Saturday, March 16, 2013

When Does Price Not Signal Quality?

By a no arbitrage argument, high prices reflect high quality.  If an apartment's rent is high but its structure quality and location is bad, why would anyone pay that?  In this case, rent would fall.  If an apartment's rent is low but its quality is high,  multiple bidders would show up and the free market price would be bid up to reflect its quality.

I raise these issues because a UCLA colleague of mine challenges me that a location's quality of life cannot be inferred by its rent.   I want to explore this claim in this post.

If there is rent control, then he is correct.  But, if free markets are allowed to operate does price signal quality?  If a person chooses to live in A rather than B then her willingness to pay for community's A's attributes relative to community B must be greater than or equal to the rental premium for living in A over B.  In this sense, data on the rent differentials across areas  and data on where people choose to live places bounds on a person's willingness to pay for non-market goods. This was a key point in Sherwin Rosen's hedonic work.

Economists understand that there are "infra-marginal" people.  Suppose that your Aunt lives in Santa Monica.  You will not be charged a higher price for rent in Santa Monica because of this.  This is an idiosyncratic feature of Santa Monica that will keep you there even if there is an increase in crime in your local area.     In contrast, a "marginal person" is equally happy living in any neighborhood given current rental prices. Rental prices have adjusted so that there are no possible gains from moving.  This means that rents perfectly signal quality for the "marginal group".

Consider an apartment owner who currently rents to Betty for $900 per month.  She gains $950 worth of happiness living in Santa Monica because she loves the unique coastal climate (and the statisticians can measure this) and is willing to pay $900 for this and she loves being close to her Aunt and would be willing to pay $50 for this access.

Suppose that Matt is willing to pay $X for the apartment.   What will be the equilibrium?  Note that in the example below, the statistician only observes what rents people pay, she doesn't know their willingness to pay.

If X < 900, then Betty rents the apartment and the statistician never can recover that Betty values being close to her Aunt.  The rent remains at $900 a month.

If  900< X<950 -="" 900="" a="" access="" and="" apartment="" as="" aunt="" because="" betty="" bid="" bound="" city="" did="" didn="" features="" for="" have="" he="" her="" i.e="" idiosyncratic="" in="" increase="X" increases.="" is="" it="" keep="" knows="" lower="" makes="" match="" matt="" monica="" move="" must="" nbsp="" not="" now="" of="" on="" other="" p="" pay="" reasons="" remain="" rent="" rents="" rise="" s="" santa="" sees="" she="" some="" statistician="" t="" that="" the="" then="" to="" whose="" will="" willingness="">
If  X > 950,  then Matt gets the apartment and the statistician knows that an upper bound on Betty's willingness to pay for the idiosyncratic features =  X-900 because Betty refused to match Matt's offer.

This example shows how economists use market data to learn about "unobservables".   Prices directly signal quality and prices and observed choices (does Betty keep the apartment) can be used to recover what must be the value of idiosyncratic neighborhood attribute.s