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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
),( ttt VUmH • 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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