Earnings Losses and Labor Mobility Over the Life Cycle

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1 June 2017 Earnings Losses and Labor Mobility Over the Life Cycle Philip Jung, Moritz Kuhn

2 Impressum: CESifo Working Papers ISSN (electronic version) Publisher and distributor: Munich Society for the Promotion of Economic Research CESifo GmbH The international platform of Ludwigs Maximilians University s Center for Economic Studies and the ifo Institute Poschingerstr. 5, Munich, Germany Telephone +49 (0) , Telefax +49 (0) , office@cesifo.de Editors: Clemens Fuest, Oliver Falck, Jasmin Gröschl group.org/wp An electronic version of the paper may be downloaded from the SSRN website: from the RePEc website: from the CESifo website: group.org/wp

3 CESifo Working Paper No Category 4:Labour Markets Earnings Losses and Labor Mobility Over the Life Cycle Abstract Large and persistent earnings losses following displacement have adverse consequences for the individual worker and the macroeconomy. Leading models cannot explain their size and disagree on their sources. Two mean-reverting forces make earnings losses transitory in these models: search as an upward force allows workers to climb back up the job ladder, and separations as a downward force make nondisplaced workers fall down the job ladder. We show that job stability at the top rather than search frictions at the bottom is the main driver of persistent earnings losses. We provide new empirical evidence on heterogeneity in job stability and develop a life-cycle search model to explain the facts. Our model offers a quantitative reconciliation of key stylized facts about the U.S. labor market: large worker flows, a large share of stable jobs, and persistent earnings shocks. We explain the size of earnings losses by dampening the downward force. Our new explanation highlights the tight link between labor market mobility and earnings dynamics. Regarding the sources, we find that over 85% stem from the loss of a particularly good job at the top of the job ladder. We apply the model to study the effectiveness of two labor market policies, retraining and placement support, from the Dislocated Worker Program. We find that both are ineffective in reducing earnings losses in line with the program evaluation literature. JEL-Codes: E240, J630, J640. Keywords: life-cycle labor market mobility, job tenure, earnings losses, worker- and matchspecific skills. Philip Jung TU Dortmund University Germany Dortmund philip.jung@tu-dortmund.de Moritz Kuhn University of Bonn Germany Bonn mokuhn@uni-bonn.de First version: June, 2011 This version: June, 2017 We thank seminar participants at various institutions and conferences for useful comments. We especially thank Rudi Bachmann, Christian Bayer, Steven Davis, Georg Duernecker, Mike Elsby, Fatih Guvenen, Marcus Hagedorn, Berthold Herrendorf, Andreas Hornstein, Philipp Kircher, Tom Krebs, Lars Ljungqvist, Iourii Manovskii, Giuseppe Moscarini, Daniel Sullivan, Gianluca Violante, and Ludo Visschers for many suggestions and insightful comments. The usual disclaimer applies.

8 1980

9 % 2% 5% 1% % 3% /

10 /

11 mean tenure 3 5 median tenure / + 2 / + 2 h h h h π h i,t log log(w i,t ) γ a i,t π h i,t = β log(w i,t ) + γ a i,t + ε i,t,

12 i t β h (0.0004) (0.0005) (0.0016) (0.0019) β log β log

13 β < 1 T T R a x ε = {e, n} e n

14 {ε, a, x} x = {x w, x m } x w x m x m g(x m ) g 1 σ 2 m x w x min w x max w x w x w x + w x + w p u (a) x w 1 p u (a) x w x w = { x w x + w 1 p u (a) p u (a), p u (a) = 0 x w = x max w p u (a) = (1 δ)p u (a 1) x w 1 p d x w p d x w p d = 0 x w = x min w x w { x x w p d w = x w 1 p d.

15 E s [ ] s E m [ ] m a x = {x w, x m } y y = f(x w, x m ) + η s η s H(η s ) π2 3 ψ2 s ω π s H(ω) = (1+exp( ω ψ s )) 1 Ψ s (π s ) ηdh(η) π ω s π f J(x w, x m, a) a x ( J(x w, x m, a) = (1 π f )(1 π s (x w, x m, a)) f(x w, x m ) + + (1 π eo (x w, x m, a))βe s [J(x w, x m, a )] Ψ s (π s ) 1 π s (x w, x m, a) w(x w, x m, a) ). π f π s η s w Ψ s(π s) Ψ 1 π s(x w,x m,a) s Ψ s (π s ) = ψ s (π s log(π s ) + (1 π s ) log(1 π s )) Ψ s

