Wednesday, February 11, 2009

Fooled by Search: The Great Housing Bubble

In the housing market, people .... just do not know how to judge the overall level of prices. Much more salient in their minds is the rate of increase of prices.

--Robert J. Shiller, Irrational Exuberance, 2nd Ed., 2005. p. 208

In the United States housing market, data suggest that temporary movements in demand are related to permanent movements in house prices, whereas theory predicts that temporary movements in demand should be related to temporary movements in prices. Alternatively, the data suggest that a permanent change in demand leads to a permanent change in the growth rate of prices, whereas theory would predict only a change in the price level of houses. The data and theory are in disagreement. The disagreement is especially striking if we think that market tightness, or the number of buyers relative to sellers, impacts prices via the bargaining process between buyers and sellers. The divergence of data from theory explains almost three-fourths of the rise of detrended housing prices in the bubble that starts in 1998.

The failure of theory can be explained by a behavioral inefficiency, where buyers and sellers who are currently in the market (irrationally) interpret prices of past transactions as the permanent value of a house. If buyers and sellers behave as such, then high demand for houses causes prices to be bid up relative to past prices. Future buyers and sellers then interpret the resulting price change as a change to the permanent value of a house. In this way temporary demand movements cause permanent movements in prices. If demand remains high, then prices continue to be bid up, so that there is an increase in the growth rate of prices. In this way, a permanent increase in demand results in a permanent increase in the growth rate of prices.

As I argue below, interpreting past prices as the permanent value of a house is irrational if the housing market suffers from `search frictions', which are the frictions in the decentralized trade of houses that cause market tightness to impact prices via the bargaining process. When these frictions are present, an increase in demand, even if there is no change to the fundamental value of house, will increase the price of a house by the interactions between sellers and buyers bidding up the price of a house since sellers know that they can easily find another buyer. However, when future market participants interpret that price change as a change in the fundamental value of a house, they are fooled. In essence they are fooled by `search frictions' into thinking that there has been an increase in the fundamental value of a house. As Shiller's quote states, households have a hard time understanding price levels, instead, they understand price increases.

In an estimated model, the irrational interpretation of past prices as the fundamental value of a house is responsible for over half of the rise in house prices from 1998 to 2006. To see this, figure Figure One plots the real price growth from the data along with an estimated counterfactual where the irrational assumption has been removed, marked `Rational Counterfactual.' The counterfactual is the model's prediction for the increase in prices due to high demand for homes over this period, if households had rationally interpreted that part of the past price increases were due to search frictions. Figure One also plots trend price growth. Removing the trend growth of prices, almost three-fourths of the rise in prices can be explained by households' ignorance of search frictions on past prices.

To see the relationship between prices and demand in the data, examine Figure Two. The most striking feature is the line marked `price level,' which is the real price of houses as reported by the Office of Federal Housing Enterprise Oversight (OFHEO), with inflation and the trend growth in prices removed (trend growth is assumed to be the average growth from 1976 to 2003). Clearly, the level of housing prices relative to trend is significantly greater than any that have been observed since the OFHEO series started. Also on the figure are turnover and price growth. Price growth is the percentage increase in prices from year to year, while turnover is the total sales of houses (new and existing, single family) over the total owner stock of homes (consists of owner-occupied houses plus vacant houses for sale as reported by the Census Bureau). Besides the bubble, we easily see in figure two that turnover moves with price growth, not the price level. Note that this is not an implication from the relative magnitudes of the curves, rather, it is the difference in the timing of the peaks and valleys of the curves: the price level lags turnover, while price growth and turnover move together. The correlation between price growth and turnover is 0.89 and turnover explains 79\% of the changes in price growth.

Turnover and price growth moving together suggests that movements in demand drive the housing market. When demand rises, more homes are sold and prices rise. Note that movements in supply would cause prices and turnover to move in opposite directions. The high correlation between turnover and price growth means that temporary movements in demand are related with a permanent change in prices. Alternatively, a permanent increase in demand is related with a permanent increase in the growth rate of prices. To see this in the data, in figure two, examine the period from 1998 to 2002. We see that turnover rose above its long-run level and stayed there for three years. In those same years we see an approximate permanent change in the growth of detrended prices from zero, being on trend, to something much larger.

Example of Turkish Bazaar

Turning to the theory, let's consider a Turkish bazaar where rugs are sold. There are a fixed amount of sellers who know that they can buy rugs for a certain price in the wholesale market. Each day buyers arrive and search for a rug to buy from a seller. Each rug is slightly differentiated and buyers have particular tastes in their rug preferences. Buyers keep searching from seller to seller looking for a rug to buy. Once a buyer finds a rug she likes, she bargains with the seller over a price. The price is influenced by how easily the buyer can find another seller from which to buy a rug. The sellers and buyers may not know all of the other buyers and sellers, but they can see the level of market tightness, given by the number of buyers to sellers, by observing how many buyers are stopping by each store. The tighter is the market, meaning the more buyers there are, the easier it is for a seller to sell the rug to someone else. In bargaining, both the buyer and seller know this, so increased market tightness leads to higher prices.

