## Saturday, July 9, 2011

### Housing bubble impact a function of the local market

Over the past year, I have developed a theory about house prices that helps explain why different local housing markets reacted differently to the burst of the housing bubble.

The non-linearity of supply and demand to price
The key to understanding price action in the housing market is to realize is that price is not a linear function of the change in supply and demand. That is, given a constant multiplier Y, a change in supply of X% will not always result in a -Y*X% change in price. We can see this in an extreme case with the oil market: in the latter half of 2008 the price per barrel dropped from \$150 to \$30 with less than a 5% reduction in demand relative to supply. Part of this was the rapid disappearance of irrational exuberance among futures traders, but most of it was due to excess inventories resulting from the recession in the west: in the presence of inelastic demand, the price will rise dramatically when demand exceeds supply by even a small amount, and drop just as dramatically when there is any excess supply fighting over dollars.

In the graph to the left, the price of oil at its peak is represented by the points ("3") immediately to the left of the supply=demand line: demand exceeded supply by a small amount. Similarly, the price of oil at its trough is represented by the points ("4") immediately to the right of the supply=demand line: supply exceeded demand by a small amount.

But we know that oil price is not linear to this relationship and can never go negative because there is some cost to digging the stuff out of the ground. So the relationship between supply minus demand and price must look something like the graph below, though I have exaggerated the inflection of the curve to make the point plain.

The red lines in both graphs represent equality of supply and demand: to the left of the red lines, demand exceeds supply and to the right supply exceeds demand. What the green line in the second graph represents is the price for a given difference between supply and demand. The gradual slope of the left tail in this graph represents the inability of the market to support a higher price even as supply is ratcheted down (resulting in shortages and substitution), while the gradual slope of the right tail represents the minimum production cost.

How this applies to housing
In rural areas far from desirable city jobs, supply of available housing always far outstrips demand: these areas are represented by the right side ("2") of each graph. Even if supply decreases or demand increases by a large amount, price doesn't change all that much: it is dominated by production/transfer cost and a small profit margin determined by competition in the local market. Prices in these places did not decrease to any appreciable degree during the bursting of the housing bubble.

Similarly, in desirable cities (think Boston, San Francisco, New York, D.C.), far more people want to live in the city than actually can because there simply aren't enough units to accommodate them all and zoning laws typically restrict the growth in the supply of units. Even if supply decreases or demand increases, the local price is already dominated by the maximum amount that those who want to live there can afford. This can be seen by the small profit potential of renting out a multi-unit house on a 75% or 80% mortgage: most of these houses are barely cash-flow positive, if at all. Furthermore, anecdotal evidence from real estate professionals and prospective buyers monitoring the housing market in Cambridge and Somerville, cities adjoining Boston, is that house prices there have stagnated but (with the exception of damaged/distressed houses) have not dropped to any appreciable degree.

The interesting areas are those near the supply=demand line. Let's break this down to pre- and post-bubble burst in the most extreme case: think of those areas where, in the early 2000's, you thought people were crazy to suffer 2 hour one-way daily commutes. At the time, these places were just to the left of the supply=demand lines ("3"): people who could not afford to live in or near the city but who needed to be within commuting distance of their city jobs built 4000ft² McMansions, and drove up the prices of existing housing stock, out on the edge of the sticks.

Demand did not have to drop much for these areas to move to the other side of the supply=demand line (from "3" to "4"): this resulted in a huge price drop as the supply of houses suddenly exceeded demand. These areas were the first to lose demand, as they are the least convenient locations for commuters who, post-bubble, either no longer had a job to support their underwater mortgage or could now afford to move to a closer suburb or downsize to the city itself. The prices in these places dropped to the greatest degree, but the same is true to a lesser extent in most suburbs except the most desirable ones.

I have been able to find maps of foreclosed mortgages by county, but none showing average sale price percentage changes by city/town to help corroborate this theory. If anyone knows of a source for such information, please post it here.