16 π eo a x w x m V e (x w, x m, a) V n (x w, a) b p ne (x w, a) κ o η o x m {V n (x w, a ), E m [V e (x w, x m, a )] κ o + η o } η s η o π2 3 ψ2 o Ψ ne (q ne ) η o q ne x m q ne (x m; x w, a) = ( 1+exp ( ( ) )) 1 ψ 1 o β V n (x w, x m, a ) (E m [V e (x w, x m, a )] κ o ). x m V n (x w, a) V n (x w, a) = b + {}}{ p ne (x w, a) ( ) q ne (x m; x w, a) (βe m [V e (x w, x m, a )] κ o ) g(x m) x m + (1 p ne (x w, a)q ne (x m; x w, a))βv n (x w, a )g(x m) +p ne (x w, a) Ψ ne (q ne )g(x m) x m x }{{} m }{{} b

17 p ne q ne π ne (x w, a) = p ne (x w, a)q ne (x m; x w, a)g(x m) x m V e (x w, x m, a) = (1 π f )(1 π s (x w, x m, a)) ( w(x w, x m, a) + V S e (x w, x m, a) ) + ((1 π f )π s (x w, x m, a) + π f ) V n (x w, a), V S e (x w, x m, a) (1 π f )(1 π s (x w, x m, a)) w(x w, x m, a) V S e (x w, x m, a) V n (x w, a) b p eo (x w, x m, a) q eo (x m; x w, x m, a) Ψ eo (q eo ) V S e (x w, x m, a) = {}}{ p eo (x, a) ( ) q eo (x m; x, a) (βe m [V e (x w, x m, a )] κ o ) g(x m) x m + (1 p eo (x, a)q eo (x m; x, a))βe s [V e (x w, x m, a )] g(x m) +p eo (x, a) Ψ eo (q eo )g(x m). x m } x {{} m }{{} x m q eo p eo π eo (x w, x m, a) = p eo (x w, x m, a)q eo (x m; x w, x m, a)g(x m) x m

18 [w, π s, q eo (x m)] = arg max J(x w, x m, a) 1 µ (x w, x m, a) µ s.t. a, x w, x m (x, a) = V e (x, a) V n (x, a) S(x, a) = (x, a) + J(x, a) S (x w, x m, a) = V S e (x w, x m, a) V n (x w, a) S S (x, a) = E s [βs(x w, x m, a )] E m [β (x w, x m, a )] P (x, a) = w(x, a) + S (x, a) J P (x, a) = f(x) w(x, a) + (1 π eo (x, a))βe s [J(x, a )] S P (x, a) = P (x, a) + J P (x, a) w(x w, x m, a) π s (x w, x m, a) q eo (x m; x w, x m, a) ( ( 1 π s (x w, x m, a) = 1 + exp ψ 1 s S P (x, a))) ( ) w(x w, x m, a) = µ S P Ψ s (π s ) (x, a) + S (x w, x m, a) 1 π s (x w, x m, a) ( ( ))) 1 (S S (x, a) + κ o q eo (x m; x w, x m, a) = 1 + exp ψ 1 o. π s q eo w π s S P J P (x, a)

19 S P Ψ s S Ψ s S κ o {ε, a, x} κ = p vn (x w, a)β x m κ = p vo (x w, x m, a)β x m q ne (x m; x w, a)e m [J(x w, x m, a )] g(x m) q eo (x m; x w, x m, a)e m [J(x w, x m, a )] g(x m), κ p vn (x w, a) x w a p vo (x w, x m, a) x w x m a m = κv 1 ϱ u ϱ v u ϱ κ

20 ( ) ϱ n(xw, a) p vn (x w, a) = κ n = κ n θ n (x w, a) ϱ, v n (x w, a) ( ) ϱ l(xw, x m, a) p vo (x w, x m, a) = κ o = κ o θ o (x w, x m, a) ϱ, v o (x w, x m, a) l(x w, x m, a) v o (x w, x m, a) θ o (x, a) n(x w, a) v n (x w, a) θ n (x w, a) p eo (x w, x m, a) = κ o θ o (x w, x m, a) 1 ϱ p ne (x w, a) = κ n θ n (x w, a) 1 ϱ

21 p u p d

22 separation rate separation rate newly hired age profile selection skill accumulation age profile age newly hired age profile age profile age separation rate job-to-job rate no risk of skill loss skill accumulation newly hired age profile selection age profile age risk of skill loss newly hired age profile age b σ m ψ s σ m b ψ s δ

