Saturday, February 02, 2013

The Social Cost of Income Inequality

Robert Frank and I are discussing the important topic of the cost of income inequality in these three posts available here.  In this blog post,  I'd like to make a few technical points.   To start, there are three broad reasons to be concerned about rising income inequality in capitalism.  First, the usual point about inequality stoking envy, and equity concerns as we all aspire to "Keep Up With the Joneses".  Second, is the political economy research line that extreme income inequality allows the super rich to purchase political power.   This is exciting work but I have nothing new to say here.  Third, is the Robert Frank "Arms Race" hypothesis that returning to the ugly Nash Equilibrium --- in an unequal world --  people are spending more and more money and time on goods they don't want in order to compete for scarce slots (jobs at Facebook, admission to elite private schools and Ivy League schools).   If we could solve this arms race, he argues, this would be a Pareto Improvement.   I will focus my remarks on this claim.

Consider the following stylized example:

Suppose that a UCLA graduate can purchase a $400 suit.  He prefers to wear jeans and he will never wear this suit again.  The graduate is aware that he is competing for a specific slot at a firm and he anticipates that his rival competitors for the job are going to wear the fancy suits.   Frank sets up a Prisoner's Dilemma and argues that "wasteful spending" will occur because these two young guys can't collude to both not wear the suit.  Professor Frank argues that rising income inequality makes this situation even worse as the rich wear better suits and the middle class have to waste more money buying a $600 suit to allow them to compete.   So, the equilibrium of this game is that the UCLA guy will waste his $ on a suit. He gains no direct utility from the suit but purchasing the suit is an input in raising the probability that he gets the job.

But, markets have two sides.  Why does the firm expect that the worker wears a suit and looks good?   A fan of non-cognitive skills might argue that looking good sends a signal that you are sane, poised person so these are inputs in a signalling game.    Alternatively, the firm may not solely seek to maximize its profit --- it may seek attractive people because the boss enjoys being surrounded by beauty.   Alternatively, the firm --- say it is in management consulting, might be able to charge clients more if its employees are very attractive.

University of Chicago research offers some optimistic push back against Frank's concern. Gary Becker's work on the economics of discrimination predicts that if the industry is perfectly competitive then a firm that only hires attractive people will eventually go bust because it will be paying them a higher wage.   Sherwin Rosen's work on two sided matching models would predict that if there are counter-culture people with tattoos and long hair and no suit that seek jobs that they won't lose the "Arms Race'.  There will be other counter-culture firms who will hire these individuals.  Implicit in Frank's work is that there is a single index of worker quality and that all firms rank workers on this index in the same way.  Diversity among firms reduces the social cost of Frank's employment Arms Race.  In Frank's single index model, workers must purchase the expensive market input (the suit) to rise in the rankings.  But there are other ways to rise. Steve Jobs didn't wear a suit!

I believe that Dr. Frank's concern is that households are working more and more hours to purchase goods they don't directly want.  This is his "rat race" competition.  In typical economics, we teach that you know your utility function and go to the market to purchase these good.  In contrast, Frank is telling a household production function story that you purchase some goods such as SAT test tutors, big home, fancy suit because these are inputs in your "status function" and "find a job function".   So, your utility function is defined over status and finding a job.  You hire the SAT tutor for your kid to achieve these goals not because you gain direct pleasure from the lesson. He argues that if we could all pre-commit not to buy these goods, we would all be happier because this is "relative competition".   He is arguing that reduced income inequality would help to slow down the Arms Race for relative status commodities.

Implicit in his work are a series of single index assumptions of quality. He implicitly is assuming that all firms rank workers using the same single index model and that all consumers achieve their status (how big is your house, where did your kid go to college?) using the same single index of producing self respect.  In a diverse world, this isn't right.   The onus is on him to produce empirical evidence documenting this strong claim.  Industrial organization economists contrast vertical single index models of quality with horizontal models of quality that admit comparative advantage and multi-dimensional sorting.   Frank's fixation on the single index approach merits serious empirical research.  I can be the ugliest guy in the world but if play chess well or if I'm respected at my church , I may have plenty of self esteem.  This is an example of multi-dimensional attributes that Frank's approach can't handle.

He is also taking his "zero sum game" very seriously.    Why aren't there more good school districts? Why can't the number of excellent universities and their number of slots increase? What is the limit to growth?  Professor Frank needs to team up with an industrial organization economist to study this issue.  He focuses on the demand for status, the demand for schools and neighborhoods but doesn't bother to model supply. In the labor market he talks about the supply of job seeking workers but doesn't discuss labor demand and equilibrium outcomes.  His theory focuses on one side of each market he considers.

 So, Dr. Frank is advancing a very interesting hypothesis that challenges standard neo-classical logic but he is  having too much fun.  If he sits down and thinks about firm heterogeneity and worker heterogeneity, two sided matching, equilibrium, and supply responses then he will reconsider how seriously he takes his core push.

For Dr. Frank to convince me that his thesis is correct, I would need to believe the following conditions;

1. There is a vector of consumption goods such as business suits and SAT tutors that people purchase even though they offer no direct utility to consumers.

2. This vector of consumption goods is growing more expensive over time because the super rich are creating a ratchet effect (i.e wearing better suits to interviews for Harvard Admissions).

3.   Those who control the scarce slots of jobs at firms or Harvard Admissions, rank individuals with respect to the same index of "quality" and this index of quality is mainly based on purchased consumer goods (such as suits and SAT tutors) rather than by personal investments in cognitive and non-cognitive skills.

4. Building on #3, all allocators of the scarce slots use the same single quality index for judging individuals.  This assumption eliminates the possibility that a kid who is  a great chess player but doesn't have a suit can be accepted at University of Chicago but rejected at Harvard.

5.  There is no arbitrage opportunity for a new set of private universities or private firms to enter the industry and hire those who scored low on the original "quality rule".  (This rules out the Becker theory of discrimination optimism).  This also rules out certain shapes of the supply curve such as constant returns to scale. By denying the possibility of entry of firms, Frank assumes a vertical supply of "slots".

6.  For individuals in the rat race, the only way to achieve self esteem is to score high on the societal single index of quality.  (This rules out comparative advantage and people gaining respect from their local community that celebrates a specific skill an individual may have.)  For example, if I'm a terrible researcher at UCLA but fun to have lunch with; my colleagues may enjoy having me around.

If these 6 conditions hold, then I agree with Dr. Frank about the social cost of inequality in the #3 rat race case.   Relax any of these assumptions and I disagree.