Lecture 2: Frictional unemployment I. The matching function

Frictional unemployment We have seen foundations for « classical unemployment » Frictional unemployment arises from continuous reallocation of workers between jobs In the models we have seen, unemployment would fall to zero absent the rigidities We need to enrich these models

Questions we want to ask What fraction of average unemployment is frictional? Does frictional unemployment play a useful social role? If so, what is the efficient level of unemployment? How is frictional unemployment affected by growth, creative destruction, etc…? Does the frictional component fluctuate?

The matching function Costly process of allocation unemployed workers to vacant positions The matching function is the production function for the flow of new hires The inputs are: –The stock of unemployed workers looking for jobs –The stock of vacant jobs looking for workers

Hirings per unit of time It is assumed to have the properties of a production function: –Constant returns to scale –Increasing in its arguments –Concave

The dynamics of unemployment

The Beveridge curve u v du/dt = 0

Properties of the Beveridge Curbve Steady state relationship between u and v Downward sloping Convex The analysis can also be made in the (u,θ) plane where θ = v/u

The Beveridge curve u θ du/dt = 0

Closing the model: labor demand

Closing the model: posting vacancies

The equilibrium value of θ

The equilibrium trajectory: u θ du/dt = 0

Labor demand shocks The θ falls when –c goes up –r goes up –φ goes up –y goes down In steady state, this is associated with moves along the Beveridge curve

A fall in labor demand: u θ E E’

In (u,v): u v E E’

Reallocation shocks We model it as an increase in s The Beveridge curve shifts out (why?) The labor demand curve shifts down An increase in s is also a negative labor demand shock (why?)

An increase in s: u θ E E’

In (u,v): u v E E’

A deterioration in the matching process The Beveridge curve shifts out again No effect of labor demand Contrary to a (pure) reallocation shock, labor flows fall

Business cycles We can approximmate them by repeated switches between two values of y They lead to loops around the Beveridge curve Vacancies « lead » the cycle Unemployment lags the cycle

The Loop: u v

Long-term unemployment The model can be used to have heterogeneous search intensity among the unemployed LTU: lower search intensity than STU And fraction of LTU larger after recessions  the Beveridge curve deteriorates Persistent effects of transitory shocks

How do we do it?