23 π f κ o κ o ψ o κ o κ o ψ o µ κ n κ κ n κ

24 65 15 f(x) = exp(x m + x w ) 1 x m σ m σ w = 0.3 σ w p u σ w β 4% ϱ = 0.5 p u 20 δ σ w p u 9 log δ log p d 1.6 log σ w p d σ m 17% 32% 55 σ w σ w

25 p u ψ s µ p d κ o b δ ψ o κ σ m π f κ o κ n p u p d δ σ m ψ s κ o ψ o π f µ b κ κ o κ n x m ψ s Ψ o κ o ψ o x m

26 b κ 56% κ o κ u π f 8% 10%

28 mean tenure median tenure

32 log log log log

33 log log

34 %

35 37% 11% 25% 13% 0.9% 1.8%

36 50% 5%

38 40

39 31% 25% 21% 48%

42 g(x m ) 14.7% 12% 4% 85.8%

43 x w x m

45 p d = 0 t t = 0 g(x m ) τ τ τ τ τ π ne τ π ne τ τ τ g(x m ) τ t τ t = 0

46 t V w u τ V w u τ 7.5% 4.2% V w u t τ τ τ t = 0 τ = 12

47 τ τ τ t = %+11.5% = 26.7% 26.6%

48 70 60 displaced average nondisplaced x m

51 π adj = π α 1 2α α π

52 / + 2 log log

53 t t + 1 I T i,t log w i,t I T i,t 1 i t T i t I T i,t = βw i,t + 55 a=20 α a I a y=2004 γ y I y + u i,t. u i,t I a I y β t y it log log log i t X it α i γ t Dit s s

54 y = βx it + α i + γ t + 10 s= 2 D s it + u it u it s = 2 s = 10 θ min θ 50 ( ) 2 πs (a, θ) ˆπ s (a) 50 ( ) 2 πeo (a, θ) ˆπ eo (a) 50 ( ) 2 πne (a, θ) ˆπ ne (a) + + ˆπ a=20 s (a) ˆπ a=20 eo (a) ˆπ a=20 ne (a) 50 ( π NH s (a, θ) ˆπ NH ) 2 s (a) 50 ( π NH eo (a, θ) ˆπ NH ) 2 eo (a) 60 ( t(a, θ) ˆt(a) (a) ˆπ eo (a) ˆt s (a) a=21 ˆπ NH s a=21 a=25 ) 2 π s (a, θ) θ π eo π ne t(a, θ) a θ NH

61 π g = π b = 0.04 w g > w b γ γ = 0.01

62 π g π g = π b = 0.03 π g = π b = 0.003

63 π g = π b π g π b = 0.2 γ = π g = π b = 0.03

66 ψ o ψ o ψ o κ o

68 H µ η π 2 3 ψ2 η ω ω η h(η) η = = [ ] ω η H(η) [ ] ω η H(η) ω H(η) η ( 1 + exp ( η µ )) 1 η ψ η ωh( ω) exp ( ψ 1 η (η µ η ) ) y = exp ( ψ 1 η (η µ η ) ) η = ψ η y 1 y ω η h(η) η = ω H( ω) ψ η ω y y = ω H( ω) ψ η [ log(1 + y) ] ω ω [ ( ( η µη η h(η) η = ωh( ω) ψ η log 1 + exp = ω H( ω) + ψ η log(1 H( ω)) ψ η )) ] ω ( ) η µη exp = H(η) ω ψ η 1 H(η) ω = ψ η (log H( ω) log(1 H( ω))) + µ η ω ω ) η h(η) η = ψ η (H( ω) log(h( ω)) + (1 H( ω)) log(1 H( ω)) + H( ω) µ η

