping foreclosed properties off the market.

There is no survey of banks and households that we can use to estimate the size of the possible shadow inventory. However, we can get a sense of it from the quarterly Housing Vacancies survey. This survey is the source for the data on owner-occupied and rental vacancy rates, and it provides a breakdown of vacant units beyond these headline vacancy rates. Table 1 provides the breakout of vacant housing units from Census. When census reports vacancy rates they exclude `Seasonal Vacant’ and `Held-off Market.’ The category Held-off market consists of three sub-categories: `Occasional Use’, `Usual Residence Elsewhere (URE)’ and `Other Reasons.’ These excluded categories are generally quite boring. They are generally increasing, following a trend, but display almost no cyclicality.


I say almost because the sub-category vacant held-off for other reasons has become quite interesting of late. Figure one plots the % of the housing stock that is vacant held-off the market for other reasons. My measure of the housing stock is the sum of total occupied, vacant for sale, vacant for rent, vacant sold or rented and vacant held-off market for other reasons. In the last two years this category of vacant units has surged from 2.3% to 2.9%. This suggests that there is a large shadow inventory equal to roughly 0.6% of the total housing stock, or 736,000 units.


Figure 2 plots the total residential vacancy rate with and without the shadow inventory (vacant units held off the market for other reasons). The total residential vacancy rate is the % of the housing stock that is vacant irrespective ownership status. The red line in figure 2 is the total vacancy rate solely from vacant for rent and vacant for sale, excluding the shadow inventory. The black line in figure 2 denotes the vacancy rate when the shadow inventory has been added to the vacant units for rent or sale. In the current crisis we see that the vacancy rate excluding the shadow inventory seems to be stabilizing while the vacancy rate including the shadow inventory seems to still be rising.


A rising vacancy rate is a potential bad omen for the recovery of the housing market. Ultimately, it is vacant units that are putting pressure on the cost of housing services, be it rents or house prices. Common sense suggests that stabilization of the vacancy rate is a necessary but not sufficient condition for stabilization of house prices. This suggests that inclusion of the shadow inventory implies that the housing market still has a long way to go before prices stop falling.

An interesting feature of the data is that the presence of a shadow inventory is not a new phenomenon. In figure 1 we see that during the crisis in 1974 there also was a surge in vacant held off market. In figure 2 we also see that the rise in the vacancy rate including the shadow inventory is more pronounced during the 1974 crisis. This suggests that movement in the shadow inventory is always part of the cyclical process of the housing market. The shadow inventory is just more visible during the severe downturns. Therefore, there may not be too large of an error in forecasts based upon historical estimates that ignore the shadow inventory.

The nature of the shadow inventory is not clear. The measure from the Census data is only vacant homes, so it does not consist of any owners who are waiting to put their house on the market. The vacant homes most likely consist of a large amount of foreclosed homes that are not listed as for sale. They could also be the former homes of the elderly who have moved to assisted living. When the housing market is in a downturn, the offspring of the elderly may take their time preparing a house before putting it on the market.

The vacant homes could also be abandoned homes. I was only just born during 1974 so I have no personal memory of that downturn, but it seems likely that it was during this period when there was an acceleration in the abandonment of vacant housing units in the cities that contributed to the inner city blight back then. Currently there is a same abandonment going on the midsize former industrial cities of the Midwest. For instance, the New York Times just had a recent piece about abandoned homes in Flint, see "An Effort to Save Flint, Mich, by Shriking It." Therefore, it is not clear whether the vacant units held off market for other reasons are a viable shadow inventory of future homes to be sold, or just an indication of a higher rate of depreciation via abandonment.

IU Econonics Forum

We had an Economics Forum at IU on Friday afternoon. There were several excellent talks put on by very bright economists with ties to IU. Here is a link to all presentations. George von Furstenberg's talk goes over the legal grounds upon which the growth in power of the Treasury, the FDIC and the Fed rests. Unfortunately his comments and turns of phrase cannot be completely gleaned from his slides.

Myself, I tried to explain how standard open-market operations were used to influence the overnight market for liquidity. I attempted to construct an example of IU undergrads lending excess cash to each other to have while they go on dates. The collateral they put for the overnight trades is video games. High quality video-games can be thought of as short-term Treasuries. A guy called Ben uses video-games to control the supply of excess cash--too much cash and the dating market overheats--too little cash and too few people go on dates.

We can think of the onset of the crisis by imagining there are a set of students at IU who go on dates, but don't get to trade directly with this guy Ben. Instead, they create their own video games that work as collateral in the overnight market. Particularly, a couple of guys started to issue `sub-prime' video games. Initially people liked these games, but in the summer 2007 people playing the games realized they were junk. These games were now lemons, and the overnight lending market froze up. Things got so bad in September 2008 that Ben's trading in money and high-quality games become impotent. Essentially, people preferred to keep their money, rather than lend it out or go out on dates. Money and high quality video games were now perfect substitutes, now serving as a store of value. The students at IU were afraid that if they lent, they would become insolvent and they would never be able to go on dates again. Ben doesn't like this situation, so he has now started to trade other types of video-games for money. For instance, he trades lower quality games and games that last longer--such as fantasy or war games that take longer to finish. This creates more liquidity for video-games, but if it will convince the students to go out on dates, we do not yet know. It's not clear how this liquidity solves the insolvency and lemons problems. It does however stem the liquidity problems that have arisen from the insolvency and lemons problems.

Intermediate Macro Blog

I've started my Spring teaching. As a byproduct I'm using a blog for the Intermediate Macro class (undergrad). I start off most classes by going over data relevant to the current crisis. While the data is not directly housing related, I'll post links to them since I think most people will find them interesting.

So far I've posted two entries.

