Incorporating Local Public Health Dynamics into The Rosen/Roback Spatial Equilibrium Model

 Imagine if there is an infectious disease that spreads within cities but not across cities.   Throughout the COVID crisis, the city specific infection rate has varied across cities at each point in time.  In a city facing a rising infection rate, people can adapt by either engaging in costly self protection (self isolating) or through public health interventions — such as vaccinating the local population.  In this case, public health substitutes for private health protection investments.  To be safe, one can either isolate and not be vaccinated or continue with life as usual and be vaccinated.

Suppose that there are two generations, the young and the old.  The old have already chosen where to live and they don’t move across cities. The young must choose where to live their adult lives. They have full information about each city’s productivity, amenities real estate prices, and quality of life and one element of quality of life is local infection risk. There are other quality of life factors such as air pollution and local climate and topography.

In spatial equilibrium, young people must be indifferent between living in the different cities. Those cities with higher death risk will feature lower housing prices.  The old’s quality of life will rise and fall with the infectious disease risk but the current young will be indifferent.  The young will engage in dynamic programming and will anticipate that they are “locking in” to a given city and they will do their best to forecast each city’s quality of life in the future when they are old. If there is a city whose quality of life is expected to decline (perhaps due to persistent infectious disease risk), then they will demand even lower rents to compensate them for moving there now.

Economists should note that in this model public health expertise represents a city production function parameter. Effective public health in a city lowers the marginal cost of a city providing a low infection rate for everyone in that city.  Land owners in the city benefit from such location specific productivity.  Increases in such productivity raise the well being of the old who are “stuck there”.

For a more formal discussion of these issues in a different setting, read my co-authored 2019 NBER paper.

In our 2015 paper, Dora and I document the historical mortality gains that cities achieved back in the 1930s by investing in clean water infrastructure.  

If infectious disease spreads across cities,  does spatial compensating differentials theory offer useful ideas?  Are we compensated by labor and real estate market for taking the risk of moving to an increasingly risky city?  If every spatial market faces the same rise in risk, then the answer is no.  If people are unaware of these changing risks, then the answer is no.  

Finally, now suppose that only 50% of the population believe that public health efforts have a causal effect on improving one’s health. For example, suppose that 50% of the population do not believe that vaccines are effective.  In this case, a new type of spatial separating equilibrium will emerge as like minded people will move to the “safe cities” and follow the advice of the public health experts.  Real estate prices may not rise much in these cities if the young who do not adhere to the public health expert advice do not want to move to those cities.  

This Tiebout separation (based on differences in beliefs about the effectiveness of public health expertise) is a cousin of my 2017 paper.   

Climate change will increase the risk of temperature extremes. Induced innovation could offset some of this threat. This paper explores the demand and supply for climate adaptation innovation in a market economy. Such innovation attenuates the past relationship between the population death rate and extreme heat. Climate change induces this innovation because the rising temperatures increase demand for self protection products and for profit firms respond to these incentives. We then augment the model to introduce “climate skeptics”. Such skeptics reject the claim that the world’s average temperature is rising and thus do not increasingly demand adaptation products. In an economy featuring no government to enact optimal taxation, we quantify how rational agents are affected by the presence of climate skeptics.