In New York City, Hong Kong, Shanghai and London and Paris,  rich people live in apartments.  President Trump owns several apartments in Manhattan.  Poor people also live in apartments.  These apartments are of different sizes, located in different areas and in different buildings and apartments are of different quality levels as well.  In the United States, the vast majority of people live in spread out single family homes.

The majority's choice to not live in multi-family apartment buildings has social consequences.  If more of us lived in apartments in multi-family buildings, then we would walk more and use public transit more and our most productive cities would offer greater economic gains for more people. 

In this blog post, I want to sketch out a thought experiment.  For every American adult, let's consider what his/her willingness to pay for living in a house versus an apartment.  What elements of the structural utility function differ between the two?   What attributes are bundled into a house versus an apartment and why do the private attributes of a house offer greater utility than if the same attributes (such as a swimming pool) are part of an apartment complex where you share this club good with your neighbors.

1. Homes have private backyards  --- While this is true, the market indicates that people do not greatly value their backyard. When you run a hedonic pricing regression of;
home price =  controls + b1*indoor space  +  b2*outdoor space  + U  , where indoor space and outdoor space are measured in square footage;  b1 is much greater than b2.  This indicates that people do not pay much for outdoor space and that in the absence of zoning that a developer would convert the outdoor space into more indoor space.  There is an arbitrage opportunity that zoning does not allow to be engaged in.  

I am sure that in hot places that home buyers are willing to pay more for a backyard if they have a swimming pool there. There are scale economies with respect to such pools. If you trust your neighbors, you can have a common pool that you all enjoy together.  As crime falls in cities, more people (see central park in NYC) are willing to have their kids play in public rather than in private (i.e your own backyard).

So, note my key point here --- the same housing attribute (having a swimming pool) --- yields different marginal utility depending on whether you trust your neighbors or not.  If you trust them less, then your demand for your private pool is higher.  Structural IO economists do not explicitly model this "marginal utility" parameter.   They use revealed preference methods to estimate a single marginal utility parameter and perhaps allow it to vary by demographic groups.  But,  if you trust your neighbors then a public pool is close to a perfect substitute for a private pool and you will be more willing to live in an apartment complex where you share the pool with your neighbors.  Trust is an attribute that the home buyer knows he/she has but the econometrician does not observe this (so this is a case of Jim Heckman's essential heterogeneity).  Heckman's work on essential heterogeneity has not been incorporated into the Sherwin Rosen 2-step hedonic research.  I recognize that a BLP style researcher could estimate a "random effects" parameter for the home's pool attribute but this approach would not yield a microfoundation for why the marginal utility distribution changes over time.  My "model" sketched here predicts that the mean marginal utility and the standard deviation of this marginal utility from having your own pool shrinks as trust in neighbors increases.

2.  Homes have more privacy  ---  In apartment buildings, one may be subject to sounds from neighbors and smells of smoke and cooking.  An interesting question is how much progress has been made in designing windows, and walls that limit these negative interaction.  Of course, there are negative externalities associated with having neighbors but market products can offset these.

3.  No collective action issues arise with a single family home --- If you live in a multi--family apartment, you are either a renter or a member of a collective that has to make some group decisions and if people differ in their preferences for local public goods (such as what plants to plant around the property or whether to replace the building's boiler)--- some members of the group will not be happy with the majority decision.   I'm not sure that this is a big deal.

4.  Homes are larger than apartments   --- This is an arbitrage again.  If you want a large apartment, can you buy two adjacent smaller apartments and blow out some walls and turn two 2 bedroom apartments into a 4 bedroom apartment?

My point here is that I believe that for more and more Americans that apartments and single family homes are becoming close substitutes.  But, there is a supply side.  Since the housing supply is durable and we have built perhaps 80 million or more single family homes that each might last for 60+ years , the transition to an apartment complex cities will take a very long time.

When real estate developers build durable structures, they are locking society into a pattern of land use that remains for decades.


So, in a society featuring lower crime and trust between strangers --- I believe that apartments and single family homes become close substitutes and then the supply side (zoning and durable capital) together determine how our cities actually look in terms of urban form.