Wage Inequality, Labor Market Participation and Unemployment

Transcription

1 Wage Inequality, Labor Market Participation and Unemployment Testing the Implications of a Search-Theoretical Model with Regional Data Joachim Möller Alisher Aldashev Universität Regensburg Stand und Perspektiven der Regionalforschung - Regensburg, November, 2004

2 Participation rates (2) Males-West Males-East Females-West Females-East

3 (3) Unemployment vs. participation (all workers) 75 labor-force-to-population ratio unemployment rate Old Laender New Laender

4 (4) Unemployment vs. participation (female workers) 80 labor-force-to-population ratio unemployment rate old laender new laender

5 (5) Wage inequality D5/D2 & D8/D5 (M) 1,6 D8/D ,4 1,2 1,0 1,0 1,2 1,4 1,6 D5/D new laender old laender

6 (6) Wage inequality D5/D2 & D8/D5 (F) 2,6 2,4 2,2 D8/D ,0 1,8 1,6 1,4 1,2 1,0 1,0 1,2 1,4 1,6 1,8 2,0 2,2 2,4 2,6 D5/D new laender old laender

7 Structure (7) Search-theoretical model Data Econometric Approach Results Conclusions

8 Search-theoretical model: Basic settings (8) Extension of standard search-theoretical approach (McCall, Mortensen, Pissarides) job offers as random drawings from a job offer distribution dynamic optimization approach model in continuous time Specific characteristics here job offer arrival rate influenced by search intensity possibility of separations exclusion of on-the-job search

9 (9) Search-theoretical model: Assumptions Wage offer distribution is time invariant and known to agents Jobs are different with respect to wages only Individuals live forever Agents are wealth-maximizing (risk neutrality) δ

10 Search-theoretical model: Specifications (10) W W Population P, number of job-seekers S, number of vacancies V; Search costs depend on search intensity θ : 1 c = c( θ) = c0 + Cθ 2 and λ ( θ) c = λ = θ Choose optimal θ and job arrival rate λ V S θ 2

11 (11) Search-theoretical model: Basic Relations (i) special case σ = 0 1 W Value of employment: Ww ( ) = ( w) δ (present value of an infinite stream of income w) (ii) σ > 0 1 W Value of employment: Ww ( ) = ( w+ σω), δ+ σ where Ω( ) is the value of search: W Reservation wage r : r = Ω r = δ Ω δ

12 (12) Search-theoretical model: Basic Relations W = = + Kr ( ) r δω b c( θ ) λ( θ ) (1) δ+ σ δ: discount rate; σ: separation rate; b θ Reservation wage: : income in case of unemployment : optimal search intensity ( ) K r : = w r + F( w)dw > 0 r 0

13 Comparative static results (1) (13) W Using FOC of optimal search intensity + substituting functions for search costs and job arrival rate in eq.(1) 1 ( ) = + [ ] 2 Φ r; b u κ1 K( r) r = 0 (1') 2C V with κ1: = ; b u : = b c0 S ( δ+ σ)

14 Comparative static results (1) (14) From Φ and 1 2 r; = b u + 1 K( r) r = 0 (1') 2C Φ < 0 one obtains the comparative static results ( ) [ κ ] r r r r r > 0, < 0, < 0, < 0 ( V / S) C σ δ r 0 < < 1 b u

15 (15) Introducing a mean-preserving spread (1)

16 (16) Introducing a mean-preserving spread (2) We include a spread parameter in the wage offer distribution: Fw ( ; s) with Fws (, )dw 0 x > 0 s Formal definition of a mean preserving spread : For any pair of 0 s and s with s < s : x wd F( w, s ) = wd F( w, s ); Fws (, )d w Fws (, )dw 1 x x

17 Effect on the reservation wage (17) Result: Reservation wage increases with spread: r > 0 s Interpretation: The spread increases the value of search!

18 Modelling participation behavior (1) (18) (i) Introducing heterogeneity: Individuals differ with respect to the value of leisure l. (ii) Differentiating between unemployment (U) and non-participation (N) two types of transfers: W unemployment benefits: t W social assistance: wealth in both cases: (U) : (N) : u i n i b = l + t c b i = l + t i u n 0 u t n

19 Modelling participation behavior (2) (19) Comparing non-participating and unemployment without searching for a job: n u n u i i (N) (U): ν : = b b = t t + c Two conditions are required to prevent corner solutions: (a) ν > 0 for a participation rate π < 1 min max (b) l + ν < w for π > 0. 0

