
KAT.TAL.322 Advanced Course in Labour Economics
September 8, 2025
Source: Statistics Finland

Source: Occupational Employment and Wage Statistics (US)
Production function F(L):FL(L)=y
Workers supply h=1 unit of labour and receive wage w if hired
Linear worker utility U(R,e,θ)=R−eθ
Equilibrium
Ld={+∞if w<y[0,+∞)if w=y0if w>y
Ls=G(w)
Continuum of jobs with varying difficulty e>0
Productivity y=f(e) such that f′(e)>0,f′′(e)<0,f(0)=0
e also corresponds to effort worker puts in if employed
Compensating wage differentials: w′(e)>0
Ld={+∞if w(e)<f(e)[0,+∞)if w(e)=f(e)0if w(e)>f(e)
Ls={1if f′(e)=θ∩f(e)−eθ≥00otherwise
At baseline worker of type θ chooses optimal effort e(θ) and earns w(e(θ))
Limit on job difficulty ˉe forces worker type θ on a lower indifference curve
Start from baseline model
Equilibrium wage wM=yηLw(wM)1+ηLw(wM) where ηLw(wM)=wMLs(wM)dLs(wM)dw
Equilibrium employment Ls(wM)=G(wM)
What happens if government mandates min wage wM<wmin<y?

Equilibrium employment and wages both rise!
Equilibrium is described by a pair (w⋆,h⋆) such that
We can graphically illustrate the equilibrium by plotting d−1(w) and E(h|w) on the next slide
Wages no longer reflect productivity differences alone
Regression of wage w on job difficulty e
lnwi=xiβ+eJ(i)α+ε
Early estimates biased by
Consider again model with varying e and two workers with fH(e),fL(e)
| Thaler and Rosen (1976) | Hwang et al. (1992) | |
|---|---|---|
| Age | 3.890 | 4.500 |
| (0.800) | ||
| Age 2 | -0.048 | -0.096 |
| (0.009) | ||
| Education | 3.400 | 4.870 |
| (0.550) | ||
| Risk | 0.035 | 0.302 |
| (0.021) | ||
| R2 | 0.41 | 0.31 |
| Price of life saved (in years of wage) | 26.54 | 227.67 |
| Mean weekly wage | 132.65 | 132.65 |
Job search frictions: even small costs enough MWP ≠ wage differentials
| Finland | ||
|---|---|---|
| MWP | Wage differentials | |
| Type of work | 0.016 | 0.107 |
| (0.180) | (0.040) | |
| Working conditions | 0.070 | 0.004 |
| (0.080) | (0.030) | |
| Working times | -0.016 | 0.048 |
| (0.070) | (0.040) | |
| Distance to work | 0.162 | -0.031 |
| (0.060) | (0.040) | |
| Job security | 0.537 | 0.068 |
| (0.220) | (0.040) | |
Estimate importance of four channels of wage heterogeneity:
| A | Variance |
|---|---|
| Total | 0.104 |
| No learning by doing | 0.096 |
| No monopsony | 0.093 |
| No premarket skill variation across jobs | 0.05 |
| No premarket skill variation at all | 0.008 |
| No search frictions | 0.007 |
| B | Variance |
|---|---|
| Total | 0.104 |
| No learning by doing | 0.096 |
| No monopsony | 0.093 |
| No search frictions | 0.086 |
| No premarket skill variation across jobs | 0.049 |
| No premarket skill variation at all | 0.007 |
| C | Variance |
|---|---|
| Total | 0.104 |
| No learning by doing | 0.096 |
| No monopsony | 0.093 |
| No nonpecuniary aspects of jobs | 0.087 |
| No premarket skill variation across jobs | 0.048 |
| No premarket skill variation at all | 0.006 |
| D | Variance |
|---|---|
| Total | 0.104 |
| No learning by doing | 0.096 |
| No monopsony | 0.093 |
| No nonpecuniary aspects of jobs | 0.087 |
| No search frictions | 0.061 |
| No premarket skill variation across jobs | 0.047 |
Firms may pay different wages to otherwise identical workers
Yit=β0+β1Xi+θi+ψJ(i)+εit
Next lecture: Human Capital on 10 Sep