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Lecture 2: Frictional unemployment I. The matching function

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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

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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?

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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

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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

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The dynamics of unemployment

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The Beveridge curve u v du/dt = 0

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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

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The Beveridge curve u θ du/dt = 0

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Closing the model: labor demand

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Closing the model: posting vacancies

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The equilibrium value of θ

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The equilibrium trajectory: u θ du/dt = 0

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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

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A fall in labor demand: u θ E E’

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In (u,v): u v E E’

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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?)

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An increase in s: u θ E E’

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In (u,v): u v E E’

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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

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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

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The Loop: u v

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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

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How do we do it?

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