Unemployment and Efficiency Wages Prof. Eric Sims University of Notre Dame

Fall 2010

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Unemployment and Efficiency Wages

Fall 2010

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Unemployment

In models up until now, there have been two ways for households to use their time: work and leisure Choice to “consume” leisure is completely voluntary In reality there is a third state, called unemployment A person is unemployed if they would like to work but can’t find work. In this sense it is involuntary To get unemployment in a model you need some kind of a friction that prevents labor market from clearing

Sims (ND)

Unemployment and Efficiency Wages

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Terminology and Definitions

n: number of people employed and working UN: number of people looking for work but not working L = n + UN: labor force (all people either working or looking for work) NL: people not in labor force (not working or looking for work) POP = n + UN + NL: total population u=

UN n+UN :

unemployment rate

participation =

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L POP

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Unemployment Rate in the US Unemployment Rate 11 10 9 8 7 6 5 4 3 2 50

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60

65

70

75

80

85

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90

95

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05

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Basic Facts

Mean unemployment rate: 5.6 percent Standard deviation: 1.5 percent Countercyclical: correlation with HP filtered output is -0.6

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Unemployment and Efficiency Wages

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Equilibrium and Unemployment

There is no unemployment in our equilibrium neoclassical model There are fluctuations in employment, but there is no involuntary non-employment. People choose to not work at a given real wage To get unemployment as it is defined here we have to think seriously about frictions in the labor market We’re going to study efficiency wages. Essentially will fix the real wage at a given level and allow for disequilibrium in the labor market.

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Unemployment and Efficiency Wages

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Efficiency Wages

Assume now that firm has some market power. Instead of being a pure price-taker, it can choose the real wage it pays workers Assume further that there are two components to the firm’s labor input: time spent working (n) and “effort”, e. Total labor input = en Assume that effort is some increasing function of the real wage: e = e (w ), e 0 (w ) > 0 Why? Moral hazard: firm can’t perfectly monitor what workers do during the day. The higher is the wage, the more costly it is to “get caught” slacking off at work (i.e. you get fired). Hence effort increasing the real wage

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Unemployment and Efficiency Wages

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Firm optimization

Firm production function is now: y = zf (k, e (w )n ). Objective is to maximize PDV of profits subject to capital accumulation. Now can choose w : maxn,n0 ,I ,k 0 ,w zf (k, e (w )n ) − wn − I
1 + z 0 f (k 0 , e (w 0 )n 0 ) − w 0 n 0 + (1 − d )k 0 1+r s.t. k 0 = I + (1 − d )k

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Unemployment and Efficiency Wages

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Characterizing Solution Just focus on FOCs with respect to n and w : n : e (w )zfn (k, e (w )n ) = w w : e 0 (w )zfn (k, e (w )n ) = 1 Both just MB = MC conditions Combine the two to get: e 0 (w )w =1 e (w ) This implicitly defines an optimal wage rate, w ∗ , that is independent of everything else in the model except the functional form of e (w ) Sims (ND)

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The Labor Market

Call the optimal real wage from the above condition w ∗ . This is now an exogenous variable Assume that this is greater than the real wage that would clear the labor market With the real wage “too high”, quantity of labor demanded will be less than the supply People who want to work at that real wage but don’t get hired (firm won’t go off its labor demand curve) ⇒ unemployment

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The Labor Market Graphically ns

w u w*

nd

n0

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n0s

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n

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The y s curve

Since we’re now long on the ns curve, the y s curve will be different Modified definition: y s curve is the set of (r , y ) pairs where the firm is on its labor demand curve and the production function holds (i.e. y = zf (k, e (w )n ) Labor demand unaffected by r ⇒ y s is vertical Mathematically, y = zf (k, e (w ∗ )n (w ∗ ) What will shift it? Only z, k, or w ∗ y d and money market same as before

Sims (ND)

Unemployment and Efficiency Wages

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The Efficiency Wage Economy ys ns

w

r

u w* r0

nd

n0

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n0s

n

Unemployment and Efficiency Wages

yd

y0

y

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Comparative Static Exercises

Changes in z 0 , g , and g 0 will have no effect on output since supply is vertical. Will only affect real interest rate, composition of output, and unemployment What about change in z?

↑ z ⇒ increases in y , c, and I . r down. n up, u down. p down Very similar to features of the data, except that real wage is not procyclical

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Implications for Policy

In RBC theory, there is no welfare justification for active use of economic policy Here there might be In general, policymakers would want to achieve the level of output that obtains in the base neoclassical model. Why? Because this is the “efficient” level of output The only way to do that is to try to lower w ∗ . w ∗ too high is the source of the inefficiency. How to do this? Does not make sense here to use “countercyclical” fiscal policy

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