20 Modelling participation behavior (3) (20) A critical value of leisure %l > 0 exists, li li l < l% > l% = l% person participates on the labor market person does not participate person is indifferent i between participating and not. Participation indifference condition: r% : = r l% = b% = b% + ν ( ) n u

21 Modelling participation behavior (4) (21) G( l ) : distribution function of the value of leisure in the population ( ) π π : = G %l with > 0 %l π : participation rate

22 Comparative static results (1) (22) The following results can be derived: %l > 0 participation increases with the mean wage w l% l% l% l% < 0; < 0; < 0; < 0 δ σ ν C and %l > 0 participation increases with the spread s

23 Extensions: Endogenous S (23) The number of job seekers is endogenous S: = πp = G( %l ) P, where P is population. Sign of comparative static effects not affected, but dampening effect.

24 Extensions: Unemployment (1) (24) Unemployment hazard rate φ i i i i ( r, s) = λ( θ ) 1 F( r, s) job offer arrival rate i i i ( r s) where θ : = θ, probability that offer will exceed the reservation wage Equilibrium unemployment rate for type i workers u i σ σ = = φi + σ λ θ (, ) 1 (, ) i ri s F ri s + σ

25 Value of leisure/ reservation wage (25) r -- low dispersion -- high dispersion Value of leisure

26 Value of leisure/ unemployment (26) u -- low dispersion -- high dispersion Value of leisure

27 Reservation wage / unemployment (27) u -- low dispersion -- high dispersion r

28 Results (28) The aggregate unemployment rate is unaffected by the spread! [the unemployment rate does not depend on the first and second moment of the wage offer distribution] However, since participation increases with the spread, the employment-to-population rate increases with a higher spread:

29 (29) Inequality and Unemployment (male, West)

30 Results (2) (30) One can show: * σ u δ + σ unemployment rate W increases with the separation rate σ W falls with the discount rate δ. if δ. is constant across regions, the regional unemployment rate can be used as an indicator of the separation rate

31 Summary of theoretical model (31) participation (labor-force-to-population ratio) increases with Wthe wage level Wthe spread in the wage offer distribution and decreases with Wjob insecurity (separation rate) as measured by the unemployment rate

32 Data (32) Sources: (i) INKAR: (aggregate) regional data on NUTS 3 level (ii) IAB-REG: 1% random sample of social security data with regional information - Data for NUTS 3 regions (excluding East and West Berlin)

33 Empirical model (1) (33) Estimated equation: π =α +α ln w +α u +α SPREAD1 r 0 1 r 2 r 3 r 4 SPREAD2 + regional type dummies +ε (allowing for different parameters in EAST and WEST) w u r r +α : average wage level in region r : unemployment rate r SPREAD1 (2) : log differences D5-D2 (D8-D5) ε r is an error term r

34 Empirical model (2) (34) Estimation with spatial econometrics methods W testing for spatial lag model (SLM) y =ρ Wy + Xβ+ y = Xβ+ε and ε=λwε+ε ε W and spatial error dependence model (SEM) W is a spatial weight matrix; data on commuter streams used for W ; 2 variants: W row normalzing (ROW) W normalizing rows and columns (RAS method)

35 Test statistics spatial correlation parameter Double-length artificial regression [ χ 2 () 1 ] Likelihood-ratio test [ χ 2 () 1 ] spatial correlation parameter Double-length artificial regression [ χ 2 () 1 ] Likelihood-ratio test [ χ 2 () 1 ] (35) spatial lag spatial error dep. male workers ROW RAS ROW RAS 0.314** ( * ) 0.340** ** (0.068) (0.071) (0.061) (0.061) test statistics H : ρ = 0 H : λ = ** ( * ) * ** ** ( * ) 9.891** ** 0.210** (0.067) female workers ( * ) (0.066) (0.074) test statistics H : ρ = 0 H : λ = (0.072) 9.561** ( * ) ** ( * )

36 Participation rates of female workers (West) (36) dependent variable : labor-force-to-population ratio (in percent) OLS spatial lag spatial error ROW** RAS(*) ROW RAS West German Regions constant unemployment rate ln wage ln(d5/d2) ln((d8/d5) KT KT KT KT KT KT KT KT N 327

37 (37) Participation rates of female workers (East) East German Regions constant unemployment rate ln wage ln(d5/d2) ln((d8/d5) KT KT KT KT KT KT KT KT N 111 s.e ln Likelihood

38 Conclusions (38) Participation behavior across regions can be reasonably explained by the model Evidence for spatial correlation Strong persistence effects are present in the behavior of female workers in East Germany Unemployment reduces participation of men, but for females only in the West If anything, the spread in the wage distribution affects participation negatively; contradiction to theory!