69 ( Ψ s (π s ) J(x w, x m, a) = (1 π f )(1 π s (x w, x m, a)) f(x w, x m ) + (1 π s (x w, x m, a)) w(x w, x m, a) ) + (1 π eo (x w, x m, a))βe s [J(x w, x m, a )] V n (x w, a) = b + p ne (x w, a) x m + x m (q ne (x w, x m, a) (βe m [V e (x w, x m, a )] κ)) g(x m) (1 p ne (x w, a)q ne (x w, x m, a))βv n (x w, a )g(x m) +p ne (x w, a) Ψ ne (q ne )g(x m) x m V e (x w, x m, a) = (1 π f )(1 π s (x w, x m, a)) ( w(x w, x m, a) + Ve S (x w, x m, a) ) + ((1 π f )π s (x w, x m, a) + π f ) V n (x w, a) V S e (x w, x m, a) = {}}{ p eo (x, a) ( ) q eo (x m; x, a) (βe m [V e (x w, x m, a )] κ o ) g(x m) x m + (1 p eo (x, a)q eo (x m; x, a))βe s [V e (x w, x m, a )] g(x m) +p eo (x, a) Ψ eo (q eo )g(x m). x m x }{{} m }{{} (x w, x m, a) = V e (x w, x m, a) V n (x w, a) = (1 π f )(1 π s (x w, x m, a)) ( w(x w, x m, a) + Ve S (x w, x m, a) V n (x w, a) ) S(x w, x m, a) = (V e (x w, x m, a) V n (x w, a) + J(x w, x m, a)) ( ) Ψ s (π s ) = (1 π f )(1 π s (x w, x m, a)) f(x w, x m ) + (1 π s (x w, x m, a)) + S (x w, x m, a) +(1 π f )(1 π s (x w, x m, a)) ((1 π eo (x w, x m, a))βe s [J(x w, x m, a )])) S P (x, a) = P (x, a) + J P (x, a) = f(x) + S (x, a) + (1 π eo (x, a))βe s [J(x, a )]. (x w, x m, a) = µ(j(x w, x m, a)+ (x w, x m, a))

70 ( ) µ(1 π f )(1 π s (x w, x m, a)) f(x w, x m ) w(x w, x m, a) + µ(1 π f )(1 π s (x w, x m, a))(1 π eo (x w, x m, a))βe s [J(x w, x m, a )] + µ(1 π f )Ψ s (x w, x m, a) = (1 µ)(1 π f )(1 π s (x w, x m, a)) ( w(x w, x m, a) + V S e (x w, x m, a) V n (x w, a) ) ( ) w(x w, x m, a) = µ f(x w, x m ) + (1 π eo (x w, x m, a))βe s [J(x w, x m, a )] µ + 1 π s (x w, x m, a) Ψ s(x w, x m, a) (1 µ) ( Ve S (x w, x m, a) V n (x w, a) ). S P (x, a) S (x, a) = f(x w, x m ) + (1 π eo (x w, x m, a))βe s [J(x w, x m, a )] ( ) w(x w, x m, a) = µ S P (x, a) S µ (x, a) + (1 π s (x w, x m, a)) Ψ s(x w, x m, a) (1 µ) S (x, a) ( ) w(x w, x m, a) = µ S P Ψ s (π s ) (x, a) + S (x w, x m, a) 1 π s (x w, x m, a) π s (x w, x m, a) ( ) (1 π f ) f(x w, x m ) w(x w, x m, a) + (1 π eo (x w, x m, a))βe s [J(x w, x m, a )] ( ) (1 πs (x w, x m, a)) (1 π f )ψ s log + (1 π f ) ( w(x w, x m, a) + Ve S (x w, x m, a) V n (x w, a) ) π s (x w, x m, a) = 0 S P (x, a) = f(x)+ S (x, a)+(1 π eo (x, a))βe s [J(x, a )] π s (x w, x m, a) = ( ( )) exp ψ 1 s S P (x, a) x m q eo (x m; x w, x m, a) βe s [J(x w, x m, a )]+βe s [V e (x w, x m, a )] βe m [V e (x w, x m, a )]+κ o = ψ eo log ( ) 1 qeo (x m; x w, x m, a) q eo (x m; x w, x m, a)

71 q eo (x m; x w, x m, a)) = ( ( 1 + exp ψ 1 o (βe s [J(x w, x m, a )] + βe s [V e (x w, x m, a )] βe m [V e (x w, x m, ))) 1 a )] + κ o βe s [J(x w, x m, a )] + βe s [V e (x w, x m, a )] βe m [V e (x w, x m, a )] + κ o = βe s [J(x w, x m, a )] + βe s [V e (x w, x m, a ) βv n (x w, a )] βe m [V e (x w, x m, a ) V n (x w, a )] + κ o = βe s S(x w, x m, a ) E m (x w, x m, a ) + κ o S S (x, a) = E s [S(x w, x m, a )] E m [ (x w, x m, a )] q eo (x m; x w, x m, a)) = ( 1 + exp ( ψ 1 o (S S (x, a) + κ o ))) 1

