Wednesday, November 11, 2015

For those who were in class today

The graph I drew on the blackboard today was taken from the paper Why Is Their Mandatory Retirement?  This paper is from 1979 and the labor market was quite different then.

Below is the comparable graph from he paper.  In the graph, W* is the wage that is actually paid, W tilde is the reservation wage, and V* is the marginal value product.   That the lines are straight is simply to make the graph more readable.  But we should note the slope.  That W* is steeper than W tilde connotes a seniority premium to the actual wage.  That W tilde is upward sloping suggests that with experience there is some of accumulation of general human capital that has value when working elsewhere.  Note that in class drew that reservation wage curve as humped.  It rises for a while but then it starts to decline.  I think that is more realistic.  After some age (perhaps 55 or so) the person slows down and that trumps the human capital accumulation part.  Where the peak is surely depends on the individual and the nature of the work the person does.  Also note that at some age, the reservation wage reflects more the value of leisure than the productivity in some other job.

Likewise, I drew the marginal value product curve as humped.  I think that is more realistic, though there is no doubt that the graph below is cleaner to look at.  Economics modeling says to look at the simplest possible model that illustrates the points the author wants to make.  So Lazear's graph wins over the one I drew in class today for that reason.

Finally, I forgot to say something very important in class with respect to this graph.  As the picture is drawn, the employee does not want to retire at T because W*(T) > W tilde (T).  So in Lazear's model mandatory retirement (which is no longer legal) gets the separation of the worker from the firm to happen when it should.  Absent mandatory retirement there needs to be some other mechanism to encourage separation (perhaps certain types of pensions will do this) or one can't rely on seniority premiums as much as one could when mandatory retirement was legal.

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