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Josephine Gordon
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8 % 2% 5% 1% % / + 2 3% /

9 mean tenure median tenure /+2 / + 2

10 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, i t β β log

11 h (0.0004) (0.0005) (0.0016) (0.0019) β log

12 1 β < 1 T T R a x ε = {e, n} e n {ε, a, x}

13 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.

14 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 ) π 2 ψ 2 s/3 ω π s H(ω) = (1 + exp( ω/ψ s )) 1 Ψ s (π s ) ω ηdh(η) π f J(x w, x m, a) a x ( 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 ) ] ). π f π s η s Ψ s(π s) = ψ s (π s log(π s)+(1 π s) log(1 π s)) π s

15 w Ψ s (π s )/(1 π s (x w, x m, a)) Ψ s 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 π 2 ψ 2 o/3 Ψ ne (q ne ) η o q ne x m ( ( q ne (x m; x w, a) = 1 + exp ψ 1 o β (V n (x w, x m, a ) ( [ E m Ve (x w, x m, a ) ] ) ))) 1 κ o. x m V n (x w, a) Ψ s

16 V n (x w, a) = b + {}}{ p ne (x w, a) ( q ne (x m; x w, a) ( [ βe m Ve (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 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) x m x m q eo (x m; x w, x m, a) Ψ eo (q eo )

17 V S e (x w, x m, a) = {}}{ p eo (x, a) ( q eo (x m; x, a) ( [ βe m Ve (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 Ve (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 [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)

18 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) ( ( π s (x w, x m, a) = 1 + exp ψ 1 ( w(x w, x m, a) = µ S P (x, a) + q eo (x m; x w, x m, a) = ( 1 + exp ( 1 s S P (x, a))) ) S (x w, x m, a) ψ 1 o Ψ s (π s ) 1 π s (x w, x m, a) ( S S (x, a) + κ o ))) 1. π s q eo w π s S P S P Ψ s S Ψ s S J P (x, a)

19 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 ( ) n(xw, a) ϱ p vn (x w, a) = κ n = κ n θ n (x w, a) ϱ, v n (x w, a) ( ) l(xw, x m, a) ϱ 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)

20 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 age profile age skill accumulation age profile newly hired 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

23 σ m ψ s σ m b ψ s δ 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 = 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 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% x m

26 ψ s Ψ o κ o ψ o b κ 56% κ o κ u x m

27 π f 8% 10%

28 mean tenure median tenure

33 log log log log

34 log log

35 %

36 37% 11% 25% 13% 0.9% 1.8% 50% 12

37 %

39 40 31%

40 25% 48% 21%

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

44 x w x m

47 p d = 0

48 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

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

50 τ τ τ t = % % = 26.7% 26.6%

51 displaced average nondisplaced x m

54 π adj = π α α π 1 2α

55 / + 2 log log

56 t t + 1 I T i,t log w i,t Ii,t 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

57 y it log log log i t X it α i γ t Dit s s 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 a= ( ) πs (a, θ) ˆπ s (a) 2 + ˆπ s (a) ( π NH s (a, θ) ˆπ NH s a=21 ˆπ NH s (a) 50 a=20 ) 2 (a) + ( ) πeo (a, θ) ˆπ eo (a) 2 + ˆπ eo (a) 50 ( π NH eo (a, θ) ˆπ NH eo a=21 ˆπ eo (a) ( πne (a, θ) ˆπ ne (a) ˆπ ne (a) ) 2 (a) 60 ( t(a, θ) ˆt(a) + ˆt s (a) 50 a=20 a=25 ) 2 ) 2

58 π s (a, θ) θ π eo π ne t(a, θ) a θ NH

66 π g = π b = 0.04 w g > w b

67 γ γ = 0.01 π g

68 π g = π b = 0.03 π g = π b = π g = π b π g π b = 0.2 γ = π g = π b = 0.03

72 ψ o ψ o ψ o κ o

74 H µ η π2 3 ψ2 η ω ω η h(η) η = = [ ] ω ω η H(η) [ 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 µ η ) ) η = ψ η y 1 y η 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 ψ η = H(η) 1 H(η) ω ω = ψ η (log H( ω) log(1 H( ω))) + µ η ω

75 ω ) η h(η) η = ψ η (H( ω) log(h( ω)) + (1 H( ω)) log(1 H( ω)) + H( ω) µ η ( 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 (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) ) ( qne (x w, x m, a) ( βe m [ Ve (x w, x m, a ) ] κ )) g(x m) + ((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 Ve (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 Ve (x w, x m, a ) ] g(x m) +p eo (x, a) Ψ eo (q eo )g(x m). x m x }{{} m }{{}

76 (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) + V S e (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)) ( ) 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)

77 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 [ Ve (x w, x m, a ) ] βe m [ Ve (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) q eo (x m; x w, x m, a)) = ( ( 1 + exp ψ 1 [ o (βe s J(x w, x m, a ) ] [ + βe s Ve (x w, x m, a ) ] [ βe m Ve (x w, x m, a ) ] ))) 1 + κ o βe s [ J(x w, x m, a ) ] + βe s [ Ve (x w, x m, a ) ] βe m [ Ve (x w, x m, a ) ] + κ o = βe s [ J(x w, x m, a ) ] + βe s [ Ve (x w, x m, a ) βv n (x w, a ) ] βe m [ Ve (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

78 Transition rate Shape Slope Level Age

79 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 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 s(x j m) = 1 ( ( 1 + exp ψ 1 s m))) S(xj 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 neµe 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)]

80 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 ) π M + g(π H) 1 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 m = [ π s, T, π NH s ] = π L g(π L ) + π M g(π M ) + π H g(π H ) [ ( ) ] m = g(π j ) (Nπ j ) 2, π 4 j N 2 g(π j ) + π j N, 1 π j j = {L, M, H}. [ ] m π L, m π M, m π H [π L, π M, π H ] m = [ π s, T, π NH s ] [σ m, ψ s, b] 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

81 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 ψ o q eo µ

82 µ µ µ κ κ n κ n κ κ κ π f π f

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

84 x w

85 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 p ne s p s 1 12 p δ s p δ = s =

87 mean tenure median tenure

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

89 log

90 mean tenure median tenure

92 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)

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

94 β 1 x a ŵ(x, a) 7.5

95 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 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.

96 [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 log

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

98 th 90 th

100

101

102

103

104

105

106

107

108

Earnings Losses and Labor Mobility Over the Life Cycle

6552 2017 June 2017 Earnings Losses and Labor Mobility Over the Life Cycle Philip Jung, Moritz Kuhn Impressum: CESifo Working Papers ISSN 2364 1428 (electronic version) Publisher and distributor: Munich