72 Transition rate Shape Slope Level Age p u p d σ m σ m ψ s b x m x m η s x L m x M m x H m x L m = x M m σ m x H m = x M m + σ m x M m = 1

73 π L = π s (x L m) π M = π s (x M m ) π H = π s (x H m) σ m ψ s b π L > π M > π H > 0 π L π M π H g(π) h(π) h(π j ) = N π j g(π j ) ( ) j = {L, M, H} N = g(πl ) π L + g(π M ) 1 π M + g(π H) π H πs π s = π L h(π L ) + π M h(π M ) + π H h(π H ) = N (g(π L ) + g(π M ) + g(π H )) = N. T T = π 1 L h(π L) + π 1 M h(π M) + π 1 H h(π H) = N ( π 2 L g(π L) + π 2 M g(π M) + π 2 H g(π H) ) = π s ( π 2 L g(π L) + π 2 M g(π M) + π 2 H g(π H) ). π NH s = π L g(π L ) + π M g(π M ) + π H g(π H ) m = [ π s, T, π NH s ] [ ( ) ] m = g(π j ) (Nπ j ) 2, π 4 j N 2 g(π j ) + π j N, 1 j = {L, M, H}. π j [ m π L, m π M, m [π L, π M, π H ] m = [ π s, T, π NH s ] π H ] [σ m, ψ s, b] π s (x j m) = ( ( exp ψ 1 s S(xm))) j j = {L, M, H} S(x j m) = x j m b + β(1 π s (x j m))s(x j m) + Ψ(π s (x j m)) βπ ne µe 0 [S(x m )] ) Ψ(π s (x j m)) = ψ s (π s (x j m) log(π s (x j m)) + (1 π s (x j m)) log(1 π s (x j m)) E 0 [S(x m )]

74 δ δ κ o ψ o κ o p eo (x w, x m, a) κ o κ o a x w x m x m q eo (x m; x w, x m, a) q eo (x m; x w, x m, a) = ( 1 + exp ( ) ) 1 ψ 1 o (E s [S(x w, x m, a )] µe m [S(x w, x m, a )] + κ o ). E s [S(x w, x m, a )] µe m S[(x w, x m, a )] κ o κ o κ o κ o ψ o κ o ψ o ψ o q eo ψ o = (1 q eo) (E s [S(x w, x m, a )] µe m S[(x w, x m, ) a )] + κ o. ψ o q eo ψ o ψ o ψ o 0.5 ψ o

75 ψ o q eo µ µ µ µ κ κ n κ n κ κ κ π f π f

76 f(x) = exp(x m + x w )

77 x w x w x w = { x w x w p δ 1 p δ p δ = 0 x w = x min w p s s < 1

78 p ne s p s 1 12 p δ s p δ = s =

79 mean tenure median tenure

80 log x new w x new w x max w p new u > x max w p u p new u x new w p new u p u log x new w x new w

81 log

82 mean tenure median tenure

84 x g(x m ) q eo (x m; x w, x m, a) E m [ ] E j2j [w x w, x m, a] j2j E j2j[w x w,x m,a] w(x w,x m,a) w(x w, x m, a) π eo (x w, x m, a) π eo (x w, x m, a) p eo (x w, x m, a)

85 log log(w a+1 ) log(w a 2 ) dŵ a+1 dŵ a 1 a dŵ a a a

86 β 1 x a ŵ(x, a) ŵ(x, a) = ζ(x, a) + ι ζ(x, a) = ζ(x, a 1) + ν σ ν σ ι σ 2 ν,a = cov(ŵ(x, a), ŵ(x, a + 1)) cov(ŵ(x, a 1), ŵ(x, a + 1)) σ 2 ι,a = var(ŵ(x, a)) cov(ŵ(x, a), ŵ(x, a 1)) σ 2 ν,a

87 σ ι η s Ψ s w n (x w, x m, a) w n (x w, x m, a) = w(x w, x m, a) µ Ψ s(π s ) 1 π s. [π s (x w, x m, a), 1] w(x w, x m, a) η s w(x w, x m, a) = w n (x w, x m, a) + µη s. log w w w σ ι

88 log w(x w, x m, a)

89 log w w w

90 th 90 th

Earnings losses and labor mobility over the lifecycle

Earnings losses and labor mobility over the lifecycle Philip Jung Moritz Kuhn First version: June, 2011 This version: September, 2015 Abstract Large and persistent earnings losses following displacement