Now let's suppose that the market is in a steady-state where market tightness and thus the price is the same from day to day. Now suppose one week that there is an increase in the number of buyers. This would result in more sales, raising turnover. Prices would also increase from the increased market tightness. Now suppose the following week the number of buyers falls back down to the usual, or steady-state level. We would expect that the price of rugs would fall back down to the usual price. This analysis suggests that temporary movements in demand should only cause temporary movements in prices.

Instead we could examine the situation where the increase in buyers is permanent. In this situation, we would expect the price increase to also be permanent. This suggests that a permanent rise in demand should permanently raise the price of rugs, but it should not lead to an increase in the growth rate of the price of rugs.

To better understand the implications of the data from the housing market, place the results from figure two in the context of the rug market in the Turkish Bazaar. Consider first the temporary movement in demand. In this case, after the temporary increase in demand, if the price of rugs behaved like U.S. house prices, the price of rugs would remain high the week after the increase in demand, even though demand had fallen back to normal. In this sense, if you were shopping the week after the high demand you would end up paying too much for the rug. In fact, prices would remain high until there was a fall in demand below its usual level, driving prices back down to their steady-state level.

Next consider the permanent increase in demand. In the Turkish Bazaar this should only cause a permanent increase in the price level of rugs. However, the data on house prices would imply a permanent increase in the growth rate of prices. To put this context, if Turkish Rugs behaved like U.S. Houses, a permanent increase in the demand for Turkish Rugs would result in prices growing at a higher rate forever, or at least as long as demand remained high.

What is the difference between the Turkish Bazaar and the United States Housing Market? One explanation could be that the sellers in the bazaar do understand the price level. They know the cost to them to buy another rug in the wholesale market. Prices cannot deviate too much from the level, since some sellers would start to advertise cheaper rugs. The United States House Market does not behave this way. The equivalent of the wholesale market is new construction. But new construction is only a part of the housing market, and for certain types of houses, new construction is a very loose substitute. This would seem to be especially true in the coastal areas where bubbles have historically been more prevalent.

Instead of a wholesale market, there are new sellers (and buyers) entering the housing market each month. They probably have very little idea as to what the fundamental value of house is that would affect the price level. Efficient markets theory (Fama 1970 Journal of Finance) tells them that past prices should reflect all the relevant information, including fundamentals, for prices. But if households ignore that search frictions are part of those fundamentals they are making a mistake. This is especially true if they are then affected by search frictions in their own pricing of houses. In this sense, they recognize that search frictions affect pricing, but ignore that search frictions may have affected past prices, instead interpreting past prices as reflecting the fundamental value of a house in a frictionless world.

Another way to understand the difference, It's as if the Turkish Bazaar had new buyer and sellers each week and that the sellers had already made their own rugs. In addition, at the entrance of the market is a database with all of the transactions from the previous week. The buyers and sellers search the database looking for the prices of comparables to a rug that they are thinking about buying or selling. However, when doing this, the buyers and sellers ignore that the level of activity the previous week, which they can see, may have affected the price level of all of the rugs. When the buyers and sellers trade in the market, the current level of market tightness does affect their bargaining over prices. They then use the past prices as an anchor and bargain relative to them, not relative to a steady-state price level. Therefore, high demand causes increases in prices relative to the previous week. Each week the process repeats itself so that temporary changes in demand lead to permanent price changes, and permanent changes in demand lead to permanent changes in price growth.


To summarize, the data on the U.S. House Market is consistent with temporary movements in demand causing permanent movements in house prices, equivalently, permanent movements in demand cause permanent changes in the growth rate of prices. This contradicts rational theory that predicts that temporary movements in demand should only cause temporary movements in prices and permanent movements in demand should only reflect an increase in the price level, not price growth. This is especially true if there are search frictions in the housing market where market tightness affects the bargaining between buyers and sellers. Theory can be reconciled with the data by assuming that buyers and sellers interpret past prices as an indicator of the fundamental value of a house in a frictionless world, households are `Fooled by Search.' The past prices then serve as anchor for bargaining. The confusion between price levels and price growth is consistent with Shiller's hypothesis that households have Irrational Exuberance and interpret temporary movements in levels as permanent changes in growth rates.

In order for people to not be fooled by search, a separate housing price index could be started that adjusts the market price of houses to take into account the over and undervaluation of houses due to search frictions. This index would be a type of aggregate index that could be thought of as existing alongside a standard price index such as the OFHEO index or the Case-Shiller index. This index would give a better idea of the fundamental value of housing. Such an index could be useful for mortgage originators to use to think about valuing housing collateral. In addition, the index could help educate the public, to try and forestall the formation of Irrational Exuberance.