The first covers the fall and subsequent (and quite recent) rapid increase in savings. See "The Trainwreck".

The second post covers the changes in Households' wealth and debt from the Fed's Flow of Funds. See "Household Debt Leading up to the Crisis." The data shows quite clearly the folly in the logic a lot of people (myself included) in thinking that the high levels of mortgage debt to income were justified by the high house values--we had seen that story before and high mortgage debt to income leads to high debt to assets, just with a lag.

The Beveridge Curve in the Housing Market: The Rental Market is more out of Equilibrium than the Owner Market

The long-run equilibrium in the Housing Market is characterized by a Beveridge Curve. In Labour Economics, the Beveridge Curve denotes the negative relationship between the unemployment rate and the number of job vacancies (Rob Shimer maintains an updated curve from the labour market). In my research (slides), I have discovered a Beveridge Curve in the Housing Market given by a negative relationship between the growth rate of households and the vacancy rate. The relationship holds in the owner-occupied market, the rental market, and the total market independent of ownership status.

The relationship for all three markets is plotted in figure 1. On the x-axis is the vacancy rate and on the y-axis is the growth rate of households for each type of market. The data source is the Housing Vacancies Survey put out by the Census Bureau (data in excel). The data have been smoothed slightly due to noise (details in slides). There is a clear negative relationship between the vacancy rate and the growth rate of households in all three markets. Currently all three markets are at their all-time highs for vacancies. (I also have a Beveridge Curve by decades).

What is most striking about the current housing market is that the rental market is significantly more out of equilibrium than the owner occupied market. This suggests that in addition to falling house prices, there is significant pressure for rents to be falling as well. In fact, there is evidence of rents falling (see CalculatedRisk, NYTimes, Guardian).What we also see is that the disequilibrium started back in 2003; the writing was on the wall even back then.

We clearly have an over-accumulation of houses. The current market imbalance is not an own versus rent problem, but a house versus household problem. The price that needs adjusting is not just the rent-price ratio. What needs adjusting is the overall cost of housing services, regardless of ownership status.

We can use the Beveridge Curve to get a deeper understanding of the long-run equilibrium in the housing market. The curve can best be thought of as a supply condition. The demand for new houses comes from household formation. Let’s assume that the cost to produce homes is increasing in the growth rate of the housing stock (as is assumed by Glaeser, Gyourko and Saiz in their papers here and here). When household formation is low, the cost to produce the homes to satisfy the market is low.

There are two adjustments to clear the market when the rate of household formation falls. The first is the standard adjustment that house prices fall. The second adjustment relates to the vacancy rate. When the cost to produce a home is low, a builder may want to produce more homes, potentially adding variety. This lowers the probability of an individual house selling, but it raises the probability that an individual builder may sell one house. In essence, builders respond to the lower costs by raising supply. The higher supply shows up in a higher vacancy rate. At some point in time the vacancy rate rises enough to stem more production and the market returns to equilibrium. Therefore, we get the following result: A lower growth rate of households lowers the costs of production to meet demand, leading to lower prices and higher vacancy rates. Thus, the Beveridge Curve.

Figure 2, illustrates how we should think of the long-run relationship in the Beveridge Curve. When the current market condition is to the northeast, there is an over-supply of homes—the vacancy rate is too high relative to the rate of household formation. High prices could drive the market into this area. When the current market condition is to the southwest there is an undersupply of housing units—the vacancy rate is too low relative to the rate of household formation.

The estimated long-run Beveridge Curve, rendered by the solid lines in figure 1, gives us a value for the current over/under supply of housing units. The best way to measure the amount of over/under supply is to find the current deviation of the vacancy rate from its long run value implied by the current growth rate of households. The deviation provides a measure of over-supply in terms of a percentage of the total housing stock. For the total market, the current over-supply is 1.04% of the total housing stock, or 1.22 million units.

A better way to measure the over-supply is to normalize it by the long-run growth rate of households. We then get a measure of over-supply in terms of years of household formation. That is, the measure is the numbers of years to erase the over-supply if household formation remains at its same rate and no more houses are constructed. This is a ‘years of supply’ measure equivalent to the ‘months of supply’ concept used in New and Existing home sales.

Figure 3 graphs the oversupply for all three markets. We clearly see a large increase in over-supply starting in 2003. Almost all of the over-supply originates from the rental market. Only recently has there been an over-supply in the owner-occupied market. Currently the total over-supply is at 1.03 years of household growth; by far the largest over-supply ever. Note that for this metric, the high rates of household formation in the 1970s kept the over-supply around 1974 low, at 0.29 years. Also, for the entire sample, the rental market is where most of the adjustment takes place—most of the over/under supply is there.

Finally, let me address foreclosures. A foreclosure does not affect the over-supply in the total market. When a household loses its house through foreclosure, the result is a vacant house and a renting household. Provided that the household remains an independent household and does not become homeless or move in with relatives, the household rents out a previously vacant house. The result is no change in the equation between houses and households. This is not to say that foreclosures are not a problem. Foreclosures are affecting the financial system, they create psychological problems for households being foreclosed upon, and a foreclosure can hurt a neighborhood just like any vacant house can hurt a neighborhood. However, foreclosures do not affect the imbalance in the overall housing market. As Glaeser and Gyourko state "the tyranny of housing supply suggests that no credit market intervention of any sort is likely to be able to stop housing price declines."

In summary, there is a Beveridge Curve in the Housing Market that defines a long-run equilibrium. Currently there is an over-supply of 1.22 million units, roughly one year of supply. What is striking is that most of the over-supply is in the rental market, not the owner-occupied market. This suggests that not only does the price-rent ratio need to adjust, but rents also need to adjust.

In a few days I will be posting about what we can expect for household formation. The data used for the Beveridge Curve suggest that this is also bleak.