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Lecture 2: Frictional unemployment I. The matching function.

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Presentation on theme: "Lecture 2: Frictional unemployment I. The matching function."— Presentation transcript:

1 Lecture 2: Frictional unemployment I. The matching function

2 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

3 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?

4 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

5 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

6 The dynamics of unemployment

7 The Beveridge curve u v du/dt = 0

8 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

9 The Beveridge curve u θ du/dt = 0

10 Closing the model: labor demand

11 Closing the model: posting vacancies

12 The equilibrium value of θ

13 The equilibrium trajectory: u θ du/dt = 0

14 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

15 A fall in labor demand: u θ E E’

16 In (u,v): u v E E’

17 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?)

18 An increase in s: u θ E E’

19 In (u,v): u v E E’

20 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

21 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

22 The Loop: u v

23 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

24 How do we do it?

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