The filtering model states that the housing stock trickles down from high income to low income over time. Let me illustrate this with an example from another context. Suppose we are in the market for automobiles and there are three income categories: high, middle, and low. High income people want to buy a new car and decide to trade in their old car (which still has a significant amount of useful life). The middle income people look at the car traded-in by the high income folks. If that traded-in car is at least as good as their current car and costs less they will trade-in their old car. This trickling down of the automobile stock continues.
There is a similar process with housing that occurs because (1) Architectural style changes, (2) Technology in housing gets better, and (3) Physical deterioration happens. Though a house can be maintained to be up-to-date with new technology and physical deterioration can be slowed if maintenance costs ever exceed the price a house can fetch on the market watch out! That home will depreciate in value and a similar process will take place in the housing market, albeit with significantly higher transaction costs than the car market!
The arbitrage model is a model based on prejudicial preferences. What do I mean? The assumption that high income people like to be around other high income people and white people like to be around other white people drives this model. Imagine a border between a high and low income neighborhood (or different races). High income people along that border do not like where they are living because they are close to low income folks. But, low income people like living near high income people for some reason. This was not clearly explained in class, but, there is literature on positive spillovers from public services like police patrol, fire safety, not to mention peer effects in schools. Then we need some "shock" to disturb the equilibrium like a redrawing of school zoning for example. Once this shock happens people from the border decide to move to the interior of the higher income area. But, anticipating this those already in the interior know they will be on the new border of low and high income housing. Because of this expectation they decide to move. Where does it end? We were not told in class, but, there are at least two reasonable thoughts about closing the model (1) Transportation costs become too great to move further away, (2) The benefit to the low income group declines as lot sizes get further from the CBD which would mean spillovers would not be as great.
The filtering model provides a reasonable explanation about why we see income increase away from the central business district. Also, the filtering model suggests that we have a choice with respect to low income housing options (1) We can build low income housing explicitly, or (2) We can subsidize the purchase of new housing and the housing stock will trickle down to the low income earners.
But this is a treatment of the structure not of other meaningful housing attributes like public services and quality neighborhoods which empirically seem to be the reason people select their households. There is a looming question in all of this, how do you provide people all of these things in a scarce world? Just relying on the private market difficult trade-offs will need to be made. The governmental track record does not evoke confidence (see government's hand in the housing crisis). In addition, some attributes that spur success are less tangible, like a culture of achievement. Hard for the government to legislate that. Still another approach, underused, is the voluntary association approach. Nonprofit organizations of different kinds and churches certainly have a role.
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